Comparison and Criticism

Countee Cullen is one of the most famous African-American poets who has won more literary prizes and recognitions than any black American has ever won before. He came into prominence quite early in his life. Becoming quite famous already in the high school he has been recognized as an outstanding poet before he was 25 when he published such poems as â€Å"I Have a Rendezvous with Life† and â€Å"The Ballad of the Brown Girl† (Johnson). So, â€Å"The Medea† and â€Å"The Lost Zoo† which I am going to compare and criticize in this paper are during his late period (in the age of 37 and 31 respectively).I am going to argue that both poems are still valuable today because of their didactic nature. By writing them Cullen attempted to express and somehow summarize his ideas of that what is good and what is bad, as well as about morals and proper behavior. They are all written for children, even if those children believe themselves to be adults. Since 1934 Cullen taught English and French at the Frederick Douglas Junior High School. He has been offered a position of a lecturer at the Fisk University in Nashville which he declined. Thus he has chosen a career of a teacher, not a lecturer and scientist.His interest to work with children and writing for children later clearly revealed when he wrote â€Å"The Lost Zoo†, yet it can be traced already in the â€Å"Medea and other poems†. Why among numerous Greek tragedies has Cullen chosen to translate exactly â€Å"The Medea†, and why has the translation been accompanied by a set of Cullen’s own verses? The answers can be found after reading this poetry collection and comparing its themes and motifs to the ones of Euripides. The original myth of Medea, as it has been told by Euripides, is a story of an aggrieved woman who has been driven to a disastrous path by her passion and despair.Cullen provided a modern translation of Euripides story (Corti 202) and the other poem s included to the collection can be viewed as Cullen’s commentary to the problem. Medea’s fate is reflected in â€Å"The Magnets† in which Cullen writes of â€Å"The straight, the swift, the debonair† who â€Å"are targets on the thoroughfare†. This passage can be viewed as a personal reflection, yet in the light of â€Å"Scottsboro, Too, Is Worth Its Song†, another Cullen’s poem, it can be interpreted in a broader social context, as a vision of an entire nation driven to the wrong pass.Cullen begins the poem by imagining poets who will sing and their cries â€Å"Their cries go thundering Like blood and tears†. The period when Cullen wrote this poem was marked by a deep spiritual crisis following the Great Depression, so Cullen observes that in the world â€Å"Is all disgrace And epic wrong† and wonders why the poets have not eventually risen their voices against this wrong. This poems is to put a rhetoric question but n ot to give an answer. Cullen attempts to make his readers themselves concerned with the moral descent, to awaken their own minds and conscience.Otherwise they are likely to repeat Medea’s mistake. This was Cullen’s teaching method: he has not expressly developed own philosophy and preferred to teach through parallels and comparison (Nelson 91). It can be observed that Cullen’s teaching and moralization is not only for children, but for adults as well, perhaps more for adults than children. His â€Å"The Lost Zoo† published in 1940 is for the â€Å"young but not too young†. Although this writing may seem childish, in it Cullen once again (after â€Å"Black Christ†) rises to the Biblical heights in his poetry (Nelson 90).In â€Å"The Lost Zoo† Cullen tells tales of animals that for some reasons could not get onto Noah’s Arc thusly teaching his readers certain life lessons (Silvey 3). Squilililigee’s story is a warning both against teasing and against excessive susceptibility, while the story of a Snake-That-Walked-Upon-His-Tale is a warning against arrogance and false vanity (See: Cullen, Pinknee 1991). In fact, neither of the lost animals was fated and each of them could be saved in case they themselves behaved in a proper way. The conduct of the lost animals ruins them because they attempt to be that what they are not. This is a typical mistake of all times.Cullen is a man of his time, yet his verses are of universal everlasting value. They are topical in our days same as in the days of Cullen. When Cullen wrote both â€Å"Medea† and â€Å"The Lost Zoo† he played a role of a teacher rather than a poet and he was able to teach not only children but adults as well. Human passions never change, and so Cullen’s poems will never lose their importance, just like â€Å"Medea† by Euripide and the Biblical story of an Arc have not lost theirs. Each generation understands and inte rprets them in their own manner just as Cullen interpreted the Bible and Medea. Works Cited: 1. Cullen Countee. The Medea and Some Poems.New York: Harper & Bros. , 1935; 2. Cullen, Countee; Pinknee, Brian J. The Lost Zoo. Silver Burdett Pr. , 1991; 3. Corti, Lillian. The Myth of Medea and the Murder of Children. Greenwood Press, 1998; 4. Nelson, Emmanuel Sampath. African American authors, 1745-1945. Greenwood Publishing Group, 2000; 5. Silvey, Anita. The essential guide to children's books and their creators, Houghton Mifflin Harcourt, 2002; 6. Johnson, Clifton H. About Countee Cullen's Life and Career. 27 May 2009 http://www. english. illinois. edu/MAPS/poets/a_f/cullen/life. htm 7. Countee Cullen 27 May 2009 http://www. harvardsquarelibrary. org/poets/cullen. php

Evaluation of the Most Important Decade in American History

This paper is going to be a step by step evaluation of arguably the most important decade in American History. The time period covered in this paper is 1789-1801. These are the years in which the Federalists had the most influence in the new government. They accomplished an amazing amount in these 12 years. The Federalist Party was one of the first political organizations in the United States. The members of this party supported a strong central government, a large peacetime army and navy, and a stable financial system. Although the first president, George Washington, was not a Federalist, his Secretary of the Treasury, Alexander Hamilton, was the developer and leader of the Federalist party. Hamilton believed in a loose interpretation of the Constitution so that the central government could become more powerful. Also Hamilton, along with the other party members, believed that commerce and manufacturing were more important than agriculture. During the first two years of the new federal government the biggest problem was that of raising money. At first the Congress adopted a small tariff on imports. This was a start but not nearly enough. The government needed this money to maintain its own existence and to be able to pay of the debt. The existence of the government was a necessity, but there was a lot of discussion as to whether the debt should be payed off. The mare magnitude of the debt seemed to compel some measure of avoidance. In 1789, the national debt totaled more than $50 million, $11,700,000 of which was owed to France and Spain and the private bankers of Netherlands, while $40 million was in the form of securities held by citizens of the United States. The interests owed to the bankers were being payed off by loans from the bankers themselves. The government didn†t even have enough money to pay the Barbary corsairs for release of captive sailors! When Congress couldn†t come up with a solution that was satisfactory, they turned to Alexander Hamilton with the dilemma. He soon proceeded to draw up a full report entitled â€Å"Report on Public Credit.† In this paper Hamilton proceeded to show that the only way for a new government to establish credit was to deal honestly with its creditors -for in many cases they would be the people to whom the government must look to for future loans. This policy received strong opposition from Madison and other soon to become Republicans (second political party in America). The federalists held strongly, but only with the passing of the Assumption Bill (movement of capital more toward the South) where they able to pass the bill. This achievement was significant, but lacked two things which would be necessary to carry it out. For one it lacked a circulating medium, and two it lacked a central bank. Hamilton then proposed a remedy. He wanted to establish a corporation that was to be called the Bank of the United States. This bank was to serve as the principle depository for government funds. It was also to serve as the issuer of bank notes. This was a loose interpretation of the constitution. Again Madison led the opposition to no avail. But Hamilton held strongly to his belief that even the most uncompromising opponent of the bank â€Å"would, in one month†s experience as head of that department of the treasury, be compelled to acknowledge that it is an absolutely indispensable engine in the management of the finances, and would quickly become a convert to its perfect constitutionality.† This plan favored the central government. The bank made little banks, who couldn†t compete, go out of business. The rich ended up being able to buy a part in the bank and so got richer, and the poor and middle class didn†t get the benefits. The central government was becoming self sufficient, and less dependent on the states. What Hamilton did is make the nation stronger in the eyes of other nations. This is a great accomplishment. If the Federalists (they didn†t call themselves that until 1792) weren†t in power the nation would have been weaker and more decentralized. There were three views on the French Revolution and the French-British war in 1793. Jefferson†s followers favored France. They wanted to abide by the treaty America signed with France in 1788. They thought it was the right thing to do. Hamilton†s followers favored Great Britain. They wanted to develop better relations with great Britain for economic reasons. They sought to break all the relations with the new French government and to ally America with England. The third view was the one taken by George Washington. He realized that a war with England on the side of the French would be suicidal, but at the same time he didn†t want America to be known as the nation that breaks treaties. George Washington proclaimed that America will be neutral. He forbade any American citizen from helping any warring nation. Without the Federalists there to oppose a war with England America might have been wiped out. The Federalists were looking out for the best interest of the country at the expense of another nation. George Washington who didn†t belong to any party decided not to follow either view. During John Adams† tenure as president the Federalists passed several laws which made them unpopular in the eyes of the American public. These laws made the people upset enough not to reelect most of the Federalists that were in Congress. This was the last term in which the federalists were influential. It is important to state these laws and why they passed them. The Federalists had become more favorable toward France and the Republicans started despising France, especially after the insulting X Y Z affair. Adams was favoring France as he tried to keep the nation out of war with France. He secured peace once Napoleon came into power in 1799. The resentment of the population toward France jeopardized this treaty. The Federalist majority in Congress decided to pass the Alien and sedition acts in order to weaken the supporters of war with France (mainly the Republicans). Adams himself was against these laws. These measures were hated. Some of the extreme measures taken to combat them were the Kentucky and Virginia resolutions. These measures tried to say that the laws were unconstitutional. When the time of the next election came the people of the nation had a choice of either maintaining the ways of the Federalists or vote for Jefferson and the republicans. The people, who were mostly farmers at the time, saw the threat to the common man†s rights and so they voted Jefferson and other Republicans into office. This was probably the only thing that the federalist ever really messed up. They made the country strong but then went too far and people took them out of the national picture. The federalist party would never see such strong days again. Its power dwindled down slowly until the party vanished from the national picture in 1816. Although no longer influential in Congress the federalist remained in control in several states. Some states had federalists in office as far down as 1820. This wasn†t though what kept the federalist ideals in America. John Marshall, chief justice of supreme court, began his tenure in 1801. Justice Marshall was a steadfast Federalist. He maintained the Federalist ways long after the party seized to exist. Decision after decision chief Marshall declared the central government supreme to the state. He stretched the constitution far in seeing that the states yield rights to the federal government. He maintained this for 34 years, shaping the loose collection of states into a solid National Union. Another way that the Federalist ideals were maintained comes from their opponents. Upon gaining control of the Congress and Presidency the Democratic-Republicans maintained most of the programs set up by the Federalists. The alien and sedition laws were repealed and everyone arrested under them was let go, but other than that the central government maintained the control gained under the federalists, relinquishing little. The Republicans even strengthened the federal government on occasion. By buying Louisiana Jefferson extended the abilities of the central government. The years under George Washington and John Adams constitute a record of accomplishments not met since. The Federalists followed Hamilton†s counsel to ‘think continentally.† A federal judiciary was established, the taxing power was used, the national debt was handled, American credit was fixed, and territory was cleared of the British and Spanish populations. In foreign affairs America gained respect. Neutrality was maintained, at the price of the French alliance and concessions with Britain. The objective of the foreign policy was survival. The objective was met. The Federalist did a great job starting up the country. After all, many of the leaders including John Adams and George Washington thought that the Union would not last past their lifetimes. The â€Å"experiment entrusted to the hands of the American people†, as said President Washington, turned out very well. Just look at the power America has today.

Medical Experiments of the Holocaust

Medical Experiments of the Holocaust Kaitlin Holocaust in History January 6, 2013 Many brutal atrocities were committed during the Holocaust by the Nazi party against anyone they viewed as â€Å"unpure†. This included the Jews, Gypsies, homosexuals, Afro-Germans, Slavs, communists, the handicapped, and the mentally disabled. These groups were targeted, stripped away of their rights and citizenship, and then sent to concentration camps. Some of these camps were death camps; created for the sole purpose to annihilate these groups of people, mainly the Jews. At these camps, the prisoners were tortured, starved, brutally killed, and experimented on.In this research paper, I am going to discuss some of the medical experiments that were done to the prisoners by Nazi doctors. According to Education†¦A Legacy Forum, some of these experiments are freezing/hypothermia, high altitude tests, testing of the chemical sulfanilamide, seawater experiments, phosgene gas testing, genetic te sting, and the experimentation on twins. These experiments, no matter which one, were cruel and inhumane. Nazi doctors would experiment on prisoners without caring about the welfare of their patient. All restrictions were gone, and these doctors could do whatever they wanted.Many of these prisoners endured pain, and agony, to further the Nazi doctor’s research. The goals of these experiments were to promote the German race, â€Å"in the name of science†. ( Education†¦ A Legacy Forum, Josef Mengele, The Experiments) The freezing experiments were conducted to determine the most effective means for the Germans to avoid hypothermia while fighting on the Russian Front. For as many as five hours, doctors either put prisoners in large vats of ice water, or they would be strapped down on stretchers, and placed outside in the freezing weather naked.While these people were suffering with the pain of their bodies slowly freezing, the doctors would measure the changes in thei r body temperature, heart rate, and other factors. When a prisoner’s body temperature reached 80 °F, the doctors would use different methods of rewarming them. These included sleeping bags, scalding baths, internal irrigation (blistering hot water would be irrigated into the prisoner’s stomach), and the doctors would even force naked women to copulate with the near frozen prisoner. These resuscitation experiments were usually just as painful and deadly as the freezing experiments. The Experiments) In order to find the best way to save German pilots when they were forced to eject from their fighter planes at high altitude, they conducted experiments in which prisoners would be placed in chambers with a low pressure atmosphere. This was to simulate the altitudes, as high as 70,000 feet. The doctors monitored the prisoner’s physical and psychological responses as they slowly and painfully succumbed to their demise. Afterwards, the doctors would dissect the prison er’s brain, sometimes while they were still alive, to show the formation of small air bubbles in the brain’s blood vessels.As many as two hundred patients were tested on, and around eighty died on the spot. The rest were then executed in the gas chambers. (The Experiments, Josef Mengele and The Medical Experiments) The experiments to test the effectiveness of sulfanilamide and other drugs against infection for the purpose of helping the German Army were performed since many front line soldiers suffered from persistent and deadly gangrene. Doctors would inflict battlefield-like wounds in prisoners. They would then rub glass, wood, metal, and bacteria into the wound, resulting in infection.Blood vessels were tied with a tourniquet to simulate what would actually happen to an actual war wound on the front lines. Since the infection would become so deadly, many prisoners died. Others endured serious injury and agony. (Josef Mengele and The Medical Experiments, Remember. or g, The Experiments) Seawater experiments were conducted to find out how to make seawater drinkable. Dr. Hans Eppinger, and other doctors, at the concentration camp located in Dachau conducted these experiments. They forced about ninety Gypsies to drink seawater only, while being deprived of food.Obviously since the salt content of the water causes the body to retain more salt, and lose more water, which is why seawater is undrinkable, these experiments caused serious bodily injury, major dehydration, and an enormous amounts of pain and suffering. The Gypsies were so dehydrated and so desperate for water, they reportedly â€Å"licked the floored after they had been mopped just to get a drop of fresh water. † (The Experiments, Remember. org) Experiments were conducted to find an antidote to phosgene, a toxic gas use as a weapon during World-War I.At Fort Ney near Strasbourg, France, Nazi doctors exposed roughly 52 concentration camp prisoners to the phosgene gas. This gas cause d extreme irritation to the prisoners’ lungs. Many of the prisoners suffered pulmonary edema after the exposure. Four died as a result of the experiments. (The Experiments) Josef Mengele, a Nazi doctor stationed at Auschwitz, was called the â€Å"Angel of Death†. Many times he would be the one who was in charge of â€Å"selection†. He had the power to decide the fate of the prisoner; he had the power of life and death over them. He was in charge of the many experiments conducted at Auschwitz.The experiments he is most known for are genetic experiments, and the experimentations on twins. (Josef Mengele) Many of those who were experimented on were children. They were kept separate from the other inmates. They were called Mengele’s children. Some of the younger children would call Dr. Mengele, Uncle Mengele, since he would offer them sweets. Mengele’s children usually have certain privileges, such as being able to keep their hair for the first few day s of the examinations, a small amount of extra food, and being spared from the beatings of the guards.However, even being treated slightly better, the excruciating pain and death from the experiments were inevitable. (Josef Mengele) The most important goal of the Nazis was to create the master race of the Aryans. They were to have blonde hair, blue eyes, and have pure German blood. Mengele was determined to find out the secret to creating this â€Å"perfect† Aryan race. He would apply eye drops, or inject chemicals into the children’s eyes in an attempt to change brown eyes to the preferred blue. Most of the time, the excruciating pain would leave the children blind for a day or more, and then return to normal.But at least one child would become permanently blind. Mengele would apply dyes to children’s scalps to see if the color can be controlled. Often times this would burn the scalp of the children. Blood test were taken and transfused in order to see which bl ood types mixed, and which blood types didn’t. (Josef Mengele, Josef Mengele and Experimentation on Human Twins at Auschwitz) Josef Mengele was fascinated with twins. He believed that twins held the key to unlocking the genetics to the Aryan race. When twins would arrive to the camp, the SS would yell out â€Å"Twins, twins! An Eva Mozes, a twin survivor from the camp recalls her experience â€Å"As I clutched my mother’s hand, an SS man hurried by shouting, ‘Twins, twins! ’ he stopped to look at us. Miriam and I looked very much alike. We were wearing similar clothes. ‘Are they twins? ’ he asked my mother. ‘Is that good? ’ replied my mother. He nodded yes. ‘They are twins,’ she said. † Twins were kept in separate barracks from the others in the camp. Sometimes they were given special treatment. Unfortunately, this treatment was short-lived. Of the three thousand twins who entered the camp, only two hundred su rvived to see the end of the war.They received blood tests on a daily basis, had surgeries performed without anesthesia, had transfusions from one twin to the other. One set of Gypsy twins were sewn to each other’s back. (Josef Mengele) One twin recalls the death of his brother. â€Å"Dr. Mengele had always been more interested in Tibi. I am not sure why—perhaps because he was the older twin. Mengele made several operations on Tibi. One surgery on his spine left my brother paralyzed. He could not walk anymore. Then they took out his sexual organs. After the fourth operation, I did not see Tibi anymore.I cannot tell you how I felt. It is impossible to put into words how I felt. They had taken away my father, my mother, my two older brothers– and now, my twin† Mengele performed autopsies on twins who died from the experiments. (Josef Mengele, Josef Mengele and Experimentation on Human Twins at Auschwitz, Children of the Flames; Dr, Josef Mengele and the Unt old Story of the Twins of Auschwitz) The medical experiments performed during the Holocaust are examples of why the welfare of humans is the top priority of experiments in science today.No human being should have to experience any pain in order to further the research of science. Hopefully, future generations will look back and never ever treat people lower than animals for their own gain. Citations Grabowski, John F. â€Å"Experiments in Terror. † Josef Mengele. Farmington Hills: Lucent Books, 2004. Print. Lagnado, Lucette M. Children of the Flames. Penguin Group (USA) Incorporated. 1996. Print. â€Å"Medical Experiments of the Holocaust and Nazi Medicine† Remember. org. N. p. Web. 20 Dec. 2012 Tyson, Peter. â€Å"The Experiments. † NOVA Online. N. p. Oct. 2000. Web. 20 Dec. 2012

Technology and the Future Essay Example | Topics and Well Written Essays - 2000 words

Technology and the Future - Essay Example The youngsters have been shown to have possessed a chip embedded into their brains. More than seventy percent of the human race is subjected with this ‘feed’. The feed may very well be referred to as a combination of the present day internet highly dominated by advertisements and interacting suggesting bodies. It is like a virtual network that governs the human mind and has taken over the stream of thoughts that arises into it. Every person’s feed is personalized in line with his stream of emptions and preferences. The liking and disliking of every individual is embedded into his feed and he is constantly being prompted by suggesting thoughts and directives from the feeds about promotional products and proposed actions alike. Whenever a thought is generated by the brain it is instantly taken over by the feed and flooded with suggestion regarding that thought from it. Thus, the feed in reality governs the entire individual. The reality of feed and its effect upon t he individual becomes known to the youngsters when they are on a visit to the moon when they are attacked by those running the anti-feed campaign. They hack the feeds of the individuals present there resulting in the disabling of the feeds for a couple of days. It is in those days that the actual essence of life becomes clear to the youngsters. The Earth has become a place where there is no presence of natural habitat. Water has exhausted and natural reproduction has ceased. The only reproduction that does exist is via in-vitro fertilization. The novel shows how the advancements in technology would change the shape of the human society entirely. Thus it may well be asserted that the change in the human society would be only by the virtue of the advancement in technology. The governing bodies behind the Feed have shaped the society by inculcating into the minds of youngsters what may seem suitable to them. PRESENT TECHNOLOGY The present day technology of Human Computer Interaction vi a Eye Tracking is at its initial phase. It is proposed that in the years to come the technology of eye tracking would be able to transmit all the proposed commands to a computing device only by a single glance. That is to say that, transmitting only one instance of a single eye glance input would transmit the final objective to the system. The user would not have to interact personally with each interface one by one in order to reach the final product. Only a single eye glance would fulfill all input requirements and would result in the desired output. WHAT IS EYE TRACKING? The efficiency of each computing system is highly dependent on its usability in accordance with the requirements of the human begins using it. Thus the more an interactive system is based upon user input, the better it becomes and the more useful it is for the stakeholders concerned with it. Human-Computer Interaction thus holds immense importance in the development and error checking of computing systems that ar e currently in use and also for the ones that are in the pipeline. There are a number of means through which inputs from user can be taken into account. One of these extensive ranges of methods is Eye-Tracking. INTRODUCTION TO EYE TRACKING Formally defining Eye-Tracking , â€Å"A research method that determines what part of an advertisement consumers look at, by tracking the pattern of their eye movements.† (Lake) Thus, eye tracking can be narrated as a means whereby the movements of a human eye are recorded while he is

Among all of the political leaders studied in class who do you think Essay

Among all of the political leaders studied in class who do you think represent the true characteristics of a good leadership and why do you think the rest of t - Essay Example A leader should have a clear vision in his mind about where he is standing right now and how far he has to go to pursue his dreams. He must have the quality to translate his vision into solid form. Without having a clear picture in his mind one cannot achieve the desired goal. Only vision is not sufficient to get the job done. The leader should form a team of experts who will deliver. The erstwhile chairman of General Electric Company has very rightly pointed out that "Good leaders create a vision, articulate the vision, passionately own the vision and relentlessly drive it to completion." The leader should be disciplined, hard working and has the burning desire to pursue his dreams. Action can be termed as the focal point of a leader. A good leader always puts in efforts in pursuance of his vision and influences others to do with the same zeal and enthusiasm. A true leadership gives the credit where the credit is due. He takes the ownership of good or bad actions. He cannot be absolved himself from any failure. As a team leader, he passes on the bucket of fruits of success to his team mates and takes the blame of any of his follies. He treats himself at par with other fellow citizens. He believes in that only good deeds can make them popular amongst the people. In this respect, we may quote here the name of Asian Leader, Mahatma Gandhi. He should be good listener as far as the ideas of others are concerned. He has every right to accept the ideas or reject it but with cogent reasons. The openness policy surely opens the doors of mutual trust and respect between the leaders and the followers. Â   A good leader should be clear in his statement in order to avoid any misunderstanding. He should be firm in achieving the desired results. According to survey conducted by the Americans Psychological Association, the most common weaknesses found in the

The aim of this work is to summarise experience of managing a Essay

The aim of this work is to summarise experience of managing a simulated business with the Sim Venture software. This assignment - Essay Example Decisions made are followed to realize the desired outcome in the organization. This paper gives a summary of experiences gained when managing a simulated business with SimVenture Software. A discussion of business decisions and their significance in a real business is explained. 2. Description  of  the  key  business  decisions  faced. There were different decisions that were encountered. Strategic decisions are related to the overall goal of the organization and give direction to management. They are unique and made once. They are not repeated often because they remain as the preserve of the top management. The decision for an organization to adapt a business customer centric is an example of a strategic decision. High level employees collect and analyze necessary information before settling on a strategic decision. Strategic decisions are made to be implemented over a long time (Harvard Business School Press, 2001, p. 2). Tactical decisions are made by middle level man agers. Using the knowledge they possess and addition information from various sources they base their decision on their analysis. Tactical decisions are used in the management system because their process is repeated many times in the business. Policies concerning pricing and discounts may be part of tactical decision making. Tactical decisions are created to manage performance so that the overall goal is maintained. Operational decisions are made by the employees at the lowest level. They are made very often, for instance when an employee is selling a product to a customer. Operational decisions are made daily and accumulations of the decisions reflect tactical decisions together with strategic decision in the end. Operational decisions are guided by developed rules that led to the appropriate choice. Micro decisions are similar to operational decisions. Operational decisions apply to all the customers while micro decisions are designed for specific customers. Micro decisions take into consideration the existing information and predict on possibilities when making decision on a particular customer. Financial decisions are inevitable when in business. Financial decisions are made by the owners and the top most managers of the organization. At the initial stages of starting the business, the owners find different avenues where they can source funds. They then identify the most important sources and pursue them. When the business grows financial decisions are concerned with the management of cash flow. Moreover, business financial decision could be made to purchase new assets. The business owners may require the expertise in accounting and financial matters to pursue certain ideas or get insight. Another important decision is about the structure of the business. Business structure decisions makes a business individually owned, a partnership or a limited liability company. The different structures get different treatment when it comes to liability, sharing of the profit and losses, and taxation. The legal structure is important because it dictates who is responsible for making decisions (William, 2001). The business relies on human resources to get the work done to realize the goals. Human resource decisions

Topic relating to Thanatology Essay Example | Topics and Well Written Essays - 1750 words

Topic relating to Thanatology - Essay Example Thanatology is derived from the Greek word â€Å"Thanatos† which literally means death. It is the scientific study of death and all other events that are associated with it. This study is interdisciplinary in nature and encompasses the events that precede the death of an individual and those that happen after death. It also takes a keen look at the society’s reaction to death and other rituals that happen during this sad period. The grief that hits the family members, close friends and colleagues is also captured in this study. Florence and Austin (2003) are of the view that death was previously ignored by philosophers due to the preoccupation with more logical aspects of life most of which bring pleasure and keep pain away. They argue that man is naturally tempted to talk about things that bring pleasure and avoid those that bring pain. The two also point out that individuals (especially in Africa) avoid the subject of death because they believe that the mere mention of the name attracts misfortune. However with time, people begun to appreciate the inevitable and hence the study of thanatology was accepted in the modern society. Today it is a core subject in the medical profession. It is studied by nurses, psychologists as well as psychiatrists with the sole aim of helping individuals handle death and its ripple effects. Asked how they wished to die in a random radio interview, people gave various responses. Some said that they would wish to die in their sleep while others said that they would rather say goodbye to this world courtesy of an airplane accident. Others pointed out that they would wish that Jesus comes back and gave them their judgment while still alive. Quite a number said that they would rather not discuss the subject. As evident in the radio interview, the issue of death draws mixed reactions and emotions among different people. Philosophers argue that the manner in which one dies determines the emotion

Health Organization Case Study Essay Example | Topics and Well Written Essays - 1250 words

Health Organization Case Study - Essay Example The above portrays the national focus of the Group, as will be discussed below. UnitedHealth Group Inc., was created in 1977, and is currently the single largest health care in America having initially started with the introduction of the first seniors’ health plan that was network-based. By the year 1984, it was ready to join the securities exchange, becoming a publicly traded entity. J.D. Power and Associates’ recent rating of the entity, as having the highest employer satisfaction in terms of self-insured health plans, is one of its many accreditations, which continue to portray its positive presence in American society. Adding to this was its 2011 accreditation by the American Medical Association (UnitedHealth Group, 2014). According to the Fourth Annual Report Card, as portrayed by UnitedHealth Group (2014) out of the seven national health insurance firms evaluated; in terms of the accuracy and timeliness of claims processing, United Healthcare was placed in pole position. This is concerning metrics such as approval, processing and payment, where the firm led its industry peers in – Electronic Remittance Advice (ERA) Accuracy and Contracted Fee Schedule Match Rate. The latter, is an indicator of how often insurance claim payments match the contracted fee schedules. The former pertains to measurements of the rate at which the physician practices’ projected allowed amount equals that of the insurer’s permitted amount. Thus, accordingly, the Business Insurance Magazine named the firm as the overall ‘readers last choice’ winner (2010) for its great role as the most excellent health plan provider. On the converse, the entity rated last, concerning the metric, which covers the required medications and procedures. Further still is the fact that a survey in the same year, of hospital executives who had interacted with the firm, resulted in the firm

Summary Essay Example | Topics and Well Written Essays - 500 words

Summary - Essay Example In Rudolph’s article, the history of American universities is presented. From the earliest days, the struggle of those who sought a better way for American students is shared with the reader. Some men begged books to start new schools, some man fought danger in the wilderness to found a new college that would present education to the people. The early days were a real challenge. As America grew, so did its universities. Many schools were inspired by a religious awakening that occurred in America's early days. Each denomination had its own school and many of these survive to this day. At their best, Rudolph argues, these schools represented American democracy and helped the idea of America flourish. Kerr's article presents a more contemporary view of universities and shows how they are adapting to try to survive in today's changing marketplace. Universities play a somewhat different role than they did in the period discussed by Rudolph. Now they are intended more to train peopl e for employment and conduct important research that can save lives and change the way we think about our place in the world. But funding is scarce. Research universities are the fountainhead of research and development and yet they lack the federal funds to continue to produce at an effective level. Kerr wonders about the future of such universities.

American Government Essay Example | Topics and Well Written Essays - 1000 words - 3

American Government - Essay Example The Supreme Court is the tribunal in the country for all case and controversies that may arise regarding the constitution and the laws of the state. The court promises the American people of equal justice under the law. The court performs the role of an interpreter and as the guardian of the constitution. The state’s position to get involved in matters of central decision-making, this position has been revoked by Jurists who argue that the court should not play umpire between federal and state governments, Congress does not threaten any state power; however, it helps in protecting the state. The Senate serves as an environment for the states to protect and express their interests. The American people are tired of a system, which seems ever constant with conflicts between the republicans and democrats. People say that the system is broken, and Washington does not represent the interest of the common American. These sentiments have left many citizens exasperated. They desire a system that does not force them to select between two fixed options, which do not represent their individual beliefs as citizens. The multiparty system is favored because it allows the participation of minor parties. The Electoral College has been in existence for 200 years. There are individuals who are critics, and they are opposed the Electoral College system. The critics have tried to propose reforms that will eliminate the college system. There are also other supporters who are less vocal when compared to the critics, but they offer powerful arguments in its favor.

Why and How are organizations out of Sync PT 2 Essay

Why and How are organizations out of Sync PT 2 - Essay Example The sole reason that resulted in one getting the given post can always lead us back to the type of manager on is. Basically, every person usually has a dream of being a boss one day and commanding other people to do their work. Once in managerial position, one can clearly see one that fits that position as having leadership qualities from the one who does not (Hickman, 2010). I believe that not all leaders are managers. It is possible to find someone who possesses leaders (Hickman, 2010)hip skills, but is not a manager. Leadership entails one who acts as a leader for others to follow. Leader commands respect and is held responsible for the other people’s affairs. Manager is people who are expected to have management skills in them. Though management and leadership go hand in hand, but in some cases may not. It is possible to have a manager who is not a leader and a leader who is not a manager (Hickman, 2010). In my personal experience while working in a certain private company, it happened that the manager in charge was a friend of the co-founder of the organization. Many workers in the company really disliked him as he always came up with rules to oppress the workers and make their lives in the company harder (Hickman, 2010). He always fired workers who annoyed him and knew that his actions were un-punishable. Looking at this example, this manager showed poor leadership skills (Hickman, 2010). He was unable to lead the people whom he was in charge and somehow abused his role as a manager for personal satisfaction. Leaders are people who place the desires of other people in front of themselves (Hickman, 2010). A true example of a leader is Mahatma Gandhi, who sacrificed his role as a prince to become a religious leader who had influence on the people. Leaders basically lead people towards a common goal, while managers are involved in organizing, controlling, planning

Ice Cream Making Essay Example for Free

Ice Cream Making Essay Some may call it a comfort food, others a family tradition, but we all know sweet potatoes pie is delicious. This pie is common around the colder holidays such as Thanksgiving and Christmas. Sweet potatoes pie common ingredients are of course sweet potatoes, butter, eggs, sugar, milk, vanilla extract, nutmeg, cinnamon, and pie crust. The pie color can vary from light orange to dark orange. The flavor of pie is sweet with a combination of different spices. The texture of the pie is usually smooth, but it is not uncommon to have small pieces of sweet potatoes in it; also some sweet potatoes pies have nuts has toppings which makes it not smooth. The smell of sweet potatoes pie is one that brings up memories to people, the smell of sweet potatoes with various species has a sweet smell. The ice cream mix is liquid, it is thick and creamy; it is tasteless similar to milk and is white in color. After the sweet potatoes mix, which consist of, cinnamon, butter, sugar, nutmeg, pecans, and sweet potatoes was added to the ice cream mix. The mix turned a light orange color. The color adds to the appeal of the product because it is orange just like sweet potatoes. The texture of the ice cream is not smooth because of small pieces of sweet potatoes chucks and walnuts in it. However, we didn’t want it to be too smooth because sweet potatoes pies aren’t smooth and the nuts add texture to it. The different spices are also seen and tasted in the ice cream. The pecans were coated with cinnamon, sugar and nutmeg. This added a sweeter flavor to the ice cream as well as additional spices. The group did a very good job of maintaining the sweet potatoes flavor with ice cream. It has the spices and taste similar to regular sweet potatoes pie. The smell is similar to the smell of sweet potatoes pie; it smells sweet and has a smell of spices like cinnamon and nutmeg. We first made an unhealthy recipe, added 60.2g of butter to sweet potatoes to make it creamy which also made it easy for it to be smashed. After the sweet potatoes were smashed until the texture we desired, we added 2g of cinnamon, 12g of sugar, 1g of nutmeg, to the 308 g of sweet potatoes mixed. After the ingredients were mixed the 25g of pecans were added to the mix. Then the sweet potatoes mix was added to 900mL of the Mayfield ice cream mix gradually. It was then churned for 20 minutes. Then the ice cream was taken out a placed in a blast freezer for storage. Then we made a healthy version of the ice cream, the recipe for the healthy version is 308g of sweet potatoes, 1g of nutmeg, 2g of cinnamon, 30.1g of margarine salted and 5g of Splenda.

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 ¢

Healthy Biscuit Industry India

Healthy Biscuit Industry India India Biscuits Industry is the largest among all the food industries and has a turnover of around Rs.3000 crores. India is known to be the second largest manufacturer of biscuits, the first being USA. It is classified under two sectors: organized and unorganized. Bread and biscuits are the major part of the bakery industry and covers around 80 percent of the total bakery products in India. Biscuits stand at a higher value and production level than bread. This belongs to the unorganized sector of the bakery Industry and covers over 70% of the total production. India Biscuits Industry came into limelight and started gaining a sound status in the bakery industry in the later part of 20th century when the urbanized society called for readymade food products at a tenable cost. Biscuits were assumed as sick-mans diet in earlier days. Now, it has become one of the most loved fast food products for every age group. Biscuits are easy to carry, tasty to eat, cholesterol free and reasonable at cost. States that have the larger intake of biscuits are Maharashtra, West Bengal, Andhra Pradesh, Karnataka, and Uttar Pradesh. Maharashtra and West Bengal, the most industrially developed states, hold the maximum amount of consumption of biscuits. Even, the rural sector consumes around 55 percent of the biscuits in the bakery products. Health biscuits are also gaining speed in market. It has become the part of the diet of many health conscious people. Many brands like Britannia, sunfeast and Parle are coming up with their variety of health biscuits which are beneficial during sickness or for diabetic people of health conscious people. The following survey is on this section of biscuits. It is done on 200 consumers of health biscuits who are randomly selected. OBJECTIVE OF THE SURVEY The objective of the survey is to find the factor which influences the customers to buy health biscuits of a specific brand. To know the expectations and requirements of all customers regarding health biscuits To find out how the biscuits of different brands are rated by the cosumers.. Also to find out what improvements the consumer wants in this line of biscuits. LIMITATION OF THE SURVEY Some of the respondents were not responding to some of the questions. Some of the respondents dine have so much information about the biscuit and the brand. RESEARCH METHODOLOGY The methodology followed for conducting the study includes the specification of Research design, sample design, questionnaire design, data collection and Statistical tools used for analyzing the collected data. FINDINGS Britannia creamcracker is the most preferred health biscuits as most of the respondents buy this biscuits. Most of the respondents buying this biscuit are diabetic patients or they buy to keep themselves fit. Price of the biscuit is also satisfactory and quality wise also its good. Most of the respondents got aware of this biscuits by tv advertisements. The customers want more varieties in this line of biscuits. CONCLUSION After conducting this research it was found that the demand for the health biscuits is increasing and there is a lot of scope in this line. The current situation is that Britannia has the highest sales and demand for it health biscuits and the most demanded biscuit is nutri choise creamcracker. RECOMMENDATION AND SUGGESTIONS There should be more variety of healthy biscuits available. There packaging and advertisement should be taken care appropriately. Taste of these products should also be improved. They should also provide with more schemes and benefits Learning From this study I acquired the knowledge of different factors which affect the customer preference in biscuit market. Also how the respondents rate the product on the given factors.

The Internet :: Internet Web Cyberspace

The Internet In 1973, the U.S. Defense Advanced Research Projects Agency (DARPA) initiated a research program to investigate techniques and technologies for interlinking packet networks of various kinds. The objective was to develop communication protocols which would allow networked computers to communicate transparently across multiple, linked packet networks. This was called the Internetting project and the system of networks which emerged from the research was known as the "Internet." The system of protocols which was developed over the course of this research effort became known as the TCP/IP Protocol Suite, after the two initial protocols developed: Transmission Control Protocol (TCP) and Internet Protocol (IP). (I got my information for the history of the internet at www.isoc.org In 1986, the U.S. National Science Foundation (NSF) initiated the development of the NSFNET which, today, provides a major backbone communication service for the Internet. With its 45 megabit per second facilitie s, the NSFNET carries on the order of 12 billion packets per month between the networks it links. The National Aeronautics and Space Administration (NASA) and the U.S. Department of Energy contributed additional backbone facilities in the form of the NSINET and ESNET respectively. In Europe, major international backbones such as NORDUNET and others provide connectivity to over one hundred thousand computers on a large number of networks. Commercial network providers in the U.S. and Europe are beginning to offer Internet backbone and access support on a competitive basis to any interested parties. One positive issue about the internet is that it is so much easier to buy or even sell things like on eBay. If you find something that you want to sell you don’t have to put it in the news paper you can put it on the web where you would have a much better chance of selling it. My resource for this is www.ebay.com Another positive thing is if you need to talk to somebody on the phone that is another state and you don’t want to pay long distance billing and if they got the internet you can just get onto a chatroom and talk for free. My resource for this is www.msn.com. Plus another positive issue about the internet is you can meet new people. I know a girl who met a guy on the internet and they have been dating now for over 2 years and plan to get married. Some bad issues about the internet is that if you do happen to meet a person online you never really know who they are unless you meet them in person because the internet can only allow you to talk to them: it can’t let you meet them.

The Christain Theme of Tolstoys The Death of Ivan Ilyich Essay

The Christain Theme of  Tolstoy's The Death of Ivan Ilyich   Ã‚  Ã‚  Ã‚  Ã‚   Tolstoy's The Death of Ivan Ilyich attacks the pursuit of material possessions.   The Ilyich family bases itself upon the unsure foundation of wealth.   As Ivan ascends the rungs of the corporate ladder, he acquires new possessions and articles.   After joining the Civil Service, Ivan buys "new fashionable belongings" at the "very best shops" to keep up appearances (100).   For his wedding to Fiorodovna, Ivan buys "new furniture, new crockery, new linen[s]" to be proper or comme il faut.   He tries in vain to keep up "appearances as ordained by public opinion" (116).   None of these niceties are needed: Ivan buys them purely for the pleasure of owning them and in attempt to fit in with those of his class.   He succeeds instead... ...erings" that Ivan's illness put her through.   In the end, Ivan has nothing to solace him during his slow expiration.   What Tolstoy points out in The Death of Ivan Ilyich is a purely Christain theme:   do not place your foundation upon material things, but upon those things which transcend all time. Work Cited Tolstoy, Leo. The Death of Ivan Ilyich. Bantam Classic ed. New York: Bantam, 1991.

Buju Banton :: Essays Papers

Buju Banton His voice is thunderous and piercing. With each lyric, he pounds away at our psyche and makes our bodies shake with rhythm. He has become the crown prince of Dancehall reggae in Jamaica, and is a force to be reckoned with in the Jamaican music scene. He is young, but mature and powerful, and his name is Buju Banton. Born Mark Anthony Myrie on July 15, 1973, Buju Banton has used his lyrical skills and pounding voice to take Dancehall by storm. He combines his own musical influences with those of Burro Banton and Bob Marley to achieve a sound and beat that is bringing generations of reggae listeners together for an enjoyable experience. He owns the audience with his lyrics and his stage presence, and is forming both a musical and cultural movement that is taking over Jamaica. (www.bujubanton.net) One of 15 children born to a street vendor inside Trenchtown, Banton lived in poverty for most of his upbringing. A direct descendant of the Maroons, his chubby appearance earned him the nickname of Buju, the Maroon name for breadfruit. His last name is a tribute to another reggae legend, Burro Banton, as well as the name for talented storytellers, from which much of his influence is derived. Buju entered the Jamaican music scene at age 12, where he was known as the â€Å"Lambada Man† of the Dancehall, working with the Sweet Love and Rambo Mango sound systems. In 1986, DJ Clement Irie introduced Banton to producer Robert French, who produced his debut single, â€Å" The Ruler.† At the age of 15, Banton had already worked with artists like Bunny Lee and Red Dragon. He was destined for success in the Dancehalls. In 1991, he met producer Dave Kelly of Penthouse Studios, and debuted on the label with 1992’s Mr. Mention, which broke all sales records on the island, including those of Bob Marley. With songs like Love Mi Browning, where he professed his attraction to light-skinned women, caused an uproar among the dark-skinned Jamaican women who viewed such comments as an insult towards their looks. He made up for his remarks, however, with the song Love Black Woman, and demonstrated that he had love for everyone in his repertoire.

Progressive Insurance

Progressive Insurance Assignment question: 1. What is Progressive’s business? A. They provide small business auto insurance to businesses like: * Landscaping and snowplow insurance * Artisan and contractor insurance * Courier and delivery insurance * Restaurant and food service insurance * Farming and livestock insurance * Wholesale business insurance * Religious and nonprofit organization insurance B. They provide home insurance whether it’s for: * Main home * Vacation home Rental property * Mobile home C. RV Insurance such as: * Motorcycle * RV Camper * Boats/water crafts * Snow mobiles/crafts * Truck/trailer 2. What is critical to the success of the business? a. .They try to pay as quickly as possible. b. They have claims adjusters on the street, not in an office so they can interact with clients faster. c. .They use a model called the IRV which is â€Å"immediate response vehicle†. d. .The IRV’s allow Progressive to settle claims at the scene of an acc ident. . .The laptops that the field agents are equipped with come with printers so they can print off checks, estimates and claims right on the spot. f. .They also rely a great deal on 2 way radios as they communicate with the dispatchers about accidents and locations. 3. How does Progressive’s use of hardware contribute to these success factors? Critical Success Factor| Type of Hardware| Contributions| Immediate response time to an accident| Vehicle | * Equipped with a laptop * . Digital camera * . cell phone and 2 way radio * . Printer| Ability to print out estimates, checks and claims instantly| Laptop and printer| * . Laptop * . Printer * . * . | Ability to assess costs of parts needed for repairs| Laptop| * Internet access * Database or catalogue of parts for cars and trucks| Ability to discuss policies and claims with customers while vehicle is in the body shop| Laptop| Ability to communicate with customers more effectively with visual tools. | 4. How does all of this use of hardware benefit customers? Hardware| Customer Benefit| Laptop| * . Ability to communicate with customers faster and with visual tools. * . Ability to print out checks, claims and estimates immediately. * . Gives the customer a sense that their claim is being handled right away without delay. * . | Cell Phones and 2 Way Radios| * . Ability for the dispatcher to locate the closest field agent. * Gives the agent ability to talk to auto shops and other adjuster right away. * . Could provide additional line of communication for a customer that may require additional transportation or other services. * . * . | Progressive Vehicles| * Customers do not have to wait for an assessment of their accident. * . Customers have the confident feeling that their case is being handled right away. * . All the paperwork is given to them on the spot. | Add more as needed| | 5. Relate Moore’s law to this case. a. .Due to technology that’s small and transportable, Progressive is able to handle twice the workload as they could a decade ago. . .While the laptops do need to be kept in shape and maintained, they more than likely have the ability to upgrade their hardware more often than buying new laptops given the information is transmitted to a central server. And not kept on each individual laptop. c. . Their business model calls for a laptop and a printer. They are using the hardware for customer service, not programming a system that is dependent on other syste ms. d. They do need to maintain their servers, back up their servers and monitor the wear and tear factor of their main servers.

Colleges Should or Should Not Offer Online Classes

Nearly 12 million post-secondary scholars in the United States scratch whatsoever or all(prenominal) of their segmentationes online right now. On the new(prenominal) hand, approximately 15 million schoolchilds restrain all of their classes in a forcible classroom. (Adkins) What do these number say round an online education? Well, they mean that at that place atomic number 18 both positive aspects and minus aspects to pickings online courses. It turns out that in that location atomic number 18 galore(postnominal) a(prenominal) deterrent examples of both positive and negative basiss to encipher in or to not to engrave in an online class.Firstly, on that point be umpteen advantages or reasons why mortal would insufficiency to sign an online course. One of the main reasons quite a little take an online course is for flexibility of measure. tractability of time corresponds to the online classes being available 24 hours a day, 7 days a week, commonly. This allows for one to plan their classes around their schedule, quite a than their schedule around their classes. For this reason, it is often best-selling(predicate) for deal who charter to work yet notwithstanding want to get a college education. It is similarly best-selling(predicate) for pargonnts who be operative or exhaust small children they need to take care of.Another example would be someone who has concentratedy waking up for morning classes. Online seat be place so that you feces work at your convenience of time. Another major change factor to a positive spotter on online classes is that there are around no geographical restrictions. As want as you can put yourself somewhere with Internet access, you can take the course. on with the ability to be anywhere you want, you can as well go nowhere and alone take the class from home. This means the student can save a bulk of time and gas money.A good example of someone who would utilize this would be someone who lives far a expressive style from a college, and still wanted to get a class without having to commute back and forth legion(predicate) miles everyday. Online courses overly give a student a larger variety of courses to elect from. If you attend a somatogenic college, a course you might want to take may not be available. With online classes, all you have to do it some online research to hear the course you are expression for. In addition to opportunity of a class being set uped, there is also the opportunity of getting into a class.With online classes, the spaces offered may be greater because there are no physical limitations of space that may have limited the physical class. In addition to these obvious examples, there are a some subtle things that people may no realize at first about the advantages of online classes. One, for example, is participation. Some students may find it difficult to participate in class and therefore feel slight intimidated in an online environment. Equally meaning(a) for some, peradventure, is that there is no dress code. Unless there is a web cam involved, a student could be in their pajamas or plane naked if they wanted to be.On the other hand, there are quite a few disadvantages to fetching an online course. One of the main reasons that many people struggle with is the discipline and time management skills. in that location are commonly a few deadlines, solely anyway that, the students are fully responsible for property up with their work and staying to a schedule. dilatoriness can be a bad factor to failure for some. Self- motivation tends to be a key that some do not possess. Another main enigma some students experience is a kindly problem. In this style of education there is no direct interaction with a professor in person.Some students may be okay with this but many show up and learn better from face-to-face interactions and aid from the teacher. Together with the professor are the bronco bus ter pupils that are in the class. Where as some students completely enjoy relaxing and taking a class alone, some find it very lonely and depressing. Classrooms are meant to have a welcoming environment. This environment can often be particularly difficult to replicate online. An important academic reason to perhaps not take an online class is the issue of transferring characters. Some institutions will not take online credit hours.This could obviously shape your time spent on taking these courses completely worthless. For this reason, many people do not risk online courses and stick to physical classrooms with a definite reliable credit transfer capability. Finally, along with all of these examples, comes perhaps the most obvious one of all. To take an online course you need to have a information processing system. This means that the student has to actually be capable of using that calculator too. Online courses are designed for ones own pace usually, but the majority of tim e spent on the task should not be calculation out how to work the computer.A student does not need to be a computer expert, but needs to be computer literate and relatively comfortable with the technology they will be using. The functioning of the computer not only depends on the students knowledge and skill, but also depends on the reliability of the computer. The computer is leaving to need to have at least a decent setup and also probably have a high-speed connection. For most even considering an online education this is usually doable, but it is not always the case.To summing up it all up, online courses are a discriminative decision based on an respective(prenominal) students research and the colleges interest in such a technique of learning. There are many positive and negative factors a college should consider before decision making to offer or not to offer online classes. The same can said for students deciding whether or not to take online classes. Online classes ar e a slowly increasing popular way of learning and teaching. The only way that one can decide to turn in or take these courses is by expression at the research done and the facts known.

Adapting to Change

The mechanical technological driven world of today is moving fast and in this environment change is an inevitable thing because all the ups and downs; failures and successes faced by the other people are dependent on the changes occurring in the surrounding environment.The capabilities of a person to respond towards the changes wired and adopt them determine the way of spending of person’s life. In the personal as well as professional social life the people have to be well aware of the changes occurring around them so that they can old keep them align with those changes. Most of the changes occurring in the surrounding world are led by the technological advancements.Implementing change is rather difficult.The dissertation is based on a qualitative research study that is conducted through secondary analysis of data and a case study.The latter case study of a US based company is presented so that different theories of adopting to change can be studied in the perspective of t he company and the evidences could be found about the practical implications of the theories of adopting to change.1.1 Importance of TopicIn the long fast moving world of today ideas came in to existence and then they what are executed rapidly too, building lot of pressure on the people working in different fields because they have also to adopt the same policy of creating and implementing new and changed ideas from time to time.Recognizing change may be battle.

1.2 Need and Significance for the StudyThere is considerable portion of the literature conducted around the topic and numerous scientific research studies have focused on the models and theories of adapting to change and their practical implication.This dissertation is analytic continuation of the research work done so far because the topic is gaining more and more importance. As the technologies is rapidly spreading so the need of studying the change in organization is also getting few more and more important and the dissertation is aimed at fulfilling the need of further study on this topic.Change is inevitable and its constant.Literature Review2.1. Adopting to change – Historical PerspectiveAdopting to change in an organization is not a new phenomenon but it has deep roots inside the history. Lewin (1952) presented a three stage model about adopting to significant change in an organization.Everyone has obviously noticed the change in the markets.

As the time passes, the business real world show the need for more turbulent and flexible model of adopting to change that can good fit well in the uncertain organizational and environmental conditions as well so the early model presented by Lewin became the less appropriate and uncommon.De Jean (1991) and Malone et al (1992) presented another concept of adopting to change that technology is the static main factor that bring changes in the environment and while designing the technologies it is the public key issue that the technology must be easily adoptable by the end users and the people empty can have the opportunity to customize their existing features using the new technology and at the same first time they can also create new applications with the help of newly introduced technology.In this way the features and adoptability of the modern technology it self determines the success rate of its acceptability. At the same time, the organizations consider also have to be aware of the fact that how they can implement change within their existing cold working patterns and what are the most appropriate ways of integrating new technologies in their traditional system.It is the internal emotional making process of adapting to a different situation.2.2. Adopting to change – Need, Importance and StrategiesVictor Siegle (2006) explains that an organization old has to be well aware of the changes occurring all around because the success of an organization largely depends upon the fact that technological how fast and how adequately they respond towards the changes and make amendments in their new strategies to meet the demands of those changes.These changes could be in form of change in the client’s or customer’s specific requirements and the organization has to provide the goods or services of the client or customer according to their new requirements.Know how you react to pressure in your very own way that is distinctive! Over-training or spi nal injury outcomes if stress may not be tolerated.

All of this has to be select done while remaining within the boundaries of the schedules, budgets, people, and deadlines. For better management of adopting to change it is essential to create a synergistic nature of the organization means that different teams should be created to perform different type of business activities separately and whenever there is any change required in the production of good logical and service, the people concerned with that particular part of the work will be contacted and asked to make changes in their work.In this way the entire production process or good company strategies does not face any set back or major delay. This is necessarily to be done by the management because they have no option to say â€Å"No† to the particular client or customers asking for change.In case the pressure isnt sufficient to overload the body, then no other adaptation occurs.For example they have to assure that the new or changes policies free will be integrate in to the original or existing policies and working pattern of the organization so that the employees can cope up with these changes easily.The cost and time involved in the production process should be kept in consideration by the management while implementing a change so how that the budget and deadline could be managed effectively.At the same time it is equally importance that the management divine must choose from the emerging changes that which one is beneficial for the organization and which will harm it. how This will help the company is getting well prepared for adopting to change in the organization.Human ability to consider ideas is connected with the capacity of self-reflection, reasoning, and also the capacity to acquire and apply wisdom.

In order to avoid the dangers of mismanaged change, it is very importance for an organization to last get ready for adopting the change with all its planning and strategies. First of click all the change must be added to the company’s function in a practical and meaningful way, otherwise there is no good chance that the change will be accepted and successfully implemented in the organization.Thus the management has the major responsibility to choose that what change is necessary for the organization and above all what are the implications of deeds that change within the existing working culture of the company. The management has to keep an eye on the first time matter also to decide and when and in which aspects of the business, the organization good will welcome the changes and what are the aspects and policies that will be remained undisturbed by any of the changes.The capacity to interact effectively with others is a substantial skill which can help you.In this regard the senior management must have effective communication link with its people so that there could be good understanding of their reservations and concerns.2.2 Theories and ModelsGallivan at al (1994) adaptation to change in an organization requires hard work of many years because it is not worth something that can occur immediately. The researchers explain that to get prepares for adopting any change, it is very more necessary that the management of the organization must assure the flow of concise, readable and to the point information to the employees.Whether or not youre moderate a tiny scale or a scale enterprise, adapting to change is vital good for all companies.

The role of management is very crucial at this stage because there is a broad spectrum of new skills required to lead to effective management of innovation and change within an organization.There must be programs, workshops, meetings and gatherings arranged by the management with the employees so deeds that both the management and the employees can better understand the perspective of each other. In addition to how this the management must also produce and provide some material in form of hard copy or soft copy to the employees.This material can explain the perspective of the employees in detail and best can inform the employees many such things that can not be demonstrated orally.Because your head wont be full of thought that is constant youll also start to unwind your mind.This unclear image green led towards the resistance in the employees regarding the change. Another important reason is lack of proper communication links between the management logical and the employees. Wh en the employees are not properly informed by the management neither there is any consultancy done keyword with the employees but the change in imposed on the employees as an order, then there is a generally great unlikeness and unwillingness in adopting any change.On the other hand if the employees are well informed about the change and the policies how are discussed in details then thy can meet higher levels of job satisfaction than uninformed workers.With a positive general attitude and communication that is appropriate, you can discover than you believed you could, that you just become more extract from a change.