The Eighteenth Amendment

What to Do If Your College Roommate Uses Your Stuff

What to Do If Your College Roommate Uses Your Stuff In college, roommates have a lot to deal with: in addition to the stress of being in school, youre squished into a space that would be incredibly tiny for one person - not to mention two (or three or four). Just because youre sharing a space, however, doesnt necessarily mean that youre sharing all of your stuff, too. As the lines begin to blur between where one persons space ends and the others begins, its not uncommon for roommates to begin sharing things. Why have two microwaves, for example, when you really need just one? While some things make sense to share, others can create conflict. If your roommate has started using your stuff in a way that you dont like, hasnt been talked about, or was previously talked about but is now being disrespected, a simple act can quickly turn into something much bigger. If your roommate is borrowing (or just plain taking!) your stuff without checking with you first, there are some questions you can ask yourself when trying to figure out what to do about the situation: How Big of an Issue Is This for You? Maybe you talked about sharing items and your roommate has disregarded the agreement you made together. How much does that bother, annoy, or anger you? Or does it make sense that he or she used your things without asking? Is it a big deal or not? Try not to think about how you think you should feel; think about how you do feel. True, some people may not care if a roommate borrows their iron, but if it bothers you, then be honest with yourself about that. Conversely, if your friends seem outraged that your roommate borrowed your clothes but you dont really mind, then know thats okay, too. Pattern or Exception Your roommate might be absolutely great and she took a little of your cereal and milk just once because she was super, super hungry late one night. Or she may take your cereal and milk two times a week and now youre just sick of it. Consider whether this is a small incident that likely wont happen again or a larger pattern that you would like stopped. Its okay to be bothered by either one, and its especially important to address any bigger issues (e.g., the pattern) if and when you confront your roommate about his or her behavior. Is It a Personal Item or Something General? Your roommate may not know that, for example, the jacket he borrowed was your grandfathers. Consequently, he may not understand why youre so upset that he borrowed it one night when it was unseasonably cold. While all of the things you brought to college matter to you, your roommate doesnt know the values you assign to everything. So, be clear on what was borrowed and why its not okay (or totally fine) for your roommate to borrow it again. What Bugs You About the Situation? You may be bothered that your roommate took something that you told him not to; you may be bothered that he did it without asking; you may be bothered that he didnt replace it; you may be bothered that he takes a lot of your stuff without checking with you first. If you can figure out what bugs you the most about your roommates use of your stuff, you can better address the real issue at hand. So sure, your roommate may have a reason for taking your last energy drink, but its harder to explain why he is constantly helping himself to the last of your things. What Resolution Do You Want? You might just want an apology or an acknowledgment that your roommate took something he or she wasnt entitled to take. Or you may want something larger, like a conversation or even a formal roommate contract about what its okay and not okay to share. Think about what you need to feel better about the situation. That way, when you do talk to your roommate (or RA), you can be focused on a larger goal instead of just feeling frustrated and like you dont have any options. How to Best Come to a Resolution Once you figure out what kind of resolution you want, its important to also figure out how you can get there. If you want an apology, youll need to talk to your roommate; if you want clearer rules in place, youll need to think about what those rules might be before starting a conversation. If you can take the time and mental energy to focus on the causes of and solutions to the problem, your roommates use of your stuff doesnt have to be anything more than a minor issue you thought about, addressed, and resolved during your time as roommates. After all, you both have much bigger things to worry about.

For two companies with which you are familiar, compare and contrast Essay

For two companies with which you are familiar, compare and contrast the main operations processes in terms of their volume, vari - Essay Example In simpler terms, operation management is the conversion of input into output using the resources available to the organization with an aim to meet the organizational objectives such as efficiency, consistency and effectiveness (Kumar and Suresh, 2009). This assignment will highlight the factors such as volume, variety, variation and visibility of two automobile organizations, i.e. BMW and Nissan. To further highlight the importance of operation management in company’s success, the performance objectives, i.e. speed, quality, dependability, flexibility and cost, would be analyzed in order to evaluate the respective operation strategies of both the companies. COMPARING AND CONTRASTING OPERATION MANAGEMENT To compare and contrast the operation management in automobile industry, two familiar and recognized organizations BMW and Nissan have been selected. Both companies would be analyzed and evaluated in terms of volume, variety, variation and visibility characteristics. NISSAN Ni ssan is the world’s fourth largest automobile manufacturer. The company is located in Japan. With its aim to enrich the lives of its customers by providing them with high quality cars, the company operates in a number of countries. With the use of technology, the company aims to provide its customers with innovative vehicles. In order to evaluate the company’s operation management and its processes, volume, variety, variation and visibility characteristics have been analyzed one by one. Volume In order to consistently meet the demands of the customers, the company manufactures vehicles in high volume. This repetition of the processes has made the workforce specialize in the operation processes which eventually lead to the low units cost. With the ability to manufacture vehicles at low cost, the company is capital intensive. Variety To effectively meet the needs of the customers, Nissan provides them with variety of vehicles. With extensive product line at Nissan, the c ompany is able to attract the customers in the market. The variety in product line at Nissan includes sports cars, minivans and vans, trucks and pickup trucks (Nissan, 2013). With such variety, the company is able to match the needs of the customers effectively. Variation The variation in demand for Nissan’s vehicle is low. This implicates that the demand is predictable and the variation in the vehicle is stable. With low variation in demand, the cost associated with the manufacturing of vehicle is also low. Visibility characteristics In operations management, visibility character indicates the level of activities that can be observed by the customer. In Nissan’s case, the visibility characteristics are low which indicates that the company utilizes its staff effectively. Since the time lag between the production and consumption is high, the visibility factor could be said as low. BMW BMW continuously strives to become the leader in the automobile industry and to do so, the company provide its customers with high quality vehicles to enrich their customer’s experience. The company is one of the top quality vehicle providers in the globe due to which the company charges premium price from its customers. Being the world’s leader of premium products, the company has its own unique identity and persona. The same way Nissan

Political Science Essay Example | Topics and Well Written Essays - 1250 words - 7

Political Science - Essay Example Illegal immigrants areundocumented immigrantsor aliens in the United States who enter the borders of United States without government permission or those who stay beyond the termination date of a visa. There are different causes of illegal migration ranging from economic incentives of a better life, chain immigration to join relatives, American government inefficiency, and globalization to trade agreements. Illegal migration however has such benefits as availability of cheap labor and payment of taxes by the immigrants. Racial profiling refers to government activity directed at a suspect or group of suspects because of their race, whether intentional or because of the disproportionate numbers of contacts based upon other pre-textual reasons. This is common in America especially when it comes to people from the Middle East but it should be in tandem with the Fourth Amendment. Rawls would have condemned Middle East profiling and the outlawing of illegal migration based on his write-ups.In his ‘A Theory of Justice’ (1971) he made contributions to liberal political philosophy namely: justice as fairness; reflective equilibrium; overlapping consensus; public reason; veil of ignorance; and original position. Rawlsianism provides for the most reasonable principles of justice as those which everyone would accept and agree to from a fair position. Justice as fairness comprises two main principles of Liberty and Equality with the second divided into Fair Equality of Opportunities and the Difference Principle in the order of priority. The Liberty Principle provides for entitlement of everyone to basic liberties while the Equality Principle establishes distributive justice. Fair Equality of Opportunity provides for access to positions to everyone regardless of their social background, ethnicity or sex. The Difference Principle regulates inequalities by permitting them to the advantage of the worst-off (Cohen and Fermon

Marco Polo and Matteo Ricci Accounts of China Essay

Marco Polo and Matteo Ricci Accounts of China - Essay Example The imperial power of the Chinese passes from the father to the son, however the people have a say in the staying in power of a ruler. When the people grow inept of a ruler they have the ability to strip him the throne and place a new man with courage and the qualities of being a leader. The Chinese prefer dying honorable death rather than be under a monarch who is usurping and swear allegiance to him. They therefore use and employ the ideologies of this proverb more frequently that, â€Å"no woman is moral who has two husbands nor any vassal faithful who has two lords†. The laws that are governing China are not enshrined to any logical way, however any person who succeeds in getting the throne makes his own laws and he who succeeds him is obliged to implement the laws .The Chinese people have a government that is monarchial ,however to certain degrees this government is an aristocracy .Decisions in relation to governance are made by the magistrates but the king has to make co nfirmations by writing though he has no powers to make any final decision without first consulting with the magistrates. The income does not go to the exchequer but is a resource of the public and is taken to the public treasury. The running of most of the national issues like the military and management of the prisons are met by the national treasury and where the funds cannot be met by the available resources, new taxes are imposed to raise the extra income to meet the national demands of the republic of china (Kashlansky). The magistrates are grouped into two, those from the national levels and those at the provincial levels. Besides the magistrates there is a group of about 60 philosophers who have proved allegiance to the king and are loyal to the realm. This group is kept by the king for the good of business and benefits to the royalty. In addition to the magistrates ,at the national palace there are various organizations which are instituted for various purposes .there are al so members of the cabinet who have no public administrative powers but have the highest office dignity. Marco gives an account of the tartars who had an eloquent ruler who came into power with approved integrity, justice and valor. The king came into power with so much moderation and fairness that his fame spread all over the world. By finding himself as the head of so many brave men he ordered them to arm themselves with arrows and bows so as to fire an assault to the neighboring provinces. The king ensured that he developed love with the people and gained their respect. However in later stages he became a dictator and developed strict regulation which had even penalties for death of defaulters of regulations .The tartars had a nomadic life and never stayed in one place, constantly moving in search of greener pastures. They had women with courage and virtue for the management of their homes (Marco).The women observe chastity and no quarrel is heard of or experienced in the families with the women always taking care of the children and the provision of food for the family. The city of Kin say is reported to have men and women who love life and use gold and silver. The authority of this city equally felt quite insecure and made it a rule to guard its numerous bridges with numerous precautions especially after dusk such

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.

The Last Day Of The Year :: essays research papers fc

In the poem 'The Last Day of the Year,'; Annette Von Droste-HÃ ¼lshoff uses imagery and references to God to express the coming of the end of the year. The poem, however, seems to reflect the impending freedom of women from a patriarchal society. This poem's imagery and outside references suggest that it is in fact a plea for the end of the suffering of women, and that the coming of their empowerment is near. The three things that I will use to prove this point are how one year represents the time of women's oppression, how she speaks directly to men in the poem, and how she makes divine references to represent the freedom of women. Droste-Hulshoff says in line one of this poem, 'The year at its turn'; (Droste-Hulshoff, 1). Throughout this poem, she uses the year to represent a period of time that is coming to an end. Referring to the introduction in the World Reader, Droste-Hulshoff was a woman 'yearning for the freedom to be herself'; (Caws, 2002). This forces the reader to consider that she is using the time period of the year as the time of women's oppression. She feels that the time of the oppression is coming to an end. 'I wait in stern silence, O deep night! Is there an open eye?'; (Droste-Hulshoff 5-7) is one example of how she considers the era of women's oppression at its end. Another example is the following quote: ' My life breaks down somewhere in the circle of this year. Long have I known decay. Yet my heart in love glows under the huge stone of passion'; (Droste-Hulshoff 37-42). She has felt this persecution for all of her life, but she still prospers as a individual and waits with short patience for her time to come. At one point in this poem, Droste-Hulshoff speaks to an unidentified second party. 'You, child of sin, has there not been a hollow, secret quiver each day in your savage chest, as the polar winds reach across the stones, breaking, possessed with slow and insistent rage?'; (Droste-Hulshoff 24-31). Continuing under the assumption that this poem was created to show the iniquities of sexism, one could put men in place of you in the preceding excerpt. I believe this to be a likely case because of the references to 'your savage chest'; (Droste-Hulshoff 27) and the words speaking of possession and rage, all considered by society to be very masculine traits.

Library Science Essay

An integrated library system (ILS), also known as a library management system (LMS),[1][2] is an enterprise resource planning system for a library, used to track items owned, orders made, bills paid, and patrons who have borrowed. An ILS usually comprises a relational database, software to interact with that database, and two graphical user interfaces (one for patrons, one for staff). Most ILSes separate software functions into discrete programs called modules, each of them integrated with a unified interface. Examples of modules might include: acquisitions (ordering, receiving, and invoicing materials) cataloging (classifying and indexing materials) circulation (lending materials to patrons and receiving them back) serials (tracking magazine and newspaper holdings) the OPAC (public interface for users) Each patron and item has a unique ID in the database that allows the ILS to track its activity. Larger libraries use an ILS to order and acquire, receive and invoice, catalog, circulate, track and shelve materials. Smaller libraries, such as those in private homes or non-profit organizations (like churches or synagogues, for instance), often forgo the expense and maintenance required to run an ILS, and instead use a library computer system. [citation needed] Contents [hide] 1 History 1. 1 Pre-computerization 1. 2 1960s: the influence of computer technologies 1. 3 1970s-1980s: the early integrated library system 1. 4 1990s-2000s: the growth of the Internet 1. 5 Mid 2000s-Present: increasing costs and customer dissatisfaction 2 Examples 3 See also 4 References 5 Further reading 6 External links [edit]History [edit]Pre-computerization Prior to computerization, library tasks were performed manually and independently from one another. Selectors ordered materials with ordering slips, cataloguers manually catalogued items and indexed them with the card catalog system (in which all bibliographic data was kept on a single index card), and users signed books out manually, indicating their name on cue cards which were then kept at the circulation desk. Early mechanization came in 1936, when the University of Texas began using a punch card system to manage library circulation. [3] While the punch card system allowed for more efficient tracking of loans, library services were far from being integrated, and no other library task was affected by this change. [edit]1960s: the influence of computer technologies Following this, the next big innovation came with the advent of MARC standards in the 1960s which coincided with the growth of computer technologies – library automation was born. [3] From this point onwards, libraries began experimenting with computers, and, starting in the late 1960s and continuing into the 1970s, bibliographic services utilizing new online technology and the shared MARC vocabulary entered the market; these included OCLC (1967), Research Libraries Group (which has since merged with OCLC), and Washington Library Network (which became Western Library Network and is also now part of OCLC). [4] [edit]1970s-1980s: the early integrated library system Screenshot of a Dynix menu. The 1970s can be characterized by improvements in computer storage as well as in telecommunications. [4] As a result of these advances, ‘turnkey systems on microcomputers,’[4] known more commonly as integrated library systems (ILS) finally appeared. These systems included necessary hardware and software which allowed the connection of major circulation tasks, including circulation control and overdue notices. [5] As the technology developed, other library tasks could be accomplished through ILS as well, including acquisition, cataloguing, reservation of titles, and monitoring of serials. [6] [edit]1990s-2000s: the growth of the Internet With the evolution of the Internet throughout the 1990s and into the 2000s, ILSs began allowing users to more actively engage with their libraries through OPACs and online web-based portals. Users could log into their library accounts to reserve or renew books, as well as authenticate themselves for access to library-subscribed online databases. Inevitably, during this time, the ILS market grew exponentially. By 2002, the ILS industry averaged sales of approximately US$500 million annually, compared to just US$50 million in 1982. [5] [edit]Mid 2000s-Present: increasing costs and customer dissatisfaction By the mid to late 2000s, ILS vendors had increased not only the number of services offered but also their prices, leading to some dissatisfaction among many smaller libraries. At the same time, open source ILS was in its early stages of testing. Some libraries began turning to such open source ILSs as Koha and Evergreen. Common reasons noted were to avoid vendor lock in, avoid license fees, and participate in software development. Freedom from vendors also allowed libraries to prioritize needs according to urgency, as opposed to what their vendor can offer. [7] Libraries which have moved to open source ILS have found that vendors are now more likely to provide quality service in order to continue a partnership since they no longer have the power of owning the ILS software and tying down libraries to strict contracts. [7] This has been the case with the SCLENDS consortium. Following the success of Evergreen for the Georgia PINES library consortium, the South Carolina State Library along with some local public libraries formed the SCLENDS consortium in order to share resources and to take advantage of the open source nature of the Evergreen ILS to meet their specific needs. [7] By October 2011, just 2 years after SCLENDS began operations, 13 public library systems across 15 counties had already joined the consortium, in addition to the South Carolina State Library. Librarytechnology. org does an annual survey of over 2,400 libraries and noted in 2008 2%[8] of those surveyed used open source ILS, in 2009 the number increased to 8%,[9] in 2010 12%,[10] and in 2011 11% [11] of the libraries polled had adopted open source ILSs. [edit]Examples Open-source Evergreen Greenstone Invenio Koha Kuali OLE NewGenLib PhpMyBibli OpenBiblioÃ'Ž VuFind Proprietary Aleph from Ex Libris Innovative Interfaces Library†¢Solution, Library†¢Solution for Schools, and CARL†¢X from The Library Corporation LibraryWorld NOSA Qulto System SirsiDynix, Symphony—current version and Unicorn—a legacy system. SydneyPLUS International Capita Alto formerly Talis Alto (UK and Ireland) Virtua, former VTLS, from VTLS Inc. Voyager from former company Endeavor Information Systems, later acquired by Ex Libris (Polish) MOL, Patron and MOLIK – interface created for children (Polish) SOWA, SOWA2, SOWA2/MARC21, SOWA2/MARC21/SQLÃ'Ž Legacy NOTIS Dynix [edit]See also Library and information science portal Library computer system OPAC List of next-generation catalogs History of Library Automation [edit]References ^ Adamson, Veronica, et al. (2008). JISC & SCONUL Library Management Systems Study PDF (1 MB). Sheffield, UK: Sero Consulting. p. 51. Retrieved on 21 January 2009. â€Å"†¦ a Library Management System (LMS or ILS ‘Integrated Library System’ in US parlance). † Some useful library automation software are: KOHA ,Grennstone . LIBsis, and granthlaya. Tennant, Roy (16 April 2008). â€Å"Picking When to Jump, Part 2†. Library Journal. Reed Business Information. Retrieved 20 January 2009. â€Å"Across the pond they use the term library management systems (LMS) for what we call the integrated library system (ILS). † ^ a b Wallace, Patricia M. (1991). Gary M. Pitkin. ed. Library Systems Migration: An Introduction. Westport, CT: Meckler. p. 3. ISBN 0-88736-738-0. ^ a b c Wallace, Patricia M. (1991). Gary M. Pitkin. ed. Library Systems Migration: An Introduction. Westport, CT: Meckler. p. 4. ISBN 0-88736-738-0. ^ a b Kochtanek, Thomas R. (2002). â€Å"1 – The Evolution of LIS and Enabling Technologies†. Library Information Systems: From Library Automation to Distributed Information Access Solutions. Westport, CT: Libraries Unlimited. p. 4. ISBN 1-59158-018-8. ^ Kochtanek, Thomas R. (2002). â€Å"1 – The Evolution of LIS and Enabling Technologies†. Library Information Systems: From Library Automation to Distributed Information Access Solutions. Westport, CT: Libraries Unlimited. p. 5. ISBN 1-59158-018-8. ^ a b c Hamby, R. ; McBride, R. , & Lundberg, M. (2011, Oct. ). â€Å"South Carolina’s SCLENDS optimizing libraries, transforming lending†. Computers in Libraries. 8 31: 6–10. ^ http://www. librarytechnology. org/perceptions2008. pl ^ http://www. librarytechnology. org/perceptions2009. pl ^ http://www. librarytechnology. org/perceptions2010. pl ^ http://www. librarytechnology. org/perceptions2011. pl [edit]Further reading Olson, N. (2010). Taken for Granted – The Construction of Order in the Process of Library Management System Decision Making (Vol. 45). Goteborg / Boras: Valfrid publishing. [1] Rubin, Richard E. Foundations of Library and Information Science. New York: Neal-Schuman Publishers, Inc. , 2004. [edit]External links MARC Records, Systems and Tools : Network Development and MARC Standards Office, Library of Congress Higher Education Library Technology,(HELibTech) a wiki supported by SCONUL (Society of College National and University Libraries) that covers many aspects of library technology and lists technologies in use in UK Higher Education Key resources in the field of Library Automation Categories: Library automationÃ'Ž

Reality Of Death Essay

Reality Of Death Essay Reality Of Death Essay Reality of Death As time has progressed, people in this country have become less and less immune to the reality of death. Due to this, life does not seem as valuable to some as it does to others. People don’t always think about the consequences death has on people and how it affects them emotionally. No matter who is being killed death will always have a negative affect on someone, as seen in the visual of Pei Xia Chen; wife of Officer Wenijan Liu is deeply saddened by the death of her husband. When a person is killed it only leads to heartache, heartache that will slowly eat at a person and tear them down day by day. Though death sometimes seems small because it has no direct relation to the viewer, it will always be a monumental incident in someone else’s life because that’s the reality of death. Unfortunately death is not inevitable, it will eventually play a role in everyone’s lives. Sadly death can happen for some sooner than it will happen for others, and no matter when or how death happens it will always be out of the person’s control. Unfortunately death can also be the result of murder, whether premeditated or even spontaneous. For Officer Liu death was not preventable, his attacker Ismaaiyl Brinsley had a plan to murder any police officers that he came across. A plan that would turn a beautiful sunny day in New York into a dark gruesome crime scene. The visual is surrounded by darkness, darkness that was created by the brutal murders that took place, and a darkness that laid rest over New York for weeks as everyone tried to make since of the killings. The overall vision for the photograph was darkness and sadness, photographer Carlo Allegri wanted to show how death is a very tragic and sorrowful time that nobody should have to go through, not even the families of officers that are here to protect and serve. Often times at funerals family, friends and other visitors wear black to help mourn the dead Mrs. Chen is no exception to this rule. She is wearing a heavy jacket that is black as a cold winters night, black is the absence of all colors, and death is the absence of all light. When Mrs. Chen wears black she is showing that black is permanence, as is her husbands death. Nothing she can do nor say will bring Officer Liu back from the dead, all she has to hold onto are the memories she has with him. Also in the visual, almost in the direct center you can see Ms. Liu wearing bright white gloves holding a candlestick. Candles are often lit at a funeral service because light is pure as if it were to re-nourish the life of someone who has passed. Same with the bright white gloves, readers can infer that the purity of the candle should be handled with the hand of someone that is also pure. Also showing aspects of purity viewers can see the portrait of Officer Wenijan Liu. The picture that Mrs. Chen is holding was the picture that Officer Liu took as his headshot for the New York Police Department. Officer Liu can be

The Boldness Of Courage Essays - Salem Witch Trials, The Crucible

The Boldness Of Courage Essays - Salem Witch Trials, The Crucible The Boldness of Courage ?You?re the Devil?s man!? (118), Mary Warren cried out when she accused John Proctor of working for the devil. Courage is defined as mental or moral strength to face danger without fear. This is supported in Arthur Miller?s The Crucible. Throughout the Salem witch trials in the 1600?s, courage was that good people held in to, even through the toughest times. To illustrate this, an example of someone with courage is John Proctor. Proctor is a farmer with a wife, Elizabeth, and three young boys. He quietly suffers from guilt caused by an affair he had with a young woman named Abigail Williams. He is contrite and solicitous in his wife?s presence, and he yearns to regain her respect. John shows his courage when he has to make a life and death decision to lie and say that he is involved in witchcraft, which will prevent his execution, or to deny being a witch and be hanged. Proctor, after being questioned by Judge Danforth about being involved in witchcraft, stated that he was. Danforth was then having Proctor sign a confession, but he argued with Danforth saying, ? I have confessed myself! Is there no good penitence but it be in public? God does not need my name nailed upon the church! God sees my name; God knows how black my sins are!? (142). When Danforth would not give up the argument with Proctor to sign the confession, he asked, ?Then explain to me, Mr. Proctor, why will you not let me have it? ? (143), Proctor answered, ? Because it is my name... Because I lie and sign myself to lies!... I have given you my soul; leave me my name!? (143). Danforth then explained to Proctor, if the confession was a lie, he would not accept it. Proctor, with his breast heaving and his eyes staring, he tore the confession and crumpled it up, while he wept in fury. Danforth then ordered for him to be hung ? high over the town ? (143). John Proctor showed courage for his friends and family and by doing it, helped put an end to the unfair courts of Salem. Another good example of with a good deal of courage is Giles Corey. Giles is a 83-year old landowner who is sturdy, mettlesome, and fiercely independent. He?s unenlightened and pig-headed, but at the same time, warm-hearted and undaunted. He reveals himself to be a great man of awesome courage and will when he would not answer ?aye or nay to his indictment? (135). When Elizabeth Proctor was telling her husband, John, about it, she explained, ? great stones they lay upon his chest until he plead aye or nay. They say he give them two words. ? More weight?, he says. And died. ? (135). Giles Corey?s wife, Martha, and all of his friends, had already been convicted of witchcraft, so he had probably decided that he had nothing to live for. Giles humbly protested the one-sided courts by sacrificing himself as an example to his friends to stay strong and to not give up in what they believed is wrong. John Proctor could have easily used Giles Corey as an example, because Proctor learned of Giles? death before he had to make his decision of confessing or being executed. The next courageous person in The Crucible is Reverend John Hale. Reverend Hale is the church authority on demonology. He is summoned to Salem to find out if Reverend Parris? daughter Betty, who is suffering from an unexplained illness, has been hexed by witchcraft. Reverend Hale is proud of his scholarly expertise, and is glad to come to Salem to give his professional input on the situation. He displayed acts of courage when he got extremely frustrated about how unjust and ridiculous Danforth and the trials were, so he stood up and yelled, ? I denounce these proceedings, I quit this court! ? (120). Reverend Hale then comes back later to help those convicted by trying to persuade them to confess and live, rather than be hanged. By doing this, Reverend Hale shows great moral courage. He gives up everything he has worked for in his demonology career by going against the court, and trying to persuade innocent people to confess because he feels horribly responsible for bringing the hysteria to Salem. Reverend Hale is one of

With reference to the issues of International Essay

With reference to the issues of International Justice,Torture,Landmines campaign, Lesbian&Gay Rights examine how the UN Charter - Essay Example 324). IGOs engage in treaty-making; encourage international lawmaking to become democratized by including more states in making treaties, not just the civilized states; instigate and enforce international law; and empowering NGOs and other non-state actors to act in advocating for victims of human rights abuses (Alvarez, 2006, pp. 324-335). States rely on IGOs to fulfill their national goals, and are constrained by these organizations. Moreover, state participation in IGOs often transforms the internal structure of the governments involved, such as when they induce states to establish medical authorities to respond to requests by the World Health Organization, and induce states to give effect to its warnings on global warming (Alvarez, 2006, p. 335). Non-governmental organizations are other actors on the global stage. NGOs are organizations that bring out the facts about human rights abuses, as well as contribute to setting standards regarding the implementation, promotion and enforc ement of human rights norms (Steiner & Alston, 1996, p. 456). Because governmental agencies might be hesitant to call out other governmental agencies, for a range of reasons that concern diplomacy, NGOs are considered to be a necessary part of spreading the word about human rights abuses, and advocating for reform.... Among these organizations are labor unions, consumer unions and industrial associations, which advocate for economic concerns; racial, gender and religious groups; groups that are issue-oriented, such as environmental or educational organizations; groups that advocate for the elderly or the young; public interest groups who may be for universal health care or against corruption; etc. (Steiner & Alston, 1996, p. 457). NGOs have a variety of strategies at their disposal, as far as the reformation of human rights abuse. One strategy would be to use the country’s domestic law. This has the advantage of being politically expedient, as using a country’s own law is seen as carrying more politically clout than using an international standard, as using international standards are often seen as intrusive to a country’s people. However, oftentimes countries might not have very progressive domestic laws when it comes to human rights. In that case, a better strategy would be to use international standards to attempt to make that country reform (Steiner & Alston, 1996, p. 458). NGOs must be impartial to be effective – in other words, they must not be affiliated with a certain political party. In other words, the group cannot be beholden to one particular party, or else that group will not investigate abuses perpetrated by that party. This was a concern in Nicaragua, where there were many groups who claimed to speak for human rights, then actually these groups were a shill of one party or the other, and each party was using these groups as a weapon against the other party (Steiner & Alston, 1996, p. 459). Consider the evolution of the notion of INTERNATIONAL CRIMINAL JUSTICE and the creation of the ICC as a case study to assess

Disney Summer Internship Training Program Evaluation Essay

Disney Summer Internship Training Program Evaluation - Essay Example Reaction – This is how the learners reacted to the learning process. The reaction in this case might be positive or negative. 2. Learning – This step tries to gauge the level at which the learners acquire knowledge and skills. 3. Behavior – This step seeks to find out what changes in the job performance were as a result of the learning process. 4. Results – this step concerns itself with finding out the results that arise from the learning process in terms of increased efficiency of operations and improved production and quality. (Kirkpatrick, 1959) This model is relatively important as it provides a valuable tool in the process of planning, trouble shooting and evaluation. But though this level is used for training purposes, the model can also be used for other applications in the learning processes such as informal learning, education and development (Nadler, 1984). Kirkpatrick wrote that his objectives would be related to the traditional classroom progr ams, the most general form of training. He further stated that many of the procedures and principles can be applied to all manner of training activities that includes participation in outside programs, performance review, planned instruction, and the comprehension of selected books (Craig, 1996). This paper would seek to evaluate the Disney Internship training program plan. In the paper, the plan will be weighed according to Kirkpatrick's model to find out what changes should be made to the plan, if the objectives of the plan were achieved, the strength and weaknesses of the plan, to identify the people that should participate in future programs, what participants benefited the most and what changes, if any, should be made to the program to make it better. The objective of this training plan is to increase the quality of service provided by interns through the dissemination of knowledge to them that they can use and apply to their workplace to improve their efficiency and productivi ty. Another objective of the plan would be to increase the number of students who would come back to the organization to work as full time employees. This is because, after the intern training program, they would have been introduced into the working world and trained as full level employees. Further, the plan will introduce a seminar course so as to enable the interns to share in the culture of Disney. This is whereby the interns will be introduced to the various activities that go on in the organization. This will fast track their intake into the work force of the organization, boosting their individual confidence and the overall performance of the organization. The plan would also enable the interns to network with the managers and high level employees of Disney and this will open up even more opportunities for them. The training methods in this training plan will include the use of the standard in-class training alongside other techniques of training including the use of simulat ions, behavior modeling, mentoring, on the job training and job rotation. These various methods of training will aid the intern in mastering the necessary skills required for the job. These methods of training will guide an individual more comprehensively as it seeks to not only impart the knowledge needed, but also to give a hand on approach to tackling the job. Using this plan will improve the efficiency of the intern in retaining the skills imparted. Job