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 ¢

Evolution Of Society In The Mi :: essays research papers

The New Way of Thinking   Ã‚  Ã‚  Ã‚  Ã‚  The height of the Middle Ages signified a revolutionary way of thinking among the people. The people of the day were breaking out of the old, controlled lifestyle, to which they were accustomed, and they began expressing themselves in many different ways. The people began breaking out of the normal, monotonous lifestyle and they began becoming individuals. The women began taking on new roles. They became independent and lived on their own. The soldiers began losing their prestige, and their life drastically changed. The clergymen took on more of a secular role, which prompted a new way of thinking toward the church. During the Middle Ages, peoples’ ideas began changing, which prompted a whole new outlook on society.   Ã‚  Ã‚  Ã‚  Ã‚  The role of women drastically changed in the Middle Ages. Women became more independent. Society became more focused on money. So women also became very focused on money, â€Å"†¦going to bed with a nice young man and earning your first mina? And I’m going to spend some of it right away to buy you a new necklace† (Turner, p. 39). Women became interested in jewelry and clothes, â€Å"†¦you’d soon be able to support me, and buy your own jewellery, and have lots of money and servants and gorgeous clothes† (Turner, p. 39). Instead of women relying on men to subsidize their major needs, if women were unmarried or widowed, they began taking care of their own needs, â€Å"When he died, I sold his hammer and tongs and anvil for two minas, and that kept us going for a while. Then I did various jobs like dressmaking and spinning and weaving, to scrape together enough for us to live on. But all the time I was struggling to bring you up, this was what I was hoping for† (Turner, p. 39). Women became fascinated with trying to keep the attention of men, even if it meant making them jealous, â€Å"†¦if he thinks someone rich is after you. He’ll be more upset, and start offering you better terms. He won’t want his rival to outbid him† (Turner, p. 42). So women began taking on a more independent role. Their fascination with money and prestige grew, and they wanted the attention of men, no matter what the cost. The role of women in society drastically began changing in the Middle Ages and a new way of thinking towards women developed. Evolution Of Society In The Mi :: essays research papers The New Way of Thinking   Ã‚  Ã‚  Ã‚  Ã‚  The height of the Middle Ages signified a revolutionary way of thinking among the people. The people of the day were breaking out of the old, controlled lifestyle, to which they were accustomed, and they began expressing themselves in many different ways. The people began breaking out of the normal, monotonous lifestyle and they began becoming individuals. The women began taking on new roles. They became independent and lived on their own. The soldiers began losing their prestige, and their life drastically changed. The clergymen took on more of a secular role, which prompted a new way of thinking toward the church. During the Middle Ages, peoples’ ideas began changing, which prompted a whole new outlook on society.   Ã‚  Ã‚  Ã‚  Ã‚  The role of women drastically changed in the Middle Ages. Women became more independent. Society became more focused on money. So women also became very focused on money, â€Å"†¦going to bed with a nice young man and earning your first mina? And I’m going to spend some of it right away to buy you a new necklace† (Turner, p. 39). Women became interested in jewelry and clothes, â€Å"†¦you’d soon be able to support me, and buy your own jewellery, and have lots of money and servants and gorgeous clothes† (Turner, p. 39). Instead of women relying on men to subsidize their major needs, if women were unmarried or widowed, they began taking care of their own needs, â€Å"When he died, I sold his hammer and tongs and anvil for two minas, and that kept us going for a while. Then I did various jobs like dressmaking and spinning and weaving, to scrape together enough for us to live on. But all the time I was struggling to bring you up, this was what I was hoping for† (Turner, p. 39). Women became fascinated with trying to keep the attention of men, even if it meant making them jealous, â€Å"†¦if he thinks someone rich is after you. He’ll be more upset, and start offering you better terms. He won’t want his rival to outbid him† (Turner, p. 42). So women began taking on a more independent role. Their fascination with money and prestige grew, and they wanted the attention of men, no matter what the cost. The role of women in society drastically began changing in the Middle Ages and a new way of thinking towards women developed.

Christianity and Slavery In Early American Literature Essay

In the 18th -19th centuries religion had a great influence on culture and literature. The American society created a unique culture influenced by its norms and traditions, historical and political development, Christianity and slavery. Dogmas and norms of the society were embodied in the religious tradition and transferred into literature. Religion and slavery did not independently becoming an integral part of culture. Thesis Early American Literature reflects cultural norms and tradition of the society and shows that blacks and whites were united by virtues and religious dogmas of Christianity. Early American Literature show that with the help of literature, people embodies their beliefs and hopes, ideas and ideals. Christianity and church was a strong force which dictated social norms and social order. For instance, the poetry by Phillis Wheatley vividly depicts the importance of morality and religion for both whites and blacks. In the poem â€Å"On Virtue† he writes: â€Å" Virtue, thro’ my youthful years! / O leave me not to the false joys of time! / But guide my steps to endless life and bliss† (Wheatley, 1996). In other poems he depicts characters as devoted parishioners who follow all values and commandments. Phillis Wheatley can be considered as â€Å"a moral poet† of his time unveiling social contradictions and moral values of slaves and their hopes. He describes the roles of God and goodness in life of slaves. In ISAIAH Wheatley describes: â€Å"For man the wrath of an immortal God: / â€Å"To execute th’ Eternal’s dread command / â€Å"My soul I sacrific’d with willing hand† (Wheatley, 1996). These examples show that religion and Christianity determines lives of slaves in spite of the fact that church and Christianity were used to defense and legitimatize the institution of slavery. Many characters in his poems wonder why anyone would understand a difference between slaves and masters, blacks and whites. Morality is depicted through religious ritual and values followed by slaves. It is not surprising that religious dogmas became the code of behavior for many women who needed strong arguments to prove their decisions. Also, the Christianity was used to maintain defense of domesticity and the role of women as mother and wives only. In â€Å"To his Honour the Lieutenant-Governor, on the Death of his Lady† Wheatley writes: â€Å"ALL-Conquering Death! by thy resistless pow’r, /Hope’s tow’ring plumage falls to rise no more! /Of scenes terrestrial how the glories fly, / Forget their splendors, and submit to die! † (Wheatley, 1996). This theme underlines the fact that all people are mortal. Even trying to challenge destiny, people cannot change ordered hierarchy of the world, and is punished with an eternal hell. In the speech, Frederick Douglass addresses a very important problem of racial inequality in America and its impact on the society. In his speech â€Å"the Fourth of July†, Frederick Douglass depicts social and political situation and ridicules low morals and false values existing in the society. As the most important he bases the main arguments on the principles of liberty, moral and religious norms. He appeals to emotions of listeners through the theme of God and morality. Douglass states: â€Å"this, for the purpose of this celebration, is the 4th of July. It is the birthday of your National Independence, and of your political freedom. This, to you, is what the Passover was to the emancipated people of God† (Douglass, 2002). Distinction between spiritual and temporal power creates a space for freedom, in which an individual can fight for freedom Works of two African-American writers and abolitionists show that slaves believed in God and followed Christian morality in their life. For slaves and free black men religion was a moral guard which shaped their behavior. Christianity played a crucial role in lives of all slaves. Both abolitionists depict that religion and church exercise power, keep their traditions and values. It is important to note that during 19th century religion had a great influence on social life and was often used as a theme and framework in literature (Fogel, 1989). Douglass gives some overview of the cultural situation of that time and people’s attitude towards the slavery. This speech is very important as it appeals to everyone both blacks and whites. In general, it is possible to say that in Douglass gives a vivid explanation of the slavery that relates with accuracy to the real events. He depicts that everyone must die eventually, and so the natural roots of democracy are therefore in mortality, whether due to natural causes or to the bloodshed of internecine warfare. Douglass blames church stating that it supports slave-owners and slavery. On the other hand, he states: â€Å"the venomous creature is nursing at the tender breast of your youthful republic; for the love of God, tear away, and fling from you the hideous monster, and let the weight of twenty millions crush and destroy it forever! † (Douglass, 2002). He separates Christianity and the American church underlining that â€Å"The American church is guilty, when viewed in connection with what it is doing to uphold slavery† (Douglass, 2002). In his speech, a spirit of mischievous and subversive anarchy runs through the entire work. This duality in views and ideals allowed slavery to continue. The short story of Edgar Poe â€Å"The Masque of The Red Death† vividly portrays the fear of death and fate. The protagonist of the story, the Prince Prospero fights with death trying to outwit it. Although, Poe depicts that it is a vein sacrifice that is painful and sorrowful causing terrible sufferings and emotional burden for the Prince. He looks around and sees the ordinariness of their existence. â€Å"The Red Death† or plagues is a symbol of death depicting that human beings cannot escape death. â€Å"The scarlet stains upon the body and especially upon the face of the victim, were the pest ban which shut him out from the aid and from the sympathy of his fellow-men† (Poe, n. d. ). Previously, the Prince had been a man who was somehow placed above ordinary mortals, who, either through his depth of suffering or his nobility of nature felt and suffered more than readers could be expected to do in everyday life. The hero also suffers death at the end, his downfall being a result of a fatal flaw in his character, a trait which he cannot help as it is a part of his makeup, but which causes the tragedy and eventually his death. The themes of fate and death show that being a part of culture religion was reflected in literary works. Poe portrays that behavior of people was religiously determined and that the key to suc ¬cessful ideas was in the understanding of religious dogmas and values. In general, Poe’s concern is for degrees of personal freedom results when a man, struggling against death, is pushed further back, achieving little in his struggle for life, and having degrees of free ¬dom removed from him. Mortality is undergone in order to expand the human spirit, to delve into matters previously kept hidden, to grow through fear. The fear before unknown and punishment were the main causes allowing slavery to continue. â€Å"The Black Cat† belongs to a literature of horror portraying a world of an alcoholic suffered from uncontrollable rage and violence. In the intoxicated state the unnamed narrator cannot control his aggression and hangs his favorite black cat. In a period of time, he tries to kill another cat with an axe, but kills his wife who tries to protect the animal. In this story, Poe portrays two different worlds: reality and fantasy that resulted in terrible crimes. Also, Poe unveils the theme of human relations: people love each other and make friends, but if they deprive their friends they are finished. (Poe, Black Cat, 2005). â€Å"A Black Cat† is a symbol of death and fate, fear and Hell. Similar to this explanation, the existence of the institution of slavery, in which white men played the dominant role and wielded control, placed slaves at the mercy of God and destiny. Christian traditions and consciousness allowed slavery to continue for a long time. Christian-conscious world was used as a strong force that affected all aspects of life. Fear of death and punishment limited actions of slaves and forced them to subdue religious norms and traditions. In reality, Christian-conscious world was the only dominated institution which affected life of whites and blacks through culture and traditions. In literature, religion helped to develop and sustain morality by promoting moral reasoning and by exemplifying values and behaviors that were conducive to human dignity. In â€Å"Pudd’nhead Wilson† Mark Twain describes the role of fate and destiny in life of a slave. The events took place in the Dawson’s Landing. Through the characters of Tom and Roxy Mark Twain shows that the fate and fear of unknown are determined by social traditions and religious norms. He writes: â€Å"he was not committing any sin that God would remember against him in the Last Great Day† (Twain, 2001). Tom comes to know that every moment and every act share the same fate. The anticipation of his life dissolves the feeling of overriding importance. Mark Twain explains: â€Å"Consider the flea! –incomparably the bravest of all the creatures of God, if ignorance of fear were courage. Whether you are asleep or awake he will attack you .. you are to him as are the massed armies of the earth to a sucking child† (Twain, 2001). The literary woks under analysis show that church worked hard to distinguish religious values of slaves and masters and their respective on peoples. Christianity was the â€Å"law of life† for defenders. The distance between these groups and a largely secular but still vaguely society is such that the preservation of the former from the evils of the latter has been achieved by the erection of considerable social barriers. Religious piety and submission were beliefs that were more marginal components of the ideology depicted by the early American writers. But, truly said it was not an ideology we understand it but obsession. The religious mores and Christian dogmas were such that traditional practice isolates slaves from the wider society. Christianity can be seen as one of the main causes of slavery and oppression. Works Cited Page 1. Douglass, F. The Fourth of July. 2002. Available at: http://douglassarchives. org/doug_a10. htm 2. Fogel, R. W. Without Consent or Contract: The Rise and Fall of American Slavery. W. W. Norton, 1989. 3. Poe. E. The Masque of the Red Death. n. d. Available at: http://bau2. uibk. ac. at/sg/poe/works/reddeath. html 4. Poe, E. The Black Cat. 2005. Available at: http://www. online-literature. com/poe/24/ 5. Twain, M. Pudd’nhead Wilson. 2001. Available at: http://emotionalliteracyeducation. com/classic_books_online/puddn10. htm 6. Wheatley, Ph. Poems on Various Subjects, Religious and Moral. 1996. Available at: http://www. gutenberg. org/dirs/etext96/whtly10. txt

Group Reflection Exercise Essays

Group Reflection Exercise Essays Group Reflection Exercise Essay Group Reflection Exercise Essay In the recent group activity, I was a member in a group of four. I had been absent from class when the groups were allocated and the two members present were given the task of choosing each of our roles. I felt they chose the more difficult roles for themselves, the introduction and conclusion, although I base that on the knowledge of my own strengths and weaknesses, with no knowledge of theirs. They assigned the work conflict to me, which I thought was a logical choice, given my occupation as a police officer.I believe we worked well together, particularly as we had only very recently met and were four distinctly different personalities. We communicated using email, as we had a number of work and/or study commitments in the week the presentation was due, which prevented us from meeting in person. The group member who had offered to produce the PowerPoint presentation, had a last minute computer problem. I suggested we each write our own section for the PowerPoint and asked the introducing member if he minded putting it together. He was happy with that and presented an easy to follow highlight of our talk.I thought our presentation was relevant and the exercise was quite successful, given that we were only able to meet during the practicals. Our negotiation techniques were clearly identified and explained by our introducing member and our concluding member related them back specifically to the scenarios. : The only area I can identify that may have made the exercise better, was if we had been able to meet as a group, prior to the presentation. That would have given us the opportunity to rehearse and make any changes that may have been needed. That is something I would put more effort into achieving in the future.

The Qing Dynasty

The Qing Dynasty The Qing dynasty, also known as the Manchu, ruled the Imperial China between 1611 and 1911. Not only did the dynasty perfect imperialism in China, but also went on to extend the borders of China during the 267 years (Historical Legacies). After witnessing numerous successes in the 18th century, the Qing dynasty began to experience both internal and external problems that led to its disintegration in the 19th century.Advertising We will write a custom essay sample on The Qing Dynasty specifically for you for only $16.05 $11/page Learn More Western pressure, economic debacles, overpopulation, revolts, a complicated governance system, the rise of Sun Yat-Sen, and peasant upheavals are some of the changes that made it difficult for the Qing dynasty to respond to confrontations of the 19th century and effectively reform China. The court’s decision to cut-off China from the rest of the world led to a decline in radicalism in technological developments and e nhancements, thus preventing it from becoming a world superpower. The cut-off made it easier for Europeans to conquer China and other less fortunate nations, making China fall under European colonization. The extraordinary invasion of their nation infuriated the Chinese, who demanded immediate evacuation of their land. The Europeans took advantage of the situation to demand compensation for their efforts, and they ended-up reaping Chinese land and tones of silver. When they went to war in the 1800s, Europeans effortlessly overcame the resistance by the Qing navy and army. Foreign advancements and attacks continued from countries like France, Britain, Germany, and Japan. The isolation policy by the colonial court proved to be a great undoing for the Qing dynasty. Attempts by some organizations like Boxers to apply guerilla tactics in repelling the Europeans were futile given the superior nature of weapons that the Europeans possessed. Of great surprise was the Boxers’ rebellio n to the ruling Qing dynasty. The opposition by the Chinese peasants weakened the dynasty, such that it was unable to address the challenges of the 19th century and reform China as well. Historical Legacies held that â€Å"†¦massive peasant uprisings†¦Ã¢â‚¬  distorted the plans of the Qing dynasty to effectively reform China. These numerous internal and external wars provided a weak platform for the Qing dynasty to counter the 19th century’s challenges and reform China. Clearly, the focus to guard their borders against invasion by foreigners coupled with the inferior weapons made it difficult for the Qing dynasty to address numerous challenges that it faced in the 19th century. Moreover, the exclusion of China from the rest of the world brought backwardness in improvements, which resulted in inability to face the challenges, such as control by foreign nations.Advertising Looking for essay on asian? Let's see if we can help you! Get your first paper with 15 % OFF Learn More The perception by the imperial court that European technologies were ‘evil’ also made the Qing dynasty to lag behind in technological advancements. According to the radicals, the challenges of the 19th century, such as invasion by the Europeans required modern technologies. China failed to industrialize at a time other nations were engaging in mass production of products using machines during the Industrial Revolution. Corruption and mismanagement of funds by officials within the imperial court system brought difficulties in the way the Qing dynasty responded to challenges of the 19th century. The imperial treasury became bankrupt, and was unable to counter any challenge due to inadequate financial power. The radicals believed that the root cause of the weakness of the Qing dynasty emanated from the inefficient systems of the imperial government. In addition, the doubling of the financial expenditures of the Qing dynasty resulted in weak financial conditions, as income remained constant. From the economic perspective, practices by the Ching ruler and the doubled expenditures resulted in a weak economic foundation. An example of a failure that emanated from this situation is the inability to expand the system of law courts to the district level. Apart from corruption and embezzlement of funds, dissatisfaction by the Han people on the ruling system of the Manchu brought disunity within the greater Qing dynasty. Historical Legacies attests that â€Å"Unity was inherently fragile, hence the perpetual fear of break-up in Chinese history.† Disunity was a great impediment to resolving challenges that the empire faced in the 19th century. Apparently, there was an amendment of the extravagant law of the Qing dynasty and establishments of the most comprehensive cultural ruling. These cultural rulings were Confucianism, which was a set of ethical beliefs acquired from the teachings one of the Chinese scholars called Co nfucius. Actually, the most important belief was in learning and practicing the ways of Dao who they believed to be their God. The Han Empire had several dictators who made people to experience extreme hardship in their lives during the periods that these tyrants ruled the Empire. Evidently, Liu Bang known as Lee Guang founded the Han dynasty, and went on to exasperate his subjects in various ways. Since he was the military leader and even defeated his rivals, he employed force on the subjects. When the Opium war began, the ordinary Han Chinese had little interest in defending the dynasty; this disloyalty exposed the loss of the Mandate of Heaven by the ruling dynasty.Advertising We will write a custom essay sample on The Qing Dynasty specifically for you for only $16.05 $11/page Learn More The decentralization of the political system, at the same time, devolved corrupt and selfish individuals who worked for their own benefits against the interests of the d ynasty. Evidently, decentralization produced disloyal Chinese subjects at the grass-root levels. With autonomous administrations, the provinces went on to declare independence from the imperial Machu court simultaneously. The disloyalty infiltrated the military through numerous reforms. This made it difficult for the Qing dynasty to get full protection assurance from the military. Regional military forces did not support the Manzhus, as they were sensibly autonomous of the Pecking’s control. From this aspect, Qing’s dynasty attempts to reform China met rebellion from the disloyal subjects. Qing dynasty also lacked competent leaders or officials to carry out the reforms needed to counter the 19th century’s challenges. Insincerity of leaders in promoting reforms made the dynasty to lag behind in the reform process that was taking place in key nations across Europe and Asia. Empress Dowager messed with the ruling of the empire when she channeled military funds to b uilding of a grand Summer Palace. With no funds to develop the Chinese military, the dynasty was unable to marshal enough and competent troops to face foreign armies who were invading the territory. Her leadership style influenced key government administrators to a mass wealth at the expense of the cries of starving commoners who could be significant in the fight against external control from the Europeans. Dishonesty among the government officials and the Empress shifted the attention of the Qing dynasty to personal gains, with little or no attention to the commoners. The Qing leadership maintained high levels of unethical practices, such that focusing on challenges that faced the country became a tertiary affair. Maintaining the huge Chinese population also proved to be a great problem for the Qing dynasty. With little resources to sustain the population, the Qing dynasty could not pay attention in reforming the country. This internal problem shifted the focus of the Qing dynasty from addressing challenges like pressure from foreigners and issues of foreign immigrants. China remained weak for the last 100 years, and with the huge population, the dynasty could not offer quality health care and education. High illiteracy levels contributed to the inability of the Qing dynasty to address challenges of the 19th century that required expansive knowledge. In line with this, the negative perception of the western culture made the dynasty to go slow on adopting modern education systems (Historical Legacies 321). The education system concentrated on training for the Imperial Examinations, and not to learning aspects that enhanced rational thinking and autonomy, as propelled by the western education. Reforms of the 19th century had immense connections with modern education, which the Qing rulers opposed its implementation. Empress Cixi is one ruler who did not understand why one should go through the education system. During such periods, concubines were easily endors ed to succeed their predecessors. Qing dynasty’s inability to embrace modern education worked against its reform programs in China.Advertising Looking for essay on asian? Let's see if we can help you! Get your first paper with 15% OFF Learn More From internal problems to external dynamics, the Qing dynasty was not able to address the issues that it faced in the 19th century resulting in its fall. Corruption, disloyalty, radicalism, insincerity, lack of modern education system, and overpopulation are the factors that made it difficult for the dynasty to focus on solving the problems of the 19th century and reform China. Even though the Qing dynasty succeeded in other areas, it failed to handle key issues that could have reformed China. â€Å"Historical Legacies.† Some Historical Pointers. 321 – 2014 – Module 2