Ayurvedic Medicine v. Western Medicine Essay Example

Ayurvedic Medicine v. Western Medicine Essay Example Ayurvedic Medicine v. Western Medicine Essay Ayurvedic Medicine v. Western Medicine Essay Medicine: the science or practice of the diagnosis, treatment, and prevention of disease (in technical use often taken to exclude surgery). For centuries medicine has been the backbone of health care and prevention of disease. In the West most forms of medicine are chemical based and man-made but on the other hand many people also use more homeopathic forms of medicine containing natural herbs and plants to cure ailments some of these can be categorized into Ayurvedic medicine. In a further analysis of these two forms of medication one can determine, if there is, which type is more effective and suitable for todays day and age. From the stone ages humans have been practicing health care for the most part in rudimentary ways. There is indication of Neolithic people using herbs and other plants as forms of medicine for thousands of years. This begs the question if our ancestors were correct in their first method of technique or if the advancements in Western medicine since then have proven to be more effective? A form of modern day medicine that follows the patterns of the Neolithic people is Ayurvedic medicine. This form of medicine originates in India about 5000 years ago and focuses on the body, mind, and environment trying to bring a balance amongst these three factors and thus hoping that this will bring forth a healthy being. â€Å"Ayur means â€Å"life† and â€Å"vedic† means â€Å"knowledge† in Sanskrit in essence Ayurveda hopes to bring knowledge of life to the way of medicine. Since this form of medicine was first practiced in India many philosophies of Hinduism are woven into the way Ayurveda is practiced. Hinduism deals a lot with the spiritual world and how the body and soul connects with the universe. Much like concepts in Hinduism, â€Å"the concepts of universal interconnectedness, the bodys constitution (prakriti), and life forces (doshas) are [also] the primary basis of ayurvedic medicine. † (Johns Hopkins) . These three doshas are categorized by one: Vata; which controls bodily functions dealing with motion. Two: Pitta; which controls the body’s metabolic functions. Three: Kapha; which controls growth in the body. Through these pathways those who practice Ayurveda try and achieve a homeopathic method of restoring or preventing disease. Hindus believe that to reach salvation, or moksha, one has to find the right balance in life and follow that path. Ayurvedic treatments follow a similar pattern where one must find the imbalance in ones life and treat that at its core. Ergo bringing balance back to these doshas. Many of these methods include a wide range of therapies, meditation, dietary changes, yoga, etc. Aside from the treatments methods Ayurveda medicinal products also greatly differ from that of the West. Where Western medicine is man-made and evidence based, Ayurvedic medicine is all natural taken from herbs, plants, spices etc. For example; Triphala, a common Ayurvedic medicine is a full combination of plants. This particular medicine is made by combining three different types of fruit bearing plants (without the seed). Ayurvedic medicine, like this medication, all follow a fully plant based foundation. When using these kinds of medicine the years of education that go behind it is still important. In the United States and Canada there are no Ayurvedic training and licensing standards set nor are there any practitioners but â€Å"in India, there are many undergraduate and postgraduate colleges for Ayurveda, where the training can involve up to five years of study† (Altmedicine). Ayurvedic medicine has proved to help in many situations in a case study I read from the Jiva Ayurvedic treatment center a forty year old woman suffering from cancer used the Rasayana and Sroto Shodhak Chikitsa treatment, which combined minerals, herbs, and spices for a longer lifespan and to boost immunity. It was recorded that â€Å"her bone scan, brain scan, and the thorax-abdominal scan reports showed up normal results, indicating that her condition was stabilizing with the treatment† (Jiva). This case is just one example of the many times Ayurvedic medicine has been effective in helping prevent and treat disease. On the other hand though, as technology has improved and the study of the body has reached new depths Western medicine has discovered startling new medications that have paved way to the eridcation of some of the most fatal diseases and prevented many others. Western medicine is an applied science where the patient is treated by various health care professionals, coming in contact with numerous technologies, and ingesting a chemical based medication. To sum up Western medication in the most laman of ways: clinical judgement is used to find a prognosis and diagnosis for a patients ailment and thus drugs and sometimes radiation or of the like are used to treat or prevent the disease. Although many of todays medicines are made from plants it undergoes a chemical  process to create the end result most of us use. The research and development that goes into creating a new drug is much more extensive than Ayurvedic medications because of the time and money invested as well as the compounds used to create the drug are much more extreme than most of the herbs and spices used in Ayurvedic treatments. In the United States, in every country for that matter, Western medicine has been the foundation of health care and been constantly advancing. Since the days of plants based medications and eradicating diseases like polio, to using new technology to detecting cancer earlier and discovering newer and newer vaccinations Western medication has been ever-changing. Unlike Ayurvedic medication, Western medicine has been known to work quicker and more effectively. Possibly because there is more evidence in favor of Western medicine as well as practitioners and researchers choosing that path to study and follow with more people there is a more time and money invested. Though this may be the opinion of some, both medicines have proven their merit in many cases. With an evident pattern among both these styles of medication where both try to prevent or cure illness the method amongst these two medicines are highly different. With such different methods there will undoubtedly be side effects that highly differ amongst these two styles. Ayurvedic medicine in some cases have showed a high count of metal in the medications used for treatments. Research indicated that â€Å"one in five Ayurvedic medicines commonly used by followers of the ancient Indian health philosophy were found to contain the metallic poisons lead, mercury or arsenic† (Reuters). After studying these toxic metals it is unclear as to how exactly these metals get into the medications. Some researchers believe that it can be found in the soil that these herbs and plants are found and thus contaminates them or another possibility is the human pollution especially common in a lead polluted country like India. Most commonly it may be a manufacturing accident or even intentional injection. Dr. Robert Saper of the Boston University School of Medicine and Boston Medical Center commented that â€Å"theres some studies that show that some herbs have a very promising anti-diabetic effect, anti-high blood pressure effect, [and] a cholesterol-lowering (effect). † Evidence showing that though these medicines may hold metals, if researchers of Ayurvedic practice can remove the toxicity of these drugs than there is a promising future for Ayurvedic  medicine and, if the right processes are harvested, can possibly be a leading system for generations to come. Western medicine on the other hand hold a different set of side effects that have a far wider range. Because Western medicine is based more on a chemical process to create the drug the body becomes much more susceptible to negative reactions. Allergic reactions can be fatal; â€Å"antibiotics such as those in the sulfonamide and penicillin families cause allergic reactions in around five per cent of the population† (Betterhealth). Another common issue with Western drugs is that people get highly addicted to them and it can cause ulcers or adverse long term effects like in the case of Advil; if used to an extreme it can cause stomach ulcers because the acidity in the drug strips away stomach lining. This is clear evidence showing that the acidic levels in many of the more modern medicine have a serious negative effect on patients. Relying on anything can be harmful because as the saying goes; too much of a good thing can be bad. For Western medication, creating a new drug means doing hours of research and testing the drugs and once this is done the drug would have gone through numerous synthesis’ before finally being put on the market. Unlike Ayurvedic medicine, the United States has stricter regulations on the drugs that are produced as final products. The Food and Drug Administration, or the FDA has to approve the drug after its first stage of clinical testing, first on animals then on humans. After the passing those tests the FDA can deem the drug fit for consumption and is allowed to sell in the market. Most people would imagine that once testing is complete all side effects should be known and if there is a serious problem with the drug then the FDA wouldn’t approve it, correct? Well the biggest issue that arises is that most of these drugs may have hidden effects that researchers don’t find, because they didn’t know to even look for it. Some of these effects can be so fatal that the drugs needs an immediate recall off the market but in most cases the drug might go back to the first phase of testing or it is added to the list of side effects this drug has. For an individual trying to decide which method to try when dealing with a medical issue theres a lot of factors to consider with all these different issues with both styles of medicine is it hard for one to decide which method will be the best for them. From what I have learnt from my research if someone wants to pick a style of medicine it is impacted by one important element: time. The timing is very significant. Meaning that depending on how far along the medical issue is be that it might be diabetes or cancer both have phases and with a combination of these both styles prognosis can be much more optimistic. Bibliography. Abbott, R. B. et al. Medical student attitudes toward complementary, alternative and integrative medicine Evidence-based Complementary and Alternative Medicine (2010) How We Discover New Medicines. . N. p. , 06 Aug 2013. Web. 6 Dec 2013. gsk. com/research/how-we-discover-new-medicines. html . . John Hopkins University . Web. 6 Dec 2013. . ummedu. . University of Maryland Medical Center . Web. 6 Dec 2013. . Vilinius, Lithuania. Jiva Ayurveda. . N. p.. Web. 6 Dec 2013. . Wong, Cathy . Ayurveda. . N. p. , 13 Aug 2013. Web. 6 Dec 2013. . . www. chopra. com. The Chopra Center. Web. 6 Dec 2013. .

3 More Types of Not Only . . . but Also Errors

3 More Types of Not Only . . . but Also Errors 3 More Types of Not Only . . . but Also Errors 3 More Types of Not Only . . . but Also Errors By Mark Nichol Errors of faulty parallelism in sentences in which â€Å"not only† and â€Å"but also† help delineate complementary phrases come in three general categories, as shown, explained, and corrected below. 1. This problem not only relates to accessibility but also to completeness, accuracy, and validity of the data. In a simple sentence employing â€Å"not only† and â€Å"but also,† a verb that applies to both phrases must precede â€Å"not only†: â€Å"This problem relates not only to accessibility but also to completeness, accuracy, and validity of the data.† (Otherwise, the assumption is that a verb distinct from the one following â€Å"not only† will appear after â€Å"not also† in parallel to the first one, as in â€Å"This problem not only relates to accessibility but also applies to completeness, accuracy, and validity of the data.†) 2. This step presents not only a technical change, but introduces risks associated with migrating to the cloud. In this example, parallel verbs should follow the respective setup phrases â€Å"not only† and â€Å"but also†: â€Å"This step not only presents a technical change but also introduces risks associated with migrating to the cloud.† (Note, too, the deletion of the comma and the introduction of also.) 3. In this way, the courts have been central, not only to the preservation of American freedom, but also to its expansion. In â€Å"not only . . . but also† constructions, a comma is often inserted before â€Å"but also† (or before but alone when also is not included, as in the example above), but the punctuation mark is unnecessary because what follows it is not an independent clause or a parenthetical phrase. Here, the first comma is correct, the second one (assuming the third is omitted) is defensible for emphasis but is extraneous, and the third is a mistake, as explained in the first sentence in this discussion: â€Å"In this way, the courts have been central not only to the preservation of American freedom but also to its expansion.† Furthermore, the appearance of the second and third commas together is a double error; the inclusion of this pair of punctuation marks erroneously implies that what is contained within is parenthetical. (To test for the validity of the punctuation, view the sentence without the intervening phrase: â€Å"In this way, the courts have been central but also to its expansion† is ungrammatical, so the commas are incorrect.) Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Grammar category, check our popular posts, or choose a related post below:Avoid Beginning a Sentence with â€Å"With†A While vs AwhilePreposition Mistakes #1: Accused and Excited

Constuiton and Criminal Law Research Paper Example | Topics and Well Written Essays - 2250 words

Constuiton and Criminal Law - Research Paper Example Civil cases, moreover, involve persons and groups seeking to resolve lawful disagreements. In an illegal case, the state, using the prosecutor, instigates the suit, whereas in a public case the casualty brings the suit. People convicted of a crime may be confined, fined, or both. Though, persons found legally responsible in a civil case may just have to relinquish property or forfeit money, but are not confined (Siegel, 2010). What is a Crime? A crime is any omission or act in desecration of a civic law threatening or commanding it. Despite the fact that there are a number of common law crimes, majority of the crimes in the United States are made by the state, local, and federal regimes. Criminal laws differ clearly from one state to another. There is still a Model Penal Code that works as a good beginning place to have a knowhow of the fundamental structure of criminal legal responsibility. Crimes consist of both felonies that are more solemn offenses like, rape or murder and misdem eanors that are less solemn offenses like, jaywalking or petty theft. ... All statutes unfolding criminal activities can be divided into their diverse elements. Most offences with the exemption of strict-liability crimes comprise of two basics: an act and a mental state. Prosecutors have to provide evidence of each and every constituent of an offense to yield a conviction. In addition, the prosecutor must prove to the judge or jury beyond a reasonable uncertainty of every verity necessary to make up the crime charged. In public cases, the petitioner needs to prove that a defendant is legally responsible only by more than 50% or a preponderance of the evidence (Gardner & Anderson, 2006). Murder, Violence and Property Crimes The detailed US violent crime rate comprise of only aggravated physical attack, while the Canadian violent crime rate comprise all sorts of physical attack, as well as the much more numerous physical attack level 1, which is physical attack not using a weapon and not leading to severe bodily harm. Crimes against property comprises of bre aking and entering to people’s houses and getting away with their properties without assault. According to a survey done in 2004 by the Bureau of Justice Statistics, from the year 1981 to 1999, the United States had a lesser surveyed housing burglary level in 1998 than Australia, Canada, Scotland and England. Treason, Terrorism, and Wartime Criminal Justice In the account of the United States, the acts of terrorism, sedition, and criminal justice in times of war took on different forms. From the treason Act of 1798 to the present warfare on terror, the bill and its alterations have been challenged to guarantee national defense. To comprehend this it is better

Research paper Example | Topics and Well Written Essays - 250 words - 3

Research Paper Example Another reason for pursuing admission in SIU is the extensive scholarship programs that are used by the university to help its students. The scholarships provided by the university are on a rise and these scholarships promote students in working hard in order to attain scholarships. The university has high number of accreditations from several different accreditation agencies which is a solid reason to become a part of SIU. Other than the popularity of the University among dental students, the university has huge number of programs for the development of those who want to pursue a career in the field of dentistry. It provides students with both practical and theoretical knowledge and application for the development of high quality dental professionals. The university does not only develop the cognitive skills of its students, it even participates in physical development of its students. Due to their educational and athletic offerings I am persuaded to be a part of SIU and look forwar d towards the accomplishment of my

Wildlife Tourism and Environmental Impacts Research Paper

Wildlife Tourism and Environmental Impacts - Research Paper Example Inasmuch as wildlife tourism provides opportunities for wildlife protection, it also creates negative impacts on the environment. This paper shall discuss wildlife tourism and its environmental impacts. It shall review various research materials on wildlife tourism, summarising the main issues on this topic and the general impacts on related activities which pertain to wildlife tourism. The United Nations Environment Programme (UNEP, 2006) discusses that wildlife tourism is related to wildlife watch, mostly those of large mammals or flocks of birds; however, all types of animals are also included in this type of tourism. Wildlife watching is set apart from hunting and fishing and is confined to observations on animals; interactions in some cases are also seen, including the touching and feeding of these animals (UNEP, 2006). Wildlife tourism has grown significantly in recent years and it has evolved in its features to include other optional activities which tourists can choose to include in their package (UNEP, 2006). In some instances, wildlife tourism also includes hunting or fishing and in some instances viewing animals in zoos and confined parks (UNEP, 2006). This paper shall include both wildlife watching and wildlife tourism (with hunting and fishing) and the term wildlife tourism shall include wildlife watching. In the study by Roe, Leader-Williams, and Dalal-Clayton (1997), the authors discuss that wildlife tourism is usually associated with wildlife management and economic enterprises which support conservation, most especially in developing nations. The proliferation of other forms of tourism has occurred alongside the increased recognition of the need to secure sustainable development and ecotourism has been considered as a stable means of implementing sustainability (Roe, et.al., 1997).

The Mystery Behind Sudoku Mathematics Essay

The Mystery Behind Sudoku Mathematics Essay Puzzle games can be very enjoyable and is popular amongst kids as well as adults. Many of you may know the game Sudoku; where by the goal of the game is to fill in the remaining empty cells with each number from 1-9 appearing no more than once from each column, each row and each of the nine sub-grids. Sudoku is a type of logic-based numerical puzzle game that has a unique solution once completed. The most common form of a Sudoku is constructed as a 99 grid with nine 33 sub-grids and is primarily partially completed. Sudoku has become appealing among puzzle enthusiasts and involves complex thinking and practice. Available daily in newspapers, mobiles and many more, this addictive and brain-teasing puzzle game has become one of the most popular games to play since the time of the Rubiks cube. This dissertation discusses the mathematical side involved in Sudoku. There is no mathematics in actually solving a Sudoku but more of how it is used from a creators side. The 99 grid will be considered in the majority of the report; however a glimpse into other size grids will be discussed briefly also known as variants. Mathematicians have been questioning How many unique solutions are there in a Sudoku? Essentially meaning what are the possible ways of filling in an empty Sudoku grid so that each row, column and sub-grid contains the numbers 1 through 9. Your first thought of an answer may be a couple of thousands, but as you understand the concepts behind a Sudoku, you begin to grasp a whole new aspect. Combinatorics and permutation group theory are largely interwoven with analysing Sudoku. For that reason, I aim to explore these theories and understand how it applies to the methods of enumerating Sudoku grids. In particular I will be looking at Felgenhauer and Jarviss approach to enumerating all possible Sudoku grids where they employ several mathematical concepts. Furthermore I will uncover the importance of Latin squares and its use of constructing Sudokus. There are many constraints in regards to when are similar solutions considered different such as solutions of similar structure, symmetry etc. Preserving symmetries are known as relabeling symbols, band permutations, reflection, transposition and rotation. Burnsides Lemma theorem is one of their techniques in computing the number of essentially different solutions. Many difficult problems are of the type called nondeterministic-polynomial known as an NP-complete problem. This will direct me onto the debate on whether Sudoku is an NP-complete problem. Sudokus can take many forms and shapes. These are called Sudoku variants and consist of rectangular regions, Sudokus with a large region having no clues (numbers), an empty row, column or sub-grid and many more! Here I will research the logic behind irregular Sudokus as well as examining any occurring patterns or whether it has occurred by chance. 1.2 Latin squares and Sudoku Sudoku is also a special case of Latin squares. The Swiss mathematician, Leonhard Euler made many fundamental discoveries during 1782 including Latin squares. A Latin square is an N x N matrix where by a set of N characters are arranged such that each row and column contains one of each character. This is also in the case of a Sudoku, when complete, with an additional constraint that the nine sub-grids must hold the numbers 1-9. A reduction can be made to any Latin square by permuting the rows and columns. This arrangement is an aspect of combinatorics and is most commonly referred to as enumeration. Enumerative combinatorics is a classic area of Combinatorics and involves counting the number of infinite class of finite sets. Counting combinations and counting permutations are two of the most common forms. The number of valid Latin squares is known to be approximately 5.525 x 10 ²Ãƒ ¢Ã‚ Ã‚ ·. Write about Colbourns proof 1.3 Combinatorics and Permutation group theory Combinations and permutations have slightly different meaning. Combinations are the number of different ways of selecting n objects from a set but the order of events is not important. From a set of 3 objects, lets call these 1, 2 and 3. If for example I was asked to pick the number of ways of selecting 2 objects out of the 3, there would be three combinations 12, 23 and 13. 12 = 21 since the order of each pair is not important. A permutation on the other hand does consider the position. Therefore if I was to use the above example, there would be six permutations. A simpler way to calculate a larger set would be to use formula 1: Formula 1. = = Where is the combination formula, is the permutation formula, n is the total number of objects and r is the number to be arranged Both methods are one way of computing the number of possible Sudoku solutions and this will be looked at later in the report. Chapter 2 Enumerating possible Sudoku solutions 2.1 Distinct Sudoku solutions There are many approaches to enumerating possible Sudoku solutions. To enumerate every possible Sudoku solution, a Sudoku differs from another if they are not identical. Thus all solutions will be consider unless they are like for like. Felgenhauer and Jarvis was the first to enumerate the Sudoku grid solutions directly in 2005. There approach was to analyze the permutations of the top row used in valid solutions. Their knowledge of the complexity in computing the number of Latin squares has made them aware of how they should go about getting an answer with fewer computations. Hence by using relabeling this could shorten the number of counts. To make it easier, each sub-grid is given an abbreviation seen in figure 3. B1 B2 B3 B4 B5 B6 B7 B8 B9 Figure 1. Abbreviated sub-grid with top band (Felgenhauer and Jarvis, 2006) Firstly they consider every solution to filling in blocks B2, B3, given that B1 is in standard form. To work out every possible way of arranging B1 on its own would essentially be computing the number of permutations of 9 symbols. There are 9! of filling in B1. The main operation they use is called relabeling. 1 2 3 4 5 6 7 8 9 Figure 2. B1 in standard form (Felgenhauer and Jarvis, 2006) Felgenhauer and Jarvis have found that B2 and B3 is the same as the transpose of B2 and B3. Therefore the number of ways of arranging B1, B2 and B3 and B1, B2 and B3 to a complete grid is equally the same. This means that computing one set of possibilities will cut down the number of solutions. Inevitably, there are few pairs of B2 and B3 that needs to be worked out and as well as using reduction the number of possibilities for the top band of a Sudoku grid is 9! x 2612736 = 948109639680. The next section involves brute force computation. As running through all 2612736 possibilities would be exceedingly tedious for B2 and B3, Felgenhauer and Jarvis attempts to identify configurations of the numbers in these blocks which give the same number of ways of completing to a full grid. This in return, will cut down the number possibilities. Permuting B2 and B3 in every way such that the result gives a unique solution will preserve the number of complete grids. This is the same for B5 and B6, and B8 and B9. However this changes B1 from its standard form, so an additional relabeling of B1 needs to be performed. Another approach to reducing the number of possibilities is to permute the columns in each block and permute the rows of any block. Reducing the number of possible ways by permuting. Lexicographical reduction Permutation reduction Column reduction As a result of these methods, Felgenhauer and Jarvis have found that there are approximately 6670903752021072936960 à ¢Ã¢â‚¬ °Ã‹â€  6.671 x 10 ²Ã‚ ¹ Sudoku solutions. In light of this result, there are fewer solutions than Latin squares due to the fact that there is that extra restriction of 9 sub-grids. That being said, there will be no shortage of Sudoku puzzles any time soon. Verification of this result has been confirmed by several other mathematicians Ed Russell to be more precise. 2.2 Essentially different Sudoku grids Whether symmetrical Sudoku grids are considered as two separate solutions is another method of enumerating the possible solutions. In this case, the only solutions are ones that are essentially different. Lets say two Sudoku grids are equivalent if one is a transformation of the other by applying any number of symmetries. If however, no such chain of symmetries can occur between two grids, it is essentially different. Two Sudoku grids are the same if we can get from one to the other by applying some sort of symmetry. For instance, take figure 3 4 below; the set of 3s in the first grid can be interchanged by the placements of the set of 1s, effectively producing the second grid. Figure 3. Valid Sudoku grid Figure 4. Another valid Sudoku grid from Figure 1 As well as this, a solution is said to be the same as another if any two columns or rows are swapped. The first column and second column in figure 3 can be exchanged to give figure 5. The two solutions are said to be symmetrical because the transformation still produces a valid Sudoku grid. Figure 5. First and second column swapped from Figure 1. Another form of symmetries includes rotational grids. A rotation of Figure 3 by 90 degrees generates a new valid Sudoku grid shown in Figure 6. Figure 6. Rotational of 90 degrees from figure 1 Any of these operations performed on a valid grid maintains the property of it being valid and this is known as symmetries of a grid. When an object is subject to these operations, certain properties are preserved. An example would be if one performs symmetry on to a Sudoku grid and repeats this operation once more, the final transformation is itself symmetric. In addition a symmetrical object can be transformed back to its original state by another form of symmetry. Performing several symmetries on a Sudoku grid can also be achieved by grouping its neighbouring pair. So the first symmetry can be paired with the second or the second can be paired with the third and so on. The resulting transformation is nevertheless the same either way. From these properties, it is inevitable to say that the set of symmetries of any Sudoku grid form a group. A group is a set G if it satisfies the following properties: CLOSURE If f and g are elements of G, then f ·g is also an element of G. ASSOCIATIVITY If f, g, and h are elements of G, then f ·(g ·h)=(f ·g) ·h must satisfy. IDENTITY ELEMENT There is an element e in G such that g ·e=e ·g=g for all g in G. INVERSE For any element g of G, there is another element d of G such that g ·d=d ·g=e, where e is the identity element. (The element d = g-1.) The symmetry group is thus generated by the transformations of: re-labelling the nine digits, permuting the three stacks (3 vertical blocks of a Sudoku), permuting the three bands (3 horizontal blocks of a Sudoku), permuting the three columns within a stack, permuting the three rows within a band, and any reflection or rotation. These can be combined to form other elements of the group and together they comprise of the symmetry group G. Given that any element of G can be mapped so that it takes one grid to another, we can say that the set of valid Sudoku grids has a finite number of elements. Thus G has finitely many symmetries. The association between symmetrical Sudoku grids are in fact an equivalence relation and satisfies the following three properties: for grids A, B and C in set G Reflexivity A = A Symmetry If A = B then B = A Transitivity If A = B and B = C then A = C Let A be any valid Sudoku grid, we must consider all the grids that are equivalent to a valid Sudoku grid A. To do this, we firstly have to group together grids that are essentially the same so that we can partition the set of grids. This will break the set of Sudoku grids into subsets, with groups that contain no relating elements within each other. The term subset can be called equivalence classes and is denoted by X/G. In any equivalence class, there are elements that are equivalent to each other by symmetry. The total number of elements in X/G is equal to the number of essential Sudoku grids. To calculate the number of essentially different Sudoku grids, we shall look at all the symmetries neglecting the re-labelling of the nine digits for the time being. The number of distinct symmetries founded by Russell and Jarvis (2006) is said to contain 3359232 (pg 4). In this finite group H, we need to take the average number of grids fixed by an element of H, up to re-labelling. Next we need to verify the number of fixed points of all elements in H. Russell and Jarvis have found that there are 275 classes of symmetries using a software package called GAP. It is interesting to note that some of the elements in H have the same number of fixed grids. In other words, we only need to count the number of fixed points for one symmetry for each of the 275 classes. However there exist symmetries in H that have no fixed points. Subsequently, there is no need to count the number of fixed grids for those that have no fixed points. That being said, there are only 27 out of 275 classes that co ntain fixed points, meaning fewer computations. Rotman. J. J (1995) demonstrate that if X is a finite G-set and |X/G| is the number of G-orbits of X, then Formula 2 holds where, for gцG, X is the number of xцX fixed by g (pg 58-61). Using this notion, we have established that the number of valid Sudoku grids is of a finite set and X/G is the number of essentially different Sudoku grids, so we can obtain the number of essentially different Sudoku grids by using the Burnside Lemma Theorem. Formula 2. Burnside Lemma Theorem (Rotman, 1995) Burnside Lemma Theorem is a useful tool when dealing with symmetry with a set of countable objects. When used to enumerate the essentially different Sudoku grid, the set of equivalent grids form an orbit of the symmetric group. The number orbits are essentially the number of different grid solutions. This may sound slightly (ALOT) trickier to compute, nonetheless Russell and Jarvis have shown that the number of essentially different Sudoku grids is 5,472,730,538 with the implementation of Burnsides Lemma Theorem. Chapter 3 Nondeterministic polynomials 3.1 NP-complete and Sudoku Sudokus may relate to a variety of problems, in particularly, whether Sudoku is an NP-complete problem. It is known that NP-complete problems are one of the most complicated cases in NP, also referred to as nondeterministic-polynomial. Its rival, P problems relates to NP as both being in the same complexity class. Mathematicians have yet to solve whether NP-complete problems can be solved in polynomial time or more commonly whether P = NP. Consequently being one of the greatest unsolved mathematical problems. The majority of computer scientists believe that P à ¢Ã¢â‚¬ °Ã‚   NP, as a result would mean that NP-complete problems are significantly trickier to compute than to verify. Unfortunately, nobody has yet found an efficient algorithm, not even with the use of computers available today. A problem is said to be NP-complete when its solution can be proved in polynomial time. And if that problem can be solved in polynomial time, all problems in NP can be solved too. An interesting characteristic of NP-complete problems is that the time frame to solve the problem increases rapidly as the size of the problem gets larger. If that is the case and Sudokus are NP-complete, solving a Sudoku of higher order (say 17 ² x 17 ²) will become increasingly challenging algorithmically then the standard 3 ² x 3 ² version were talking trillions of years. It has been shown that Sudoku does belong to the category of NPC problems by Takayuki Yato of the Univeristy of Tokyo (2003). An exchange for the notation ASP-completeness (shorthand for Another solution problem), led the proof of NP-completeness of ASP. Their proof uses reduction in order to obtain the required polynomial-time ASP from the problem of Latin squares by Colbourn (1984) who has verified, the NP-completeness of ASP of Latin square completion Another accountable source by Provan states that, It is known that solving general-sized Sudoku puzzles is NP-hard, even for square grids with blocks consisting of the sets of rows and columns (Latin Squares) or for p2 x p2 grids with blocks consisting of rows, columns, and the p2 partitioned p x p subsquares. Mathematical programmes such as the 0-1 linear programming and the knapsack problems are also cases of NP-complete problems. A full list of other problems that are NP-complete can be found in Garey and Johnson (1979). Chapter 4 Sudoku Variants 4.1 Variation The classic form of a 99 Sudoku are polyominoes. There are other variations of Sudokus that can be applied to the rules of Sudoku. There are puzzles of the size 66 with 23 regions or a 1212 grid of 43 regions. More so, there are other fascinating Sudoku variants such as Greater than Sudoku. Chapter 5 Personal Critical Review The progress I have made during the duration of this project, have been fairly slow but surely getting there. Having said this on many occasions, I have still not conquered my time management skills! The project started very slow which meant I was behind schedule. Nevertheless my organisational skills have kept me on balance. The GANT chart has been of great help in doing so. What has kept me going throughout this project in particular would be self discipline and motivation. This project has proven that I am capable of working to my own initiative, but also well within a group; my time during the group project. Furthermore, my time on this project has definitely promoted a better mentality of my future ambitions. I have learnt that it is crucial to read a lot, as well as reading as broadly as I can. This in turn have aided in the running of my project. With other coursework deadlines, I made that a priority and had no time to meet with my supervisor. I understand that meeting with my supervisor is equally important because a supervisor is there to encourage and to advice on any difficult obstacles I may encounter. An area of interest to proof whether NP-complete problems can be solved in polynomial time, was left open as future work. This could be the next step of extending this report that little bit further. Chapter 6 Conclusion A challenging problem for further research is to proof whether NP-complete problems can be solved in polynomial time. This has yet to be solved and anyone who has a formal proof will be rewarded $1 million dollars by The Clay Mathematics Institute.

Promotional Strategies Essay -- essays research papers

â€Å"How do I get my product/service out there?† This is a question that many people who plan to begin their own businesses, or even larger companies who have already established a name for themselves, frequently ask. Your product or service may be the latest and greatest on the market today, but that doesn't help you if no one knows it exists. You need to find someway to make yourself and your product known. That is where promotion comes into play. But what exactly is promotion? Well, www.dictionary.com defines promotion as: The act of promoting or the fact of being promoted; advancement. Encouragement of the progress, growth, or acceptance of something; furtherance. Advertising; publicity. Essentially this covers everything from commercials to magazine ads and even free items given out at exhibitions and trade shows. Promotion is preformed many different ways by many different people but when it all comes down to it there is really only one purpose. To get your name out there. Now you're probably wondering which kind or promotional strategy would be best for your product, and you would be right to wonder about this. Not every product can be marketed in the same way. Truth be told the promotional strategy is based solely on the product or service. There is no list of defined laws for promotion. The best I can do is give some examples of promotion and explain some points. The rest is really up to you. For simplicity sake all of my promotional examples are taken from the gaming software aspect of the Information Technology field. More specifically the games programmed for gaming consoles such as the Playstation and GameCube. To start things off we'll discuss the media aspect of promotion. But just what makes a promotion successful? And how many types of promotions are out there? The Handbook Of Market Segmentation says: Successful advertising calls for investing your dollars wisely. Advertising expenditures should be allocated to those media vehicles which can best deliver to target markets. Scores of different media can be used. One advertising company claimed that more than 14,000 choices exist. Obviously, most of these media are obscure, impractical, or unimportant. For simplicity, media can be divided into three major classes: 1.Bro... ... into a promotion for a product that hasn't been completed yet. Nintendo decided the best course of action would be to take shots of what they already have completed, put it to some good sounding dramatic music, just to show viewers what this game will have to offer. After all of this you have to ask yourself â€Å"Is all of this stuff really worth it?†. Most companies would say definitely. Promotional items make sure that people have physical objects to remember your product by, and as for the commercials, well, Alan Bruce said it best in his article â€Å"Marking 50 Years Of Memorable TV†: If the TV medium has reason to celebrate anything lately, it's commercials like these. And industry groups just that marking the 50th anniversary of those ineluctable ads whose history is as memorable – for better or worse – as that of the TV programming itself. Bibliographies 1.Weinstein, Art. The Handbook of Market Segmentation. New York: The Haworth Press, 2004 2.Bruce, Alan. "Marking 50 Years of Memorable TV The Commercials" Christian Science Monitor. 3 Mar. 1995: Vol: 87, Issue: 67 3.Videos care of www.nintendo.com

Know Rhymesâ€Know Reasons

My parents are nerds.   I don’t mean they were nerds as kids and grew out of it; I mean my parents were nerds from the moment each was born, though their adolescence, and right into adulthood.   Today, my parents remain true to their heritage: they are full-fledged, adult nerds. As most people are aware, nerd hood requires a few supplies and traits: along with the requisite pocket protectors, the over-exuberance for all things academic, and thick glasses, both of my parents are bookworms.   Luckily, certain genetic traits skip a generation, and I can honestly say that I am not a nerd; however, I am a bookworm, and I am not ashamed to admit it because much of my life has been influenced by the things I have read. I grew up with Dr. Seuss.   My father used to spend time every week reading the latest Dr. Seuss book with me.   He’d tuck me into bed, and then I read to him aloud as the story unfolded one rhyme and one intriguing illustration at a time.   My goal was not so much to get to the end, but to learn new words, and each new word I learned was marked by my father with a bright, yellow highlighter. In this way, the progress I made became more tangible, and for all I know, that habit of my father’s allowed me the freedom to read all of my books with a dictionary and a highlighter by my side and never to feel as if doing so was a waste of time or a burden: new word were an adventure, and I loved learning them.   I don’t recall developing a particular favorite Dr. Seuss book as a child, but as I got older, I began to get the urge to unpack the box of my highlighted books and relive a little of my youth. The box of Dr. Seuss books had been stored in the family shed, and the years had taken their toll.   The change in temperature had caused the books to warp and mold, but they had not gone completely to waste: at least one family of rodents had nested in the box, shredding the pages of my early education for their own progeny’s needs.   One lone book remained untouched: Horton Hears a Who, and as I opened this last book of my childhood and began to read, I was struck by the power of the story.   Hidden in the text was one of the most important lessons I’ve ever learned: a single voice of the tiniest girl was strong enough to make a difference.   As hokey as it may sound, I leaned the degree to which an individual can impact the world that day as I read that book.   Perhaps I am a nerd. I won’t waste time by detailing the degree to which I read during grade school, junior high school, and high school; I will only clarify that while I admit to being bookish, I was also an athlete, participated in student body, and had a social life.   I was, however, not done with Dr. Seuss. I hit a wall with Shakespeare, and I felt the burden of reading for the first time in my life.   While many students had grown accustomed to that wall, I had never dealt with it, so by the time it happened to me, the stakes were high: I was in college, and I wasn’t getting it.   I had never skipped a reading—never worried about my English or literature courses. Suddenly, I was ready for a slug of the stuff Romeo had taken.   I did the only thing I could think of: looking for commiseration, I complained to my parents about how stupid Shakespeare was, pointed out that no one could really be sure he’d written his plays, and wondered out loud why anyone needed to read stuff that’s written like that anyway. My father would have none of it, but he suggested to me that anyone who had grown up on Dr. Seuss and Shel Silverstein had no business complaining about or being confused by Shakespeare.   Like many messages delivered when one isn’t ready to receive them, the point my father had tried to make was lost on me for awhile—buried by the frustration of not having been appeased.   Several days later, I tried to give in to the notion that there might be something familiar in the rhythm and rhyme of Shakespeare if only I’d do what my father had suggested: read it out loud and listen—really listen. I struggled at first trying to work through the colloquial terms.   I fought to remember that the ends of a line of text didn’t necessarily equal the end of a sentence.   I battled with Shakespeare’s sentence structure trying to remember that it was rarely subject-verb-object.   It was like running through sand that was waist deep.   Until it wasn’t.   Suddenly, everything fell into place: it was like I had learned a foreign language.   The words made sense; the story began to unfold around me; I got it; I liked it.   The only thing I can compare it to is sitting in a theater watching a sub-titled movie: there is a point at which the reading becomes so automatic that it is no longer a conscious effort but automatic.   It was just like that. Later, I met the wall that was Henry James.   I was reading Portrait of a Lady, and I had spent far too much time trying to decipher the first scene of the text.   When I realized that James had spent over a page beating around the bush to say that three men were at tea, I wanted to scream.   I wanted to ask the guy why he’d wasted so much ink and so many words simply to point out to the audience that it was tea time, but instead of there being women there, there were men—but I had a book to wade through, and Mr. James was long dead, so I moved on. Having figured out the context of the opening if the book, I went back and started anew, and I realized that I wanted to sit and talk to the man who had chosen such wonderfully descriptive words—a man who had taken such great care to spend the time to so completely describe the fact that three men were at tea.   I remember thinking to myself that if he were a painter, and he painted the way he wrote, that I would love his work like I loved Claude Monet’s Impression Sunrise.   Years later, when I began to read everything I could by and about Henry James, I had a private laugh over his affinity for painters—Monet in particular. Having cracked Shakespeare and James, I was never again afraid of a book’s language or  length.   I picked up Middlemarch and Tom Jones and Vanity Fair and loved each of them for  different reasons, but one day, I picked up Sherwood Anderson’s Winesburg, Ohio, and like  Horton Hears a Who, I found a story that changed the way I viewed the world.   â€Å"The Book of the  Grotesque† made me think about truth, and the way in which each individual forms his or her  own truth and twists it to suite personal needs.   It made me consider that each person’s  quest for and claiming of truth can send ripples into the world, and these ideas changed me. Recently, I have discovered Flannery O’Connor, and while I struggle with the racial issues that threaten to ruin her works for me, I feel the now-familiar tingle beginning that I have grown to recognize as the discovery and excitement that only a well-written book can bring me.   I may have to break down and buy a pocket protector just to use as a book mark. What about writing?   Well, if one day all of the things I have jotted down in hopes of emulating the people previously mentioned ever manages to make its way to a publisher, I will blame that on the books I have read and the people who wrote them.   I will speak of the fact that when I walk into a bookstore, I marvel at all of the people who have managed to get published and allow myself an instant to believe it might someday happen for me as well. As I pick my words and paint my own pictures, I wonder if I have it in me to write the thing that for the right person will make a difference—the thing that might one day be highlighted in bright yellow—the page marked with a sticky note.   Maybe this year I’ll try my hand at NaNoWriMo.   

crime and media essays

crime and media essays Corrections has been a field dominated primarily by men. Women entering in this field have had to struggle against the resistance presented when entering these types of jobs. Criminal justice and women have been terms that have not been heavily associated. However women do play a major role in the criminal justice system, whether they are the offenders, victims or criminal justice professionals. The role of women in criminal justice often depicts women as the victims in order to keep in place the ideologies of women being subordinate, feeble, and unable to take care of themselves against their aggressor. Women are not only victimized women also play roles of the offenders and criminal justice professionals contrary to popular belief. Although women have made strives to progress they still represent lowest line of sworn in officers Women are very versatile in their involvement with the criminal justices system. It is also important for us a as society to understand that women are major functions in the criminal justice system although their isnt an enormous amount of literature about it. Women are represented in every dimension of the criminal justice system. The depictions of women in the media are influential factors for women who have chosen this male dominated work force. The traditional role of women being housewives and mothers have in some ways hindered the process of them becoming a dominant work force in the field of corrections. In film it is very noticeable how women are depicted as helpless or are in need of some type of assistance from her male counterpart. In the Hale article about women in videos the treatment of women tends to be a social control. It romanticizes the way women and men are especially in uniform. For example the man is usually the hero in the film usually he rescues the woman. The scenario hardly ever plays in the other direction. I personally cant think of ...

Forming the Past Tense of Regular Verbs

Forming the Past Tense of Regular Verbs The tense of a verb suggests the time of its action- present, past, or future. We rely on the past tense to show that an action has already been completed. Adding -d or -ed to Form the Past Tense In the following sentences, the verbs in bold are in the past tense: Wallace moved into his new house last Saturday.Yesterday I visited him for tea. Both move and visit are called regular verbs because they have the same past-tense ending of -ed. If the present form of a regular verb ends in -e, we add -d to form the past tense: Wallace and Gromit move frequently. (present tense)Wallace and Gromit moved into their new house last Saturday. (past tense) If the present form of a regular verb ends in a letter other than -e, we usually add -ed to form the past tense: I visit Wallace and Gromit every Tuesday evening. (present tense)Yesterday I visited them for tea. (past tense) Note that a spelling rule comes into play with verbs ending in -y. If the present form of a regular verb ends in -y preceded by a consonant (for example, cry, fry, try, carry), change the y to i and add -ed to form the past tense (cried, fried, tried, carried): Wallace and Gromit carry the cheese and crackers into the kitchen. (present tense)Wallace and Gromit carried the cheese and crackers into the kitchen. (past tense) Because all regular verbs have the same -ed ending in the past tense no matter what the subject is, subject-verb agreement is not a problem. The Different Sounds of the -ed Ending Dont let the sound of an -ed ending ever trick you into making a spelling error when you form the past tense. While we do hear a d sound at the end of some verbs (for example, moved and visited), we hear a t sound at the end of others (promised, laughed). Also, if you have a habit when you speak of clipping off word endings, dont do this when you write. No matter what sound you hear or fail to hear when you pronounce a regular verb in the past tense, be careful when you write to add -d or -ed at the end. EXERCISE: Forming the Past Tense of Regular Verbs The first sentence in each set below contains a verb in the present tense. Complete the second sentence in each set by adding -d or -ed to the verb in parentheses to form the past tense. When youre done, compare your responses with the answers at the end of the exercise. Carrot Top uses unusual props in his comedy act. Recently he (use) a double-wide toilet seat.Halleys Comet appears every 76 years. It last (appear) in 1986.We rarely punish the children. However, we (punish) them yesterday for spray-painting the dog.Wallace likes knitting and reading the newspaper. Even as a boy, he (like) to invent things.Wallace enjoys Wensleydale cheese and a nice cup of tea. When he was younger, Wallace (enjoy) cheddar cheese.I usually purchase a season ticket from the box office. Yesterday I (purchase) a ticket over the Internet.Gromit graduates from college today. Last year he (graduate) from Dogwarts University.Please carry this invention upstairs for me. I (carry) it into the house.Mookie and Buddy cry when they are hungry. Last night they (cry) for over an hour.Gromit tries very hard to be helpful. He (try) too hard last week. ANSWERS:1. used; 2. appeared; 3. punished; 4. liked; 5. enjoyed; 6. purchased; 7. graduated; 8. carried; 9. cried; 10. tried.

Culture of Employers and Employees Essay Example | Topics and Well Written Essays - 1000 words

Culture of Employers and Employees - Essay Example The American employees are motivated by flexible work timings and good salary packages. As most of these employees tend to have more than one job at a time to earn more, flexible work schedules appeal to them. These employees care about money and freedom of expression. They expect their employers to be flexible in terms of work deadlines. The goal of these employees is to save enough money to live a luxurious lifestyle. These employees are good customers and shop frequently. They are influenced by latest technology, and products of acknowledged and reputable brands. They have an instinct towards living green, safe and healthy, though they are not quite as much prudent in their activities to ensure this. Their assumptions are that they belong to a multicultural society, where they have to accept all kinds of religions, norms, values, and traditions. The affect of these assumptions on their work is that they have freedom of expression and allow others the same. Nairobi, Kenya The cultu re of Nairobian workers deems work second to home. These employees are generally very friendly, and helpful towards one another. They understand one another’s problems and try to extend their help if possible. At a certain point in time, if a Nairobian worker has an issue at home and another at the office of equal importance, the worker would first attend the issue at home and then at the office. â€Å"It is considered a perfectly acceptable reason to show up late for an assignment and for deadlines to be missed just so workers can keep their personal affairs in good order† (â€Å"Cultural Information – Kenya†). Nairobian employers motivate the workers by providing them with relaxed work schedules (Kumba). Nairobian employees expect employers to provide them with flexible work schedules and they care about their families a lot. The goal of Nairobian workers is to earn sufficient for their families. They assume that their employers understand their feeling s towards their families. This has a slightly negative effect on their work as they tend to arrive late at work or leave for home before the break off time. They may not be there at the workplace in the time of urgency. Paris, France The employees in Paris are culturally diverse, but not quite as much as the ones in New York. They communicate with one another mostly in French and occasionally in English. French business culture emphasizes upon formality, respect, mutual trust, and courtesy. In order to be motivated for work, French employees need to be respected. â€Å"Respect of colleagues and bosses motivates workers in France† (Woodward and Shandwick). These employees care about personal image and reputation, and are able to deliver their best in an emotionally satiating and psychologically fulfilling work environment. The French employees have the goal to excel in their profession while keeping their image high. They are influenced by charismatic managers and coworkers wh o are not only well-dressed but also well-behaved. They are motivated to work hard provided that they get the right conditions, though not many are of the view that their employers are cooperative. â€Å"While 82 per cent of employees in France say that they are motivated to ‘go the extra mile’ (in other words ‘engaged’), less than two thirds (53 per cent) feel they are enabled by

Reflection Essay Example | Topics and Well Written Essays - 1000 words - 16

Reflection - Essay Example Many students feel that the meals they take for lunch are not tasty and as a result they prefer to skip the meals. According to Martin and Oakley (438), care programs that provide the learners with meals that have proper nutrition will succeed to make the learners ready for their studies. Learners should enjoy high nutritious meals before they get to school because this will help them to easily transition to meals offered in school. The physical environment of the school is ideal for learning. While in school, the students are to access the services of a well organised classroom, play ground and dining hall. When activities change, students change their physical setting, making them able to relate the activity they are doing with the environment. A student like Samuel for example is able to differentiate the different setting with the activities to be undertaken. The physical setting of the classroom makes students ready to learn. According to Cashin and Cooper, interaction between the teachers and the students improves the environment of learning compared to using online platforms to teach students on language. The positive interactions between the students and the mentor make the students motivated to learn. The mentors are also able to demonstrate their interest to participate in the learning process of the students and to provide the students with sufficient mentorship. From the experience of interacting with the students, the general performance of the students improve substantially when new innovative mentoring techniques are used in an alternating manner. Some of the effective techniques used include brainstorming sessions, note taking sessions and group activity sessions. While note taking enables the students to further master the language, other techniques like group activities make the students to motivate each other to learn more. Teacher’s participation