Pen-3 Model Essay Example | Topics and Well Written Essays - 500 words

Pen-3 Model - Essay Example PEN 3 Model Culture is defined as a set of beliefs, behaviors, objects and others that are common to a group of people (Schaefer, 2009). Cultural aspects also include religion, language, values, laws, norms and the like. It is learned by the people by imitating the elders and/or enforcement by means of stigma and praises inside the society. Because of this, it is logical to say that culture can also affect health, as the health of an individual is also affected by culture and in turn also affects the health of the society. The health of the society is vital and it should be assessed regularly to monitor the needs of the people. A healthy population is a healthy civilization. Some diseases, like AIDS, are spread because of behavior. AIDS is transmitted by having unprotected sex or by using soiled needles contaminated by the HIV in medical procedures. These are all controllable and the spread can actually be contained when the people can just adjust their behavior. Behavior, like promi scuity, is an aspect of culture. Therefore, a disease that is spread by culture can also be corrected by culture. The sub-Saharan territory in Africa has the largest population of people with AIDS. The adult prevalence of AIDS in the 2005 was at 5.0% and it continues to grow (UNAIDS).

U. S. student population Essay Example for Free

U. S. student population Essay The sources indicate that there are key individual differences among learners which standardized testing may not be sensitive to. Racial discrimination can occur within the confines of a testing facility when certain questions included in the test are more favorable to certain ethnic, religious, or social groups or if they are less favorable to others. This weakness of standardized tests have already been acknowledged back in the Clinton administration when the Educational Commission claimed that SAT scores do not reveal all of the competencies of those who take them. A particular example that depicts the failure of standardized tests in measuring individual work competence is the case of Hope who was an able education student who could not pass licensure testing despite of her high marks in practical examinations and demo teaching exercises because she has a disorder that makes her read slower than normal. Presentation America is the melting pot of human diversity. Its population is composed of so many different ethnicities, religions, cultures, socioeconomic and sociopolitical stratifications that its minorities are the majority. It is needless to say that these differences naturally find their way in all aspects of American life, especially in education. However the problem arises when the way that the school system expects students to perform is to be measured by standards that are not fair to all. Standardized testing is the administration of a single, uniform evaluation upon all the members of the population. From standardized tests, a performance of the individual relative to the group can be measured and inferences as to which college he or she qualifies in are made. This means that the results of standardized tests basically dictate what a student is good enough to do in the academic world. It is therefore of utmost importance that such tests are conducted in a fair, undiscriminating manner and that the tests themselves give equal chances to all to be able to show what they can do. However, the individual differences of students in terms of their language proficiencies, learning, styles, and social and cultural inclinations seriously lead to such standardized tests being biased towards or against certain groups. The American public school system is composed of a great many students who are using English as a Second Language. These people who come from Asia, the Middle East, or Latin America have as much right as the next student to be able to perform to the best of his or her ability during standardized tests. However, when it is considered that all such tests are worded in formal English, the discrimination against these groups becomes apparent. A student can be a genius at calculus but if he does not understand terminologies used because he is more used to dealing with their Spanish or Arabic counterparts, it can be expected that he would perform poorly in a calculus exam. There is no question that the English language should be a part of standardized testing and it is, but allowing students who cannot speak English so well no alternatives in taking tests on other topics such as science and mathematics means that the system is forcing them to take English exams regardless of what subject is written on the test booklet. In any subject, learning is not supposed to be limited within the confines of the pencil and the paper. In science, experiments are conducted in order to verify laws while enhancing students’ competence with various equipment. The competencies that students gain in this manner cannot be tested by multiple choice questions on an SAT examination. The worlds future rocket scientists may not be so keen at memorization but they could be excellent at practical application of theories and concepts. However, standardized testing may well cut off any chances that they could have to become NASA pilots just because they are not good at multiple choice tests, something that they would hardly need when they’re up in space! Different students have different learning styles, this applies to how students are evaluated as well. If standardized testing would restrict evaluation to just pencil and paper multiple choice items, then it is closing its doors to all the many other learners who just happen to be naturally attuned to other equally important aspects of learning. Lastly, points of discrimination can be within questions themselves. A standardized test that concentrates too much in using examples in football games when giving details to math problems would confuse those who do not follow the game from answering the questions correctly. Including opinionated, political details to questions about comprehension can distract students from responding. All of these biases should be weeded out of any test that is to be administered to the U. S. student population. Standardized testing is supposed to have the value of giving everyone an equal shot. It is supposed to promote equality among all existing groups and fairness towards obtaining opportunities. However, evidences sow that the exact opposite may be happening. The current use of standardizes testing is disenfranchising various lingual, learning, and cultural groups from being able to fully express their academic competence. This is a grave problem for the educational system which should be addressed promptly and effectively. Students, educators, and government should all work together to be able to revamp this system of evaluation to standards that are truly fair.

Difference of Squares of Two Natural Numbers

Difference of Squares of Two Natural Numbers One of the basic arithmetic operations is finding squares and difference between squares of two natural numbers. Though there are various methods to find the difference between squares of two natural numbers, still there are scopes to find simplified and easy approaches. As the sequence formed using the difference between squares of two natural numbers follow a number patterns, using number patterns may facilitate more easy approach. Also, this sequence has some general properties which are already discussed by many mathematicians in different notations. Apart from these, the sequence has some special properties like sequence difference property, difference sum property, which helps to find the value easily. The sequence also has some relations that assist to form a number pattern. This paper tries to identify the general properties, special properties of finding difference between the squares of any two natural numbers using number patterns. A rhombus rule relationship between the sequences of numbers formed by considering the difference between squares of the two natural numbers has been defined. A new method to find a2 b2 also has been introduced in some simple cases. This approach will help the secondary education lower grade students in identifying and recognizing number patterns and squares of natural numbers. Mathematical Subject Classifications: (2010) 11A25, 11A51, 40C99, 03F50 DIFFERENCE BETWEEN SQUARES OF TWO NATURAL NUMBERS RELATIONS, PROPERTIES AND NEW APPROACH Introduction Mathematics, a subject of problem solving skills and applications, has wide usage in all the fields. Basic skills of mathematical applications in number systems used even in day to day life. Though calculators and computers have greater influences in calculations, still there is a need to find new easy methods of calculations to improve personal intellectual skills. As there has been growing interest, in mathematics education, in teaching and learning, many mathematicians build simple and different methods, rules and relationships in various mathematical field. Though various investigations have made important contributions to mathematics development and education (2), there still room for new research to clarify the mutual relationship between the numbers and number patterns. In natural numbers, various subsets have been recognized by ancient mathematicians. Some are odd numbers, prime numbers, oblong numbers, triangular numbers and squares. These numbers shall be identified by number patterns. Recognizing number patterns is also an important problem-solving skill. Working with number patterns leads directly to the concept of functions in mathematics: a formal description of the relationships among different quantities. One of the basic arithmetic operations is finding squares and difference between squares of two natural numbers. Already many proofs and relationships were identified and proved in finding difference between squares of two natural numbers. We use different methods to find the difference between squares of two natural numbers. That is, to find a2 b2. Though, this area of research may be discussed by early mathematicians and researchers in various aspects, still there are many interesting ways to discuss the same in teaching. Teaching number patterns in secondary level education is most important issue as the students develop their analytical and cognitive skills in this stage. Different arithmetic operations and calculations need to be introduced in such way that they help the students in lifelong learning. Easy and simplified approaches will support the students in logical reasoning. This paper tries to identify the general properties, special properties of finding difference between the squares of any two natural numbers using number patterns. Also, this paper tries to define the rhombus rule relationship between the sequences of numbers formed by the differences of squares of two natural numbers. A new method to find a2 b2 also has been introduced in some simple cases. These may be introduced in secondary school early grades, before introducing algebraic techniques of finding a2 b2 to develop the knowledge and understanding of number patterns. This will help to recognize and apply number patterns in further level. Literature Review To find the difference between the squares of any two natural numbers, we use different methods. Also, we use various rules to find the square of a natural number. Some properties were also been identified by the researchers and mathematicians. Methods used to find the difference between squares of two natural numbers Direct Method The difference between the squares of two natural numbers shall be found out by finding the squares of the numbers directly. Example: 252 52 = 625 25 = 600 Using algebraic rule The algebraic rule a2 b2 = (a b)(a + b) shall be applied to find the difference between the squares of two natural numbers. Example: 252 52 = (25 5)(25 + 5) = 20 x 30 = 600 Method when a b = 1(2) The difference between the squares of every two consecutive natural numbers is always an odd number, and that it is equal to the sum of these numbers. Example: 252 242 = 25 + 24 = 49 Methods used to find the square of a natural number Using Algebraic Method The algebraic rules shall be used to find the square of natural number other than the direct multiplication. In general, (a + b)2, (a b)2 are used to find the squares of a natural number from nearest whole number. Example: 992 = (100 1)2 = 1002 2(100)(1) + 12 = 10000 200 + 1 = 9801 Square of a number using previous number(8) The following rule may be applied to find the square of a number using previous number. (n + 1)2 = n2 + n + (n+1) Example: 312 = 302 + 30 + 31 = 900 + 30 + 31 = 961 The Gilbreth Method of finding square(9) The Gilbreth method uses binomial theorem to find the square of a natural number. The rule is n2 = 100(n 25) + (50 n)2 Example: 992 = 100(99 25) + (50 99)2 = 7400 + 2401 = 9801 Other than the above mentioned methods various methods are used based on the knowledge and requirements. Properties of differences between squares of the natural numbers 2.3.1. The difference between squares of any two consecutive natural numbers is always odd. To prove this property, let us consider two consecutive natural numbers, say 25 and 26 Now let us find 262 252 262 252 = (26 + 25)(26 25) [Using algebraic rule] = 51 x 1 = 51, an odd number 2.3.2. The difference between squares of any two alternative natural numbers is always even. To prove this property, let us consider two alternative natural numbers, say 125 and 127 Now let us find 1272 1252 1272 1252 = (127 + 125)(127 125) [Using algebraic rule] = 252 x 2 = 504, an even number Some other properties were also identified and discussed by various mathematicians and researchers. Number Patterns and Difference Between the Squares of Two Natural Numbers Discussions and Findings Some of the properties stated above shall be proved by using number pattern. Number patterns are interesting area of arithmetic that stimulates the logical reasoning. They shall be applied in various notations to identify the sequences and relations between the numbers. 3.1. Sample Table for the difference between squares of two natural numbers To find the properties and relations that are satisfied by the sequences formed by the differences between the squares of two natural numbers, let us form a number pattern. For discussion purposes, let us consider first 10 natural numbers 1, 2, 3 à ¢Ã¢â€š ¬Ã‚ ¦ 10. Now, let us find the difference between two consecutive natural numbers. That is, 22 12 = 3; 32 22 = 5; and so on. Then the sequence will be as follows: 3, 5, 7, 9, 11, 13, 15, 17 and 19. The sequence is a set of odd numbers starting from 3. i.e., Difference 1: {x| x is an odd number greater than or equal to 3, x ÃŽ N} In the same way, let us form the sequence for the difference between squares of two alternative natural numbers. That is, 32 12 = 8, 42 22 = 12, and so on. Then the sequence will be: 8, 12, 16, 20, 24, 28, 32 and 36 Thus the sequence is a set of even numbers and multiples of 4 starting from 8. i.e., Difference 2: {x| x is an multiple of 4 greater than or equal to 8, x ÃŽ N} By proceeding this way, the sequences for other differences shall be formed. Let us represent the sequences in a table for discussion purposes. In Table 1, N is the natural number. S is the square of the corresponding natural number. D1 represents the difference between the squares of two consecutive natural numbers. That is, the difference between the numbers is 1. D2 represents the difference between the squares of two alternate natural numbers. That is, the difference between the numbers is 2. D3 represents the difference between the squares of 4th and 1st number. That is, the difference between the numbers is 3, and so on. 3.2. Relationship between the row elements of each column Now, let us discuss the relationship between the elements of rows and columns of the table. From the above table, Column D1 shows that the difference between squares of two consecutive numbers is odd. Column D2 shows that the difference between squares of two alternate numbers is even. The other columns show that the difference between the squares of two numbers is either odd or even. From the above findings, the following properties shall be defined for the difference between squares of any two natural numbers. 3.3. General Properties of the difference between squares of two natural numbers: The difference between squares of any two consecutive natural numbers is always odd. Proof: Column D1 proves this property. This may also be tested randomly for big numbers. Let us consider two digit consecutive natural numbers, say 96 and 97. Now, 972 962 = 9409 9216 = 493, an odd number Let us consider three digit consecutive natural numbers, say 757 and 758. Thus, 7582 7572 = 574564 573049 = 1515, an odd number This property may also be further tested for big numbers and proved. For example, let us consider five digit two consecutive natural numbers, say 15887 and 15888. Then, 158882 158872 = 252428544 252396769 = 31775, an odd number Apart from these, the property shall also be easily derived by the natural numbers properties. As the difference between two consecutive numbers is 1, the natural number property The sum of odd and even natural numbers is always odd, shall be applied to prove this property. The difference between squares of any two alternative natural numbers is always even. Proof: Column D2 proves this property. This may also be verified for big numbers by considering different digit natural numbers as discussed above. Apart from this, as the difference between two alternate natural numbers is 2, the natural numbers property A natural number said to be even if it is a multiple of two shall also be used for proving the stated property. The difference between squares of any two natural numbers is either odd or even, depending upon the difference between the numbers. Proof: The other columns of Table 1 prove this property. In Table 1, as D3 represents the sequence formed by the difference between two natural numbers whose difference is 3, an odd number, the sequence is also odd. Thus, the property may be proved by testing the other Columns D4, D5, à ¢Ã¢â€š ¬Ã‚ ¦ Also, the addition, subtraction and multiplication properties of natural numbers prove this property. Example: 112 62 Here the difference (11 6 = 5) is odd. So, the result will be odd. i.e. 112 62 = 121 36 = 85, an odd number 122 82 Here the difference (12 8 = 4) is even. So, the result will be even. i.e. 122 82 = 144 64 = 80, an even number 3.4. Special Properties of the difference between squares of the two natural numbers Table 1 also facilitates to find some special properties stated below. Sequence Difference Property Table 1 shows that the sequences formed are following a number pattern with a common property between them. Let us consider the number sequences of each column. Let us consider the first column D1 elements. D1: 3, 5, 7, 9, 11 à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ As D1 represents the difference between the squares of two consecutive natural numbers, let us say, a and b with a > b, the difference between them will be 1. That is a b = 1 Let us consider the difference between the elements in the sequence. The difference between the numbers in the sequence is 2. Thus the difference between the elements of the sequence shall be expressed as, 2 x 1. Thus, Difference = 2(a b) Now, let us consider the second column D2 elements. D2: 8, 12, 16, 26, à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ As D2 represents the difference between the squares of two alternative natural numbers, the difference between the natural numbers, say a and b is always 2. That is a b = 2 If we consider the difference between the elements in the sequence, the difference is 4. Thus, the difference between the elements in the sequence shall be expressed as 2 x 2. That is, difference = 2 (a b) In the same way, D3: 15, 21, 27, 33, à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ à ¢Ã¢â€š ¬Ã‚ ¦ D3 represents the difference between squares of the 4th and 1st numbers, difference is 3. That is a b = 3 The difference between the numbers in the sequence is 6. Thus, difference = 2 x 3 = 2(a b) All other columns also show that the difference between the numbers in the corresponding sequence is 2 (a b) Thus, this may be generalized as following property: The difference between elements of the number sequence, formed by the difference between any two natural numbers, is equal to two times of the difference between those corresponding natural numbers. Difference Sum Property: From Table 1, we shall also identify another relationship between the elements of the sequence formed. Let us consider the columns from table 1 other than D1. Consider D2: 8, 12, 16, 20, à ¢Ã¢â€š ¬Ã‚ ¦ This sequence shall be formed by adding two numbers of Column D1. i.e. 8 = 3 + 5 12 = 5 + 7 16 = 7 + 9 20 = 9 + 11 And so on. Thus, if the difference between the natural numbers taken is 2, then the number sequence of the difference between the two natural numbers shall be formed by adding 2 natural numbers. Consider D3: 15, 21, 27, à ¢Ã¢â€š ¬Ã‚ ¦ This sequence shall be formed by adding three numbers from Column D1. i.e. 15 = 3 + 5 + 7 21 = 5 + 7 + 9 27 = 7 + 9 + 11 And so on. Thus, if the difference between the natural numbers taken is 3, then the number sequence of the difference between the two natural numbers shall be formed by adding 3 natural numbers. This may also be verified with respect to the other columns. Table 2 shows the above relationship between the differences of the squares of the natural numbers. Now the above relation shall be generalized as If a b = k > 1, then a2 b2 shall be written as the sum of k natural numbers As Column D1 elements are odd natural numbers, this property may be defined as If a b = k > 1, then a2 b2 shall be written as the sum of k odd natural numbers As these odd numbers are consecutive, the property may be further precisely defined as: If a b = k > 1, then a2 b2 shall be written as the sum of k consecutive odd natural numbers 3.5. New Method to find the difference between squares of two natural numbers Using the above difference sum property, the difference between squares of two natural numbers shall be found as follows. The property shows that, a2 b2 is equal to sum of k consecutive odd numbers. Now, the principal idea is to find those k consecutive odd numbers. Let us consider two natural numbers, say 7 and 10. The difference between them 10 7 = 3 Thus, 102 72 = sum of three consecutive odd numbers. 102 72 = 100 49 = 51 Now, 51 = Sum of 3 consecutive odd numbers i.e., 51 = 15 + 17 + 19 Let we try to find these 3 numbers with respect to either the first number, let us say, a or the second number, say, b. Assume, for b As general form for odd numbers is either (2n + 1) or (2n 1), as b 15 = 2(7) + 1 = 2b + 1 17 = 2(7) + 3 = 2b + 3 19 = 2(7) + 5 = 2b + 5 Thus, 102 72 shall be written as the sum of 3 consecutive odd numbers starting from 15. i.e. starting from 2b + 1 This idea may also be applied for higher digit numbers. Let us consider two 3 digit numbers, 101 and 105. Let us find 1052 1012 Here the difference is 4. Thus 1052 1012 shall be written as the sum of 4 consecutive odd numbers. The numbers shall be found as follows: Here b = 101 The first odd number = 2b + 1 = 2(101) + 1 = 203 Thus, the 4 consecutive odd numbers are: 203, 205, 207, 209 So, 1052 1012 = 203 + 205 + 207 + 209 = 824 This shall be verified for any number of digits. Let us consider two 6 digit numbers 100519, 100521. Let us find 1005212 1005192 Here the difference is 2. Thus 1005212 1005192 shall be written as the sum of two odd numbers. Applying the same idea, The first odd number = 2(100519) + 1 = 201039 Thus the 2 consecutive odd numbers are: 201039, 201041 1005212 1005192 = 201039 + 201041 = 402080 The above result shall be verified by using other methods. For example: 1052 1012 1052 1012 = 11025 10201 = 824 (Using Direct Method) 1052 1012 = (105 + 101) (105 101) = 206 x 4 = 824 (Using Algebraic Rule) Thus, this idea shall be generalized as follows: a2 b2shall be found by adding the (a b) consecutive odd numbers starting from 2b + 1 This shall also be found using the first term a. As a > b, let us consider (2n 1) form of odd numbers. From Table 1, 102 62 = 13 + 15 + 17 + 19 = 64 Here, 2a 1 = 2(10) 1 = 19 2a 3 = 2(10) 3 = 17 2a 5 = 2(10) 5 = 15 2a 7 = 2(10) 7 = 13 Thus, as the difference between the numbers is 4, 102 62 shall be written as the sum of four consecutive odd numbers in reverse order starting from 2a 1. Thus proceeding, this may be generalized as, a2 b2shall be found by adding the (a b) consecutive odd numbers starting from 2a 1 in reverse order Finding the first number of each column Let us check the number pattern followed by the first numbers of each column. From Table 1, the first numbers of each column are: 3, 8, 15, 24 à ¢Ã¢â€š ¬Ã‚ ¦ Let us find the difference between elements of this sequence. The difference between two consecutive terms of this sequence is 5, 7, 9 à ¢Ã¢â€š ¬Ã‚ ¦ i.e. D2 D1 = 8 3 = 5; D3 D2 = 7; D4 D3 = 9 and so on. As D2 represents the difference between two alternate natural numbers, (say a and b) which implies that the difference between a and b is 2. Now, 5 = 2 (2) +1 i.e. 2 times of the difference between the numbers + 1 In the same idea, D3 D2 = 15 8 = 7 As D3 represents the difference between squares of the 4th and 1st natural numbers, (say a and b) which implies that the difference between a and b is 3. Thus, 7 = 2(3) + 1 This also shows that the difference shall be found by = 2 times of the difference between the numbers + 1 Thus, The first term of the each column shall be found by adding the previous column first term with 2 times of the difference between the numbers + 1 Finding the elements row wise The elements of the table shall also be formed in row wise. If we check the elements of each row, we can find that they follow a number pattern sequence with some property. Let us consider the elements of row when N = 5: 20, 40, 60, 80 20 = 2 x 5 x 2 Here, 5 represent the row natural number. 2 represent the difference between the elements using which the column is formed. Thus Row element = 2 x N x difference In the same way, 40 = 2 x 5 x 4 = 2 x N x difference Thus, the elements shall be formed by the rule: Row Element = 2 x N x difference This shall be applied for middle rows also. For example, let us consider the row between 5 6: The elements in this intermediate row are: 11, 33, 55, 77, 99 Here N is the mid value of 5 6. i.e. N = 5.5 Let us consider the elements and apply the above stated rule. 11 = 2 x N x difference = 2 x 5.5 x 1 In the same way other elements shall also be formed. Thus the elements of the table shall be formed in row wise using the stated rule. Rhombus Rule Relation Let us consider the elements in D2, D3 and D4. Consider the elements in the rhombus drawn, 24, 33, 39 and 48 24 + 48 = 72 33 + 39 = 72 Thus the sums of the elements in the opposite corners are equal. The other column elements also prove the same. Thus, Rhombus Rule Relation: Sum of the elements the same row of the sequence of alternative columns is equal to the sum of the two elements in the intermediate column Application of the Properties in Finding the Square of a number The square of a natural number shall be found by various methods. Here is one of the suggested methods. This method uses nearest 10s and 100s to find the square of a number. This method is also based on the algebraic formula a2 b2 = (a b)(a + b) If a > b, b2 = a2 (a2 b2) If b > a, b2 = a2 + (b2 a2) Example: Square of 32 As we need to find 322, let us assume b = 32. The nearest multiple of 10 is 30. Let a = 30 Here b > a. b2 = a2 + (b2 a2) 322 = 302 + (322 302) Using the Difference Sum Property, 322 = 900 + 61 + 63 = 1024 Example 2: Square of 9972 Let b = 997 Nearest multiple 10 is 1000. Let a = 1000 Here a > b, so b2 = a2 (a2 b2) 9972 = 10002 (10002 9972) Using Difference Sum Property, 9972 = 1000000 (1995 + 1997 + 1999) = 994009 Conclusion Though this method shall be applied to find the difference between squares of any two natural numbers, if the difference is big, it will be cumbersome. Thus, this method shall be used for finding the difference between squares of any two natural numbers where the difference is manageable. The properties shall be used for easy calculation. This properties and approach shall be introduced in secondary school lower grade levels, to make the students to identify the number patterns. This approach will surely help the students to understand the properties of squares, difference and natural numbers. The new approach will surely help the students in developing their reasoning skills. Limitations As number systems, number patterns and arithmetic operations have wide applications in various fields, the above properties, rules and relations shall be further studied intensively based on the requirements. Thus, new properties and relations shall be identified and discussed with respect to other nations.

Monopolies Must be Eliminated in America :: Argumentative Persuasive Argument Essays

Monopolies Must be Eliminated in America      Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In this day and age, competition (to a certain extent) is considered healthy and, in many instances, encouraged.   Every day, adults and teenagers alike struggle to outdo other well-qualified applicants in the job market.   Even children as young as four years old can be found competing on the little league field.   As one can see, competition is an integral part of everyday life; however, what happens when competition ceases to exist?   It wouldn’t be very challenging or rewarding if an applicant received every job for which he applied.   And a child wouldn’t enjoy playing baseball against himself.   Even though it is hard to imagine a world without competition, there are a number of American media businesses that have no or relatively little competition in the market.   In the best interest of the public, monopolies, as these competition-less companies are called, need to be eliminated immediately.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   According to Ben H. Bagdikian, monopolies form for two main reasons: money and influence.   It is common sense that the company with a very large number of consumers is going to produce more revenue than the small, independently owned business with a lesser number of customers.   The advertising agency Backer Spielvogel Bates recently conducted a four-year study of 2,746 companies.   This study showed that the companies with 1.5 times the sales of their nearest challengers were 52 percent more cost-effective.   Also, it is important to recognize the fact that influence also plays a key role in the motives of monopolistic companies.   It is believed that if a certain company can have a marked influence over the public’s news, ideas and culture, then this corporation will have a much better chance of wielding a significant amount of influence over the public concerning government issues.   If this certain media company can manipulate all public ideas and information, it only makes sense that this business will also make a considerable difference when it comes to political news (Bagdikian 1997). I agree with Bagdikian when he states that monopolies form due to a want for money and a need for power by influencing the public.   It is an undeniable fact that money and power influence people in numerous ways.   In an attempt to be the best, I believe that many companies simply came to the conclusion that they would have to â€Å"crush† any attempts that were made by a competing company.

“Gaston” by William Saroyan Essay

The short story â€Å"Gaston† by William Saroyan is a creative story that portrays the better parts of life of a torn family. The father and the daughter in the story are spending quality bonding time during the frame of the story. What began as just the simple act of a meal of peaches turned into a thoughtful insight of there lives. Throughout the story the concepts of fear love and loss of both the father and his daughter are portrayed through Gaston. The imaginative father plays an important role in the story. He created a life for the bug within the peach that held so much meaning and importance to backbone of the story. Preparing the day with his daughter as she naps he purchases seven peaches for an afternoon snack. While eating the â€Å"bad† peach he comes across a bug that has made his home within the seed of the peach. He gives the critter the name â€Å"Gaston† and refuses to squash him. I feel that we can relate this situation of the bug to the relationship between the father and his daughter. The fathers fear of losing his daughter and or making her unhappy is very strong. Just in the way he jumps at the fact she wants a bad peach. And finding something good within the bad peach is like finding something good coming out of the divorce situation. The fathers love for his daughter is prominence, we can assume how much he cares for her when he tells her â€Å"the important thing is what you want, not what I want† (63). His love for her helps overcome the loss of his family and home. I believe that when he states â€Å"the poor fellow hasn’t got a home, and there he is with all that pure design and handsome form, and nowhere to go† (62), he talks about his self. The daughters concept of love grown within the story. Her first reaction to the bug was â€Å"ugh† and wanting to squash it. She formed a bond with the critter when her father was ar ound and explained to her how special the bug is.

Spanish Prepositional Pronouns

Spanish Prepositional Pronouns The easy part about learning the grammar of pronouns in Spanish is that they follow a structure similar to the pronouns of English, serving as subjects as well as objects of verbs and prepositions. The tricky part, at least for people whose first language is English, is remembering which pronouns to use. While English uses the same pronouns as objects of prepositions and for direct and indirect objects of verbs, Spanish has a different set of pronouns for each usage, and those sets overlap. The subject pronouns and prepositional pronouns are identical except in the first-person singular and familiar second-person singular forms. How To Use Prepositional Pronouns As you can probably guess, prepositional pronouns are those that come after prepositions. In a sentence such as Tengo una sorpresa para ella (I have a surprise for her), para (for) is the preposition and ella (her) is the prepositional pronoun. Here are the prepositional pronouns of Spanish along with examples of their usage: mà ­ (first-person singular, equivalent of me): El regalo es para mà ­. (The gift is for me.)ti (informal second-person singular, equivalent of you; note that there is no written accent on this pronoun): El regalo es para ti. (The gift is for you.)usted (formal second-person singular, equivalent of you): El regalo es para usted. (The gift is for you.)à ©l (third-person masculine singular, equivalent of him or it): El regalo es para à ©l. (The gift is for him.)  Miro debajo à ©l.  (I am looking under it.)ella (third-person feminine singular, equivalent of her or it): El regalo es para ella. (The gift is for her.)  Miro debajo ella.  (I am looking under it.)nosotros, nosotras (first-person plural, equivalent of us): El regalo es para nosotros. (The gift is for us.)vosotros, vosotras (second-person informal plural, equivalent of you): El regalo es para vosotros. (The gift is for you.)ustedes (second-person formal plural, equivalent of you): El regalo es para ustedes.  (Th e gift is for you.) ellos, ellas (third-person plural, equivalent of them): El regalo es para ellos. (The gift is for them.) Sà ­ as a Pronoun There is also another prepositional object that is occasionally used. Sà ­ is used to mean himself, herself, the formal yourself, the formal yourselves, or themselves as the object of a preposition. For example, à ©l compra el regalo para sà ­, he is buying the gift for himself. One reason you dont see this usage often is since the meaning is usually expressed using the reflexive form of the verb: Se compra un regalo, he is buying himself a gift. Pronouns for It Either à ©l or ella can mean it as the object of a preposition, although as a subject there is no Spanish word used for it. The word used depends on the gender of the noun it replaces, with à ©l being used for masculine nouns and ella being used for feminine nouns.  ¿Dà ³nde est la mesa? Necesito mirar debajo ella. (Where is the table? I need to look under it.) ¿Dà ³nde est el carro? Necesito mirar debajo à ©l.  (Where is the car? I need to look under it.) Similarly, ellos and ellas, when used as a preposition pronoun meaning them, can be used to represent things as well as people. Use ellos when referring to nouns that are masculine, ellas for feminine nouns. Ellos also is used when referring to a group that includes both masculine and feminine nouhs. Contigo and Conmigo Instead of saying con mà ­ and con ti, use conmigo and contigo. Él va conmigo.  (He is going with me.)  Ella va contigo.  (She is going with you.) You also should use consigo instead of con sà ­, although this word isnt very common. Él habla consigo. (He  talks with himself.) Exceptions: Prepositions Followed by Subject Pronouns Finally, note that yo and tà º are used with the following six prepositions instead of with mà ­ and ti, respectively: entre (between)excepto (usually translated as except)incluso (including or even)menos (except)salvo (except)segà ºn (according to) Also, hasta is used with the subject pronouns when it is used in the same way as incluso. Examples: Es la diferencia entre tà º y yo. (Its the difference between you and me.)Muchas personas incluso/hasta yo creen en las hadas. (Many people including me believe in fairies.)Todos excepto/menos/salvo tà º creen en las hadas. (Everybody except you believes in fairies.)Es la verdad segà ºn yo. (Its the truth according to me.)