Topology Essay -- Mathematics Geometry Essays

Topology Topology is the study of those properties of geometric figures that are unchanged when the shape of the figure is twisted, stretched, shrunk, or otherwise distorted without breaking. It is sometimes referred to as "rubber sheet geometry" (West 577). Topology is a basic and essential part of any post school mathematics curriculum. Johann Benedict Listing introduced this subject, while Euler is regarded as the founder of topology. Mathematicians such as August Ferdinand MÃ ¶bius, Felix Christian Klein, Camille Marie Ennemond Jordan and others have contributed to this field of mathematics. The MÃ ¶bius band, Klein bottle, and Jordan curve are all examples of objects commonly studied. These and other topics prove to be intricate and fascinating mathematical themes. Topologists are mathematicians who study qualitative questions about geometrical structures. They ask questions like does the structure have any holes in it? Is it all connected, or can it be separated into parts? Topologists are not concerned with size, straightness, distance, angle, or other such properties. An often-cited example is the London Underground map. This will not reliably tell you how far it is from Kings Cross to Picadilly, or even the compass direction from one to the other. However, it will tell you how the lines connect between them, using topological rather than geometric information (What 1). Furthermore, if one figure can be distorted into another figure without breaking, then the two figures are described as being topologically equivalent to each other. Two examples of topologically equivalent figures are a coffee cup and doughnut, and groups of the letters of the alphabet. First, an object shaped like a doughnut is a torus. A torus can... ...and. New York:Oxford University Press, 1993. "Felix Christian Klein." Available Online. http://www-groups.dcs-and.ac.uk/~history/Mathematicians/Klein.html. Accessed 12/4/99. Flegg, Graham. From Geometry to Topology. New York: Crane, Russak, and Company, Inc.,1974. "Jordan Curve Theorem and its Generalizations." Available Online. http://www.math.ohio-state.edu/~fiedorow/math655/Jordan.html. Accessed 12/6/99. "Marie Ennemond Camille (1838-1922)." Available Online. http://ukdb.web.aol.com/hutchinson/encyclopedia/91/M0046091.htm. Accessed 12/6/99. "What is Topology?" Available Online. http://www.shef.ac.uk/~pm1nps/Wurble.html. Accessed 12/4/99. West, Beverly Henderson, and others. "Topology." The Prentice-Hall Encyclopedia of Mathematics. 1982. 21: 577-585. Yaglom, I.M. Felix Klein and Sophus Lie. Boston: Birkhauser Boston, 1988.

Piri Thomas’ “Alien House” Essay

Throughout the short story Alien Turf, Piri, a little Puerto Rican boy who just moved to an all-Italian neighborhood encounters many obstacles. Piri will face rejection and inadequacy. He gets teased, and beaten up, but still, he stays strong and acts older than he really is. At the end of the story, Piri is encountered with a strong sense of compassion from Rocky, an Italian boy who had previously beaten him up. The boys realized that racism is only skin deep, but each person may be a kind, caring human being. In the beginning of the story, all Rocky saw was a Puerto Rican invading his Italian neighborhood. According to him, only Italians belonged in the neighborhood, and Puerto Ricans, like Piri and his family, should be ultimately banned. Racism is a belief that one race is the primary determinant of human traits and capacities. Racial differences may produce an inherent superiority of a particular race. Rocky fully lived by this in the beginning, and even throughout most of the story. What is compassion? According to the Merriam-Webster Dictionary, compassion is sympathetic consciousness of others’ distress together with a desire to alleviate it. Some other people may see compassion as being sympathetic toward someone or something when they are struggling or having some sort of problem. If this is what compassion means, then Rocky truly showed compassion for Piri at the end of the story. During the last fight that the Italian boys got into with Piri was when everything changed. One of the boys screamed to Piri from down the street, â€Å"You even buying from us paisans, you must wantta be an Italians.† Usually, he would just run away from them, but this day was different. Piri, sticking up for himself, screamed back to them, â€Å"I wouldn’t be a guinea on a motherfucking bet!† Rocky and his gang were shocked that he said this. The boys started fist fighting and Piri hit Tony in the stomach as hard as he could, watching him fall to the ground. Tony grabbed a handful of asphalt and threw it in Piri’s face. Rocky hit Tony in the face, knowing that his friend had crossed the line. Rocky showed compassion by sticking up for Piri. He took Piri’s hand saying,  Ã¢â‚¬Å"Comon kind, lemme take you home. Rocky recognized that yes, Piri was a little bit different because he was Puerto Rican, but he was also a human being. He realized that racism is only skin deep, and everybody has feelings. Piri was also touched in this instant. He never would have thought that any of the boys, especially Rocky, the leader of the gang, would ever stick up for him. To his amazement, not only did Rocky yell at his friend, but he also threw a couple of punches at him. Compassion was displayed in this because Rocky new that even though he really didn’t like the fact that there was a little Puerto Rican boy that moved into his neighborhood, he could not dismiss the fact that what his friend did was wrong. He was going to help this little boy out. Rocky experienced a true epiphany during this part of the story. His views about everything were disregarded in that instant when his friend threw the asphalt in Piri’s face. He knew that if they really wanted to, they could have beaten Piri up real bad since he couldn’t see, but Rocky knew that it would not be a fair fight. Rocky also recognized the fact that Piri needed his compassion and care in that instant, and that was exactly what he was going to do.

TBD Devastator - Douglas TBD Devastator

TBD Devastator - Douglas TBD Devastator TBD-1 Devastator - Specifications: General Length: 35 ft. Wingspan: 50 ft. Height: 15 ft. 1 in. Wing Area: 422 sq. ft. Empty Weight: 6,182 lbs. Loaded Weight: 9,862 lbs. Crew: 3 Number Built: 129 Performance Power Plant: 1 Ãâ€" Pratt Whitney R-1830-64 Twin Wasp radial engine, 850 hp Range: 435-716 miles Max Speed: 206 mph Ceiling: 19,700 ft. Armament Power Plant: 1 Ãâ€" Pratt Whitney R-1830-64 Twin Wasp radial engine, 850 hp Range: 435-716 miles Max Speed: 206 mph Ceiling: 19,700 ft. Guns: 1 Ãâ€" forward-firing 0.30 in. or 0.50 in. machine gun. 1 Ãâ€" 0.30 in. machine gun in rear cockpit (later increased to two) Bombs/Torpedo: 1 x Mark 13 torpedo or 1 x 1,000 lb. bomb or 3 x 500 lb. bombs or 12 x 100 lb. bombs TBD Devastator - Design Development: On June 30, 1934, the US Navy Bureau of Aeronautics (BuAir) issued a request for proposals for a new torpedo and level bomber to replace their existing Martin BM-1s and Great Lakes TG-2s. Hall, Great Lakes, and Douglas all submitted designs for the competition. While Halls design, a high-wing seaplane, failed to meet BuAirs carrier suitability requirement both Great Lakes and Douglas pressed on. The Great Lakes design, the XTBG-1, was a three-place biplane which quickly proved to possess poor handling and instability during flight. The failure of the Hall and Great Lakes designs opened the way for the advancement of the Douglas XTBD-1. A low-wing monoplane, it was of all-metal construction and included power wing folding. All three of these traits were firsts for a US Navy aircraft making the XTBD-1 design somewhat revolutionary. The XTBD-1 also featured a long, low greenhouse canopy that fully enclosed the aircrafts crew of three (pilot, bombardier, radio operator/gunner). Power was initially provided by a Pratt Whitney XR-1830-60 Twin Wasp radial engine (800 hp). The XTBD-1 carried its payload externally and could deliver a Mark 13 torpedo or 1,200 lbs. of bombs to a range of 435 miles. Cruising speed varied between 100-120 mph depending on payload. Though slow, short-ranged, and under-powered by World War II standards, the aircraft marked a dramatic advance in capabilities over its biplane predecessors. For defense, the XTBD-1 mounted a single .30 cal. (later .50 cal.) machine gun in the cowling and a single rear-facing .30 cal. (later twin) machine gun. For bombing missions, the bombardier aimed through a Norden bombsight under the pilots seat. TBD Devastator - Acceptance Production: First flying on April 15, 1935, Douglas quickly delivered the prototype to Naval Air Station, Anacostia for the beginning of performance trials. Extensively tested by the US Navy through the remainder of the year, the X-TBD performed well with the only requested alteration being an enlargement of the canopy to increase visibility. On February 3, 1936, BuAir placed an order for 114 TBD-1s. An additional 15 aircraft were later added to the contract. The first production aircraft was retained for testing purposes and later became the types only variant when it was fitted with floats and dubbed TBD-1A. TBD Devastator - Operational History: The TBD-1 entered service in late 1937 when USS Saratogas VT-3 transitioned off TG-2s. Other US Navy torpedo squadrons also switched to the TBD-1 as aircraft became available. Though revolutionary at introduction, aircraft development in the 1930s progressed at a dramatic rate. Aware that the TBD-1 was already being eclipsed by new fighters in 1939, BuAer issued a request for proposals for the aircrafts replacement. This competition resulted in the selection of the Grumman TBF Avenger. While TBF development progressed, the TBD remained in place as the US Navys frontline torpedo bomber. In 1941, the TBD-1 officially received the nickname Devastator. With the Japanese attack on Pearl Harbor that December, the Devastator began to see combat action. Taking part in attacks on Japanese shipping in the Gilbert Islands in February 1942, TBDs from USS Enterprise had little success. This was largely due to problems associated with the Mark 13 torpedo. A delicate weapon, the Mark 13 required the pilot to drop it from no higher than 120 ft. and no faster than 150 mph making the aircraft extremely vulnerable during its attack. Once dropped, the Mark 13 had issues with running too deep or simply failing to explode on impact. For torpedo attacks, the bombardier was typically left on the carrier and the Devastator flew with a crew of two. Additional raids that spring saw TBDs attack Wake and Marcus Islands, as well as targets off New Guinea with mixed results. The highlight of the Devastators career came during the Battle of the Coral Sea when the type aided in sinking the light carrier Shoho. Subsequent attacks against the larger Japanese carriers the next day proved fruitless. The TBDs final engagement came the following month at the Battle of Midway. By this time attrition had become an issue with the US Navys TBD force and Rear Admirals Frank J. Fletcher and Raymond Spruance possessed only 41 Devastators aboard their three careers when the battle began on June 4. Locating the Japanese fleet, Spruance ordered strikes to begin immediately and dispatched 39 TBDs against the enemy. Becoming separated from their escorting fighters, the three American torpedo squadrons were the first to arrive over the Japanese. Attacking without cover, they suffered horrific losses to Japanese A6M Zero fighters and anti-aircraft fire. Though failing to score any hits, their attack pulled the Japanese combat air patrol out of position, leaving the fleet vulnerable. At 10:22 AM, American SBD Dauntless dive bombers approaching from the southwest and northeast struck the carriers Kaga, Soryu, and Akagi. In less than six minutes they reduced the Japanese ships to burning wrecks. Of the 39 TBDs sent against the Japanese, only 5 returned. In the attack, USS Hornets VT-8 lost all 15 aircraft with Ensign George Gay being the only survivor. In the wake of Midway, the US Navy withdrew its remaining TBDs and squadrons transitioned to the newly arriving Avenger. The 39 TBDs remaining in the inventory were assigned to training roles in the United States and by 1944 the type was no longer in the US Navys inventory. Often believed to have been a failure, the TBD Devastators principal fault was simply being old and obsolete. BuAir was aware of this fact and the aircrafts replacement was en route when the Devastators career ingloriously ended. Selected Sources Aviation History: TBD DevastatorHistory of War: TBD Devastator Boeing: TBD Devastator

Naval Commander Donald DuBrul

At 7:50 a.m., Naval Commander Donald DuBrul was about to complete his 4 a.m. to 8 a.m. watch on board the USS Argon. The ship was stationed in the Navy Yard towards the entrance to Pearl Harbor in Hawaii. He began wondering if the next man would show up for his shift. In the distance, a band onboard the USS Nevada could be heard playing the Star-spangled Banner for the flag-raising ceremony that was about to commence. The singleman paced waiting for his chance to have his watch end when he turned east to look out over the harbor. Directly east, Ford Island could be seen with its battleship yard full and past that, the ammo dump and tank farm. Over the music being played on the Nevada, a plains whine could be heard. Commander DuBrul looked up just in time to see an explosion on Ford Island. His immediate thought was that some American pilot was about to be court marshaled; until another plane flew in and unloaded its cargo. The first wave of Japanese torpedo planes ! came into full view as they passed through the clouds aiming for the battleship yard. The time was 7:53 a.m. The seaman stood in astonishment as flames lept from the ships. He was awakened by a voice over the loud speaker yelling, Air Raid Pearl Harbor! This is no drill! The air was filled with the whine of dive bombers and the sounds of antiaircraft guns beginning to start their counterattacks. One of the more prized battleships, the Arizona, took a torpedo right down its exhaust stack where it blew up. Seamen dove off ships trying to swim to safety, only to be burned by waves of fire in the harbor that contained burning oil. Onboard the Nevada, the band kept playing as the ship prepared to escape the harbor. In fear of blocking the exit, it turned and beached itself. At about 9 a.m., after two waves of Japanese dive bombers took their toll on the once great US Navy, the chaos had finally ended (DuBrul). A date which will ...

Relationship Marketing Term Paper Example | Topics and Well Written Essays - 1000 words

Relationship Marketing - Term Paper Example The term paper "Relationship Marketing" talks about the strategies to develop strong associations with customers through providing information which matches their requirements and desires. In the business viewpoint, relationship marketing is concerned with appealing, developing and retaining customers’ relations. Relationship marketing is based on developing a mutually advantageous exchange between industry associates. The growth of relationship marketing was accelerated by the literature of management advisors. The present concept of relationship marketing drifted from ‘organizational behavior’ and ‘industrial marketing’ where reliance among organizations has been the basis for a successful business to business coalitions. According to Iacobucci and Hibbard, the relationship in commerce can be of three kinds, which are: â€Å"Business Marketing Relationships† (BMR), â€Å"Interpersonal Commercial Relationships† (ICR), and â€Å"Business to Customer Relationships† (B-to-C). In BMR the business associations are characterized by long-standing, close and deep connections between fairly symmetric associates. BMR requires assurance, faith, and reliance in understanding business relations. ICR is characterized by the relationships between service organizations and end users. ICR can occur between two relatively balanced associates and it is long-term in nature. The consequences of effective ICR include increased satisfaction and productivity. Finally, B-to-C is demarcated by technology oriented relations among business and individual consumers.

Global economic environment &marketing Essay Example | Topics and Well Written Essays - 1500 words

Global economic environment &marketing - Essay Example Secondly, the fact that there was emphasis on the achievement of fairness rather than focusing of liberalization of trade also resulted in disagreement among member states. The fact that certain nations had bargaining power over others and this power was being shifted to other member countries caused a rift between members. Some of these issues reflect on the case study. For instance, one of the guidelines of the organisation was fairness. However, countries usually want to maintain the bargaining power over others irrespective of the fact that globalization has resulted in change and new markets where countries which were not major players in the past are currently significant players in the market. 4.2 In the international market, free trade cannot be fair. This is as a result of the fact that each country wants to protect its indigenous business establishment thus governments end up providing an added advantage over other business organisations in the international market (Salvato re, 2012. For instance, countries such as the United States of America are known to offer subsidies to farmers in order to give them an upper hand in the import and export sector. Question Five 5.1 Various a factors contributed to the economic crisis in Thailand to spread to other south East Asia countries making it a contagion. One of the major factors that contributed to this is that most of the respective governments in the region did not deal with the increasing balance of benefits in turkey, overheating pressures the stock market and property bubbles early enough. The fact that pegged / fixed exchange rates went on for too long was also a major contributor since it resulted in a false sense of stability that encouraged firms in the region to lend huge sums of money to those in Thailand. Finally, the fact that financial markets in the region were not regulated and supervised at the time was also major contributor 5.2 Countries in the region would have been able to prevent such a crisis if they implemented certain policies. Firstly, more supervision and regulation would have helped in ensuring that balance deficits that were present would not have risen to that level (Jackson, 1999). Secondly, countries in the region should have come up with measures that would ensure that stock market and property bubbles could be withstood since they would have been forecasted. Finally, the region would have adopted exchange rates that were not fixed. They would allow the exchange rate of currencies in the region to be determined by the forces of demand and supply. This would have helped greatly since a fall in the Thai baht would indicate something was wrong. Report Introduction There are various indicators that are used to determine the economic position in which a country or a region is in. Such indicators are instrumental in policy and decision making especially for business establishments that operate internationally. Such companies are able to determine if their bus iness ventures will be successful by evaluating indicators such as GDP. This part of the paper will focus on how different indicators have affected particular regions and how they are interpreted by an organisation Gross domestic product (GDP) is an indicator in macroeconomics that is used to measure the economic state of a country. It is the value of all goods and services recognised officially produced within a specific country in a stipulated period. In general, it is used to determine

Impact of Globalisation on the Nature of Work in Developing Countries Essay

Impact of Globalisation on the Nature of Work in Developing Countries - Essay Example negatively much more than the male counterparts in the same countries because they are less likely to be able to take up the skilled employment opportunities. Widening Income Gaps There are other disadvantages which come with globalisation. As globalisation creates employment for the skilled people and takes away the same from those who are not professionally trained, this will continue to widen the income gap and these developing countries will end up without a middle class. A country without a middle class is usually at risk of economic and political instabilities, and this is why the issue of globalisation persists.6 Globalisation will continue to expand the gap between the poor and the rich as the few people in the developed countries who have been rich enough to get an education continue to take the top jobs, either locally or even internationally, and be richer, and the majority who do not have an education continue to be jobless and without income.7 Those poor people will not be capable of educating their children, and the trend will continue. On the other hand, the few who are at the top of the socioeconomic ladder will be able to instruct their children, and this means that the few rich will continue to get richer while the majority poor will continue to be poorer. India’s labour market was one of the first to hugely benefit from globalisation as it was the preferred destination for business process outsourcing. As a result of many western camping in Indian cities looking for educated jobless individuals to do their call centre work, many young and educated men benefited and started earning salaries they could not have dreamt of, especially for a call agent. The problem with this was that not everybody in India is educated and when these opportunities came,... This report stresses that â€Å"education differences have played a big role in turning globalisation opportunities into curse for developing countries†. This is a big issue in developing countries because in these countries, few people are educated and thus cannot take advantage of these opportunities brought about by globalisation. Developing countries also have women who are generally much less educated than their male counterparts. This is unlike in the developed world where the gap between the educated males and females is closing up. This means that women in developing countries will be affected negatively much more than the male counterparts in the same countries because they are less likely to be able to take up the skilled employment opportunities. Globalisation has also helped in boosting the local employment numbers in developing countries through supporting local businesses. This paper makes a conclusion that globalisation has both positive and negative impacts. With regard to the labour market, globalisation has brought both favourable and adverse impacts. However, the negative impacts seem to be outweighing the positive ones and, if not put in check, these negative impacts may end up having a serious implication for the global economy rather than only for the developing world. As a result, it is necessary that the issue of globalisation be looked at seriously and any future problems be solved in order to avoid a negative effect on the global economy.