Valuations On Distressed Firms And Assets Finance Essay - Free Essay Example

Sample details Pages: 14 Words: 4251 Downloads: 9 Date added: 2017/06/26 Category Finance Essay Type Research paper Did you like this example? What is valuation? From the first days on this planet humanity evaluates. Ancient people thought about: how many fruits and vegetables they should take in exchange for a meat and not take too few. With currency system development, everything has been evaluated in money. Don’t waste time! Our writers will create an original "Valuations On Distressed Firms And Assets Finance Essay" essay for you Create order But the same problem stayed: how to find fair value and not to make yourself a fool. Thousand years passed, many concepts, price theories were devised, but there is still no unique approach. And probably as physics goes more and more deeply into substance, failing to find ultimate particle, economists face or do the same. Often during the course of business many companies are in a situation wherein they find it difficult to maintain their normal course of business. In such cases they are termed as distressed firms. However, show must go on. Either someone with financial power buys them out or the firm will be liquidated. It is an interesting and sophisticated work. Ascertaining the value of a distressed company is very crucial for those who are interested in the company. Interested parties require this information to determine what the actual underlying value of the business is and what discounts are to be made over this value to get an accurate picture of the business value of the firm. First of all, in this article we will pay attention for distressed company valuation as special case, which required its own approach. Of course, usual valuation techniques can be used for distressed companies, but these results are very unstable. Various studies have shown that using valuation techniques for the valuation of distressed firms have produced results which are in the range of 20% to 300% of the actual value. This is a large difference and is not acceptable in any business transaction. For example in the case of Sahara Airlines there was a large difference in the bids of Jet Airways and Kingfisher Airlines. This emphasizes the underlying difficulty in estimating the value of distressed firms. Valuation technique may result in 300% of the true value of the distressed firm True Value of the Firm 20% Estimate of the firms value through valuation techniques. VALUATIONS In finance, valuation is the process of estimating the potential market va lue of a financial asset or liability. Valuations can be done on assets (for example, investments in marketable securities such as stocks, options, business enterprises, or intangible assets such as patents and trademarks) or on liabilities (e.g., Bonds issued by a company). Valuations are required in many contexts including investment analysis, capital budgeting, merger and acquisition transactions, financial reporting, taxable events to determine the proper tax liability, and in litigation. Methods of Corporate Valuation There are several methods which are widely used in the industry for analysing the value of any firm. Many-a-times several methods are used to get a better idea of the underlying value of the firm. The focus of this paper is valuation of distressed assets, so we will not go into details of the traditional approaches DISTRESSED FIRMS One of the simplest definitions for a distressed firm is any firm that in near future wont be able to fulfil its obligations. Firm in this case may either go bankrupt and consequently liquidate its asset or it may undergo restructuring. In any case it is important to identify the true value of the firm. Other definition of a Distressed Asset is as follows. Assets are usually considered distressed when their value is severely depressed for a reason particular to the issuer and not because of general market conditions. CHARACTERISTICS OF A POSSIBLE DISTRESSED FIRM Financial distress is typically an unanticipated event. It is really difficult to identify the potential firms which are on the verge of default. But there are peculiar indicators which can give an idea about the health of the firm. Businesses transitioning along a continuum of financial health from going concern to distressed, often exhibits one or more of the following characteristics: Over-leveraged balance sheet A high debt to Equity Ratio and debt to Asset ratio is a first signal of the upcoming problem. Sometimes it may be due to bad management or it may be due to aggressive Merger and Acquisition strategy. For example after the acquisition of the Tata Steel, its balance sheet is over leveraged. Covenant and/or payment defaults If a firm fails to meet its debt or other obligations on time then it is an indication of poor health of the firm or poor management of resources. Lack of internal controls Many a times due to lack of systems and procedures there is a lack of internal control in the firm. Loss of a major customer, supplier, or key employee Sometimes a company gets a major chunk of its business from one key customer. Similarly there is one key supplier who supplies a raw material critical for the production. In such cases if there is a loss of such customer or supplier then entire operations of the company are in jeopardy. This is what Reliance did when it was the single supplier of one of the critical raw materials for plastic industry. Management seeking bridge financing for quick fixes If the management of the company is having a short term approach and is looking for quick fix solutions instead of long term solutions. Discovery of fraud Discovery of fraud is a very good indication of an unhealthy firm. For example in the case of Satyam, when its erstwhile promoter Ramalinga Raju tried to get Maytas Infra under Satyam, many analysts were sceptical about the companys health. Product failure Sometimes companies get most of their revenue from one single product. Also many companies tend to invest all their resources in a single product. In such cases if the product fails then the entire firm is doomed to fail. Obsolete business model If a firm fails to innovate and continues its business with same model then after sometime its business model will become redundant and obsolete. Firms with obsolete business models are always next in line to fail. Cyclical downturn Many industry sectors have a common phenomenon of cyclical downturn. There is a recession in the industry after every cycle of say 10 or 15 years. Strong companies are able to overcome such scenarios but the weaker players succumb to it. Volatility in raw material and energy costs In some sectors proportion of raw material cost is a very high. In such cases if the prices of raw materials jump steeply then the business becomes unviable. An example of such sector is Airlines industry which is highly dependent on the prices of the OIL. External shock to economy External factors may also influence the health of the company. These may be macro level factors like government policies or it can be events like terrorist activities. For example health of the hospitality industry is directly related to influx of tourists which in turn is related to peace in the country. After every major terrorist activity, Indian Hotel companies see a steep decline in their Occupancies. Although these characteristics are true for any distressed firm, but it doesnt means that if any firm shows any of these characteristics then it is going to bankrupt. For example a firm may make payment defaults but it doesnt means that the firm will have to be liquidated now. In fact in such cases the above characteristics just give a preliminary indication that finances of a particular firm are not in place. In such cases a deeper analysis of the firms financials is required. ADJUSTMENTS in DISTRESSED ASSET VALUATIONS Additional adjustments to a valuation approach, whether it is market-, income- or asset-based, are necessary in almost all the instances. These adjustments help in gauging a more accurate valuation for a distressed Asset. These involve: Excess or restricted cash Other non-operating assets and liabilities Lack of marketability discount Control premium or lack of control discount Above or below market leases Excess salaries in the case of private companies. There are other adjustments to the financial statements that have to be made when valuing a distressed company. Typical adjustments used to recast the financial statements for a distressed company include: Working capital adjustment Deferred capital expenditures Cost of goods sold adjustment Non-recurring professional fees and costs Certain non-operating income/expense items ADAPTING DISCOUNTED CASH FLOW VALUATION TO DISTRESS SITUATIONS When will the failure to consider distress in discoun ted cash flow valuation have a material impact on value? If the likelihood of distress is high, access to capital is constrained (by internal or external factors) and distress sale proceeds are significantly lower than going concern values, discounted cash flow valuations will overstate firm and equity value for distressed firms, even if the cash flows and the discount rates are correctly estimated. In this section, we will consider several ways of incorporating the effects of distress into the estimated value. Simulations In traditional valuation, we estimate expected values for each of the input variables. For instance, in valuing a firm, we may assume an expected growth rate in revenues of 30% a year and that the expected operating margin will be 10%. In reality, each of these variables has a distribution of values, which we condense into an expected value. Simulations attempt to utilize the information in the entire distribution, rather than just the expected value, to arrive at a value. By looking at the entire distribution, simulations provide us with an opportunity to deal explicitly with distress. Before we begin running the simulations, we will have to decide the circumstances which will constitute distress and what will happen in the event of distress. For example, we may determine that cumulative operating losses of more than $ 1 billion over three years will push the firm into distress and that it will sell its assets for 25% of book value in that event. The parameters for distress will vary not only across firms, based upon their size and asset characteristics, but also on the state of financial markets and the overall economy. A firm that has three bad years in a row in a healthy economy with rising equity markets may be less exposed to default than a similar firm in the middle of a recession. The steps in the simulation are as follows: Step 1: The first step involves choosing those variables whose expected values will be replaced by distributions. While there may be uncertainty associated with every variable in valuation, only the most critical variables might be chosen at this stage. For instance, revenue growth and operating margins may be the key variables that we choose to build distributions for. Step 2: We choose a probability distribution for each of the variables. There are a number of choices here, ranging from discrete probability distributions (probabilities are assigned to specific outcomes) to continuous distributions (the normal, lognorm al or exponential distribution). In making this choice, the following factors should be considered: The range of feasible outcomes for the variable; (e.g., the revenues cannot be less than zero, ruling out any distribution that requires the variable to take on large negative values, such as the normal distribution). The experience of the company on this variable. Data on a variable, such as operating margins historically, may help us determine the type of distribution that best describes it. While no distribution will provide a perfect fit, the distribution that best fits the data should be used. Step 3: Next, the parameters of the distribution chosen for each variable are estimated. The number of parameters will vary from distribution to distribution; for instance, the mean and the variance have to be estimated for the normal distribution, while the uniform distribution requires estimates of the minimum and maximum values for the variable. Step 4: One outcome is draw n from each distribution; the variable is assumed to take on that value for that particular simulation. To make the analysis richer, we can repeat this process each year and allow for correlation across variables and across time. Step 5: The expected cash flows are estimated based upon the outcomes drawn in step 4. If the firm meets the criteria for a going concern, defined before the simulation, we will then discount the cash flows to arrive at a conventional estimate of discounted cash flow value. If it fails to meet the criteria, we will value it as a distressed firm. Step 6: Steps 4 and 5 are repeated until a sufficient number of simulations have been conducted. In general, the more complex the distribution (in terms of the number of values the variable can take on and the number of parameters needed to define the distribution) and the greater the number of variables, the larger this number will be. Step 7: After every simulation, a value will be generated depending upo n whether it is a going concern or a distressed firm as the case may be. To calculate the value of the firm, take the average of all the simulated values. From simulation, probability of default can also be assessed along with the effects of distress on the underlying value of the firm. But there are some limitations to this approach. The most basic limitation is the identification of the inputs which are required for the analysis. In practice, it is difficult to choose both the right distribution to describe a variable and the parameters of that distribution. If the assumptions are not proper then although the outcome may look impressive but it will be of no value. Therefore, complete care should be taken to extract the maximum results. MODIFIED DISCOUNTED CASH FLOW VALUATION Discounted Cash Flow valuation can be adjusted to reflect the effects of firms distress on the valuations of the firm. We will use both Expected cash flows as well as discount rates to get an accurate valuation of the distressed firm. Estimating Expected Cash flows To consider the effects of distress into a discounted cash flow valuation, we have to incorporate the probability that a firm will not survive into the expected cash flows. In its most complete form, this would require that we consider all possible scenarios, ranging from the most optimistic to the most pessimistic, assign probabilities to each scenario and cash flows under each scenario, and estimate the expected cash flows each year. Where ÃÆ' Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬jt is the probability of scenario j in period t and Cashflowjt is the cashflow under that scenario and in that period. These inputs have to be estimated each year, since the probabilities and the cash flows are likely to change from year to year. A shortcut, albeit an approximate one, would require estimates for only two scenarios the going concern scenario and the distress scenario. For the going concern scenario, we could use the expected growth rates and cash flows estimated under the assumption that the firm will be nursed back to health. Under the distress scenario, we would assume that the firm will be liquidated for its distress sale proceeds. Our expected cash flow for each year then would be: Where ÃÆ' Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Going concern, t is the cumulative probability that the firm will continue as a going concern through period t. The probabilities of distress will have to be estimated for each year and the cumulative probability of surviving as a going concern can then be written as follows: Where ÃÆ' Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬distress, t is the probability that the firm will become distressed in period t. For example, if a firm has 20% chance of distress in year 1 and a 10% chance of distress in year 2, the cumulati ve probability of surviving as a going concern over two years can be written as: Cumulative probability of survival over 2 years = (1- .20) (1 .10) = .72 or 72% Estimating Discount Rates: In conventional valuation, we often estimate the cost of equity using a regression beta and the cost of debt by looking at the market interest rates on publicly traded bonds issued by the firm. For firms with a significant probability of distress, these approaches can lead to inconsistent estimates. Consider first the use of regression betas. Since regression betas are based upon past prices over long periods (two to five years, for instance), and distress occurs over shorter periods, we will find that these betas will understate the true risk in the distressed firm. With the interest rates on corporate bonds, we run into a different problem. The yields to maturity on the corporate bonds of firms that are viewed as distressed reach extremely high levels, largely because the interest rates are computed based upon promised cash flows (coupons and face value) rather than expected cash flows. The presumption in a going concern valuation is that the promised cash flows have to be mad e for the firm to remain a going concern, and it is thus appropriate to base the cost of debt on promised rather than expected cash flows. For a firm with a significant likelihood of distress, this presumption is clearly unfounded. As an extreme example, consider estimating a beta for Enron at the end of 2001. The beta estimate from Bloomberg, using 2 years of data, was 1.45. Over three-quarters of this period, Enron was viewed (rightly or wrongly) as a healthy firm with positive earnings. It is only in the last part of the regression period that you see the effects of distress on stock prices and the debt to equity ratio of the firm. What are the estimation choices for distressed firms? To estimate the cost of equity, we have two options that provide more reasonable estimates than regression betas: CAPM Betas adjusted for distress Instead of using regression betas, we could use the bottom-up unlevered beta (the weighted average of unlevered betas of the businesses that the firm operates in) and the current market debt to equity ratio of the firm. Since distressed firms often have high debt to equity ratios, brought about largely as a consequence of dropping stock prices, this will lead to levered betas that are significantly higher than regression betas. If we couple this with the reality that most distressed firms are in no position to get any tax advantages from debt, the levered beta will become even higher. Levered beta = Bottom-up Unlevered beta (1 + (1- tax rate) (Debt to Equity ratio)) Note, though, that it is reasonable to re-estimate debt to equity ratios and tax rates for future years based upon our expectations for the firm and adjust the beta to reflect these changes. Distress factor Models In addition to the standard factor for market risk, we could add a separate distress factor to the cost of equity. In effect, this would make the cost of equity for distressed firms much higher than healthy firms in the same business. In fact, some have attributed the higher returns earned by firms with low price to book ratios to distress; low price to book stocks, they argue, are more likely to be distressed. Other studies, however, contest this notion by noting that portfolios of distressed firms have earned lower returns than portfolios of healthy firms historically. To estimate the cost of debt for a distressed firm, we would recommend using the interest rate based upon the firms bond rating. While this will still yield a high cost of debt, it will be more reasonable than the yield to maturity when default is viewed as imminent. To compute the cost of capital, we need to estimate the weights on debt on equity. In the initial year, we should use the current market debt to capital ratio (which may be very high for a distressed firm). As we make our forecasts for future years and build in our expectations of improvements in profitability, we should adjust the debt ratio towards more reasonable levels. The conventional practice of using target debt ratios for the entire valuation period (which reflect industry averages or the optimal mix) can lead to misleading estimates of value for firms that are significantly over levered. Limitations of Approach The biggest roadblock to using this approach is that even in its limited form, it is difficult to estimate the cumulative probabilities of distress (and survival) each year for the forecast period. Consequently, the expected cash flows may not incorporate the effects of distress completely. In addition, it is difficult to bring both the going concern and the distressed firm assumptions into the same model. We attempt to do so using probabilities, but the two approaches make different and sometimes contradictory assumptions about how markets operate and how distressed firms evolve over time. INVESTING IN DISTRESSED ASSETS The most common situation of a distressed asset is a commercial loan on which the issuer has defaulted on payments of principal or interest. Distressed asset investing generally, and emerging markets distressed investing in particular, are undertaken by a small number of firms. Implementing the strategies successfully requires specific skills and particular e conomic structures. For those firms with the appropriate professional skills and capital base, however, the strategies can be extremely profitable. Investing in such assets has become particularly more popular after the recession wherein many firms are in distressed state. There is still huge underlying value in assets of many such companies and proper valuation of these dark horses can lead to windfall gains for investors. Different types of Distressed Asset Investing Distressed investments can be categorised by the type of exit foreseen. In other words, what is the strategy for cashing out? Event-driven distressed investments. These are directional investments in distressed and special event situations in sovereign and corporate securities, for which some event is on the horizon which will transform the nature of and increase the value of the assets. The event can be a restructuring of a companys or countrys debt, a liquidation of a companys assets, or a buyback of outstanding debt by an issuer or by individuals. Capital gain from the investment is provided either through re-pricing upon occurrence of the event, or through the proceeds of a restructuring. Valuation-driven distressed investments. These are directional investments made in distressed situations where a transformative event is not at sight. The exit may be either through the market (re-pricing due to credit strengthening), cash flow, or an event (re-pricing upon an event or t hrough the proceeds of a restructuring). Some investors may buy distressed assets simply because the price seems too good to pass up, but this can be dangerous: what is cheap today may be cheap tomorrow, unless there is a reason for the value to rise. Valuation-driven investments should therefore be made only when a clear reason for triggering an increase in value can be ascertained, even if the timing of the increase is uncertain. Distressed investing usually involves the purchase of debt, but equity analysis is relevant for two reasons. First, the assets are usually non-performing, and therefore the theoretical yield is less important than the potential for capital gains; successful distressed debt investments will produce equity-like returns. Second, equities are increasingly being distributed to creditors as part of the package of assets coming out of debt restructurings; in this way, control of a companys debt pre-restructuring may later lead to equity control. Distres sed investing strategies may be combined with other complementary but uncorrelated investment strategies in liquid instruments. This can diversify portfolio risk, create hedging opportunities, and provide useful liquidity. Distressed investments are rarely possible to sell short, so any hedges for long positions or outright short positions must be undertaken in the context of a different, liquid investment strategy. Example of a Successful Distressed Investment A very famous Thai Oil Company at one point of time in the late 1990s had over $2 billion of debt outstanding. Company was not able to meet the obligations and had defaulted. After the default the market price of the debt fell and it was being traded at 30% of the actual face value. But here the company reorganized its finance and made a smart move. The company itself bought almost 50% of its outstanding debt at a price between 50-90% of the original face value. Company also agreed on a debt restructuring, in which it issued clean debt and gave  ½ of its equity to creditors. Thus improvements in the business and decrease in the outstanding debt led to rerating of its debt ratings. Now the debt was rating at par and thus made its once worth less equity very valuable. CONCLUSION Distressed firms, i.e., firms with negative earnings have a strong likelihood of failure; present a challenge to analysts valuing them because so much of conventional valuation is built on the pr esumption that firms are going concerns. But in the case of distressed firms this very assumption doesnt holds true. In this paper, we have examined how discounted cash flow has to be adjusted with respect to the valuation of distressed assets. With discounted cash flow valuation, we suggested two ways in which we can incorporate distress into value simulations that allow for the possibility that a firm will have to be liquidated and modified discounted cash flow models, where the expected cash flows and discount rates are adjusted to reflect the likelihood of default With relative valuation, we can adjust the multiples for distress or use other distressed firms as the comparable firms. In addition to this in the last section we talked about investing in such assets. From this we can say that trading in distressed assets that too particularly in emerging markets can be highly profitable, given the growth prospects naturally existing in such regions. But before dealing with di stressed firms it is very important to understand how to evaluate such firms. If the valuations can be done accurately then it can lead to windfall gains.

A Day Away From Her Final Exam - 1489 Words

Team Lyle – Elizabeth Scalco, Tyler Kerr, James Sylvia, Cory Casal Extenuating Circumstances Jessica is college student, who is a day away from her final exam in a very critical class. In the class, she is on the borderline of an A or B, but she needs to get an A in order to look like a solid prospect for medical school. Unfortunately, Jessica just had a devastating death in the family the week of the final, which has caused her to lose complete focus on her schoolwork. With her critical final exam the next day, she realized she is not prepared. With that in mind, Jessica comes up with a plan to cheat during the final. She recruits the help of her friend Candi to cheat on the final exam with her. They decide to communicate the answers to†¦show more content†¦Jessica explains that she just had a death in the family that has affected her a lot. She continues to say that she has not been able to study due to the death. Jessica also tells Dr. Lopez that she had asked Candi to help her out. Candi adds that she felt so bad for Jessica and all tha t she had to go through, so she felt obligated to help her friend out. Dr. Lopez knows Jessica and Candi pretty well and they have become fairly close over the semester. She would not have expected two of her brightest students to commit such an act of dishonesty. As Dr. Lopez continues to ponder the circumstances, she recalls that there were signs of Jessica slipping into depression. As a young adult, Dr. Lopez struggled with depression, so she knows the signs and what Jessica is going through. Dr. Lopez knows the impact of failing Jessica will have on her future. However, she is very concerned about the spiraling downfall of Jessica’s mental health. As a new professor at the university, Dr. Lopez does not want to get caught in a cheating scandal if she lets the two girls go. She has just 24 hours to turn in her final grades. How should Dr. Lopez handle the situation? Discussion Questions 1.) In your opinion, what should Dr. Lopez do? 2.) Based on Jessica’s circumstances, should the incident be looked at with further consideration by Dr. Lopez? 3.) It is clearly stated in The Honor Code of Institutions of Higher Education that cheating is wrong. Using a

Midsummer Night’s Dream Free Essays

Midsummer Night’s Dream was written by William Shakespeare in the mid 1590s and probably before Romeo and Juliet. It is a hilarious comedy and the plot conveys the creative genius of the great playwright. It is indeed a ‘comedy of errors’ where the mistakes of a well-meaning immortal being have the most unexpected and extremely captivating and enchanting effects. We will write a custom essay sample on Midsummer Night’s Dream or any similar topic only for you Order Now The characters are inspired from many sources such as Greek mythology, English country folklore and rich and diverse texts. However the plot, unlike many other Shakespearean plays which are inspired from older plays, is very original. The comedy is entirely Shakespearean and the signature style of the Bard is evident. The plot is made more interesting and the comedy is made more pronounced by the many literary devices and symbols used by Shakespeare. The most interesting of these is the effect created by the existence of another play within the play. One set of characters in Midsummer Night’s Dream – a band of Athenian craftsmen, is rehearsing a play they wish to perform at the wedding of the Theseus (the Duke of Athens) to Hippolyta, his beloved. The play that these craftsmen wish to perform is the most lamentable comedy and most cruel death of Pyramus and Thisbe. This paper attempts to explore the way this inner play mirrors the actions of Midsummer Night’s Dream. The story of Pyramus and Thisbe has been taken from tragic poetry by Ovid. Pyramus and Thisbe were young lovers whose liaison was not acceptable to their parents as they belonged to feuding families. They spoke to each other through a hole in the wall that separated them. One night, a lion happens to attack Thisbe. While she manages to escape, the lion tatters her mantle to shreds. Pyramus sees her tattered mantle and thinks that his lover is dead. In anguish, he commits suicide without waiting to verify his troubled assumptions. Later, when Thisbe finds his corpse, she also commits suicide. The concept of the ‘double suicide’ and the extreme tragedy that it creates has been used in Midsummer Night’s Dream to create an altogether different and an almost contrasting effect. Shakespeare has used the tragedy of Pyramus and Thisbe in a most unconventional manner so that it has the most interesting consequences upon the analysis of the play Midsummer Night’s Dream. We examine these consequences in the following parts of the paper. The most important effect that the concept of ‘play within a play’ creates is that it highlights the outer plot of the unfortunate events in the life of the young Athenian lovers. The story of Pyramus and Thisbe is a very tragic tale and would bring tears to the eyes of most audience. But the unintentionally hilarious portrayal of this tragic story by a group of inexperienced craftsmen, ill-suited as actors, makes a tragedy seem funny. Similarly, the untoward incidents that happen to the fours lovers are horrible and almost terrifying if seen out of context of the play. But by sheer genius of the playwright and antics of certain characters like Puck and Bottom, the tale is converted into something the audience can laugh at. Thus the inner plot (i.e. the performance of the tragic play in a comic manner) mirrors the outer plot (i.e. the almost tragic incidents in the forest presented in a funny manner). The Athenian craftsmen have decided to enact the tragedy of Pyramus and Thisbe for the Duke’s wedding. This fact heightens the comedy in a very endearing way. The craftsmen are not suited to the enactment of such a refined play. They are poor actors; they have bumbling speech; they have such ludicrous concerns about the performance that they create a very funny prologue for their play. They are concerned that the lion might frighten the ladies in the audience; the suicide of Pyramus might not be taken well and are also concerned about how they will create the effect of moonlight and the wall that separates the lovers. To take care of these concerns, they insert an explanation in the prologue of the play insisting that the lion is not real and the actor playing Pyramus is not indeed dead. It creates an uproarious effect. However, they mean well, a fact acknowledged even by the Duke at the end of their performance. Another effect of the inner plot is that it underlines the creative brilliance of Shakespeare. He uses the inner plot perfectly to mirror the outer plot, even as we find that the inner plot does not have any effect on the outer plot. The parallel inner plot just creates a comical side track even as unwittingly it mirrors the main plot. The play about Pyramus and Thisbe is performed on stage after all the issues and problems have been successfully resolved the main play is nearing a happy ending. The performance thus has no impact on the actual plot of the play. But the funny performance heightens the feeling of well- being created by the resolution of all the problems that the main characters encountered. Midsummer Night’s Dream is a brilliant comedy. The effect of the inner plot contributes a lot to the play. This complex literary device used by Shakespeare creates a riotous effect. Perhaps the brilliance of the play is accorded more luster due to this clever ‘play within a play’ ploy used by the playwright. The analysis of this device makes the play even more endearing as each reading reveals more subtle ways in which the inner plot mirrors the out one. That is why, perhaps, this play remains one of the most famous of Shakespearean comedies. REFERANCES (1)  Ã‚   David Garrison, Chapter 10 – Shakespeare’s Pyramus and Thisbe in Midsummer Night’s Dream, â€Å"Gongora and the â€Å"Pyramus and Thisbe† Myth from Ovid to Shakespeare†, Publisher: Juan de la Cuesta, Newark, DE, 1994, pg143 (2)  Ã‚   Jonathan Bate, â€Å"Shakespeare and Ovid†, Oxford University Press, 1994                         How to cite Midsummer Night’s Dream, Essay examples

Codification in English for Origins and Development- myassignmenthelp

Question: Discuss about theCodification in English for Origins and Development. Answer: Introduction Codification is an essential process through which a language is standardized. It helps the language to gain a form that is easily understandable by everyone. Even the people who do not use that specific language as their mother tongue can use it with ease if a specific structure is clearly defined. Grammar is the tool that is used to standardize a language and further modifications are done by reshaping words and phonetics. Two of the most important tools to facilitate in the codification process are grammar and the making of dictionaries (Braine 2014). Grammar helps to give a formidable structure to the language which makes it easy to understand and fathom how the language operates; while dictionaries help to give an idea as to which are the accepted words in the language and helps to create the vocabulary of the language. Dictionaries also help to make the user know the meaning of the words of the language, which helps to understand which words are best suited for a purpose and ac cordingly employ those words to deliver the opinions and facts in the best possible way (Sung 2016). The paper seeks to give answers as to these aspects regarding how the English language was codified and how and why were grammar standardized and dictionary books were created. History of English language codification The linguistic term codification normally refers to the different methods that are used to standardize a language, English for the case of the current paper, which was coined by Einar Haugen, a popular linguist. It was defined as the process leading to minimal variation in form. This means that the language is more or less of the same form across the places where it is spoken. Creating dictionaries, guides about how to use different styles and guidelines of using the language, a structure put forth by grammar books are all tools that are used to standardize a language (Brems 2015). Codification is a continuous and ongoing process; but the most important period was during the 18th century, where a huge number of grammar books and dictionaries were being published, all trying to give the language a proper structure. Among these, the most notable were Samuel Johnsons Dictionary of the English Language, published in the Great Britain in 1755, and Noah Websters The American Spelling Book, published in 1783 in the United States. Codification is often seen as the final process in the standardization of a language. During the 16th and 17th centuries, the English language was given a lot of attention in the attempt to standardize it. The victory of Henry the 8th over the Catholic church led to a fall in its control over education and that made the importance of Latin to fall in terms of use (Kroskrity 2015). The language of the emerging nation of England as a state required it to be standardized in order to be used widely. In 1523, one of the first grammar books, A Shorte Introduction of Grammar was published by William Lily, that took an attempt to give a standard idea of language. The stark disparity in the number of grammar books that were published before and after 1600 is huge and is one of the best evidences that more people were trying to standardize the language (Mosel 2014). The first grammar book that tied to give a logical explanation regarding how does English work as a language or tried to give a p roper idea about the spelling and syntax of the language was Bullokars Bref Grammar for English. This was the first book that described how English should be and not just how it was. Ways to standardize There are a few ways and methods that are put into action to standardize languages. Some being: Dialect leveling: This refers to the process of lingual standardization by reducing, or even eliminating, the differences that a language has in different regions. This happens over a period of time and several generations. English across the countries are increasingly becoming generic and loosing local characters. This may be attributed to the advent of the internet. Linguistic imperialism: This is when one language is imposed on the speakers of another language and subjugate them to use this new language instead their native one. The primary example of this would the expansion of English language. Purism: This means holding a very conservative perspective regarding the use and development of a language. The problem with English in this aspect is, despite some vehement defenders, it is not at all pure and has inputs from numerous other languages, words it has molded and incorporated as its own. Linguistic insecurity: This happens when the users of a certain language are not confident enough to think that their use of the language is not up to the mark of the standard form of the language. This feeling of insecurity prompts them to alter their unique way of using the language and bring it in accordance to how other people use it (Weber 2015). This makes everyone trying to speak or use the language in the same way, making the language standardized. Prescriptivism: This notion refers to the belief that one language, or dialect of the same language, is superior to the others and ought to be promoted more. This is another form of purism, that hails a particular dialect and form an d dismisses another. This makes some users of a language to be more controlling and tend to try and make others speak and use the language as they see fit and the only proper way. Necessities for dictionaries Dictionaries are one of the two pillars that uphold the basic tenets of any language. A dictionary helps an individual to be autonomous, who does not need to be reliant on others in order to properly use the language. Dictionaries help to shape a language in many ways. Dictionaries are essentially the compilation of words that are accepted in a language and can best explain what one wants to mean. A proper notion and knowledge about these words can help to translate better: without the knowledge on words, it is tricky to communicate with people who speak another language, simply because translations are rendered useless. Dictionaries help an individual to use proper grammar as well as giving ideas and knowledge about the background of a word and also how it should be pronounced and the word family it belongs to, the properties of that segment of words and also the best ways and situations to use them (Algeo and Butcher 2013). Dictionaries also help to give the knowledge regarding the different forms of the same word: how it is spoken as a verb or as a noun or as an adverb. Dictionaries were being commissioned more and more in numbers during the period of the industrial revolution in Europe. In that time, there was a great need to educate the people because the lifestyle was changing fast and with that the outlook and views on different things were quickly changing. Every country had people who were writing their own and selling dictionaries. With the industrial revolution came the advent of scientific research and new discoveries, inventions, innovations were being done every day. This was one of the most important reasons to develop and standardize English as a language (Pennycook 2017). The need to communicate about the new scientific discoveries and to expand the knowledge. English helped in this aspect and it was necessary to give a proper form that would enable the scientists to discuss about the new researches that were going on around the world. Books being expensive during that time, dictionaries were the only option through which the idea and the knowledge about the language could be spread. This had another political aspect to it: the rise of English as a language resulted in the reduction of Latin as in popularity. This was used by the royal families and churches to write books and scrolls. English suddenly made everyone able to read and knowledge was rendered to be free. This simultaneously paved the path for the monarchy to fall and the rise of the educated middle class was initiated. There are many criteria for a word to be included in a dictionary. The process is lengthy and requires a lot of requirements to be fulfilled. At the very beginning, it must be observed very carefully which words are used the most and how are they being used (Aarts, Chalker and Weiner 2014). This gives important insight regarding how important is a particular word. One good way to achieve this is by reading daily publications in every possible way. Online or digital publications are also given a lot of emphasis in todays world as the internet has been seen to be the reason for the establishment of many words in popular culture. If any of these new words are found to be in use for a long period of time and if they are even started to be used in official work as well, albeit not being included in the dictionary even then, then these words are tried to be given a proper definition (Knowles 2014). To observe and understand the trends and situations where these words are used can help to u nderstand what purpose do these words serve and may they be used. The definitions are established on this and any further use of the words are kept in accordance with the explanations of the words (Kubota 2014). The sources of these words are of paramount importance as they hold the key to understand the use of the words. Noting down the sources of these words is called citations and gives important understanding regarding just how much used is the word. These citations are then compiled and alphabetic segments are divided into according to alphabets. While new words are being incorporated into the dictionary, already existing words are also examined to see whether there have been any changes in their definition or what they represent. Throughout the history of language, numerous words have gone through a drastic change in terms of what they define or refer to. The words are then included into the dictionary with a clear description, how should it be pronounced and what is the best situation to use it. Prescriptivism and descriptivism of the dictionary This term, as defined earlier, refers to the notion that one language or dialect is better than another and leads to subjugation of one of them. But in a broad and general sense, most of the words that are used today or are part of the dictionaries, are descriptive. The only words that come across as prescriptive are mostly slangs or are non-standard. Prescriptive words are used these days only in cases of being misused. Descriptivism means taking an objective approach towards the language, while prescriptivism is more like a set of rules that dictate what should be the structure of the language (Gray 2014). In the modern world, it is hard for anything to have such a hard and fast rule. This makes almost all the modern day dictionaries to be descriptive rather than prescriptive. References Aarts, B., Chalker, S. and Weiner, E., 2014.The Oxford dictionary of English grammar. Oxford University Press. Algeo, J. and Butcher, C.A., 2013.The origins and development of the English language. Cengage Learning. Braine, G. ed., 2014.Teaching English to the world: History, curriculum, and practice. Routledge. Brems, L., 2015. Martin Hilpert, Construction Grammar and its Application to English.English Text Construction,8(1), pp.132-136. Gray, W., 2014. Codification, Decodification and Recodification: History, Politics and Procedure. InCodification in International Perspective(pp. 3-10). Springer International Publishing. Knowles, G., 2014 .A cultural history of the English language. Routledge. Kroskrity, P.V., 2015. Designing a dictionary for an endangered language community: lexicographical deliberations, language ideological clarifications. Kubota, R., 2014. Standardization of language and culture.Rethinking language and culture in Japanese education: Beyond the standard, pp.19-34. Mosel, U., 2014. Corpus linguistic and documentary approaches in writing a grammar of a previously undescribed language. Pennycook, A., 2017.The cultural politics of English as an international language. Taylor Francis. Sung, C.C.M., 2016. Exposure to multiple accents of English in the English Language Teaching classroom: from second language learners' perspectives.Innovation in Language Learning and Teaching,10(3), pp.190-205. Weber, J.J., 2015. What Is a Language? InLanguage Racism(pp. 21-49). Palgrave Macmillan UK.

Space Exploration Essay Example For Students

Space Exploration Essay H By: Jigar Bhakta Space Exploration Essay: FROM THE PAST TO THE FUTURE Ever since the beginning of time, mankind has been fascinated with wonders of space. Before the mid-1900s, all mankind could do was gaze at the stars from Earth and wonder what it would be like to go into space. Man would look through telescopes and make theories on how the universe worked. During the mid-1900s, mankind finally was able to send a man into space and explore the wonders of space first hand. So why do humans explore space? Well, it is our fascination with the unknown. We will write a custom essay on Space Exploration specifically for you for only $16.38 $13.9/page Order now At first, all mankind did was look up and wonder how things became what they are now. We started to think that all celestial bodies revolved around the Earth, and the Earth was the center of the entire universe. Galileo Galelie later disproved this theory. Even with growing knowledge in the field, it was not until 1957 when the first Earth orbiter, the Soviets Sputnik 1, was sent into space and placed in orbit at an altitude of 1,370 miles and weighed 184 pounds. Later in that year, the Soviets sent Sputnik 2 into space with a dog named Laika. Laika was the first animal to venture into space. Then in 1985, the United States successfully sent their very own satellite into space. In 1960, the Soviets launched to dogs into space and successfully returned them to Earth. From this point started the space race. The space race was a challenge between the USSR and the United States to see who could land a man on the moon first. In 1961, the first man in space was cosmonaut Yuri Gagarin who was in space for 60 minutes before returning to Earth in Vostok 1 and was sent by the USSR. Astronaut Shepard flew the first manned sub-orbital space-flight by the Americans. The first true American orbital flight was by John Glen and he stayed in space for five hours in Mercury 6 in 1962. Then in 1963, the USSR sent the first woman into space; her name was Valentina Tereshkova-Nikaleva. They also had the first person to take a space-walk in 1965. In 1968, the National Aeronautics and Space Administration or NASA tested the first Saturn 5 rocket, which would be used for the Apollo missions. The first manned Apollo missions and the first flight around the moon took place in 1968. Finally, on July 21, 1969, the United States placed the first man on the moon winning the space race. The challenge for mankind at present is placing a human on Mars. We have already sent probes on to Mars and roamed some of its terrain with the rover known as Sojourner. Sojourner was taken to Mars on NASAs Mars Pathfinder and was the first wheeled vehicle to operate on another planetary surface. The Mars pathfinder sent photographs, atmospheric measurements, and a few other important data that will contribute to taking a man to Mars. While pathfinder sent data, Sojourner examined rocks and soil samples with a camera and Alpha Proton X-ray Spectrometer, providing useful data on chemical compositions and radiation bounced back from rocks and dust. The mission finally ended when the Pathfinder stopped responding to commands from NASA. NASA has sent two other probes to Mars, but both malfunctioned and were destroyed on impact on the Martian surface. The US and a few other countries have joined together and are constructing the International Space Station or the ISS. The ISS is scheduled to be completed in 2004 and will be continuously occupied by up to seven crewmembers. The space station is envisioned to be a world-class research facility in which scientist can study Earth and space, as well as explore the medical effects of long durations of weightlessness in space and the behavior of materials in a weightlessness environment, and the practicality of space manufacturing techniques. Now, the future of space exploration depends on many factors. Some of these factors are as followed: how much technology advances, how political forces change rivalries as well as partnerships with other nations, and how important space exploration is to the general public. .u70aae7260d66494fce7489c237220890 , .u70aae7260d66494fce7489c237220890 .postImageUrl , .u70aae7260d66494fce7489c237220890 .centered-text-area { min-height: 80px; position: relative; } .u70aae7260d66494fce7489c237220890 , .u70aae7260d66494fce7489c237220890:hover , .u70aae7260d66494fce7489c237220890:visited , .u70aae7260d66494fce7489c237220890:active { border:0!important; } .u70aae7260d66494fce7489c237220890 .clearfix:after { content: ""; display: table; clear: both; } .u70aae7260d66494fce7489c237220890 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u70aae7260d66494fce7489c237220890:active , .u70aae7260d66494fce7489c237220890:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u70aae7260d66494fce7489c237220890 .centered-text-area { width: 100%; position: relative ; } .u70aae7260d66494fce7489c237220890 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u70aae7260d66494fce7489c237220890 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u70aae7260d66494fce7489c237220890 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u70aae7260d66494fce7489c237220890:hover .ctaButton { background-color: #34495E!important; } .u70aae7260d66494fce7489c237220890 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u70aae7260d66494fce7489c237220890 .u70aae7260d66494fce7489c237220890-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u70aae7260d66494fce7489c237220890:after { content: ""; display: block; clear: both; } READ: Teenage peer pressure drugs and alcohol Essay NASA is working on a single-stage-to-orbit (SSTO) vehicle, but . Space Exploration Essay Example For Students Space Exploration Essay Ever since the beginning of time, mankind has been fascinated with wonders of space. Before the mid-1900s, all mankind could do was gaze at the stars from Earth and wonder what it would be like to go into space. Man would look through telescopes and make theories on how the universe worked. During the mid-1900s, mankind finally was able to send a man into space and explore the wonders of space first hand. So why do humans explore space? Well, it is our fascination with the unknown. At first, all mankind did was look up and wonder how things became what they are now. We started to think that all celestial bodies revolved around the Earth, and the Earth was the center of the entire universe. Galileo Galelie later disproved this theory. Even with growing knowledge in the field, it was not until 1957 when the first Earth orbiter, the Soviets Sputnik 1, was sent into space and placed in orbit at an altitude of 1,370 miles and weighed 184 pounds. Later in that year, the Soviets sent Sputnik 2 into space with a dog named Laika. Laika was the first animal to venture into space. We will write a custom essay on Space Exploration specifically for you for only $16.38 $13.9/page Order now Then in 1985, the United States successfully sent their very own satellite into space. In 1960, the Soviets launched to dogs into space and successfully returned them to Earth. From this point started the space race. The space race was a challenge between the USSR and the United States to see who could land a man on the moon first. In 1961, the first man in space was cosmonaut Yuri Gagarin who was in space for 60 minutes before returning to Earth in Vostok 1 and was sent by the USSR. Astronaut Shepard flew the first manned sub-orbital space-flight by the Americans. The first true American orbital flight was by John Glen and he stayed in space for five hours in Mercury 6 in 1962. Then in 1963, the USSR sent the first woman into space; her name was Valentina Tereshkova-Nikaleva. They also had the first person to take a space-walk in 1965. In 1968, the National Aeronautics and Space Administration or NASA tested the first Saturn 5 rocket, which would be used for the Apollo missions. The first manned Apollo missions and the first flight around the moon took place in 1968. Finally, on July 21, 1969, the United States placed the first man on the moon winning the space race. The challenge for mankind at present is placing a human on Mars. We have already sent probes on to Mars and roamed some of its terrain with the rover known as Sojourner. Sojourner was taken to Mars on NASAs Mars Pathfinder and was the first wheeled vehicle to operate on another planetary surface. The Mars pathfinder sent photographs, atmospheric measurements, and a few other important data that will contribute to taking a man to Mars. While pathfinder sent data, Sojourner examined rocks and soil samples with a camera and Alpha Proton X-ray Spectrometer, providing useful data on chemical compositions and radiation bounced back from rocks and dust. The mission finally ended when the Pathfinder stopped responding to commands from NASA. NASA has sent two other probes to Mars, but both malfunctioned and were destroyed on impact on the Martian surface. The US and a few other countries have joined together and are constructing the International Space Station or the ISS. The ISS is scheduled to be completed in 2004 and will be continuously occupied by up to seven crewmembers. The space station is envisioned to be a world-class research facility in which scientist can study Earth and space, as well as explore the medical effects of long durations of weightlessness in space and the behavior of materials in a weightlessness environment, and the practicality of space manufacturing techniques. Now, the future of Space Exploration Essay depends on many factors. Some of these factors are as followed: how much technology advances, how political forces change rivalries as well as partnerships with other nations, and how important space exploration is to the general public. .u30a987f63aec3ff2042dcc70b44233cc , .u30a987f63aec3ff2042dcc70b44233cc .postImageUrl , .u30a987f63aec3ff2042dcc70b44233cc .centered-text-area { min-height: 80px; position: relative; } .u30a987f63aec3ff2042dcc70b44233cc , .u30a987f63aec3ff2042dcc70b44233cc:hover , .u30a987f63aec3ff2042dcc70b44233cc:visited , .u30a987f63aec3ff2042dcc70b44233cc:active { border:0!important; } .u30a987f63aec3ff2042dcc70b44233cc .clearfix:after { content: ""; display: table; clear: both; } .u30a987f63aec3ff2042dcc70b44233cc { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u30a987f63aec3ff2042dcc70b44233cc:active , .u30a987f63aec3ff2042dcc70b44233cc:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u30a987f63aec3ff2042dcc70b44233cc .centered-text-area { width: 100%; position: relative ; } .u30a987f63aec3ff2042dcc70b44233cc .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u30a987f63aec3ff2042dcc70b44233cc .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u30a987f63aec3ff2042dcc70b44233cc .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u30a987f63aec3ff2042dcc70b44233cc:hover .ctaButton { background-color: #34495E!important; } .u30a987f63aec3ff2042dcc70b44233cc .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u30a987f63aec3ff2042dcc70b44233cc .u30a987f63aec3ff2042dcc70b44233cc-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u30a987f63aec3ff2042dcc70b44233cc:after { content: ""; display: block; clear: both; } READ: The Yellow Wallpaper Gender Roles Essay NASA is working on a single-stage-to-orbit (SSTO) vehicle, but until it is until then, NASA plans to us the space shuttle fleet to the year 2012. . Space Exploration Essay Example For Students Space Exploration Essay Approaching the end of Apollo, my frustration often surfaced. No one in America seemed to care that we were giving up, surrendering the future of the next generation of young people with stars in their eyes. How I wished John F. Kennedy were still alive, challenging us to dare and to dream. I feel the same way today; the boldness and scope of his vision is not to be found today in our space program and in our nation. Entering the twenty-first century, we have an unimaginable array of technology and a generation of young Americans schooled in these technologies. With our powerful economy, we can do anything we set our mind to do. Yet we stand with our feet firmly planted on the ground when we could be exploring the universe. Three decades ago We will write a custom essay on Space Exploration specifically for you for only $16.38 $13.9/page Order now Americans placed six flags on the Moon. Today we no longer try for new and bold space achievements; instead we celebrate the anniversaries of the past. Our work is unfinished Gene Kranz, Failure Is Not An Option Theres a certain something about science which is part of its appeal to me and to many others. Call it a willingness to dream, if you will. Sometimes a dream may be amusing, as with the molecular creations (dodecahedrane, cubane, superphane, basketane, and of course buckminsterfullerene) described in Designing the Molecular World by Philip Ball. Sometimes a dream may be visionary and bold, as with the dream to finally understand the physics that underlies our world. Theres definitely something interesting about the fact that the fundamental particles of the universe can be drawn in a chart on a T-shirt, or that the equations behind classical electromagnetism can be scribbled on a scrap of paper. For some 400 years, scientists have dared to dream that they can understand and explore the universe, ever since Galileo peered into the night skies with a simple telescope. I read a large amount of books and magazines; in addition to the science books that fill my bookshelf, I subscribe to Scientific American and Discover and several other scientific magazines. They all are, in some way, connected with the dreams of science, whether it be the dreams of the past (scientific history) or dreams about the future of science. How excited I was when I saw the March 2000 issue of Scientific American, which at the top had the words Special Report: Sending Humans to Mars! How incredibly nifty. However, I was considerly less enthusiastic when I actually read the articles inside. In the article How to Go to Mars, George Musser and Mark Alpert mention, In all the proposals for sending humans to Mars, the crucial first step is launching the spacecraft into a low Earth orbit (200 to 500 kilometers up). The basic problem is that any manned craft using present-day propulsion technologies will need a huge supply of propellant to get to Mars and hence will be extremely heavy: at least 130 metric tons and possibly twice that much. Thats fine. No one ever said that attaining dreams was easy. But I was absolutely shocked when I looked at the chart on the following page. This chart is one of the most dismal and saddening things Ive ever seen. Its a horizontal bar chart divided into two parts: an upper one labeled Existing Launch Vehicles and a lower one labeled Proposed Launch Vehicles; the bars in each part are different colors to emphasize which vehicles currently exist and which are proposed. The horizontal scale reads Lift Capacity (metric tons to low Earth orbit) and goes from 0 to 100. Yes, thats rather distressing already. The existing launch vehicles, the Titan 4B and the Space Shuttle, we are told by this chart, can lift 22 and 23 metric tons, respectively. The proposed launch vehicles, the Delta 4 Heavy, the VentureStar, and the Magnum, can lift 23, 25, and 80 metric tons, respectively. The Magnums bar is obviously emphasized, being almost four times longer than the diminutive bars above it. Wow. 80 metric tons to low Earth orbit. The caption to the side, reads, Current launch vehicles cannot meet the needs of a human mission to Mars. .u2a118edecf65ebef5096ab2b42e9b807 , .u2a118edecf65ebef5096ab2b42e9b807 .postImageUrl , .u2a118edecf65ebef5096ab2b42e9b807 .centered-text-area { min-height: 80px; position: relative; } .u2a118edecf65ebef5096ab2b42e9b807 , .u2a118edecf65ebef5096ab2b42e9b807:hover , .u2a118edecf65ebef5096ab2b42e9b807:visited , .u2a118edecf65ebef5096ab2b42e9b807:active { border:0!important; } .u2a118edecf65ebef5096ab2b42e9b807 .clearfix:after { content: ""; display: table; clear: both; } .u2a118edecf65ebef5096ab2b42e9b807 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u2a118edecf65ebef5096ab2b42e9b807:active , .u2a118edecf65ebef5096ab2b42e9b807:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u2a118edecf65ebef5096ab2b42e9b807 .centered-text-area { width: 100%; position: relative ; } .u2a118edecf65ebef5096ab2b42e9b807 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u2a118edecf65ebef5096ab2b42e9b807 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u2a118edecf65ebef5096ab2b42e9b807 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u2a118edecf65ebef5096ab2b42e9b807:hover .ctaButton { background-color: #34495E!important; } .u2a118edecf65ebef5096ab2b42e9b807 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u2a118edecf65ebef5096ab2b42e9b807 .u2a118edecf65ebef5096ab2b42e9b807-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u2a118edecf65ebef5096ab2b42e9b807:after { content: ""; display: block; clear: both; } READ: Communist Manifesto Essay Paper Boosting a 130-ton Mars craft into low Earth . Space Exploration Essay Example For Students Space Exploration Essay On May 25, 1961, John F. Kennedy delivered one of the most memorable State of the Union addresses in the history of the United States. I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to the earth (http://www.cs.umb. edu/jfklibrary, President John F. Kennedys Special Message to the Congress on Urgent National Needs). With those words, Kennedy launched a new era of Space Exploration Essay in the United States. Although the National Aeronautics And Space Administration was created in 1958 by the National Aeronautics and Space Act (http://www.hq.nasa. gov, Key Documents), and the Russians already launched the first satellite into space in 1957, the US was still at a stand still on the subject. What the country needed was a wake-up call, and that is exactly what it got from one of the most celebrated speakers in its history. The new era promised much, but expected little. From USAs struggle to be the dominant world power in the Cold War Era, to the careless depletion of natural resources in the Information Age, space exploration and astronauts were and will be the real keys to the new millennium and beyond. Before looking into the future, or even evaluating the present, one must look in detail at the history of the space project. The missions that gave scientists and engineers the necessary data and experience to make new, safer, more reliable and intricate equipment were launched long before there was realistic talk of sending probes to Mars. We will write a custom essay on Space Exploration specifically for you for only $16.38 $13.9/page Order now The astronauts that helped shape the training programs, took the beatings of primitive flight tests, and died in order to serve their country were born before World War II. And even the Russian Space Program was crucial to what the space program is today. It fueled competition, and provided more resources for American engineers. Until Apollo 11, they were ahead of the Americans in almost everyway, with their launch of Sputnik, a unmanned satellite in 1957, and their countless firsts in orbiting and space walks. Yuri Gagarin was the first man in space. Although most of the missions that have been launched have been important in their own ways, some missions just stand out, whether it was the first step on the Moon, or the first mission to Mars. NASAs first high profile program was Project Mercury, an effort to learn if humans could survive in space. It was the prelude to the later missions, and it gave NASA the necessary data to build better, and more comfortable ships for humans to stay in space for extended periods of time. The first launch of the Mercury program was the LJ-1 on August 21, 1959. At thirty-five minutes before launch, evacuation of the area had been proceeding on schedule. Suddenly, half an hour before launch-time, an explosive flash occurred. When the smoke cleared it was evident that only the capsule-and-tower combination had been launched, on a trajectory similar to an off-the-pad abort (http://www. ksc.nasa.gov, Mercury: LJ-1). The first mildly successful spacecraft launch occurred September 9, 1959. Although the BJ-1 ship experienced some problems, and the timing on some of the separation procedures was off, the capsule made it back to earth some seven hours after lift-off. The capsule orbited the earth for approximately thirteen minutes (Mercury: BJ-1). Mercury mission MA-5 was the first to carry live organisms into sub-orbit. Although Enos a chimpanzee, was not a perfect substitute for a human, he served as a good test for the environmental controls of the capsule. He orbited the earth in total weightlessness for over three hours and upon landing was in perfect physical condition (Mercury: MA-5). On May 5, 1961, Freedom 7 was the first launch to carry humans into space. Alan B. Shepard, Jr. .ucfd38ada86fad34bc4a10ba248a0a7dd , .ucfd38ada86fad34bc4a10ba248a0a7dd .postImageUrl , .ucfd38ada86fad34bc4a10ba248a0a7dd .centered-text-area { min-height: 80px; position: relative; } .ucfd38ada86fad34bc4a10ba248a0a7dd , .ucfd38ada86fad34bc4a10ba248a0a7dd:hover , .ucfd38ada86fad34bc4a10ba248a0a7dd:visited , .ucfd38ada86fad34bc4a10ba248a0a7dd:active { border:0!important; } .ucfd38ada86fad34bc4a10ba248a0a7dd .clearfix:after { content: ""; display: table; clear: both; } .ucfd38ada86fad34bc4a10ba248a0a7dd { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .ucfd38ada86fad34bc4a10ba248a0a7dd:active , .ucfd38ada86fad34bc4a10ba248a0a7dd:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .ucfd38ada86fad34bc4a10ba248a0a7dd .centered-text-area { width: 100%; position: relative ; } .ucfd38ada86fad34bc4a10ba248a0a7dd .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .ucfd38ada86fad34bc4a10ba248a0a7dd .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .ucfd38ada86fad34bc4a10ba248a0a7dd .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .ucfd38ada86fad34bc4a10ba248a0a7dd:hover .ctaButton { background-color: #34495E!important; } .ucfd38ada86fad34bc4a10ba248a0a7dd .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .ucfd38ada86fad34bc4a10ba248a0a7dd .ucfd38ada86fad34bc4a10ba248a0a7dd-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .ucfd38ada86fad34bc4a10ba248a0a7dd:after { content: ""; display: block; clear: both; } READ: Tuesdays With Morrie Essay was the only crewmember, and the successful mission lasted for over 15 minutes (Mercury: MR-3). More manned flights from the Mercury series followed, highlighted by the Friendship 7, where on February 20, 1962, John Glenn was the first American in actual orbit, and he orbited the earth three times for a little under five hours (Mercury: MA-6). The last mission from the Mercury project came on May 15, 1963, where L. Gordon Cooper was in orbit in the Faith 7 for over a day. Total weightless time was over thirty-four hours, and the mission was celebrated and deemed more than successful (Mercury: MA-9). Gemini missions followed which built on the success of the Mercury flights, and basically followed the same outlines, except with a crew . Space Exploration Essay Example For Students Space Exploration Essay People have been venturing out into the universe for many years now. In addition to satellites, both women and men astronauts have traveled into space to collect data about the universe. The first human being, the first animal, and the first spacecraft in orbit, were all achievements of the Soviet Union. In 1958 a group known as The National Aeronautics and Space Administration (NASA) was founded. The first probe to escape Earths gravity was the Soviet LUNA 1, launched on Jan. 2, 1959. It passed the Moon and continued into interplanetary space. The U.S. probe Pioneer 4, launched two months later, followed the same path. Later Soviet probes either hit the Moon or passed it and took photographs of the hidden far side, relaying them back to Earth. The first man to travel to space was Yuri Gagarin. History was made on April 12, 1961, when he successfully orbited the earth in the Votsok 1. His flight lasted one hour and 48 minutes and as he circled the earth, his speed was about 17,000 mph on the Votsok 1. Following this mission, Gagarin was killed in a test airplane crash . Neil Armstrong was the first person to ever land on the moon. Born in Wapakoneta, Ohio, he graduated from college in 1955 and joined the NASA team. We will write a custom essay on Space Exploration specifically for you for only $16.38 $13.9/page Order now In 1962, he became the first civilian to enter into an astronaut training program. In 1969, Armstrong headed the Apollo 11 mission, becoing the first human being to set foot on the moon. Other astronauts the accompanied Armstrong on this mission were Edwin E. Aldrin, Jr., and Michael Collins. In 1971, Armstrong became a professor of aerospace engineering at the University of Cincinnati. Valentina Vladimora Nikolayeva Tereshkova was the first woman to enter into space. She joined a Soviet training program in the year 1961 and two years later she successfully orbited the earth 48 times in the Votsok 6. The Sputnik 1 was the first artificial satellite to orbit the earth. It was an aluminum sphere, 58 cm (23 in) in diameter, weighing 83 kg (184 lb). Its orbited around the earth lasted 96.2 minutes. At the end of 57 days the satellite returned to earths atmosphere and was destroyed by aerodynamic frictional heat. Voyager 1 and Voyager 2 were both spacecrafts that were launched to Jupiter. Voyager 2 was launched on August 20, 1977, and Voyager 1 was launched 2 weeks later on September 5, 1977. Voyager 1 made it to Jupiter before Voyager 2 because it took a shorter and quicker route. Photos Voyager 1 and 2 took proved a couple of new facts about Jupiter. One of them is that Jupiter has a ring around it, and also that Jupiters moon has a giant active volcano that spits out sulfur compounds. The moons around Jupiter were found to be icy, rocky balls, with fractures and craters. When Voyager 1 and 2 were heading back they got a few pictures of Saturns rings. These pictures proved that instread of the 3 or 4 rings that were orginally thought to be around Saturn, there are actually thousands of concentric ringlets. The Near Earth Asteroid Rendezvous, also known as NEAR, is a spaceship whose mission it is to explore an asteroid called Eros. The journey time to Eros is approximately 35 months and the cost for launching and building is $122 million. Four years of this operation will cost $40 million. Eros was picked for a couple of reasons and one of them was that it might help solve the mystery of why most meteorites do not resemble their bigger brothers in space. In the years to come, NASA will continue to launch new satellites and explore the great unknown. Some of these satellites will be so big that theyll have to be assembled in outer space. There is still lots more to discover. . Space Exploration Essay Example For Students Space Exploration Essay On May 25, 1961, John F. Kennedy delivered one of the most memorable State of the Union addresses in the history of the United States. I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to the earth (http://www.cs.umb. edu/jfklibrary, President John F. Kennedys Special Message to the Congress on Urgent National We will write a custom essay on Space Exploration specifically for you for only $16.38 $13.9/page Order now Needs). With those words, Kennedy launched a new era of Space Exploration Essay in the United States. Although the National Aeronautics And Space Administration was created in 1958 by the National Aeronautics and Space Act (http://www.hq.nasa. gov, Key Documents), and the Russians already launched the first satellite into space in 1957, the US was still at a stand still on the subject. What the country needed was a wake-up call, and that is exactly what it got from one of the most celebrated speakers in its history. The new era promised much, but expected little. From USAs struggle to be the dominant world power in the Cold War Era, to the careless depletion of natural resources in the Information Age, space exploration and astronauts were and will be the real keys to the new millennium and beyond. Before looking into the future, or even evaluating the present, one must look in detail at the history of the space project. The missions that gave scientists and engineers the necessary data and experience to make new, safer, more reliable and intricate equipment were launched long before there was realistic talk of sending probes to Mars. The astronauts that helped shape the training programs, took the beatings of primitive flight tests, and died in order to serve their country were born before World War II. And even the Russian Space Program was crucial to what the space program is today. It fueled competition, and provided more resources for American engineers. Until Apollo 11, they were ahead of the Americans in almost everyway, with their launch of Sputnik, a unmanned satellite in 1957, and their countless firsts in orbiting and space walks. Yuri Gagarin was the first man in space. Although most of the missions that have been launched have been important in their own ways, some missions just stand out, whether it was the first step on the Moon, or the first mission to Mars. NASAs first high profile program was Project Mercury, an effort to learn if humans could survive in space. It was the prelude to the later missions, and it gave NASA the necessary data to build better, and more comfortable ships for humans to stay in space for extended periods of time. The first launch of the Mercury program was the LJ-1 on August 21, 1959. At thirty-five minutes before launch, evacuation of the area had been proceeding on schedule. Suddenly, half an hour before launch-time, an explosive flash occurred. When the smoke cleared it was evident that only the capsule-and-tower combination had been launched, on a trajectory similar to an off-the-pad abort (http://www. ksc.nasa.gov, Mercury: LJ-1). The first mildly successful spacecraft launch occurred September 9, 1959. Although the BJ-1 ship experienced some problems, and the timing on some of the separation procedures was off, the capsule made it back to earth some seven hours after lift-off. The capsule orbited the earth for approximately thirteen minutes (Mercury: BJ-1). Mercury mission MA-5 was the first to carry live organisms into sub-orbit. Although Enos a chimpanzee, was not a perfect substitute for a human, he served as a good test for the environmental controls of the capsule. He orbited the earth in total weightlessness for over three hours and upon landing was in perfect physical condition (Mercury: MA-5). On May 5, 1961, Freedom 7 was the first launch to carry humans into space. Alan B. Shepard, Jr. .u2cca7caf3eb94925a9a958723da2b412 , .u2cca7caf3eb94925a9a958723da2b412 .postImageUrl , .u2cca7caf3eb94925a9a958723da2b412 .centered-text-area { min-height: 80px; position: relative; } .u2cca7caf3eb94925a9a958723da2b412 , .u2cca7caf3eb94925a9a958723da2b412:hover , .u2cca7caf3eb94925a9a958723da2b412:visited , .u2cca7caf3eb94925a9a958723da2b412:active { border:0!important; } .u2cca7caf3eb94925a9a958723da2b412 .clearfix:after { content: ""; display: table; clear: both; } .u2cca7caf3eb94925a9a958723da2b412 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u2cca7caf3eb94925a9a958723da2b412:active , .u2cca7caf3eb94925a9a958723da2b412:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u2cca7caf3eb94925a9a958723da2b412 .centered-text-area { width: 100%; position: relative ; } .u2cca7caf3eb94925a9a958723da2b412 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u2cca7caf3eb94925a9a958723da2b412 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u2cca7caf3eb94925a9a958723da2b412 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u2cca7caf3eb94925a9a958723da2b412:hover .ctaButton { background-color: #34495E!important; } .u2cca7caf3eb94925a9a958723da2b412 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u2cca7caf3eb94925a9a958723da2b412 .u2cca7caf3eb94925a9a958723da2b412-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u2cca7caf3eb94925a9a958723da2b412:after { content: ""; display: block; clear: both; } READ: Lost Boy Essay was the only crewmember, and the successful mission lasted for over 15 minutes (Mercury: MR-3). More manned flights from the Mercury series followed, highlighted by the Friendship 7, where on February 20, 1962, John Glenn was the first American in actual orbit, and he orbited the earth three times for a little under five hours (Mercury: MA-6). The last mission from the Mercury project came on May 15, 1963, where L. Gordon Cooper was in orbit in the Faith 7 for over a day. Total weightless time was over thirty-four hours, and the mission was celebrated and deemed more than successful (Mercury: MA-9). Gemini missions followed which built on the success of the Mercury flights, and basically followed the same outlines, except with a crew .

Italian Phrases for Shopping in Italy

Italian Phrases for Shopping in Italy When you arrive in Italy, shopping in any context- like at the bakery, the pharmacy, or just any negozio (store)- is inevitable. Plus, who doesn’t bring home a suitcase brimming with local oils and products that read â€Å"Made in Italy†? With that in mind, here are the basic phrases you need to know that can help you get by in any shopping situation. General Shopping Phrases/Vocabulary Quant’à ¨? - How much is it?Quanto costa? - How much is it?Quanto spendo? - How much do I spend? TIP: Use â€Å"quant’à ¨Ã¢â‚¬  or â€Å"quanto spendo† when you have many items and â€Å"quanto costa† when you have just one item. Posso pagare con il bancomat? - Can I pay with my debit card?Accettate carte di credito? - Do you (all) accept credit cards?Accettiamo soltanto i contanti. - We only accept cash.Sto cercando†¦ - I’m looking for†¦ TIP: Notice that the phrase above does not use any preposition like â€Å"per†, for example, to stand in as â€Å"for†. Some phrases in Italian don’t need the preposition in the same way that we do in English, which serves as just another friendly reminder to be careful about directly translating from English to Italian. Sto solo guardando. - I’m just looking.Poi? - Anything else?Qualcos’altro? - Something else?Basta cosà ¬. - That’s all.Vorrei†¦, per favore. - I would like†¦, please.Prendo†¦ - I’ll take†¦Ha bisogno di aiuto? - Do you need help? (formal)Mi piace. - I like it.Non mi piace. - I don’t like it. TIP: If the object you like or don’t like from the above two phrases is plural, like â€Å"le scarpe - the shoes†, then say instead â€Å"Mi piacciono† or â€Å"Non mi piacciono†. È troppo caro. - It’s too expensive.Ha qualcosa di meno costoso? - Do you have anything cheaper? (formal)È un regalo. - It’s a gift.Vuole la confezione regalo? - Would you like it gift-wrapped? (formal)È fatto a mano.  - It’s handmade.È artigianale.  - It’s artisanal/small-scale.La commessa - Shop assistant Phrases for Shopping at a Market Whether you’re going to un mercato all’aperto (an open-air market) or un supermercato (a supermarket), these phrases will help you navigate the experience. Quanto costa al chilo? - How much does it cost per kilo?Quelli come si chiamano? - What are those called?Un etto di†¦(agnello). - 100 grams of†¦(lamb).Come si puà ² cucinare†¦(il vitello)? - How does one cook†¦(veal)?(Otto) fette di†¦(prosciutto cotto), per favore. - (8) slices of...(cooked prosciutto), please.Avete...(le patate)? - Do you have†¦(potatoes)?Posso assaggiare (il pecorino), per favore? - Can I try (the pecorino), please? Phrases for Shopping at a Clothing Store Use these phrases to help you confidently shop for clothing and accessories from the trendiest shops on il corso (the main street) to i mercati delle pulci (flea markets). Sono/Porto/Indosso una taglia†¦(media). - I’m a medium.Vuole provarlo? - Do you want to try it on?Vorrei provare questi, dove sono i camerini?- I’d like to try these on, where are the fitting rooms? TIP: In the phrase above, â€Å"lo† would be used if the item were singular and masculine, like il vestito - the dress. However, if it were singular and feminine, like la sciarpa - the scarf, it would be â€Å"Vuole provarla†? While it’s important to make everything agree, don’t stress if you can’t remember the gender of the object you have. You’ll be safe with using the pronoun â€Å"lo†. Dove sono i camerini? - Where are the fitting rooms?Non mi sta bene. - It doesn’t fit me well.È comodo. - It’s comfortable.Questi (stivali) sono scomodi. - These (boots) are uncomfortable.Preferisco (la rosa). - I prefer pink.Vorrei cambiare questo, per favore. - I would like to exchange this, please.Stai veramente bene con (quel vestito). - You look great in that dress. (informal)L’alta moda - High fashion To get a more detailed description of how to shop for clothes in Italy, check out this article. Types of Stores There are an endless amount of specialty shops in Italy, so here are the names of each of the most popular ones in case you need to ask on how to get to one or need a recommendation. Il centro commerciale - Shopping centerLa bottega - WorkshopIl negozio - StoreIl negozio dell’usato - Second-hand storeL’edicola - NewsstandLa gioielleria - Jewelry shopLa profumeria - Perfume shopLa libreria - BookshopLa tabaccheria - Tobacco shop TIP: Technically this is a tobacco shop, but it is more of a convenience store where you can cigarettes, magazines, bus tickets, and recharge your phone. Il supermercato - SupermarketLa farmacia - PharmacyLa tintoria - DrycleanersLa pasticciera - Pastry shopLa macelleria- ButcherLa latteria - Milk cheese shopLa panetteria - BakeryLa rosticceria - DelicatessenIl fruttivendolo - GreengrocerLa cartoleria - Stationery shop

Request for Scholarship Essay Example | Topics and Well Written Essays - 250 words

Request for - Scholarship Essay Example Earning for the sake of well-being of my children is the dire necessity now for this divorced mother of four children. After marriage, I was a stay at home mother without the responsibility for earning. After the bitter experience of divorce, though it was a great blow in my personal life, I began to find jobs, was employed twice, and on both the occasions was laid off. I am placed at the precarious stage of my life and I am unable to take admission to any medical course without financial assistance. At the same time, I am determined to do the course to eventually get myself qualified as a Sonographer to start with and then do a course in MRI. I have been advised by my well-wishers that if I am able to do this course from a reputed medical institution like yours that will stand me in good stead for my future career opportunities. Taking into consideration my family condition, my earnest desire to enter the health field that provides immense challenges to serve humankind, and to fulfill my long-term career goals, I request you to grant me a scholarship that will cover up the entire tuition fees and other related expenses. I shall remain ever grateful for this magnanimous act by the management of Gurnick Academy of Medical Arts. I request you treat mine as a very special

Critical evaluation of an academic research article Essay

Critical evaluation of an academic research article - Essay Example The article provides a comprehensive ethical analysis through different ethical theories of product placement. An attempt has been made, throughout the article, to identify whether product placement overall is a deceptive practice or not. In this paper we will critically evaluate the research article. The key arguments of the article will be discussed and logic of arguments will be examined. Critical Analysis The article starts with an introduction of the topic in general. The introduction is very well written with the help of previous literature. No major claims are made rather readers are informed regarding the main subject of the article. Overall the article seems to be written in a logical flow with each section placed in the right order. Introduction is strong and everything said in the introduction is substantiated with existing literature. Product placement is a practice of placing a brand or a product in the scene or script of news and entertainment. Product placement has bee n seen in the Hollywood movies for a long time (Fristoe, 2005). The article is trying to evaluate whether this type of marketing is ethical or not. Implicit product placement has also been discussed in the article. The legal status of product placement is also discussed. ... The article does not clearly see product placement as deceptive but it argues that there are aspects of product placement that may not be approved by ethical theories and general public. The article raises questions about the implicit aspect of product placement. The argument made by the article with regards to the implicit product placement is that people should be aware of product placement. If this is not the case then product placement might be deceptive. Existing literature has also raised questions on implicit product placement (Spence & van Heekeren, 2005). The authors argue that when people are not aware of the persuasion then it might be unethical according to categorical imperative and Aristotelian ethics. The former teaches to treat humanity as oneself, and the latter lay burden of right or wrong on the intentions of the actor. According to both ethical theories implicit product placement is unethical, given that people are not aware of such a marketing practice. A strong point of the article is that it has questioned an assumption that is mistreated as fact in the corporate world to justify excessive marketing. Studies have shown that uneducated people might not have a clear idea about how marketing works and they might not be aware of their rights (Culnan, 2006). Marketing can also manipulate people who are not emotionally or financially mature (Laczniak & Murphy, 2006). The assumption that consumers are smart and knowledgeable is not justified and the article too raises questions about it. The authors have tried to remain impartial throughout the article and have attempted to give a genuine account of ethical issues

Answers on history (Liberalism, State Sovereignty, Marxism, The Cold Essay

Answers on history (Liberalism, State Sovereignty, Marxism, The Cold War) - Essay Example One of the questions the paper deals with is liberalism. The term liberalism has its roots in the Age of enlightenment in the eighteenth century. The intellectual and philosophical developments of that age aspired towards governmental consolidation, centralization and primacy of the nation-state, and greater rights for common people. . Its core was a critical questioning of traditional institutions, customs, and morals. The topic modern liberalism is so wide and consists of political, economical, cultural, and social aspects. It emphasizes the rights of individual and equality of opportunities and freedom of thoughts and the freedom of expression of ideas. Enlightenment thinkers believed that systematic thinking might be applied to all areas of human activity. Its leaders believed they could lead their states to progress after a long period of tradition, irrationality, superstition, and tyranny which they imputed to the Middle Ages.

Hopf Algebra Project

Hopf Algebra Project Petros Karayiannis Chapter 0 Introduction Hopf algebras have lot of applications. At first, they used it in topology in 1940s, but then they realized it has applications through combinatorics, category theory, Hopf-Galois theory, quantum theory, Lie algebras, Homological algebra and functional analysis. The purpose of this project is to see the definitions and properties of Hopf algebras.(Becca 2014) Preliminaries This chapter provides all the essential tools to understand the structure of Hopf algebras. Basic notations of Hopf algebra are: Groups Fields Vector spaces Homomorphism Commutative diagrams 1.Groups Group G is a finite or infinite set of elements with a binary operation. Groups have to obey some rules, so we can define it as a group. Those are: closure, associative, there exist an identity element and an inverse element. Let us define two elements U, V in G, closure is when then the product of UV is also in G. Associative when the multiplication (UV) W=U (VW) à ªÃ¢â‚¬Å" ¯ U, V, W in G. There exist an identity element such that IU=UI=U for every element U in G. The inverse is when for each element U of G, the set contains an element V=U-1 such that UU-1=U-1U=I. 2.Fields A field Ã’Å“ is a commutative ring and every element b à Ã‚ µ Ã’Å“ has an inverse. 3.Vector Space A vector space V is a set that is closed under finite vector addition and scalar multiplication. In order for V to be a vector space, the following conditions must hold à ªÃ¢â‚¬Å" ¯ X, Y à Ã‚ µ V and any scalar a, b à Ã‚ µ Ã’Å“: a(b X) = (a b) X (a + b) X=aX + bX a(X+Y)=aX + aY 1X=X A left ideal of K-algebra is a linear subspace that has the property that any element of the subspace multiplied on the left by any element of the algebra produces an element of the subspace. We say that a subset L of a K-algebra A is a left ideal if for every x and y in L, z in A and c in K, we have the following: X +y is in L cx is in L zà ¢Ã¢â‚¬ ¹Ã¢â‚¬ ¦ x is in L If we replace c) with xà ¢Ã¢â‚¬ ¹Ã¢â‚¬ ¦ z is in L, then this would define a right ideal. A two-sided ideal is a subset that is both a left and a right ideal. When the algebra is commutative, then all of those notions of ideal are equivalent. We denote the left ideal as à ¢Ã…  Ã‚ ³. 4.Homomorphism Given two groups, (G,*) and (H, °) is a function f: Gà ¢Ã¢â‚¬  Ã¢â‚¬â„¢H such that à ªÃ¢â‚¬Å" ¯ u, v à Ã‚ µ G it holds that f(u*v)=f(u) °f(v) 5.Commutative diagrams A commutative diagram is showing the composition of maps represented by arrows. The fundament operation of Hopf algebras is the tensor product. A tensor product is a multiplication of vector spaces V and W with a result a single vector space, denoted as V    W. Definition 0.1 Let V and W be Ã’Å“-vector spaces with bases {ei } and {fj } respectively. The tensor product V and W is a new Ã’Å“-vector space,  Ãƒâ€šÃ‚   V      W with basis { ei fj }, is the set of all elements v    w= à ¢Ã‹â€ Ã¢â‚¬Ëœ (ci,j ei    fj ). ci,j à Ã‚ µÃƒâ€™Ã…“ are scalars. Also tensor products obey to distributive and scalar multiplication laws. The dimension of the tensor product of two vector spaces is: Dim(V   W)=dim(V)dim(W) Theorem of Universal Property of Tensor products 0.2 Let V, W, U be vector spaces with map f: V x W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ U is defined as f: (v, w) à ¢Ã¢â‚¬  Ã¢â‚¬â„¢vw. There exists a bilinear mapping b: V x W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ V   W , (v,w) à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ v   Ãƒâ€šÃ‚   w If f: V x W à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ U is bilinear, then there exist a unique function, f: V   Wà ¢Ã¢â‚¬  Ã¢â‚¬â„¢U with f=f °b   Extension of Tensor Products0.3 The definition of Tensor products can be extended for more than two vectors such as; V1 à ¢Ã…  -   V2à ¢Ã…  -  Ãƒâ€šÃ‚   V3 à ¢Ã…  -   à ¢Ã¢â€š ¬Ã‚ ¦..à ¢Ã…  -   VN = à ¢Ã‹â€ Ã¢â‚¬Ëœ( biv1à ¢Ã…  -   v2à ¢Ã…  -   à ¢Ã¢â€š ¬Ã‚ ¦.à ¢Ã…  -   vn )   (Becca 2014) Definition0.4 Let U,V be vector spacers over a field k and ÃŽÂ ½ à Ã‚ µ Uà ¢Ã‚ ¨Ã¢â‚¬Å¡V. If ÃŽÂ ½=0 then Rank (ÃŽÂ ½) =0. If ÃŽÂ ½Ãƒ ¢Ã¢â‚¬ °Ã‚  0 then rank (ÃŽÂ ½) is equal to the smallest positive integer r arising from the representations of ÃŽÂ ½= à ¢Ã‹â€ Ã¢â‚¬Ëœui à ¢Ã‚ ¨Ã¢â‚¬Å¡ vi à Ã‚ µUà ¢Ã‚ ¨Ã¢â‚¬Å¡V for i=1,2,à ¢Ã¢â€š ¬Ã‚ ¦,r. Definition0.5 Let U be a finite dimensional vector space over the field k with basis {u1,à ¢Ã¢â€š ¬Ã‚ ¦.,un}   be a basis for U. the dual basis for U*is {u1,à ¢Ã¢â€š ¬Ã‚ ¦.,un} where ui(uj)= ÃŽÂ ´ij for 1à ¢Ã¢â‚¬ °Ã‚ ¤I,jà ¢Ã¢â‚¬ °Ã‚ ¤n. Dual Pair0.6 A dual pair is a 3 -tuple (X,Y,) consisting two vector spaces X,Y over the same field K and a bilinear map, : X x Yà ¢Ã¢â‚¬  Ã¢â‚¬â„¢K with à ªÃ¢â‚¬Å" ¯x à Ã‚ µ X{0} yà Ã‚ µY: 0 and à ªÃ¢â‚¬Å" ¯y à Ã‚ µ Y{0} xà Ã‚ µX: 0 Definition0.7 The wedge product is the product in an exterior algebra. If ÃŽÂ ±, ÃŽÂ ² are differential k-forms of degree p, g respectively, then   ÃƒÅ½Ã‚ ±Ãƒ ¢Ã‹â€ Ã‚ §ÃƒÅ½Ã‚ ²=(-1)pq ÃŽÂ ²Ãƒ ¢Ã‹â€ Ã‚ §ÃƒÅ½Ã‚ ±, is not in general commutative, but is associative, (ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ §ÃƒÅ½Ã‚ ²)à ¢Ã‹â€ Ã‚ §u= ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ §(ÃŽÂ ²Ãƒ ¢Ã‹â€ Ã‚ §u) and bilinear (c1 ÃŽÂ ±1+c2 ÃŽÂ ±2)à ¢Ã‹â€ Ã‚ § ÃŽÂ ²= c1( ÃŽÂ ±1à ¢Ã‹â€ Ã‚ § ÃŽÂ ²) + c2( ÃŽÂ ±2à ¢Ã‹â€ Ã‚ § ÃŽÂ ²) ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ §( c1 ÃŽÂ ²1+c2 ÃŽÂ ²2)= c1( ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ § ÃŽÂ ²1) + c2( ÃŽÂ ±Ãƒ ¢Ã‹â€ Ã‚ § ÃŽÂ ²2).  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   (Becca 2014) Chapter 1 Definition1.1 Let (A, m, ÃŽÂ ·) be an algebra over k and write mop (ab) = ab à ªÃ¢â‚¬Å" ¯ a, bà Ã‚ µ A where mop=mà Ã¢â‚¬Å¾ÃƒÅ½Ã¢â‚¬Ëœ,Α. Thus ab=ba à ªÃ¢â‚¬Å" ¯a, b à Ã‚ µA. The (A, mop, ÃŽÂ ·) is the opposite algebra. Definition1.2 A co-algebra C is A vector space over K A map Ά: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢C à ¢Ã…  -   C which is coassociative in the sense of à ¢Ã‹â€ Ã¢â‚¬Ëœ (c(1)(1) à ¢Ã…  -  Ãƒâ€šÃ‚   c(1)(2) à ¢Ã…  -   c(2))= à ¢Ã‹â€ Ã¢â‚¬Ëœ (c(1) à ¢Ã…  -  Ãƒâ€šÃ‚   c(2)(1) à ¢Ã…  -   c(2)c(2) )  Ãƒâ€šÃ‚   à ªÃ¢â‚¬Å" ¯ cà Ã‚ µC (Ά called the co-product) A map ÃŽÂ µ: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ k obeying à ¢Ã‹â€ Ã¢â‚¬Ëœ[ÃŽÂ µ((c(1))c(2))]=c= à ¢Ã‹â€ Ã¢â‚¬Ëœ[(c(1)) ÃŽÂ µc(2))] à ªÃ¢â‚¬Å" ¯ cà Ã‚ µC ( ÃŽÂ µ called the counit) Co-associativity and co-unit element can be expressed as commutative diagrams as follow: Figure 1: Co-associativity map Ά Figure 2: co-unit element map ÃŽÂ µ Definition1.3 A bi-algebra H is An algebra (H, m ,ÃŽÂ ·) A co-algebra (H, Ά, ÃŽÂ µ) Ά,ÃŽÂ µ are algebra maps, where Hà ¢Ã…  -   H has the tensor product algebra structure (hà ¢Ã…  - g)(hà ¢Ã…  -   g)= hhà ¢Ã…  -  Ãƒâ€šÃ‚   gg à ªÃ¢â‚¬Å" ¯h, h, g, g à Ã‚ µH. A representation of Hopf algebras as diagrams is the following: Definition1.4 A Hopf Algebra H is A bi-algebra H, Ά, ÃŽÂ µ, m, ÃŽÂ · A map S : Hà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ H such that à ¢Ã‹â€ Ã¢â‚¬Ëœ [(Sh(1))h(2) ]= ÃŽÂ µ(h)= à ¢Ã‹â€ Ã¢â‚¬Ëœ [h(1)Sh(2) ]à ªÃ¢â‚¬Å" ¯ hà Ã‚ µH The axioms that make a simultaneous algebra and co-algebra into Hopf algebra is à Ã¢â‚¬Å¾:   Hà ¢Ã…  - Hà ¢Ã¢â‚¬  Ã¢â‚¬â„¢Hà ¢Ã…  -H Is the map à Ã¢â‚¬Å¾(hà ¢Ã…  -g)=gà ¢Ã…  -h called the flip map à ªÃ¢â‚¬Å" ¯ h, g à Ã‚ µ H. Definition1.5 Hopf Algebra is commutative if its commutative as algebra. It is co-commutative if its co-commutative as a co-algebra, à Ã¢â‚¬Å¾ÃƒÅ½Ã¢â‚¬ =Ά. It can be defined as S2=id. A commutative algebra over K is an algebra (A, m, ÃŽÂ ·) over k such that m=mop. Definition1.6 Two Hopf algebras H,H are dually paired by a map : H H à ¢Ã¢â‚¬  Ã¢â‚¬â„¢k if, =à Ã‹â€ ,Άh>, =ÃŽÂ µ(h) g   >=, ÃŽÂ µ(à Ã¢â‚¬  )= = à ªÃ¢â‚¬Å" ¯ à Ã¢â‚¬  , à Ã‹â€ Ãƒ Ã‚ µ H and h, g à Ã‚ µH. Let (C, Ά,ÃŽÂ µ) be a co-algebra over k. The co-algebra (C, Άcop, ÃŽÂ µ) is the opposite co-algebra. A co-commutative co-algebra over k is a co-algebra (C, Ά, ÃŽÂ µ) over k such that Ά= Άcop. Definition1.7 A bi-algebra or Hopf algebra H acts on algebra A (called H-module algebra) if: H acts on A as a vector space. The product map m: AAà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A commutes with the action of H The unit map ÃŽÂ ·: kà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ A commutes with the action of H. From b,c we come to the next action hà ¢Ã…  Ã‚ ³(ab)=à ¢Ã‹â€ Ã¢â‚¬Ëœ(h(1)à ¢Ã…  Ã‚ ³a)(h(2)à ¢Ã…  Ã‚ ³b), hà ¢Ã…  Ã‚ ³1= ÃŽÂ µ(h)1, à ªÃ¢â‚¬Å" ¯a, b à Ã‚ µ A, h à Ã‚ µ H This is the left action. Definition1.8 Let (A, m, ÃŽÂ ·) be algebra over k and is a left H- module along with a linear map m: Aà ¢Ã…  -Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A and a scalar multiplication ÃŽÂ ·: k à ¢Ã…  - Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A if the following diagrams commute. Figure 3: Left Module map Definition1.9 Co-algebra (C, Ά, ÃŽÂ µ) is H-module co-algebra if: C is an H-module Ά: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢CC and ÃŽÂ µ: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ k commutes with the action of H. (Is a right C- co-module). Explicitly, Ά(hà ¢Ã…  Ã‚ ³c)=à ¢Ã‹â€ Ã¢â‚¬Ëœh(1)à ¢Ã…  Ã‚ ³c(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡h(2)à ¢Ã…  Ã‚ ³c(2), ÃŽÂ µ(hà ¢Ã…  Ã‚ ³c)= ÃŽÂ µ(h)ÃŽÂ µ(c), à ªÃ¢â‚¬Å" ¯h à Ã‚ µ H, c à Ã‚ µ C.   Definition1.10 A co-action of a co-algebra C on a vector space V is a map ÃŽÂ ²: Và ¢Ã¢â‚¬  Ã¢â‚¬â„¢Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V such that, (idà ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ²) à ¢Ã‹â€ Ã‹Å"ÃŽÂ ²=(ΆÃƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ id )ÃŽÂ ²;   id =(ÃŽÂ µÃƒ ¢Ã‚ ¨Ã¢â‚¬Å¡id )à ¢Ã‹â€ Ã‹Å"ÃŽÂ ². Definition1.11 A bi-algebra or Hopf algebra H co-acts on an algebra A (an H- co-module algebra) if: A is an H- co-module The co-action ÃŽÂ ²: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A is an algebra homomorphism, where Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A has the tensor product algebra structure. Definition1.12 Let C be co- algebra (C, Ά, ÃŽÂ µ), map ÃŽÂ ²: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ Hà ¢Ã‚ ¨Ã¢â‚¬Å¡A is a right C- co- module if the following diagrams commute. Figure 6:Co-algebra of a right co-module Sub-algebras, left ideals and right ideals of algebra have dual counter-parts in co-algebras. Let (A, m, ÃŽÂ ·) be algebra over k and suppose that V is a left ideal of A. Then m(Aà ¢Ã‚ ¨Ã¢â‚¬Å¡V)à ¢Ã…  Ã¢â‚¬  V. Thus the restriction of m to Aà ¢Ã‚ ¨Ã¢â‚¬Å¡V determines a map Aà ¢Ã‚ ¨Ã¢â‚¬Å¡Và ¢Ã¢â‚¬  Ã¢â‚¬â„¢V. Left co-ideal of a co-algebra C is a subspace V of C such that the co-product Ά restricts to a map Và ¢Ã¢â‚¬  Ã¢â‚¬â„¢Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V. Definition1.13 Let V be a subspace of a co-algebra C over k. Then V is a sub-co-algebra of C if Ά(V)à ¢Ã…  Ã¢â‚¬  Và ¢Ã‚ ¨Ã¢â‚¬Å¡V, for left co-ideal Ά(V)à ¢Ã…  Ã¢â‚¬  Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V and for right co-ideal Ά(V)à ¢Ã…  Ã¢â‚¬  Và ¢Ã‚ ¨Ã¢â‚¬Å¡C. Definition1.14 Let V be a subspace of a co-algebra C over k. The unique minimal sub-co-algebra of C which contains V is the sub-co-algebra of C generated by V. Definition1.15 A simple co-algebra is a co-algebra which has two sub-co-algebras. Definition1.16 Let C be co-algebra over k. A group-like element of C is c à Ã‚ µC with satisfies, Ά(s)=sà ¢Ã‚ ¨Ã¢â‚¬Å¡s   and ÃŽÂ µ(s)=1 à ªÃ¢â‚¬Å" ¯ s à Ã‚ µS. The set of group-like elements of C is denoted G(C). Definition1.17 Let S be a set. The co-algebra k[S] has a co-algebra structure determined by Ά(s)=sà ¢Ã‚ ¨Ã¢â‚¬Å¡s   and ÃŽÂ µ(s)=1 à ªÃ¢â‚¬Å" ¯ s à Ã‚ µS. If S=à ¢Ã‹â€ Ã¢â‚¬ ¦ we set C=k[à ¢Ã‹â€ Ã¢â‚¬ ¦]=0. Is the group-like co-algebra of S over k. Definition1.18 The co-algebra C over k with basis {co, c1, c2,à ¢Ã¢â€š ¬Ã‚ ¦..} whose co-product and co-unit is satisfy by Ά(cn)= à ¢Ã‹â€ Ã¢â‚¬Ëœcn-là ¢Ã‚ ¨Ã¢â‚¬Å¡cl and ÃŽÂ µ(cn)=ÃŽÂ ´n,0 for l=1,à ¢Ã¢â€š ¬Ã‚ ¦.,n and for all nà ¢Ã¢â‚¬ °Ã‚ ¥0. Is denoted by Pà ¢Ã‹â€ Ã… ¾(k). The sub-co-algebra which is the span of co, c1, c2,à ¢Ã¢â€š ¬Ã‚ ¦,cn is denoted Pn(k). Definition1.19 A co-matrix co-algebra over k is a co-algebra over k isomorphic to Cs(k) for some finite set S. The co-matrix identities are: Ά(ei, j)= à ¢Ã‹â€ Ã¢â‚¬Ëœei, là ¢Ã‚ ¨Ã¢â‚¬Å¡el, j ÃŽÂ µ(ei, j)=ÃŽÂ ´i, j à ¢Ã‹â€ Ã¢â€š ¬ i, j à Ã‚ µS. Set Cà ¢Ã‹â€ Ã¢â‚¬ ¦(k)=(0). Definition1.20 Let S be a non-empty finite set. A standard basis for Cs(k) is a basis {c i ,j}I, j à Ã‚ µS for Cs(k) which satisfies the co-matrix identities. Definition1.21 Let (C, Άc, ÃŽÂ µc) and (D, ΆD, ÃŽÂ µD) be co-algebras over the field k. A co-algebra map f: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢D is a linear map of underlying vector spaces such that ΆDà ¢Ã‹â€ Ã‹Å"f=(fà ¢Ã‚ ¨Ã¢â‚¬Å¡f)à ¢Ã‹â€ Ã‹Å" Άc and ÃŽÂ µDà ¢Ã‹â€ Ã‹Å"f= ÃŽÂ µc. An isomorphism of co-algebras is a co-algebra map which is a linear isomorphism. Definition1.22 Let C be co-algebra over the field k. A co-ideal of C is a subspace I of C such that ÃŽÂ µ (I) = (0) and Ά (ÃŽâ„ ¢) à ¢Ã…  Ã¢â‚¬   Ià ¢Ã‚ ¨Ã¢â‚¬Å¡C+Cà ¢Ã‚ ¨Ã¢â‚¬Å¡I. Definition1.23 The co-ideal Ker (ÃŽÂ µ) of a co-algebra C over k is denoted by C+. Definition1.24 Let I be a co-ideal of co-algebra C over k. The unique co-algebra structure on C /I such that the projection à Ã¢â€š ¬: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ C/I is a co-algebra map, is the quotient co-algebra structure on C/I. Definition1.25 The tensor product of co-algebra has a natural co-algebra structure as the tensor product of vector space Cà ¢Ã…  -D is a co-algebra over k where Ά(c(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡d(1))à ¢Ã‚ ¨Ã¢â‚¬Å¡( c(2)à ¢Ã‚ ¨Ã¢â‚¬Å¡d(2)) and ÃŽÂ µ(cà ¢Ã‚ ¨Ã¢â‚¬Å¡d)=ÃŽÂ µ(c)ÃŽÂ µ(d) à ¢Ã‹â€ Ã¢â€š ¬ c in C and d in D. Definition1.26 Let C be co-algebra over k. A skew-primitive element of C is a cà Ã‚ µC which satisfies Ά(c)= gà ¢Ã‚ ¨Ã¢â‚¬Å¡c +cà ¢Ã‚ ¨Ã¢â‚¬Å¡h, where c, h à Ã‚ µG(c). The set of g:h-skew primitive elements of C is denoted   by Pg,h (C). Definition1.27 Let C be co-algebra over a field k. A co-commutative element of C is cà Ã‚ µC such that Ά(c) = Άcop(c). The set of co-commutative elements of C is denoted by Cc(C). Cc(C) à ¢Ã…  Ã¢â‚¬  C. Definition1.28 The category whose objects are co-algebras over k and whose morphisms are co-algebra maps under function composition is denoted by k-Coalg. Definition1.29 The category whose objects are algebras over k and whose morphisms are co-algebra maps under function composition is denoted by k-Alg. Definition1.30 Let (C, Ά, ÃŽÂ µ) be co-algebra over k. The algebra (Cà ¢Ã‹â€ -, m, ÃŽÂ ·) where m= ΆÃƒ ¢Ã‹â€ -| Cà ¢Ã‹â€ -à ¢Ã‚ ¨Ã¢â‚¬Å¡Cà ¢Ã‹â€ -, ÃŽÂ · (1) =ÃŽÂ µ, is the dual algebra of (C, Ά, ÃŽÂ µ). Definition1.31 Let A be algebra over the field k. A locally finite A-module is an A-module M whose finitely generated sub-modules are finite-dimensional. The left and right Cà ¢Ã‹â€ --module actions on C are locally finite. Definition1.32 Let A be algebra over the field k. A derivation of A is a linear endomorphism F of A such that F (ab) =F (a) b-aF(b) for all a, b à Ã‚ µA. For fixed b à Ã‚ µA note that F: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢A defined by F(a)=[a, b]= ab- ba   for all a à Ã‚ µA is a derivation of A. Definition1.33 Let C be co-algebra over the field k. A co-derivation of C is a linear endomorphism f of C such that ΆÃƒ ¢Ã‹â€ Ã‹Å"f= (fà ¢Ã‚ ¨Ã¢â‚¬Å¡IC + IC à ¢Ã‚ ¨Ã¢â‚¬Å¡f) à ¢Ã‹â€ Ã‹Å"Ά. Definition1.34 Let A and B ne algebra over the field k. The tensor product algebra structure on Aà ¢Ã‚ ¨Ã¢â‚¬Å¡B is determined by (aà ¢Ã‚ ¨Ã¢â‚¬Å¡b)(aà ¢Ã‚ ¨Ã¢â‚¬Å¡b)= aaà ¢Ã‚ ¨Ã¢â‚¬Å¡bb à ªÃ¢â‚¬Å" ¯ a, aà Ã‚ µA and b, bà Ã‚ µB. Definition1.35 Let X, Y be non-empty subsets of an algebra A over the field k. The centralizer of Y in X is ZX(Y) = {xà Ã‚ µX|yx=xy à ªÃ¢â‚¬Å" ¯yà Ã‚ µY} For y à Ã‚ µA the centralizer of y in X is ZX(y) = ZX({y}). Definition1.36 The centre of an algebra A over the field Z (A) = ZA(A). Definition1.37 Let (S, à ¢Ã¢â‚¬ °Ã‚ ¤) be a partially ordered set which is locally finite, meaning that à ªÃ¢â‚¬Å" ¯, I, jà Ã‚ µS which satisfy ià ¢Ã¢â‚¬ °Ã‚ ¤j the interval [i, j] = {là Ã‚ µS|ià ¢Ã¢â‚¬ °Ã‚ ¤là ¢Ã¢â‚¬ °Ã‚ ¤j} is a finite set. Let S= {[i, j] |I, jà Ã‚ µS, ià ¢Ã¢â‚¬ °Ã‚ ¤j} and let A be the algebra which is the vector space of functions f: Sà ¢Ã¢â‚¬  Ã¢â‚¬â„¢k under point wise operations whose product is given by (fà ¢Ã¢â‚¬ ¹Ã¢â‚¬  g)([i, j])=f([i, l])g([l, j])   ià ¢Ã¢â‚¬ °Ã‚ ¤là ¢Ã¢â‚¬ °Ã‚ ¤j For all f, g à Ã‚ µA and [i, j]à Ã‚ µS and whose unit is given by 1([I,j])= ÃŽÂ ´i,j à ªÃ¢â‚¬Å" ¯[I,j]à Ã‚ µS. Definition1.38 The algebra of A over the k described above is the incidence algebra of the locally finite partially ordered set (S, à ¢Ã¢â‚¬ °Ã‚ ¤). Definition1.39 Lie co-algebra over k is a pair (C, ÃŽÂ ´), where C is a vector space over k and ÃŽÂ ´: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢Cà ¢Ã‚ ¨Ã¢â‚¬Å¡C is a linear map, which satisfies: à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"ÃŽÂ ´=0 and (ÃŽâ„ ¢+(à Ã¢â‚¬Å¾Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã¢â€ž ¢)à ¢Ã‹â€ Ã‹Å"(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Ãƒ Ã¢â‚¬Å¾)+(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Ãƒ Ã¢â‚¬Å¾)à ¢Ã‹â€ Ã‹Å" (à Ã¢â‚¬Å¾Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã¢â€ž ¢))à ¢Ã‹â€ Ã‹Å"(ÃŽâ„ ¢Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡ÃƒÅ½Ã‚ ´)à ¢Ã‹â€ Ã‹Å"ÃŽÂ ´=0 à Ã¢â‚¬Å¾=à Ã¢â‚¬Å¾C,C and I is the appropriate identity map. Definition1.40 Suppose that C is co-algebra over the field k. The wedge product of subspaces U and V is Uà ¢Ã‹â€ Ã‚ §V = Ά-1(Uà ¢Ã‚ ¨Ã¢â‚¬Å¡C+ Cà ¢Ã‚ ¨Ã¢â‚¬Å¡V). Definition1.41 Let C be co-algebra over the field k. A saturated sub-co-algebra of C is a sub-co-algebra D of C such that Uà ¢Ã‹â€ Ã‚ §Và ¢Ã…  Ã¢â‚¬  D, à ªÃ¢â‚¬Å" ¯ U, V of D. Definition1.42 Let C be co-algebra over k and (N, à Ã‚ ) be a left co-module. Then Uà ¢Ã‹â€ Ã‚ §X= à Ã‚ -1(Uà ¢Ã‚ ¨Ã¢â‚¬Å¡N+ Cà ¢Ã‚ ¨Ã¢â‚¬Å¡X) is the wedge product of subspaces U of C and X of N. Definition1.43 Let C be co-algebra over k and U be a subspace of C. The unique minimal saturated sub-co-algebra of C containing U is the saturated closure of U in C. Definition1.44 Let (A, m, ÃŽÂ ·) be algebra over k. Then, Aà ¢Ã‹â€ Ã‹Å"=mà ¢Ã‹â€ 1(Aà ¢Ã‹â€ -à ¢Ã‚ ¨Ã¢â‚¬Å¡Aà ¢Ã‹â€ - ) (Aà ¢Ã‹â€ Ã‹Å", Ά, ÃŽÂ µ) is a co-algebra over k, where Ά= mà ¢Ã‹â€ -| Aà ¢Ã‹â€ Ã‹Å" and ÃŽÂ µ=ÃŽÂ ·Ãƒ ¢Ã‹â€ -. ÃŽÂ ¤he co-algebra (Aà ¢Ã‹â€ Ã‹Å", Ά, ÃŽÂ µ) is the dual co-algebra of (A, m, ÃŽÂ ·). Also we denote Aà ¢Ã‹â€ Ã‹Å" by aà ¢Ã‹â€ Ã‹Å" and ΆÃƒ ¢Ã‹â€ Ã‹Å"= aà ¢Ã‹â€ Ã‹Å"(1)à ¢Ã‚ ¨Ã¢â‚¬Å¡ aà ¢Ã‹â€ Ã‹Å"(2), à ªÃ¢â‚¬Å" ¯ aà ¢Ã‹â€ Ã‹Å" à Ã‚ µ Aà ¢Ã‹â€ Ã‹Å". Definition1.45 Let A be algebra over k. An ÃŽÂ ·:ÃŽÂ ¾- derivation of A is a linear map f: Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢k which satisfies f(ab)= ÃŽÂ ·(a)f(b)+f(a) ÃŽÂ ¾(b), à ªÃ¢â‚¬Å" ¯ a, bà Ã‚ µ A and ÃŽÂ ·, ÃŽÂ ¾ à Ã‚ µ Alg(A, k). Definition1.46 The full subcategory of k-Alg (respectively of k-Co-alg) whose objects are finite dimensional algebras (respectively co-algebras) over k is denoted k-Alg fd (respectively  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   k-Co-alg fd). Definition1.47 A proper algebra over k is an algebra over k such that the intersection of the co-finite ideals of A is (0), or equivalently the algebra map jA:Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(Aà ¢Ã‹â€ Ã‹Å")*, be linear map defined by jA(a)(aà ¢Ã‹â€ Ã‹Å")=aà ¢Ã‹â€ Ã‹Å"(a), a à Ã‚ µA and aà ¢Ã‹â€ Ã‹Å"à Ã‚ µAà ¢Ã‹â€ Ã‹Å". Then: jA:Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(Aà ¢Ã‹â€ Ã‹Å")* is an algebra map Ker(jA) is the intersection of the co-finite ideals of A Im(jA) is a dense subspace of (Aà ¢Ã‹â€ Ã‹Å")*. Is one-to-one. Definition1.48 Let A (respectively C) be an algebra (respectively co-algebra ) over k. Then A (respectively C) is reflexive if jA:Aà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(Aà ¢Ã‹â€ Ã‹Å")*, as defined before and jC:Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(C*)à ¢Ã‹â€ Ã‹Å", defined as: jC(c)(c*)=c*(c), à ªÃ¢â‚¬Å" ¯ c*à Ã‚ µC* and cà Ã‚ µC. Then: Im(jC)à ¢Ã…  Ã¢â‚¬  (C*)à ¢Ã‹â€ Ã‹Å" and jC:Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢(C*)à ¢Ã‹â€ Ã‹Å" is a co-algebra map. jC is one-to-one. Im(jC) is the set of all aà Ã‚ µ(C*)* which vanish on a closed co-finite ideal of C*. Is an isomorphism. Definition1.49 Almost left noetherian algebra over k is an algebra over k whose co-finite left ideal are finitely generated. (M is called almost noetherian if every co-finite submodule of M is finitely generated). Definition1.50 Let f:Uà ¢Ã¢â‚¬  Ã¢â‚¬â„¢V be a map of vector spaces over k. Then f is an almost one-to-one linear map if ker(f) is finite-dimensional, f is an almost onto linear map if Im(f) is co-finite subspace of V and f is an almost isomorphism if f is an almost one-to-one and an almost linear map. Definition1.51 Let A be algebra over k and C be co-algebra over k. A pairing of A and C is a bilinear map   ÃƒÅ½Ã‚ ²: AÃÆ'-Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢k which satisfies, ÃŽÂ ²(ab,c)= ÃŽÂ ² (a, c(1))ÃŽÂ ² (b, c(2)) and ÃŽÂ ²(1, c) = ÃŽÂ µ(c), à ªÃ¢â‚¬Å" ¯ a, b à Ã‚ µ A and  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   c à Ã‚ µC. Definition1.52 Let V be a vector space over k. A co-free co-algebra on V is a pair (à Ã¢â€š ¬, Tco(V)) such that: Tco(V) is a co-algebra over k and à Ã¢â€š ¬: Tco(V)à ¢Ã¢â‚¬  Ã¢â‚¬â„¢T is a linear map. If C is a co-algebra over k and f:Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢V is a linear map,à ¢Ã‹â€ Ã†â€™ a co-algebra map F: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢ Tco(V) determined by à Ã¢â€š ¬Ãƒ ¢Ã‹â€ Ã‹Å"F=f. Definition1.53 Let V be a vector space over k. A co-free co-commutative co-algebra on V is any pair (à Ã¢â€š ¬, C(V)) which satisfies: C(V) is a co-commutative co-algebra over k and à Ã¢â€š ¬:C(V)à ¢Ã¢â‚¬  Ã¢â‚¬â„¢V is a linear map. If C is a co-commutative co-algebra over k and f: Cà ¢Ã¢â‚¬  Ã¢â‚¬â„¢V is linear map, à ¢Ã‹â€ Ã†â€™ co-algebra map F:C à ¢Ã¢â‚¬  Ã¢â‚¬â„¢C(V) determined by à Ã¢â€š ¬Ãƒ ¢Ã‹â€ Ã‹Å"F=f.   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   (Majid 2002, Radford David E) Chapter 2 Proposition (Anti-homomorphism property of antipodes) 2.1 The antipode of a Hopf algebra is unique and obey S(hg)=S(g)S(h), S(1)=1 and (Sà ¢Ã‚ ¨Ã¢â‚¬Å¡S)à ¢Ã‹â€ Ã‹Å"Άh=à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"ΆÃƒ ¢Ã‹â€ Ã‹Å"Sh, ÃŽÂ µSh=ÃŽÂ µh, à ¢Ã‹â€ Ã¢â€š ¬h,g à ¢Ã‹â€ Ã‹â€  H.   Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚  Ãƒâ€šÃ‚   (Majid 2002, Radford David E) Proof Let S and S1 be two antipodes for H. Then using properties of antipode, associativity of à Ã¢â‚¬Å¾ and co-associativity of Ά we get S= à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Sà ¢Ã…  -[ à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Idà ¢Ã…  -S1)à ¢Ã‹â€ Ã‹Å"Ά])à ¢Ã‹â€ Ã‹Å"Ά= à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Idà ¢Ã…  - à Ã¢â‚¬Å¾)à ¢Ã‹â€ Ã‹Å"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Idà ¢Ã…  -S1)à ¢Ã‹â€ Ã‹Å"(Id à ¢Ã…  -Ά)à ¢Ã‹â€ Ã‹Å"Ά= à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(à Ã¢â‚¬Å¾Ãƒ ¢Ã‚ ¨Ã¢â‚¬Å¡Id)à ¢Ã‹â€ Ã‹Å"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Idà ¢Ã…  -S1)à ¢Ã‹â€ Ã‹Å"(Ά à ¢Ã…  -Id)à ¢Ã‹â€ Ã‹Å"Ά = à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"( [à Ã¢â‚¬Å¾Ãƒ ¢Ã‹â€ Ã‹Å"(Sà ¢Ã‚ ¨Ã¢â‚¬Å¡Id)à ¢Ã‹â€ Ã‹Å"Ά]à ¢Ã‚ ¨Ã¢â‚¬Å¡S1)à ¢Ã‹â€ Ã‹Å" Ά=S1. So the antipode is unique. Let Sà ¢Ã‹â€ -id=ÃŽÂ µs idà ¢Ã‹â€ -S=ÃŽÂ µt To check that S is an algebra anti-homomorphism, we compute S(1)= S(1(1))1(2)S(1(3))= S(1(1)) ÃŽÂ µt (1(2))= ÃŽÂ µs(1)=1, S(hg)=S(h(1)g(1)) ÃŽÂ µt(h(2)g(2))= S(h(1)g(1))h(2) ÃŽÂ µt(g(2))S(h(3))=ÃŽÂ µs (h(1)g(1))S(g(2))S(h(2))= S(g(1)) ÃŽÂ µs(h(1)) ÃŽÂ µt (g(2))S(h(2))=S(g)S(h), à ¢Ã‹â€ Ã¢â€š ¬h,g à ¢Ã‹â€ Ã‹â€ H and we used ÃŽÂ µt(hg)= ÃŽÂ µt(h ÃŽÂ µt(g)) and ÃŽÂ µs(hg)= ÃŽÂ µt(ÃŽÂ µs(h)g). Dualizing the above we can show that S is also a co-algebra anti-homomorphism: ÃŽÂ µ(S(h))= ÃŽÂ µ(S(h(1) ÃŽÂ µt(h(2)))= ÃŽÂ µ(S(h(1)h(2))= ÃŽÂ µ(ÃŽÂ µt(h))= ÃŽÂ µ(h), Ά(S(h))= Ά(S(h(1) ÃŽÂ µt(h(2)))= Ά(S(h(1) ÃŽÂ µt(h(2))à ¢Ã‚ ¨Ã¢â‚¬Å¡1)= Ά(S(h(1) ))(h(2)S(h(4))à ¢Ã‚ ¨Ã¢â‚¬Å¡ ÃŽÂ µt (h(3))= Ά(ÃŽÂ µs(h(1))(S(h(3))à ¢Ã‚ ¨Ã¢â‚¬Å¡S(h(2)))=S(h(3))à ¢Ã‚ ¨Ã¢â‚¬Å¡ ÃŽÂ µs(h(1))S(h(2))=S(h(2))à ¢Ã‚ ¨Ã¢â‚¬Å¡ S(h(1)). (New directions) Example2.2 The Hopf Algebra H=Uq(b+) is generated by 1 and the elements X,g,g-1 with relations gg-1=1=g-1g and g X=q X g, where q   is a fixed invertible element of the field k. Here ΆX= Xà ¢Ã‚ ¨Ã¢â‚¬Å¡1 +g à ¢Ã‚ ¨Ã¢â‚¬Å¡ X, Άg=g à ¢Ã‚ ¨Ã¢â‚¬Å¡ g, Άg-1=g-1à ¢Ã‚ ¨Ã¢â‚¬Å¡g-1, ÃŽÂ µX=0, ÃŽÂ µg=1=ÃŽÂ µ g-1, SX=- g-1X, Sg= g-1, S g-1=g. S2X=q-1X. Proof We have Ά, ÃŽÂ µ on the generators and extended them multiplicatively to products of the generators. ΆgX=(Άg)( ΆX)=( gà ¢Ã‚ ¨Ã¢â‚¬Å¡g)( Xà ¢Ã‚ ¨Ã¢â‚¬Å¡1 +gà ¢