5-color theorem Essay Example | Topics and Well Written Essays - 500 words

5-color theorem - Essay Example There are three of them, four-color, five-color and six-color theorem. The five color theorem was proved in 1890 showing that five colors suffice to color a map. (Jensen and Toft 61) It all began with Francis Guthrie. He was a mathematician from British, who in 1952 discovered that he could color the states in the map of Great Britain by means of four colors without coloring of the neighboring countries with the same color. The problem hence arose if it was feasible to color any given map using four colors and it remained an area of interest for a while. The problem was; however, deciphered in 1879 when A. Kempe claimed to have found an explanation to the four color problem and went ahead to publish his solution and proof. In 1890; however, P. Heawood discovered an error in Kempers proof, which led to the demotion of the four color theorem as a credible theory. Heawood was unable to show that there was an error, which could have been colored with not less than five colors, but ultimately proved that Kempe was wrong in his argument. This led to a solution in the color problem with the five color theorem sufficing (Jensen and Toft 61). In order to proof the five color theorem mathematically, one relates a planar graph, G to a certain map. A vertex is placed on every area in the map. Two vertices are then connected with an edge where analogous areas share a boundary in common. This problem is then translated into a graph coloring problem. One is now required to color the graph vertices so that no border has its endpoints with a similar color. This proof relies heavily on the Euler characteristic to illustrate that there, it is mandatory to have a vertex V that is shared by at most five borders. It also relies on the fact that G is a planar. This is to denote that G may be embedded in a plane without necessarily intersecting the borders. Now take out

Foreign Language Essay -- Language

Only 9% of the U.S. population is bilingual, and less than 8% of college students enroll in foreign language courses (Baron). The United States has not put enough emphasis on the importance of foreign language education. People are not aware of the price this country pays due to a lack of language professionals. Its national security and diplomacy are lagging behind. American companies are becoming less prevalent in the international economy. Americans are isolated from culture that thrives in their communities. However, the future generations can be salvaged from this weak state with foreign language education. The teaching of foreign language in American public schools will help shape a culturally-nourished nation ready to advance into international political, economic, and social affairs. The national security and diplomatic affairs in the United States has suffered and will continue to if foreign language education is not rectified and strengthened. Perhaps the most severe tragedy on American soil, 9/11, exposed the language-related weaknesses of the U.S. government and intelligence agencies. After 9/11, the intelligence community revealed that it was only 30% prepared in languages crucial to national security (Holt). Although the government, had 123,000 hours of Arabic language recordings following the attacks, there weren’t enough linguistic professionals to analyze the information (Holt). In 2006 the FBI reported that only 33 FBI employees had limited skills in Arabic (Holt). However, they weren’t even in departments in which their skills could be used towards counterterrorism (Holt). The breach in national security is widening when intelligence agencies can only offer agents with â€Å"limited† language skills. There are intel... ...gn-language-educ_b_127588.html>. Lowery, George. "Cornell Chronicle: U.S. Should Emphasize Foreign Language Education." Cornell Chronicle Online. 24 Oct. 2007. Web. 03 Jan. 2012. . Osborn, Terry A. The Future of Foreign Language Education in the United States. Westport, CT: Bergin & Garvey, 2002. Print. Pufahl, Ingrid, Nancy C. Rhodes, and Donna Christian. "CAL: Digests: What We Can Learn From Foreign Language Teaching In Other Countries." Center for Applied Linguistics. Sept. 2001. Web. 02 Jan. 2012. . Ramzy, Austin. "Get Ahead, Learn Mandarin - TIME." TIME World. Breaking News, Analysis, Politics, Blogs, News Photos, Video, Tech Reviews - TIME.com. 26 June 2006. Web. 02 Jan. 2012. .

Therapy Management Of Rheumatoid Arthritis Health And Social Care Essay

Rheumatoid Arthritis is the most common signifier of inflammatory arthritis which was described in item for the first clip at the terminal of the eighteenth century. This systemic disease affects all cultural groups with the peak incidence in the fifth and 6th decennaries of life. It is characterized by proliferating and destructive alterations in the synovial membrane, periarticular constructions, skeletal musculuss and perineural sheaths of the host. Finally, the affected articulations become fibrosed or ankylosed because of destructive alterations in the joint construction [ 1 ] .EpidemiologyThe prevalence of the RA is about 1 % in the general population in the United States. Prevalence is similar worldwide. It affects all cultural groups with the peak incidence in adult females between the ages of 30 and 50. Disorder occurs three times more often in adult females than in work forces ) . Sing the significance and impact of RA is vitally of import, because it is a progressive destr uctive disease which leads to cram malformation, joint devastation and lasting disablement of the affected articulations [ 2, 3 ] .PathophysiologyEven though the exact cause is still unknown, research workers have found the disease is caused by auto-antibodies which affect synovial tissue. Most of the instances ( 70 % to 90 % ) are caused by the Rheumatoid Factor ( an autoantibody ) matching with IgG, itself an antibody. Most of the balance is caused by the arthritic factors attaching to IgM, IgA or IgE. This immune composite, which is a step of these arthritic factors, are engulfed by WBCs and luxuriant destructive muramidases within the lysosomes. Procollagenase, an enzyme released by neutrophils, is converted into active collagenase by the synovial fluid. Collagenase so splits the collagen of the articular surface gristle and leads to primary synovitis. This primary synovitis gives rise to a pannus which in bend signifiers villi. These villi migrate toward the joint doing its devastation and anchylosis [ 1, 4 ] . In add-on, some research workers say the disease is influenced by familial, environmental, infective factors, and autoimmunity [ 3 ] .DiagnosisThe right diagnosing is the key to the planning of intervention at any phase of a disease. Diagnosis of RA is suspected chiefly by detecting, forenoon articulation stiffness, inflammation and puffiness of the articulations of more than 6 hebdomads continuance impacting the little articulations of the custodies and pess symmetrically, synovial puffiness and hypertrophy with an infiltrate of assorted inflammatory cells including lymph cells and macrophages. Presence of serum rhe umatoid factor, radiological characteristics of RA and periarticular osteoporosis are the characteristic characteristics of the disease, apart from other characteristics such as febrility, weariness, weight loss, vasculitis and arthritic nodules. keratoconjunctivitis, dry eyes, and dry oral cavity, are excess articular and systemic characteristics of RA. Confirmation of the diagnosing is done by blood trials, joint aspiration and radiologic imagination [ 1, 2 ] .Orthopedic malformations of Rheumatoid ArthritisRheumatoid Arthritis can impact any joint in the organic structure. But it involves the peripheral articulations more frequently and really seldom affects the larger articulations. Deformities in the manus Symmetrical peripheral puffiness of phalangeal and interphalangeal articulations. Ulnar divergence of the manus is due to rupture of the collateral ligaments at the metacarpophalangeal articulations. This leads to stealing of the extensor sinews from their channels towards the ulnar side. Boutonniere & A ; acirc ; ˆâ„ ¢s ( button hole ) malformation is due to the rupture of cardinal enlargement of the fingers ensuing in flexure at the proximal interphalangeal articulations. Swan cervix malformation is due to the rupture or stretching of the palmar home base of the proximal interphalangeal articulations which enables the sinews to steal towards the dorsal side. Here there is hyperextension of the PIP articulation and flexure of the distal interphalangeal articulations. Trigger fingers and the trigger pollex are the nodules over the sinews. Deformities in the pes RA affects the whole pes which consists of forefoot mid pes and back pes. If it is in the fore pes patients may develop, hallux valgus malformation of the great toe, claw toes, callus over the back of the pes and the sole, broadening of the fore pes and the heel may demo valgus malformation. Deformities of the other articulations In the articulatio genus, patient may develop hempen anchylosis or bony anchylosis due to widespread devastation of the articular gristle by the pannus tissue. And besides causes the followerss such as flexure and valgus malformation of the articulatio genus.ManagementPharmacological direction Under pharmacological direction, Analgesics NSAIDs and DMARDs are the chief drug classs that are ordering for the intent of cut down the patterned advance of the disease and the symptoms such as redness, swelling and hurting. Normally Azathioprine, Cyclophospamide, Ciclosporin, Hydroxychloroquine, Leflunomide, Methotrexate, Penicillamine, Sulfasalazine are the major drugs which use for the direction of RA [ 3, 4 ] . Physiotherapeutic and rehabilitative direction in Rheumatoid Arthritis The chief intent of physical therapy direction for RA is to accomplish hurting alleviation and prevent joint harm and the functional loss. Physiotherapeutic and rehabilitative applications have significantly augmented medical therapy by cut downing the disabilities in day-to-day life for patients with RA. The basic PT program of attention for the patients who have RA include educate the patient, relieve hurting and musculus guarding, promote relaxation, minimise joint stiffness, maintain available gesture, minimise musculus wasting, and prevent malformation by protecting joint constructions. Inform the patient on importance of remainder, joint protection, energy preservation, and public presentation of scope of gesture ( ROM ) are the inaugural stairss of the patient instruction. Besides teach place exercising plan and activity alteration that conserve energy and minimise emphasis to vulnerable articulations will cut down the patterned advance of the disease. Application of physical therapy modes and intercessions include cold / heat applications, electrical stimulations, soft massage, immobilise in splint, relaxation technique and hydropathy are the intervention techniques which use to alleviate hurting, musculus guarding and to advance relaxation. Even though there are several physiotherapy agents that normally used in day-to-day pattern, most frequently their usage is based on the personal experiences of the physical therapist [ 5 ] . Cold is one of the most normally used physical agents which is utilizing in assorted types of creaky conditions particularly during the acute phase. Applications of cold battalions, Ice, cold air are some of the different methods of using cold therapy. Harmonizing to the pathology of RA, the enzymes ( gristle – destructing enzymes ) such as collagenase, elastaase, spreading factor and peptidase which are doing devastation of the joint construction are impacting by the temperature of local articulations. The normal intra-articular temperature is 33 0C, but it may be lift up to 36 0C in patient with RA. With temperature of 30 0C or lower, effects of these enzymes are negligibly little. Cold is impacting on the circulation of the local articulations and causes vasoconstriction which reduces the blood supply to the joint. Reduced force per unit area inside the blood vass consequences low unstable exudate which reduces swelling and hurting. Application of hot battalions is effectual for the chronic creaky hurting. Vasodilatation occurs with the heat and delivers extra blood in to the damaged tissues. Increased O and foods supply to the damaged tissues facilitate tissue mending. Heat therapy can be applied as hot battalions, dry hot towels, and every bit good as moist heat ( steam ) . Transdermal Electrical Nerve Stimulation ( TENS ) , signifier of electrical stimulation which uses to cut down the hurting perceptual experience. Harmonizing to the hurting gate theory, the electrical urges travel through the centripetal A-delta fibres which has connexions with substantia gelatinosa, elicit a negative response at T cells. Percept of hurting diminishes due to shutting of the hurting gate by negative response of the T cells. Application of electrodes over where the hurting is most intense is good to cut down the hurting perceptual experience. Passive or active assistive ROM within absolute bounds of hurting and gradual patterned advance as tolerated are required to minimise joint stiffness and maintain available gesture. Gentle grade I and II joint distraction and oscillation techniques are used to suppress hurting and minimise unstable stasis. In fact these techniques cut down the swelling significantly. Maintain normal muscular strength and prevent musculus wasting are indispensable to go independent in Activities of Daily Living ( ADL & A ; acirc ; ˆâ„ ¢s ) . Gentle isometric exercisings in hurting free places and patterned advance as tolerated minimize musculus wasting caused due to inadequate musculus work. In the interim, usage of supportive and assistive equipment for all pathologically active articulations, good bed positioning while resting, and turning away of activities that stress the articulations must be practiced to forestall progressive joint malformation. The ultimate end of physical therapy program of attention for the patients with RA is to do them independent in their ADLs. However, there are some contraindications and safeguards that physical therapist should see before administer any PT intercession to patients. Joint distraction, oscillation technique, stretching and inactive ROM should be done with the utmost attention of hurting and tissue harm. Besides application of heavy opposition over affected articulations and vigorous stretching are contraindicated particularly when articulations are swollen. The thought of the text was to give an overall description about RA and its direction schemes related to physical therapy. However, be aftering intervention Sessionss and find necessary intercessions are the responsibilities of the healer and besides it depends on patients disease position. It is far beyond the range of this text.

John F Kennedy Profile of President - Free Essay Example

Sample details Pages: 1 Words: 401 Downloads: 7 Date added: 2019/05/13 Category Politics Essay Level High school Tags: John F Kennedy Essay Did you like this example? John F. Kennedy Mini- Profile of President First Lady- Jacqueline Kennedy Onassis Nickname- Jack President- 1961- 1963 Political Party- Democrat Served- 1 term Chief executive January 20, 1961- Victory! This is the era of the youth. But, we still need the power of older generations to help us lead the way. Like my friend Dean Rusk as someone in my cabinet. Definitely, someone, I can trust! Commander-in-chief October, 1962- It is for sure a shame that people have started to lose humanity. Thanks, McGeorge Bundy for bringing the high altitude pictures taken from U-2 planes flying over Cuba. Just want to set this straight that IF the Soviets ever introduced defensive weapons, The gravest issues would arise. Chief Diplomat October 7, 1963- Why would anyone not want to have a ban on limited nuclear tests? Well as the president I have decided for the betterment of America I am going to sign the limited nuclear test-ban treaty with the Soviet Union and the United Kingdom. This is a fight which I will conquer to keep America safe! Chief of State May 29, 1961- Who agrees the American flag should be everywhere including the moon? It is an honor of mine to announce the fact that my goal is to have a landing man on the moon before the joint session of Congress. Don’t waste time! Our writers will create an original "John F Kennedy Profile of President" essay for you Create order I will be very glad to see if our nation can make it to the moon with the flag. Go America! Chief Legislators October 31, 1963- Who gives someone the right to control over someones life? No one has this right. Today, I am so glad to announce that I am signing a bill that frees thousands of Americans with mental illnesses from life in institutions. Instead of having big institutions they will be provided with community-based care instead. This gives them a better chance to recover. I have full faith that people will want this to happen. Chief of the Economy 1961- Passed a $451 million program in an effort to aid in alleviating the suffering in distressed areas hit by the unemployment where it is substantially a continuous not temporary and seasonal. As promised, will try very hard to have equal opportunities and create more job opportunities. Everyone should a way of income. Works Cited John F. Kennedy. Biography.com, AE Networks Television, 27 Oct. 2017, www.biography.com/people/john-f-kennedy-9362930. John F. Kennedy: Domestic Affairs. Miller Center, 10 Apr. 2018, millercenter.org/president/kennedy/domestic-affairs.