Child Mental Health Factors Essay

The child mental health factors are comprised of: sensory integration, emotional regulation, Attention Deficit Hyperactivity Disorder (ADHD), Oppositional Disorder (ODD) and Autism (Michigan Non Profit Association, 2002, p. 6). The children who have been diagnosed as sensitive or under-reactive to all of its five senses are perceived to be easily distracted and are displaying other challenging behaviors such as impulsiveness and problem of proper transition in between certain events (Nelson, 1999 as cited from Michigan Non Profit Association, 2002, p. 6). Other children are unable to regulate their emotions as such they are more prone to emotional outbursts whenever they are frustrated or is angry with someone (Murphy, Eisenberg and Fabes, 1999, as cited from Michigan Non Profit Association, 2002, p. 6). On the other hand, Attention Deficit Disorder (ADHD) is perceived to be more often present in male children rather than their female counterparts. However, the prevalence of ADHD is hard to recognize because of the usual connotation that children are naturally difficult to deal with most specially during their early stages of development. As such, there is a need to seek the help of psychiatrists and psychologists in order to properly address such a concern (Barreda-Hanson and Kilham, 1997 as cited from Michigan Non Profit Association, 2002, p. 6). The Oppositional Defiant Disorder (ODD) is often times found in children who manifest high rates of problematic behaviors. Albeit, it should be noted that since difficult behaviors in juxtaposition with hyperactivity are hard to recognize due to its close resemblance to ADHD (Speltz, McClellan and DeKleyen, 1999 as cited from Michigan Non Profit Association, 2002, p. 6). Children with Autism have difficulties communicating with other people. In other cases, some of them could be virtually unaware of other people surrounding them. Autism usually appears during the age of three and has an incidence of 1 every 500 children (National, 1998 as cited from Michigan Non Profit Association, 2002, p. 6).

Concept Paper or Pre-Proposal

Statement of the problem †¢Statement of the solution †¢Brief statement of how the solution will benefit the reader(s) II. Background†¢Explanation of key terms †¢Proof that you know the issues surrounding the problem †¢Proof that you know what action has been taken to solve similar problems †¢Proof that you (or someone you are associated with) can carry out the action plan III. Action Plan and Requirements†¢A set of objectives (what your plan will accomplish) †¢An action plan (who will do what when) keyed to the objectives †¢A description of what you need to implement the plan A cost/benefit analysis of the plan IV. Benefits†¢An explanation of why the plan will work †¢A set of outcomes keyed to the objectives †¢A description of how you and the reader(s) will benefit †¢Proof that you are the best person or team to carry out the action plan †¢A statement demonstrating that your plan is the best approach to solving the problem Ideas or Content Problem statement Since you will ask your reader(s) to give you something, you must first establish that there is a problem that needs to be solved. If you are responding to an agency's Request for Proposals (RFP), the problem will be given to you.This is a solicited proposal. However, if you are requesting support or approval for your own idea (e. g. , a product design,technological innovation, and/or process), you must clearly state the problem and explain why you think it is a problem. This is an unsolicited proposal. A template for a statement of purpose/solution follows: The purpose of this concept paper is to request [approval or support] in the form of [ approval, equipment, funding, personnel, resources] to solve [description of a problem] so that [benefits of implementing the solution]. Sample purpose statements: The purpose of this concept paper is to request your approval to develop a technical proposal to request funding from the National Scienc e Foundation to establish a chicken-cloning program at the University of Texas. †¢The purpose of this document is to convince you to provide the Residents' Association with $2,000 to renovate the apartment complex's existing tennis courts so that you can successfully fulfill your contractual agreement with residents and so that they can play tennis without having to needlessly chase errant balls. Background information 1.As in all technical documents, you must first identify your audience? n this case, your potential supporter(s). If you are responding to an RFP or other solicited proposal, you will know the agency or company you will be writing to, but may still need to research both the names of the people to whom the proposal should be addressed, as well as the funding history of the agency or organization. This will help you to: †¢ narrow your research down to only those areas that will appeal to your reader(s) and †¢ to formulate a plan the agency/organization wi ll be likely to support.If you are submitting an unsolicited proposal, this research is even more important. There is lots of funding available, but much of it is targeted to very specific types of projects or types of respondents. For example, one philanthropic organization might support only those projects proposed by community organizations focused on prevention of substance abuse by teenagers. An organization I worked for once sent out an RFP to fund teacher-training projects proposed by groups of educators only.Individuals or groups with money to invest in new ideas may also have limits to the cash awards they offer. If your action plan can be accomplished with $5,000 or less, you may have more potential supporters than if your project requires $50,000 or even $5,000,000. 2. Conduct market or rhetorical research (analyze your context of use) to determine what evidence you might present that could convince the reader(s) to give you what you request. 3. Collect only that evidence that will convince your reader(s) to act. . Explain key terms and orient the reader to the problem. (Use internal citations when warranted. ) 5. Prove to the reader(s) that you have researched both the problem and its solution. 6. Explain why you and/or other reputable people think the problem is important. Clear solution/action plan While developing a clear solution may seem like an easy thing to do, it may actually be quite complicated. It may help you to develop categories equivalent to those that may later be required in the final proposal (e. . , objectives, rationale, personnel, management, timeline, products, budget, evaluation, guarantees of assurance, dissemination of results). While you will not be able to provide many details at this core document stage, you must have a clear idea of: †¢who will perform what actions (personnel and management), †¢how long it will take to achieve the solution (timeline), †¢how much it will cost (budget), and †¢what reso urces you will need (approval, funds, equipment, personnel, or other resources).Good proposals present strong links between the objectives of the plan (what you hope to accomplish), the activities that will allow you to accomplish those objectives, and the means by which you will determine how well your project is going. The methods of evaluation also link directly back to the objectives; this means that as you write an objective, you must make certain its degree of achievement can be measured. You might consider using a chart similar to that in Table 2 as a planning tool. In this example, the proposal is requesting approval and funds to carry out the specified action plan.Note that the objectives refer to the plan itself, not to reader support of the plan. Table 2. Sample Proposal Planning Chart ObjectivesAction PlanEvaluation (on-going and summative) †¢To develop a web site to successfully market the services of an engineering consulting firm 1. Form a project team that inclu des managers, researchers, graphic artists, technical writers, and web authors. 2. Conduct research on the audience that will be accessing the web site. 3. Conduct research on similar successful web sites. 4. Work with managers to determine the purpose and content of the web site. . Define†successful marketing†of the firm's web site. 6. Develop a questionnaire to assess successful marketing. . . †¢Web site tally of the number of people accessing the site (hits) †¢Follow-up electronic questionnaire sent to those who contact the firm for services Needs/Requirements Clearly specify what you need from the reader(s) of your Concept Paper. You should have already stated in an introductory paragraph the specific action you want from your reader; now explain how you will use the support you request.For instance, if you request money, state how the funds will be used or distributed. The typical format for doing this is a formal budget statement. Table 3 shows a sample b udget chart for the project described in Table 2. Table 3. Sample Budget Chart ExpenseRecipientSourceAmount (per year) Project Team SalariesTeam LeaderEngineering Firm$15,000 Graphic ArtistEngineering Firm$25,000 ResearcherEngineering Firm$5,000 Technical WriterEngineering Firm$25,000 Web expertEngineering Firm$5,000In this sample chart, all funds are expected to come from the engineering firm to which the proposal is being sent. However, your proposal may be more likely to be funded if you can show matching support from other sources (cost-share). This budget reflects only personnel and their projected salaries. * As you develop your chart, consider what other needs you might have. For example, in this project, the author might want to include costs of computers, printers, scanners, digital cameras, or other production equipment needed to develop the web site.

Shangri-La Hotels

What are the key elements of Shangri-La Hotel’s strategy? Which of the five generic competitive strategies described in Chapter 5 is the company employing? What is Shangri-La’s strategy for competing internationally? 2. What policies, practices, support systems, and management approaches underlie Shangri-La’s efforts to execute its strategy? 3. How important are the company’s training and Shangri-La Care program to its success? What is your assessment of Shangri-La’s compensation policies and career growth effort? What pluses and minuses do you see? . What are the key features of the culture at Shangri-La Hotels? How important is the culture in the company’s success? Explain. What impact do the company’s mission statement and the Shangri-La Care program have on the company’s culture? 5. What core/distinctive competencies has management at Shangri-La tried to build and nurture? What challenges does the company face as it attempts to transfer its core and distinctive competencies to other cultures? How has the company attempted to resolve these challenges? Has it been successful in doing so? 6.What does the company’s financial and operational performance reveal about how successful its strategy and strategy implementation efforts have been? Should shareholders be pleased with the company’s financial performance? Why or why not? What financial and operating performance pluses and minuses do you see? 7. What challenges does Shangri-La face in expanding into Eastern China? Do you believe the company’s current policies and operating procedures will be sufficient in addressing these challenges? If so, why? If not, what else may need to be done? 8. How do the challenges associated with Shangri-La’s expansion into Europe,Australia, and North America compare with the company’s expansion in China? Do you believe the company’s current policies and operating procedures will be sufficient in addressing these challenges? If so, why? If not, what else may need to be done? 9. How big a threat does the expansion of other hotel chains into China pose for Shangri-La Hotels? What specific challenges are likely to arise as a result of this expansion? How should Shangri-La address these challenges? 10. What recommendations would you make to Symon Bridle to improve Shangri-La’s prospects for continued success? Shangri-La Hotels Shangri-La Hotels Contents Background Executive Summary Problem Statement Current Strategy External Environment VRINE Model Internal Analysis TOWS Analysis Value Chain Analysis Key Success Factors Alternatives Recommendations Implementation Plan Prologue Appendices Background Hong Kong-based Shangri-La Hotels and Resorts is Asia Pacific's leading luxury hotel group and regarded as one of the world’s finest hotel ownership and management companies. The Shangri-La story began in 1971 with its first deluxe hotel in Singapore. Today, there are  71 hotels and resorts throughout Asia Pacific, North America, the Middle East, and Europe,  representing a room inventory of over 30,000. In addition, new hotels are under development in  Austria, Canada, mainland China, India, Macau, Philippines, Qatar, Turkey and United Kingdom. Executive Summary The purpose of this report is to provide a strategic analysis of Shangri-La Hotels and its rapidly expanding business of luxury hotels into Eastern China, Europe, North America, and Australia; while still holding on to Shangri-La’s signature standards of â€Å"Shangri-La Hospitality. My analysis supports the recommendation that Shangri-La hotels have the required resources, expertise and efficiencies to successfully expand into these markets even with the tight labor markets and vast cultural differences Problem Statement Shangri-La Hotels is attempting to expand its business into other countries; however, expanding into high-wage economies’ such as E urope and North America could tarnish their brand and lead to a reduced overall profit. Current Strategy External Analysis PESTEL Analysis Political – little impact in Canada, however foreign companies may restrict trade or impose tariffs, thus increasing costs. Free trade may help or hinder companies. Favorable taxation or subsidies in other countries may assist competitors. Economic – Collectivity stage and needing to delegate (marketing). Interest rates, currency fluctuations and unemployment are factors. Social and Cultural – Foreign interest in products could be a fad. Advantage is quality. Technological – improved production/packaging technology needed Environmental- could focus on recyclable, reusable packaging. Legal- Foreign sales may require changes or inter-provincial sales may result in abiding by various provincial regulations. | Test| Competitive Implication| Performance Implication| Valuable| Does the resource or capability allow the firm to meet a market demand or protect the firm from market uncertainties| The product itself doesn’t protect the firm from uncertainties. The marketing concept of a healthy product, charming PEI and authentic ‘goodness’ is the competitive edge. Protecting the branded image and promotion is important in sustaining the market position and increasing this position. | Rare| Assuming the resource or capability is valuable, is it scarce relative to demand? Or is it widely possessed by most competitors| The preserve product can be copied. Strawberry jam has the most demand and supply meets demand in N America. Unique product combining high fruit content and liquors. | Product is easily copied; therefore it is important to differentiate fro m the competition with use of specific formulas of ingredients to have a unique taste. Inimitable and non substitutable| Assuming a valuable and rare resource how difficult is it for competitors to either imitate the resource or capability or substitute for it with other resources and capabilities that accomplish similar benefits| Preserve resource is not rare. The culture of home made natural image in the PEI setting is the rarity and could be substituted but countered with its original/ authentic brand. | Product is easily copied, so value must be in packaging/image/marketing appeal. Exploitable| For each set of the preceding steps of the VRINE test, can the firm actually exploit the resources and capabilities that it owns or controls? | One resource that the company has access to is the fresh fruit within the region, therefore there is the potential that the Company could monopolize the fruit market in the area. | Product is easily produced with access to fruit in the area. | Int ernal Analysis Functional Analysis Production Marketing Human Resources Finance Value Chain Analysis TOWS Analysis | From External Analysis| Opportunities1. New national and international markets/customers2. Custom production to utilize spare capacity3. Japanese tourism and marketplace4. Potential to tailor products to consumers in each geographical region| Threats:1. Potential entrants/substitutions claiming PEI origin2. Tariffs on exports make the product a less competitive price3. Labor intensive and seasonal labor 4. Significant currency fluctuations can impede exporting| From InternalAnalysis| Strengths:1. Quality product attracting premium pricing2. PEI ethnicity and charm3. Favorable tax status in Cda4. Increased sales and international interest5. Fresh local produce not requiring freight and storage costs6. Quality staff with low turnover. | SO strategies (use strengths to take advantage of opportunities)Increasing sales across Canada will promote PEI, incur favourable tax status vs imported products and therefore increase/improve competivenessJapanese market can be tapped with Japanese tourism in Canada (Vancouver/Toronto) without incurring the prohibitive multi levels of taxes and levies. Expansion would not only include different geographical locations but includes the potential to utilize quality staff throughout the year, rather than only seasonallyPromote company culture| ST Strategies (use advantages of strengths to overcome threats)PEI authenticity and premium gourmet product with specific marketing highlights to overshadow competitors substitutions. Selling to tourists within Canada, with no GST/PST or tariffs makes the product more attractive Selling nationally reduces freight/shipping damages and more inventory control | | Weaknesses1. Marketing plan2. Restaurant business dilutes core business3. Seasonal business4. Underutilized capacity5. Management’s lack of experience in growth management| WO strategies (use opportunities to overcome weaknesses)Custom production, expansion of selling to new markets/customers and effective marketing plan can utilize the unused capacity and even out the seasonal nature of the business Outsource canning, packing – research alternatives with environmental/recycle benefits| WT strategies (use defensive strategies to minimize weaknesses and avoid threats) Targeted marketing plan and sales agent to identify the place and promotion of the 4P’s to expand sales and sales mix. Increased sales and production would require full time staff and reduce seasonality which would increase ability to retain quality staff. | Key Success Factors Alternatives 1. Pro Con 2. Pro Con 3. Pro Con Recommendation Implementation Plan Short-Term Long-Term Prologue According to the SHANGRI-LA ASIA financial reports for 2006 through 2009 the Asian division has had an increasing net income with the exception of 2008. Proving that Shangri-La has been a success in Asia, even with the expansion into the Chinese market. Appendices Bargaining Power of Suppliers Substitute Products Bargaining Power of Buyers Threats of new entrants Competitors-Airbus/Boeing CCCComCompetitAIRBUS/Boeing Airlines Leasing companies Governmental institutions FAA, IATA, EPA Other regulating bodies Advance in short haul turboprop technology Advances in automotives industry and infrastructures High speed train Advances in telecommunications: video conferences etc†¦ Engine manufacturer Electronic, Semiconductor etc†¦ Others manufacturers such as metal, composite materials Government institutions Capital sources investors and banks FAA, IATA, EPA Other regulating bodies Mitsubishi Others emerging power Others small aircraft manufacturers Military companies: Dassault, Lockheed, ATR Mission Statement We envision a community of responsible and educated citizens who are environmentally conscious, practice social responsibility in their daily lives and inspire others to do the same. We commit to operating in an economically, socially and environmentally responsible manner whilst balancing the interests of diverse stakeholders. We strive to be a leader in corporate citizenship and sustainable development, caring for our employees and customers, seeking to enrich the quality of life for the communities in which we do business, and serving as good stewards of society and the environment. Partnering for the Future With a solid foundation and reputation for excellence in Asia Pacific, the Middle East and North America, the company's strategic plan now incorporates the goal of expanding the Shangri-La brand globally by operating deluxe hotels in gateway cities and key resorts around the world under management agreements, equity participation or ownership. Given the commitment to becoming a top-end global hotel company, the development functions of Shangri-La Hotels and Resorts are directly led by the President and Chief Executive Officer. Shangri-La has always believed in the unique characteristics encapsulated by Asian Hospitality. Our commitment to providing guests with distinctive Asian standards of hospitality and service from caring people remains our major point of differentiation from our peers and the very cornerstone of our reputation as a world-class hotel group. â€Å"Pride without arrogance† is of particular importance as we want our people to be internally proud of our achievements but outwardly humble. After all, the hallmark of true success is that it does not need to be stated. In striving to delight customers each and every time they stay with us we aim to exceed expectations through consistently providing quality and value in our products and services. That’s why we look for trendsetters, professionals who are enthused by innovation and driven by achievement. Environment Our  daily operations ensure that we mitigate the impact of climate change, uphold biodiversity in conservation/habitat restoration, adopt the best practices in preventing ozone depletion, and continually strive to improve ater-use management, waste-disposal management and indoor air quality. Health & Safety We  are committed to protecting our customers, employees, stakeholders and the greater public by providing a safe and healthy environment based on international standards. Employees Our colleagues are our number-one asset, and our source of inspiration for the greater communities with which we work. We value our stakeholders and always engage them with clarity, honesty, and respect. We require that our business partners ensure the highest standards in environmental, hygiene and labour practices. We believe that caring for others today allows them to care for themselves and others tomorrow. ‘Embrace’ aims to build, strengthen and sustain local communities through various and specific education and health projects. Each of our resorts provides a natural habitat for flourishing biodiversity. The ‘sanctuary' is Shangri-La’s project for ensuring the highest standards in marine and terrestrial habitat restoration and environmental conservation.

Organizational Learning Coursework Example | Topics and Well Written Essays - 1250 words

Organizational Learning - Coursework Example The success of strategic management requires the skills and implementation of the academic level or performance of the employees of the organization. According to Phipps and Burbach, the ability of an organization to achieve its goals greatly depends on knowledge management (Phipps and Burbach, 2010, p. 11). Knowledge management in turn engages the monitoring of databases and statistical panels regarding the dealings and operations of the firm (Beer, Voelpel, Leibold and Tekie, 2005, p. 446). For the employees to realize how to use and implement such information, they have to be fully acquainted with the skills regarding such procedures. The ability and skills of the employees of an organization greatly rely on organizational learning for full implementation and prediction of the strategies imposed. B. Purpose of the study The research model of implementing a theoretical framework was adapted by Sekeran and implemented by Chen and Huang. According to Chen and Huang, organizational le arning relates with knowledge management in the sense that the knowledge infrastructure ability of an organization influence the operations that take place in every business unit of the organization (Chen and Huang, 2007, p. 110). Therefore, depriving the discussion from this assumption, the purpose of this study is to recognize the actual relationship between information infrastructure, the knowledge procedure, and organizational effectiveness from the perception of teamwork, before asserting that organizational learning is able to foresee the success of the strategies of an organization (Sekaran and Bougie, 2009, 202). C. Variables identified i. Analysis The success of strategic management can be identified through a... This report approves that the hypothetical structure of the argument is grounded on the importance of organizational learning in the current global community. Organizational learning involves the training and evaluation of the skills and academic standards of the employees in an organization. The success of strategic management requires the skills and implementation of the academic level or performance of the employees of the organization. Knowledge management in turn engages the monitoring of databases and statistical panels regarding the dealings and operations of the firm. This essay makes a conclusion that for effective operation of tactical management policies and plans, organizations are required to fit and side with their organizational learning strategies, abilities and skills. Complete and successful management within a highly competitive and steady changing setting can only be accomplished through organizational learning in fields such as communication, management behavior of profit and non-profit organizations and knowledge management. The capacity of the staff to change in accordance with new surroundings and imposition of management strategies can be determined and improved through organizational learning. The concept derived from this study asserts that managers are supposed to be aware of the leading universal and essential changes made in organizational learning. Therefore, organizational learning is able to predict the success of strategic management, should the managers impose the right changes on staff and data management.

CONTEMPORARY CASES IN PUBLIC POLICY Essay Example | Topics and Well Written Essays - 3000 words - 1

CONTEMPORARY CASES IN PUBLIC POLICY - Essay Example In its literal sense, civic engagement is the basic right given to the citizens to utilize public resources, participate in determination of the policies which will help them in seeking for the betterment of the society and helps in reforming or replacing institutions which are unable to perform effectively and efficiently. Civic engagement is integrated with having an essential relationship with the concept of public policy due to its focus on elaboration of state and governmental policies (Reuben, 2003). It interlinks all the values, skills, ideas, beliefs, concepts and attitudes which a population holds within a state and helps in the potential formation of broad cultural, social, and economic identities within a state. It is a fact that within a democratic society, citizens form the core representation of a democratic society. Application of civic engagement and community can only be found within programs which can help in implementation of various essential areas of a state†™s consistent development. Social and community collaboration involves democratic roles where individuals of various interests and ambitions can act together for discussing their concern about various issues and can help them in giving them a chance for making changes to things which they deem to be crucial. Such moves can prove to be a source of inspirations and thought provoking ideas which include neighborhood associations, school, colleges and universities where citizens can find relevant information for their community and also create a place where they can feel their voices are being heard and they can be given an opportunity for providing their own input regarding crucial governmental decisions which are of utmost interest of the public. Engagement in public discussions that is able to clarify necessities as well as certain changes which need to be made on a regular basis. Political involvement is another vey key issue which may need to be

Arthur Miller Research Paper Example | Topics and Well Written Essays - 1500 words

Arthur Miller - Research Paper Example Miller's first play to make it to Broadway, The Man Who Had All the Luck (1944), was a dismal failure, closing after only four performances. This early setback almost discouraged Miller from writing completely, but he gave himself one more try. Three years later,  All My Sons  won the New York Drama Critics' Circle Award as the best play of 1947, launching Miller into theatrical stardom. All My Sons, a drama about a manufacturer of faulty war materials, was strongly influenced by the naturalist drama of Henrik Ibsen. Along with  Death of a Salesman  (his most enduring success), All My Sons and The Man Who Had All the Luck form a thematic trilogy of plays about love triangles involving fathers and sons. The drama of the family is at the core of all of Miller's major plays, but nowhere is it more prominent than in the realism of All My Sons and the impressionism of Death of a Salesman, a play which secured Miller’s reputation as one of the nation’s foremost playwr ights. Also in 1956, Miller married actress Marilyn Monroe. The two divorced in 1961, one year before her death. That year Monroe appeared in her last film, The Misfits, which is based on an original screenplay by Miller. After divorcing Monroe, Miller wed Ingeborg Morath, to whom he remained married until his death in 2005. The pair had a son and a daughter. Miller also wrote the plays A Memory of Two Mondays and the short A View from the Bridge, which were both staged in 1955. His other works include After the Fall (1964), a thinly veiled account of his marriage to Monroe, as well as The Price (1967), The Archbishop's Ceiling (1977), and  The American  Clock (1980). His most recent works include the plays The Ride Down Mt. Morgan (1991), The Last Yankee (1993), and Broken Glass (1993), which won the Olivier Award for Best Play. Miller also wrote the plays A Memory of Two Mondays and the short A View from the Bridge, which were both staged in 1955. His other works include After the Fall (1964), a thinly veiled account of his marriage to Monroe, as well as The Price (1967), The Archbishop's Ceiling (1977), and  The American  Clock (1980). His most recent works include the plays The Ride Down Mt. Morgan (1991), The Last Yankee (1993), and Broken Glass (1993), which won the Olivier Award for Best Play. Although Miller did not write frequently for film, he did pen an adaptation for the 1996 film version of The Crucible starring Daniel Day-Lewis and Winona Ryder, which garnered him an Academy Award nomination. Miller's daughter Rebecca married Day-Lewis in 1996. With  Tennessee Williams, Miller was one of the best-known American playwrights after WW II. Several of his works were filmed by such director as John Huston, Sidney Lumet and Karel Reiz. Arthur Miller was awarded the Pulitzer Prize in 1949 for  Death of a Salesman.  He has come to be considered one of the greatest dramatists in the history of the American Theatre, and his plays, a fusion of naturalistic and expressionistic techniques, continue to be widely produced. Arthur Miller's  Death of a Salesman  stems from both Arthur Miller's personal experiences and the theatrical traditions in which the playwright was schooled. Miller is in some way accusing a culture that encourages "wrong" values and campaigning against an uncharitable social order that deprives honest workers of constructive labor, then discards those who are no longer useful. The play recalls the

HR external consultant recommendation Essay Example | Topics and Well Written Essays - 2500 words

HR external consultant recommendation - Essay Example The HR Director has reservations about the transferability of the HR systems from an American context to the EU legislation, cultural and HR aspects. There are also concerns regarding the induction process for the expatriate workers. This paper aims at discussing the problems that Fantasia Corp will be anticipating in the process of implementing an HR system developed in the US in France. This paper will also give suggestions on how Fantasia Corp can overcome these challenges. In the last few decades, there has been a significant increase in the rate in which business organizations opt for global operations. Going for global markets present companies with more opportunities. Similarly, Fantasia Corp has also opted to expand their operations to Europe, with France being their targeted country. Recent researches reveal that organizations operating in different geographical environments usually have to operate under different HR practices and policies (Festing 2012, p. 43). This is due to the difference in social, political, cultural, and economic factors. Just like many other managerial practices, HRM is always affected by cultural beliefs. This is a factor that multinational corporations must take into consideration when intending to transfer some of their HR practices and policies to another country. Some of the practices that are socially allowed in America might not be admissible in France. This is a clear indication that some of the practices that have been successfully used by Fantasia Corp in the US might not be applicable in France. Therefore transferring the HR system used by Fantasia Corp in the US to France might have some performance consequences of their operations in France. HR researches have it that multinational corporations such as Fantasia Corp have to adapt to a certain degree to the cultural beliefs and practices of a host country. It should not be forgotten that in their operations

King Saud University Essay Example | Topics and Well Written Essays - 3000 words

King Saud University - Essay Example They offer a complete free tuition in addition of providing scholarships to both the International and Saudi Arabia students. The university is situated in vast state of modern art campus in addition of being equipped with the modern technological instructions. For Internal audit to remain important to the King Saud University management then it must always adapt to the ever changing expectations of the seven universities in addition of maintaining alignment with the objectives of the university. There should be a systematic and a structured process for developing the internal audit strategic plan for the university; the strategic plan will include the following in addition to the mission and vision of the university; For the three years strategic plan, the initial step should be â€Å"Planning to plan† it should represent the necessary work before the beginning of primary planning process. The university internal management should agree on the efforts of overall strategic planning and the significant planning steps that will be undertaken. The university organization should also consider, evaluate and review the legislative/constitutional mandate since this will determine their future as well as daily academic business. The mission and vision of the university should also be its considerations before coming up with strategic planning. For the three years strategic planning, the university should identify its purpose and mandate of existence to avoid unnecessary conflict that might arise, which can also help in channeling a productive discussion and activity. The vision statement will make the university identify how it will appear in the future after successfully implemented its strategies as well as achieving its full potentiality. The three year strategic plan should also include a developed internal audit’s strategic vision. It should identify the responsibilities functional roles, mandates, stakeholders’ needs and

TRAINING, LEARNING & DEVELOPMENT 'HELPING HANDS' CASE STUDY Essay

TRAINING, LEARNING & DEVELOPMENT 'HELPING HANDS' CASE STUDY - Essay Example It is against this background that I propose to delineate the strategic vision and mission of Helping Hand’s current corporate philosophy. It is not far fetched to suggest at this stage of my analysis that the management at Helping Hand, has almost foreclosed the significant opportunities that TL&D concept presents to business organizations at a critical phase of its growth process, by not revisiting its corporate strategy. There is an inevitable negative correlation between the gradual up-scaling of strategic corporate goals and a static TL&D policy. The outcome is not only predictably negative but also competitively disastrous. The principal stance of the Helping Hand’s senior management is that the operating capacity and efficiency of the middle management structure ought to be enhanced through a conventional and often credibility deficient technique of contracting out functional managerial tasks to outsiders who as consulting firms would rather put in place stop-gap measures. Stress management counselling services are performed by professionals who help client organizations to manage their staff well with a view to increasing worker productivity. Some of the latest techniques have been adopted, probably, by the Helping Hand’s rivals. For example, â€Å"Autogenic biofeedback in psychophysiological therapy and stress management†, has been received by stress management companies with open arms because it provides the counsellor with a more reliable tool (Lehrer and Sime, Editors, 2007, p.231). At Helping Hand, there is no such innovative strategic drive. Right now the level of staff mot ivation is at a low ebb. This is reflected in the high rate of labour attrition. Plans for diversification must be carried out with a total shake up in the existing organizational structure. Additional middle layers of management would necessarily add to the communication bottlenecks that underlie a tall chain of command. As a

Leadership Style and Performance Essay Example for Free

Leadership Style and Performance Essay An overview of the topic of leadership styles summarizes that the existing studies on how performance is affected by leadership style is separated into important phases. Early studies on leadership (frequently categorized as ‘trait’ studies on leadership) concentrated on identifying the personality traits which characterized successful leaders (Argyris, 1955; Mahoney et al. , 1960). According to them successful leaders are ‘naturally born’ and those they have certain native characteristics which distinguish them from non-leaders (see Stodgill, 1948). However, there was significant difficulty in validating these characteristics led to widespread criticism of this trait approach, signaling the emergence of ‘style’ and ‘behavioral’ approaches to leadership (Stodgill, 1948). Style and behavioral theorists shifted the emphasis away from the characteristics of the leader to the behavior and style the leader adopted. The primry conclusion of these studies is that adoption of democratic or participative styles by leaders are more successful (see, for example, Bowsers and Seashore, 1966). In this sense, these early studies are focused on identifying the ‘one best way of leading’. Similarly to trait theories, the major weakness of style and behavioral theories is the ignorance of how important role situational factors play in determining the effectiveness of individual leaders (Mullins, 1999). It is this limitation that gives rise to the ‘situational’ and ‘contingency’ theories of leadership (for example, Fiedler, 1967; House, 1971; Vroom and Yetton, 1974) which shift the emphasis away from ‘the one best way to lead’ to context-sensitive leadership. Although each study emphasizes the importance of different factors, the general tenet of the situational and contingency perspectives is that leadership effectiveness is dependent on the leader’s diagnosis and understanding of situational factors, followed by the adoption of the appropriate style to deal with each circumstance. However, recent studies on leadership have contrasted ‘transactional’ leadership with ‘transformational’. Transactional leaders are said to be ‘instrumental’ and frequently focus on exchange relationship with their subordinates. In contrast, transformational leaders are argued to be visionary and enthusiastic, with an inherent ability to motivate subordinates. Although the brief summary above indicates that research into leadership has gone through periods of skepticism, recent interest has focused on the importance of the leadership role to the success of organizations. Fiedler (1996), one of the most respected researchers on leadership, has provided a recent treatise on the importance of leadership by arguing that the effectiveness of a leader is a major determinant of the success or failure of a group, organization or even an entire country. It has been argued that one way in which organizations have sought to cope with the increasing volatility and turbulence of the external environment is by training and developing leaders and equipping them with the skills to cope. These claims are based on the assumption of a direct link between leadership and organizational performance. This assumption requires critical review. Widely celebrated cases of a direct leadership–performance link may be found in numerous anecdotal accounts of improvements of company performance attributed to changes in leadership (see, for example, Nicholls, 1988; Quick, 1992; Simms, 1997). However, empirical studies into the links between leadership and performance have been lacking. One notable exception is the detailed study of the impact of leadership on performance in the somewhat surprising context of Icelandic fishing ships. Thorlindsson (1987) suggests that variations in the performance of different fishing ships, under identical conditions, can be accounted for by the leadership skills of captains. Over a three-year period, Thorlindsson revealed that the leadership qualities of the ship captains accounted for 35 to 49 per cent of variation in the catch of different crews. Other studies which examine the links between leadership and performance coincide with the re-emergence of the ‘one best way to lead’ debate. Of particular relevance is the resurgence of interest into charismatic leadership, which is frequently referred to as transformational leadership (Bass and Avolio, 1993). A number of researchers theorize that transformational leadership is linked to organizational performance. Conceptually, it is argued that the visionary and inspirational skills of transformational leaders motivate followers to deliver superior performance. In summary, much of the above evidence presented as supporting the claim of a leadership–performance link is anecdotal and frequently over-concentrates on the ‘transformational’ role of leaders in corporate successes. It would appear that few studies have responded to the observation of Porter and Mckibbin (1988) that much of the research reported as supporting this claim is either inconclusive or empirically suspect. The limited or inconclusive character of research findings in this area suggests the need to investigate further the nature of the relationship between leadership and performance. Several different categories of leadership paradigms have been suggested by various researchers. For example, Bass (1985) stated that there are four dimensions of transformational leadership, three dimensions of transactional leadership, and a non-leadership dimension of laissez-faire leadership (Bass, 1985). Avery (2004) suggested categorizing leadership into four leadership paradigms, while Goleman (1995) prefers six leadership paradigms. Despite Bass’s (1985) model being acclaimed as making a major contribution to leadership, his theory has been criticized for various reasons (Yukl, 1999). One criticism is that his model overemphasizes the importance of one or two leadership paradigms (e. g. transactional and visionary), omitting the classical and organic paradigms Bass asserts that visionary (transformational) leaders are nearly always more effective than transactional leaders, but others (e. g. Judge and Piccolo, 2004; Wallace, 1997) dispute this. While this in itself does not invalidate the concept of visionary leadership, Bass attributes more to visionary (transformational) leadership than perhaps he should. As Avery (2004) suggested, both transactional and visionary leadership are valid forms of leadership, but visionary leadership may be applicable more broadly, including in situations where there are insufficient resources for the manager to rely on supplying external rewards (Judge and Piccolo, 2004), or where the situation is complex and ambiguous, and relies strongly on follower knowledge and commitment. Avery suggests that there are other situations in which transactional leadership is the appropriate form of leadership, such as when followers are unwilling or unable to commit to the leader’s vision. In contrast with Bass’s (1985) model, Avery’s (2004) paradigms provide a broad basis allowing for different forms of leadership that have evolved at different times and in different places. The paradigms are useful for showing that there is no single best way of thinking about leadership, rather that different kinds of leadership reflect social and historical roots. Avery’s paradigms allow leadership to depend on the context, respond to organizational needs and preferences, and involve many interdependent factors that can be manipulated (Bryman, 1992; Shamir and Howell, 1999; Yukl, 1999). Avery (2004) proposes 13 indices to differentiate between her four paradigms: classical, transactional, visionary, and organic. The nine indices included in this review are decision making, range of staff’s power, power distance between leader and the staff, key player of the organization, source of staff’s commitment, staff’s responsibility, situation of management and leadership in the organization, situation of diversity in the organization and situation of control in the organization. These nine criteria are considered more relevant for differentiating the four leadership paradigms than the other four criteria. Each paradigm is discussed in turn, including the distinguishing characteristics using the above nine criteria. Classical leadership is probably the oldest paradigm with its origins in antiquity, and is still used in contemporary organizations (Avery, 2004). This paradigm reflected the prevailing view in the business literature until the 1970s when the human relations movement led to more of a focus on followers and their environment. According to Avery (2004), classical leadership refers to dominance by a pre-eminent person or an ‘elite’ group of people. This leadership can either be coercive or benevolent or a mixture of both. This happens because the elite individual or group commands or maneuvers other members to act towards a goal, which may or may not be explicitly stated. The other members of the society or organization typically adhere to the directives of the elite leader, do not openly question their directives, and execute orders largely out of fear of the consequences of not doing so, or out of respect for the leader, or both (Avery, 2004). Classical leadership has some limitations. The first occurs where the leader cannot command and control every action, particularly as situations become more complex and beyond the capacity of one person; or when additional commitment from followers is needed to get a job done, such as in reacting to changing circumstances; or when ideas about leadership change and followers no longer accept domination, or follower commitment starts to wane for other reasons. Another limitation is that this paradigm often relies on the idea of a ‘great person’, implying that only a select few are good enough to exercise initiative, and this belief can encourage followers to deskill themselves nd idealize the leaders. Followers then seek and hold little power, leave the leader accountable for organizational outcomes, and make relatively little contribution to the organization (Avery, 2004). According to the nine distinguishing indicators, under the classical leadership paradigm leaders normally use an autocratic style for making decisions, involving followers in the decision making process never or very little; they do not empower followers. Followers have almost no power in the organization and as classical leaders tend to be highly directive, followers can be unskilled. The source of followers’ commitment comes from their fear of or respect for the leaders; the technical system becomes more regulating; the operations in the organization become more routine and predictable; and the organization is highly controlled by the leaders (Avery, 2004). A transaction or exchange process is the basis of the commonly employed transactional leadership paradigm (Evans and Dermer, 1974; House and Mitchell, 1974). The transactional leader recognizes subordinates’ needs and desires, and then clarifies how those needs and desires will be met in exchange for subordinates’ work. By clarifying what is required of subordinates and the consequences of their behaviors, transactional leaders are able to build confidence in subordinates to exert the necessary effort to achieve expected levels of performance. According to Judge and Piccolo (2004), three dimensions of transactional leadership are contingent reward, management by exception-active, and management by exception-passive. Contingent reward is the degree to which the leader sets up constructive transactions or exchanges with followers. The leader clarifies expectations and establishes the rewards for meeting these expectations. In general, management by exception is the degree to which the leader takes corrective action on the basis of results of leader-follower transactions (Judge and Piccolo, 2004). As noted by Howell and Avolio (1993), the difference between management by exception-active and management by exception-passive lies in the timing of the leader’s intervention. Active leaders monitor follower behavior, anticipate problems, and take corrective actions before the behavior creates serious difficulties. Passive leaders wait until the behavior has created problems before taking action (Howell and Avolio, 1993; Judge and Piccolo, 2004). According to Avery (2004, p. 34), under the transactional leadership paradigm, leaders adopt a consultative style for making decisions. They engage in different degrees of consultation with individual followers, but the leaders remain the final decision-makers. Leaders do not very often empower followers, and followers have very low power in the organization apart from being able to withdraw from or contribute more of their labor. Compared with classical leadership, under transactional leadership the source of followers’ commitment comes from the rewards, agreements, and expectations negotiated with the leader rather than from their fear of, or respect for, the classical leader. The technical system becomes more regulating, the operations in the organization become more routine and predictable, and the organization is mostly highly controlled by the leaders. Avery (2004) argues that under transactional leadership, the followers’ knowledge base can be somewhat higher than under classical leadership. Compared with classical leaders, transactional leaders require staff somewhat more skilled on specific tasks. In the last three decades, visionary (transformational, charismatic) leadership has received increasing attention (Bass, 1985, 1998; Burns, 1978; Conger and Kanungo, 1987; House, 1977). It added a new dimension to organizational studies, namely the visionary aspect of leadership and the emotional involvement of employees within an organization. The basic notion is that a visionary leader can create an impression that he or she has high competence and a vision to achieve success. Subordinates are expected to respond with enthusiasm and commitment to the leadership objectives, and may be recruited because they share the vision. Bass (1985, 1998) developed a theory of visionary or transformational leadership whereby the leader inspires and activates subordinates to perform beyond normal expectations. According to Avery (2004), visionary leadership has limitations, even with the current literature’s overwhelmingly positive view of it. Nadler and Tuschman (1990) pointed out that the unrealistic expectations followers often place on visionary leaders can create disappointment if things do not work out. Followers can become dependent on visionary leaders, believing that the leader has everything under control. Also, innovation can be inhibited if people become reluctant to disagree with a visionary leader. Avery (2004, p. 39) distinguishes the visionary leadership paradigm from the other three paradigms as follows. First, leaders employ a collaborative style for making decisions. They share problems with their followers and seek consensus before the leaders make the final decision. Visionary leaders empower their followers, giving followers a much higher level of power in the organization than classical and transactional leadership. This is essential because the leader needs the followers’ input and commitment to realize his or her goals. Followers of visionary leadership need sufficient power to work autonomously towards a shared vision. The source of followers’ commitment comes from the influence of the leaders’ charisma and/or the shared vision, the technical system becomes still more complex, operations become more uncertain and unpredictable, and the organization is jointly controlled by the leaders and their followers. Regarding the followers’ knowledge base, visionary leadership requires skilled and knowledgeable workers who are attracted to, and share the leader’s vision, and can contribute to realizing the vision. The fourth paradigm, organic leadership, is relatively new to organizational studies. Recently introduced by Drath (2001) and expanded by Avery (2004), organic leadership is likely to blur the formal distinction between leaders and followers. This paradigm relies on reciprocal actions, where team members work together in whatever roles of authority and power they may have, not based on position power (Hirschhorn, 1997; Raelin, 2003; Rothschild and Whitt, 1986). Employees become interacting partners in determining what makes sense, how to adapt to change, and what is a useful direction. Rather than relying on one leader, organic organizations are likely to have many leaders. Multiple leaders are valuable because as people cope with heterogeneous and dynamic environments, the knowledge and issues become too complicated for only a few leaders to understand (Avery, 2004). Organic leadership allows for people with different degrees of expertise on current issues to emerge and be accepted by the group as leaders. In addition, under organic leadership, there may be no formal leaders and the interaction of all organizational members can act as a form of leadership, held together by a shared vision, values, and a supporting culture. Under this paradigm where an organization has no formal leadership structure, an integrator role may emerge to actively link together the many parts of the organization (Avery, 2004). The emphasis is on emerging leadership rather than on people being appointed to leadership positions. However, Kanter (1989) argued that the downside of organic leadership that advocates autonomy, freedom, discretion and authorization may result in loss of control and greatly increased uncertainty. It is important to recognize that organic leadership is about generating a form of self-control and self-organization, where people have a clear sense of purpose and autonomy within a particular context (Meindl, 1998). This idealized organic leadership paradigm requires differentiating from classical, transactional, and visionary leadership concepts by not relying on formal leaders. Furthermore, the enterprise has to trust in the capacity of its members to solve problems and make decisions in the interests of the organization. This idea clearly relies upon self-leading organizational members (Avery, 2004). According to Avery’s (2004, p. 39) distinguishing characteristics, under organic leadership an organization adopts a mutual agreement style for making decisions. Decisions need not be unanimous but can be based on consensus. The members have a high degree of power as a result of this shared leadership. Accountability and responsibility are shared as well. The source of followers’ commitment is based on the values and visions shared by all the members in the organization; a strong, shared culture; a technical system that is highly complex; operations in the organic organization become more self-organizing and unpredictable; formal control is provided by peer pressure and group dynamics, and a shared culture, vision, and values. Members are self-managing. Organic leadership seems particularly appropriate for professional and knowledge workers in dynamic, chaotic situations. This leadership paradigm relies on attracting and retaining highly trained and knowledgeable staff with self-controlling capabilities.

Priemgetallen

Priemgetallen Voorwoord Het stond vast, ons onderwerp werd priemgetallen. Onze kennis in verband met priemgetallen reikte niet verder dan de getallen die deelbaar zijn door 1 en zichzelf. En we vroegen ons af wat er nog meer over te zeggen valt. Na even te surfen op het internet bleek al snel dat er veel informatie te vinden was. Priemgetallen hebben vele wiskundigen door de geschiedenis geboeid. Zo heb je Euclides, Fermat, Mersenne, Euler. Dit waren stuk voor stuk grote wiskundigen die geboeid waren door priemgetallen en er velen jaren over nagedacht hebben. Het grote voordeel aan een onderzoekscompetentie (OZC) met twee maken, is dat je elk maar de helft moet doen. Maar met als nadeel dat je verschillende afspraken moet maken, het werk eerlijk moet verdelen en samenkomen om alles te overlopen en tot in de details uit te werken. Onze OZC is in vier hoofdstukken ingedeeld. Eerst hebben we het over de geschiedenis van de priemgetallen en over de wiskundigen die er mee bezig waren. Hoe men steeds nieuwe priem getallen blijft vinden zien we in hoofdstuk 2. Hoofdstuk 3 gaat over de eigenschappen van de priemgetallen. Zo hebben we eerst het vermoeden van Goldbach, de belangrijkste stelling bij de priemgetallen. Daarna gaan we het hebben over de soorten priemgetallen en priemgetallen met speciale eigenschappen. Tenslotte gaat hoofdstuk 4 over de toepassingen van priemgetallen, en dit blijkt vrij veel te zijn. We hopen dat het voor u een even interessante en leerrijke ontdekkingsreis door de priemgetallen zal worden als dat het voor ons was. Hoofdstuk 1 De geschiedenis van de priemgetallen Wanneer precies de priemgetallen ontstaan zijn, kan nooit met zekerheid gezegd worden. Het zou kunnen dat de Babylonià «rs de eerste ontdekkers waren. Wel staat vast dat rond 400 voor Christus, Pythagoras de priemgetallen had gedefinieerd als getallen alleen deelbaar door 1 en zichzelf. Daarmee staat hij bekend als de uitvinder van de priemgetallen. In 530 v.C. stichte hij in het zuiden van Italià « een gemeenschap die zich onder andere bezighield met wiskunde. Er was een grote interesse in natuurlijke getallen en hun eigenschappen. Natuurlijke getallen en hun verhoudingen waren volgens de gemeenschap de basis van het leven en het heelal. Dankzij hun grote interesse, ontdekten ze iets bijzonder over bepaalde getallen. Stel een getal voor als een aantal knopen. Je kan dan sommige getallen rangschikken als een rechthoek, zoals het getal 6 (een rechthoek van 2 op 3 knopen). Er zijn getallen die je onmogelijk kan rangschikken als een rechthoek, zoals het getal 5. Er werd zo het verschil gemaakt tussen de rechtlijnige en de rechthoekige getallen. Deze rechtlijnige getallen worden nu priemgetallen genoemd. Rond 300 v.C. kwam Euclides, à ©Ãƒ ©n van de grootste wiskundigen uit de oudheid. Hij schreef een 13-delig werk De Elementen, waarin onder andere een bewijs staat dat er oneindig veel priemgetallen bestaan. Bewijs: Veronderstel dat er een grootste priemgetal pn bestaat. Dan maken we een lijst van alle priemgetallen: 2, 3, 5,,pn. Definieer dan N = 2, 3, 5, , pn. N + 1 is niet deelbaar door 2 want N is dat wel. De rest is 1. N + 1 is niet deelbaar door 3 want N is dat wel. Ook hier is de rest 1. N + 1 is niet deelbaar door 5, 7,,pn. De rest is telkens 1. Als N + 1 niet deelbaar is dan moet N + 1 zelf priem zijn. Als het wel deelbaar is, dan bestaat er een priemgetal p dat N + 1 deelt maar dat niet was opgenomen in de lijst, dus moet dat priemgetal p groter zijn dan pn. Hierdoor is er dus geen grootste priemgetal en zijn de priemgetallen oneindig. In 200 v.C. werd De Zeef van Erastosthenes (zie 2.4.1) beschreven en daarna bleef het een aantal eeuwen stil rond priemgetallen. In de 16de eeuw veronderstelde Pierre Fermat dat 22n- 1 enkel priemgetallen opleverde. Indien n een priemgetal voorstelde. Marin Mersenne dacht hetzelfde over 2n 1. In 1753 toonde Goldbach aan dat geen enkele formule voldoet om alle priemgetallen te definià «ren. Vanaf de 19de eeuw werd er intensief op zoek gegaan naar grote priemgetallen en de mogelijkheden om ze toe te passen in de samenleving. Hoofdstuk 2 Het zoeken naar priemgetallen Welke getallen zijn priem? De definitie: Een priemgetal is een natuurlijk getal dat slechts 2 verschillende delers heeft. Die delers zijn 1 en het getal zelf. In het begin is het simpel. Je kan getallen à ©Ãƒ ©n voor à ©Ãƒ ©n gaan uitproberen. Zijn ze niet deelbaar door een ander getal dan 1 en zichzelf, dan is het een priemgetal. Zo zijn 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 alle priemgetallen kleiner dan 100. Veel mensen vragen zich af waarom 1 ook niet gewoonweg een priemgetal is. Natuurlijk heeft 1 maar à ©Ãƒ ©n deler en geen twee. Dan waarom is de definitie niet gewoon een natuurlijk getal dat enkel gedeeld kan worden door 1 en zichzelf? Wel hierdoor zou de hoofdstelling van de rekenkunde (Elk natuurlijk getal valt te ontbinden in priemfactoren op juist à ©Ãƒ ©n manier) niet meer gelden. Een natuurlijk getal zou dan op oneindig veel manieren kunnen worden geschreven als een product van priemgetallen. Eà ©n voor à ©Ãƒ ©n de getallen gaan uitproberen om na te gaan of ze priem zijn is na een tijdje toch vrij vervelend. Het zou daarom wel handig zijn een patroon in een lijst van priemgetallen te herkennen. Helaas is er tot op het heden geen enkel goede formule gevonden. Euler, in de 18de eeuw, vond de formule f(x) = x ² + x + 41 en alle f(x) zijn priem. Maar het werkt enkel voor x∈(0 t/m. 39). De principià «le hoofdtheorie De principià «le hoofdtheorie houdt in dat de kans een getal x priem is, ongeveer gelijk is aan 1/ln(x), voor een x groter dan rond de 5000. Als x rond het getal 10000 ligt, dan is de kans dat het priem is ongeveer 1/9. Ligt een getal ergens bij de 1.000.000.000 dan is de kans ongeveer 1/21. Dit betekent dat de priemgetallen zeldzamer worden naarmate we kijken naar grotere getallen. Mersenne-getallen Marin Mersenne onderzocht in het begin van de 17de eeuw ook de priemgetallen en hij probeerde net zoals Fermat een formule op te stellen. Ook hij is er niet in geslaagd, maar hij heeft wel ander belangrijk werk verricht. Hij was de eerste die zich volledig toelegde op de formule Mp = 2p -1, waarin p priem is. Euler had deze formule opgesteld in De Elementen. Deze formule werkt niet altijd. Toch is al jarenlang het grootst bekende priemgetal altijd een Mersenne-priemgetal geweest. Vanaf juni 2009 zijn er 47 Mersenne-priemgetallen bekend. Het grootst bekende priemgetal is 243112609 -1. Het was het eerste bekende priemgetal met meer dan 10 miljoen cijfers! De vlugge testen De zeef van Erastosthenes De zeef van Eratosthenes is de oudste methode voor het vinden van priemgetallen. Ze is ontstaan circa 240 voor Christus. Het werkt heel simpel. Je schrijft bijvoorbeeld alle getallen op van 2 tot en met 120 Dan nemen we het eerste getal, 2, en arceren we alle veelvouden van dit getal, groter dan het getal zelf in het rood. We nemen nu het volgende, nog niet gearceerde getal, 3, en arceren alle veelvouden van 3 in het groen. De veelvouden van 4 zijn reeds gearceerd dus kunnen we deze overslaan. Daarna arceren we alle veelvouden van 5 (blauw), van 7(geel) en van 9 (groen) De resterende getallen arceren we in het paars en dit zijn de priemgetallen van 1 t/m. 120 Met deze methode kan je alle priemgetallen t/m. n achterhalen door alle veelvouden t/m. n te arceren. Dit valt ook te bewijzen: Stel dat de zeef maar van 2 t/m 100 gaat. Stel dan dat er toch een samengesteld getal x ≠¤ 100 nog niet gearceerd is. Omdat x samengesteld is, geldt x = a.b , met a ≠¤ 100 of b ≠¤ 100. (Als a en b beide groter zijn dan 100 , is a.b = x immers groter ( 100) ²=100). x Is dus een veelvoud van een getal kleiner dan 100, Al deze veelvouden hebben we gearceerd. Elk niet gearceerd getal kleiner dan 100 kan dus niet samengesteld zijn, en moet een priemgetal zijn. Het ontbinden in priemfactoren Euclides bewees eveneens in De Elementen dat elk natuurlijk getal te ontbinden valt in priemfactoren op juist à ©Ãƒ ©n manier (als we de volgorde verwaarlozen). Dit wordt ook wel de hoofdstelling van de rekenkunde genoemd. Valt een natuurlijk getal niet te ontbinden in priemfactoren, dan is het getal priem. Bijvoorbeeld met het getal 211. Je kijkt of het deelbaar is door 2,3,5,7,11 en 13. Omdat 17 > 211mag je bij 13 stoppen. Het getal 221 is niet deelbaar door deze 6 priemgetallen, dus is het zelf priem. Deze methode wordt alleen gebruikt voor getallen met maximum 25 cijfers. Fermat In de 17de eeuw stelde Pierre de Fermat dat elk getal van de vorm Fn = 22n+ 1 (met n ∈ N een priemgetal is. Echter in 1732 zei Euler dat dit onzin is. Het werkt enkel voor n = 0 t/m 4. Je hebt enkel 2 proefdelingen nodig om deze factor te vinden. Euler toonde aan dat elke deler van een Fermat-getal Fn met n > 2 de vorm 2n+2.k + 1 heeft. In het geval van F(5) is dat 128.k + 1. De getallen 129, 385 en 513 zijn niet priem dus gaan we 257 en 641 uitproberen, met succes. Waarschijnlijk zijn alleen de eerste 5 Fermat-getallen werkelijk priemgetallen. Fermats kleine stelling daarentegen is van meer nut. Het houdt in als p een priemgetal is, dan geldt voor ieder geheel getal a dat ap = a(mod p) Als het priemgetal p geen deler is van a, dan heeft ap-1/p een rest van 1. Stel dat je een bepaald getal a hebt. Als je een priemgetal p kunt vinden waarvoor ap-1/p niet als rest 1 oplevert, dan is a deelbaar door p en dus samengesteld. Bijvoorbeeld: a=4 en p=5; dan is 1024/5 = 1020 + 4. De rest is 4, dus is het getal 1024 samengesteld en niet priem. Jammer genoeg werkt de stelling niet altijd in de andere richting, maar door deze kleine stelling van Fermat kunnen we al meteen een hele hoop getallen elimineren als priemgetallen. De andere getallen kunnen daarna verder gecontroleerd worden. PRPs De hedendaagse computertests hebben hun snelheid niet alleen te danken aan de snelle hardware, maar veeleer aan de software. Men gaat eerst een aantal waarschijnlijkheidstesten uitvoeren. Ze gaan op zoek naar pseudo-priemen. De getallen die deze testen doorstaan. De simpelste test werkt met de kleine stelling van Fermat. (zie 2.4.3) Het omgekeerde van die stelling is niet altijd geldig. Als voor een gehele a en k geldt dat ak = a(mod k) dan is k niet noodzakelijk een priemgetal. Vroeger was elke k een pseudo-priemgetal. Nu is het alleen nog maar een pseudo-priemgetal als het nog meer testen doorstaat en toch geen priemgetal blijkt te zijn. Een getal k dat in een test slaagt waarin a=2 noemt met een 2-PRP (waarschijnlijk priemgetal, een vertaling van probable prime). Als de test slaagt met a=3 noemt met het een 3-PRP enzovoort. Omdat deze priemtesten veel sneller verlopen dat de exacte controles, gaat men er meerdere na elkaar uitvoeren. Men begint bij a=2, dan a=3 enzoverder. Als een getal k positief test over verschillende testen, dan is het waarschijnlijk dat het ook een priemgetal is. Bijvoorbeeld: Een 2-PRP met k=341. Het blijkt geen priemgetal te zijn want het is deelbaar door 11 en 31. Er zijn 1.091.987.405 priemgetallen kleiner dan 25.000.000.000, maar slechts 21.853 pseudo- 2-PRP priemgetallen. Dus een getal k kleiner dan 25 miljard, die in een 2-PRP-test slaagt, in 99.998% van de gevallen ook werkelijk priem is. En hoe groter k wordt, hoe groter de slaagkans wordt. SPRPs Wanneer k het getal is dat we onderzoeken of het priem is, d oneven is en s positief. Dan is in k 1 = 2s.d , k een sterk waarschijnlijk priemgetal (vertaling van strong probable prime) als aan à ©Ãƒ ©n van de volgende condities voldaan wordt op basis a. ad = 1(mod k) (ad)2r = -1(mod k) waarbij r positief is en r Ook hier zijn alle getallen k > 1 die niet in de test slagen, niet priem. En de getallen die wel slagen kunnen priem zijn. Deze waarden voor k zijn dus niet priem. Zo een SPRP-test is redelijk snel, zeker als het gecombineerd wordt met het zoeken naar de kleinste priemfactoren. Het is aangetoond dat dergelijke testen in 75% van de gevallen priemfactoren oplevert. Op zichzelf is een SPRP-test dus tamelijk zwak, maar als we enkele van deze testen combineren, maken we een krachtige test voor kleine getallen k, die priemheid aantonen. Wat wilt zeggen dat een getal zeker priem is of zeker niet. Bijvoorbeeld: Als k k priem. Als k k priem. Als k k priem. Als k k priem. Als k k priem. Als k k priem. Deze resultaten geven ons een manier om een zeer snelle priemheidstest te maken. We beginnen met het zoeken naar de kleinste priemfactoren, daarna voeren we SPRP-testen uit op basis 2, basis 3, tot wanneer een van de bovenstaande criteria is bereikt. Bijvoorbeeld, als k De klassieke testen Merkwaardig is dat de grootste priemgetallen tot nu toe gevonden, p-1 of p+1, zeer makkelijk te ontbinden zijn. Dit komt omdat dit priemgetallen zijn waarvan het gemakkelijk is om te bewijzen dat ze priem zijn. Bij deze klassieke testen kunnen we aantonen dat een getal priem is. Dit zijn dus geen waarschijnlijkheidstesten, maar bewijzen van de priemheid. Stelling 1 (Lucas-Kraitchik-Lehmer) Lucas heeft op het einde van de 19de eeuw de kleine stelling van Fermat omgevormd tot een praktische test, die later versterkt werd door Kraitchik en Lehmer. Stel n > 1. Als voor iedere priemfactor q van n-1 er een natuurlijke a bestaat zodat an-1 = 1(mod n) a(n-1)/q ≠  1(mod n) dan is n priem. Dit is zowat de basis van alle moderne priemtesten. Stelling 2 (Pocklington) Stelling 1 heeft een volledige ontbinding in priemfactoren nodig van n-1. Pocklington had daar een oplossing voor. Stel n-1 = qkr waar q priem is en r niet deelt. Als er een natuurlijk getal a bestaat zodat an-1 = 1(mod n) en de g.g.d. van(an-1q- 1,n) = 1, dan heeft iedere priemfactor q van n de vorm qkr + 1. Stel dan n-1 = FR, waarbij F > R, g.g.d. (F,R) = 1 en de ontbinding van F gekend is. Als voor iedere priemfactor q van F er een a > 1 bestaat zodat an-1=1(mod n) g.g.d. (an-1q- 1,n) = 1 dan is n priem. Er kunnen verschillende a gebruikt worden voor ieder priemgetal q. Deze formules zijn de basis van de bekendere formules, zoals die van Pepin en Proth. Pepins test Pepin heeft in 1877 een formule gevonden die Fermat-getallen (van de vorm 22n+1) op de priemheid test. Stel dat Fn het n-de Fermat-getal is met n > 1. Fn is priem als en slechts als 3(Fn-1)/2 = 1(mod Fn). Bijvoorbeeld: F2 = 222+ 1 = 17 Dan is 3(17-1)/2 = 38 =6561 = 1(mod 17) Want (6561+1)/17 = 386 Proths test Proth maakte in 1878 de formule: n =2kh +1 met 2k > h. Als er een natuurlijk getal a bestaat zodat a(n-1)/2 = -1(mod n), dan is n priem. Lucas-Lehmertest Om na te gaan of een Mersenne-getal, een priemgetal is kan je de Lucas-Lehmer test gebruiken. Als p een priemgetal (groter dan 2) is, is het Mersenne-getal 2p -1 priem, als S(p-1) deelbaar is door 2p -1, waarbij S(n+1) = S(n) ² -2 en S(1)=4. Bijvoorbeeld: Als we willen weten of M3 = 7 een priemgetal is, dan zoeken we S(2).   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  S(2) = S(1) ²-2   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  = 4 ²-2   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  = 14 Dan controleren we of 14 deelbaar is door 2p -1 = 7. Dat klopt dus 7 is een priemgetal. De theorie voor de test heeft Lucas uitgevonden rond 1870. Hij heeft dan de test vereenvoudigd in 1930 tot wat hierboven uitgelegd staat. Voor heel grote Mersenne-getallen wordt het wel moeilijk de test uit te voeren. Zelfs moderne computers kunnen slecht overweg met zeer grote getallen. APR, APRT-CL In 1970 begon Williams samen met enkele anderen op een andere manier de priemheid te testen. Ze gingen nu niet meer de factoren van n-1 gebruiken, maar factoren van n2+1, n ²+n+1, n ²-n+1 en nm 1 waarbij soms m heel groot was, zoals 5040. Elk priemgetal q waarvoor q 1 een deler is van 5040 (welke n niet deelt) moet dan n5040 1 delen. Er is aangetoond dat er altijd een m is waarvoor geldt dat m q die nm 1 delen met q 1 een deler van m op zijn minst een product geven dat gelijk is aann. Zo goed als altijd ligt m rond de 100.000.000 voor een n die een 3000-tal cijfers bevat. GIMPS GIMPS (Great Internet Mersenne Prime Search) is een project waarbij men zoekt naar steeds grotere Mersenne-priemgetallen. Dankzij GIMPS kunnen we enorm grote getallen controleren op priemheid, doordat het werk wordt verdeeld onder een aantal deelnemers. Het project heeft tot op het heden 12 Mersenne-priemgetallen gevonden. Iedereen die een computer heeft en over internet beschikt kan deelnemen. Er is wel veel tijd voor nodig, à ©Ãƒ ©n priemheidstest kan gemakkelijk een hele maand duren. GIMPS is een efficià «nt systeem, het zoeken naar Mersenne-getallen gebeurt in verschillende stappen. Het aanmaken van een lijst met priemgetallen (want de formule die ze gebruiken is 2p-1 met p als priemgetal) Het zoeken naar de priemfactoren, wat op verschillende manieren kan gebeuren. Bij GIMPS zullen ze de exponent eerst omzetten naar het binair talstelsel. Bijvoorbeeld: 223 1 wordt getest en wordt daarbij gedeeld door 47. In het binair is 23 = 10111. Daarna passen ze de volgende werkwijze toe (het binair rekenen): De Pollard-methode om te ontbinden in priemfactoren. De P-1-methode werkt nogal simpel. In stadium 1 kiezen ze een vaste B1. Als q = 2kp + 1, dan zal het P-1-ontbinden in factoren deze factor q bepalen zolang alle factoren van k kleiner zijn dan B1. Dan wordt x = 3E.2.P berekend. Daarna controleren ze de g.g.d. van(x 1,2p -1) om te zien of er een factor is gevonden. In stadium 2 gebruiken ze een ander vast getal, B2. Hier zal de factor q gevonden worden als k exact à ©Ãƒ ©n factor heeft tussen B1 en B1 en alle andere factoren van k kleiner zijn dan B1. (Dit stadium maakt gebruik van zeer veel geheugen) GIMPS gebruikt deze methode om de grote factoren te vinden. Bijvoorbeeld 22944999 1 dat deelbaar is door 314584703073057080643101377. B1 en B2 worden gekozen door kansberekening. De Lucas-Lehmer test. (zie : 2.5.2.2) Om een getal te controleren zijn er heel veel vermenigvuldigingen nodig. Er worden zorgvuldig algoritmes geschreven die gebruikt worden om zeer snel te vermenigvuldigen. De kans dat zo een Lucas-Lehmer test succesvol een priemgetal ontdekt is ongeveer 1/80000. De zoektocht naar het grootste priemgetal Sommige mensen hebben er een hobby van gemaakt steeds op zoek te gaan naar het grootste priemgetal. De traditie is al gaande sinds 300 v.C. toen Euclides zijn werk De Elementen schreef. Hij merkte op dat de perfecte getallen (positieve getallen gelijk aan de som van zijn delers) nogal dicht lagen bij de priemgetallen van de vorm 2p -1 voor een priemgetal p. Vanaf toen begon de jacht op de Mersenne-priemgetallen. Grote getallen van deze vorm zijn al bestudeerd door grote wiskundigen zoals Fermat, Mersenne, Euler, Lucas, Leibniz enzovoort. Veel mensen willen de eer om hun naam bij het lijstje te voegen. De traditie om grote Mersenne-priemgetallen te vinden zal zeker blijven duren. En er valt heel wat meer met mee te bereiken. Er zijn programmas om priemgetallen te zoeken bij het testen van hardware. Dit wordt al gedaan sinds het ontstaan van de computer. Zo werden stukjes software van het GIMPS project (Zie 2.7) gebruikt door Intel om de processors Pentium II en Pentium Pro te testen alvorens ze verscheept werden. De software dat priemgetallen berekent, belast de processor meer dan andere programmas doen en duurt niet lang om uit te voeren. Als je een heel groot priemgetal invoert, moet de processor een miljoen berekeningen uitvoeren om na te gaan of het wel klopt. En hoe meer priemgetallen er gevonden worden, hoe meer de verdeling ervan kan worden bestudeerd en worden begrepen. Er is al veel onderzoek gedaan naar patronen in de verdeling van priemgetallen. Tevens is het allemaal niet voor niks. Er wordt een serieuze geldprijs van minstens $ 150.000 uitgereikt aan degene die als eerste het priemgetal vindt bestaande uit 100-miljoen cijfers. De eerste die er eentje kan vinden bestaande uit een miljard cijfers, krijgt zelfs een prijs van minstens $ 250.000. Het grootste priemgetal is dus heel bruikbaar en gewild. Hoofdstuk 3 Een priemwereld vol verrassingen Inleiding Zoals al gebleken is zijn er oneindig veel priemgetallen maar kunnen we deze nog onderverdelen in aparte groepen? Ja, er zijn zelfs zeer veel onderverdelingen met elk hun specifieke eigenschappen. Zo heb je de palindroompriemgetallen, Mersennepriemgetallen, Illegale priemgetallen, Maar eerst beginnen we met het uitleggen van enkele vermoedens in verband met priemgetallen. Enkele vermoedens Inleiding Er zijn vele stellingen in verband met priemgetallen. Deze gaan van zeer simpel tot echte breinbrekers. We vooral de meest bekende en de meest belangrijke stellingen voor de priemgetallen bespreken. En daarom beginnen we ook met de stelling die van het grootste belang was voor de priemgetallen, namelijk het vermoeden van Goldbach. Het vermoeden van Goldbach Goldbach was een Duitse wiskundige en is in 1690 geboren in Kà ¶ningsberg. Hij werd zelfs leraar bij de Tsaar in Moskou omdat hij een zeer belangrijke wiskundige was in zijn tijd. Deze job gaf hem dan ook de mogelijkheid veel te reizen zodat hij overal in contact kwam met andere belangrijke wiskundigen zoals Euler, Leibniz. Hij bleef in contact met deze geleerden door middel van brieven. Ook het begin van zijn vermoeden schreef hij in 1792 in naar Euler. In deze brief schreef hij dit vermoeden: Als een geheel getal n > 5 is dan kan dit getal geschreven worden als de som van 3 priemgetallen. Bij deze 3 priemgetallen kan herhaling optreden. Wat wel vreemd is aan het hele verhaal is dat Euler een brief terugschreef met daarin de stelling dat dit vermoeden geldt voor ieder getal n > 2 maar toch is het vermoeden enkel bekend als het vermoeden van Goldbach. Euler beschouwde de stelling van Goldbach als waar maar hierbij was de stelling nog niet bewezen. Zelfs nu is de stelling nog niet bewezen desondanks er als publiciteitsstunt 1 miljoen dollar aan te verdienen was. Maar dit betekent niet dat er geen belangrijke ontdekkingen zijn gedaan. In 1939 bewees Schnirelmann dat je elk even getal groter dan 2 geschreven kan worden als een som van ten meeste 300000 priemgetallen. In 1995 bewees Ramarà © dat een som van maximum 7 priemgetallen meer dan genoeg is. Het oude vermoeden van Goldbach Dit is het vermoeden dat Goldbach als eerst vermelde in zijn brief naar Euler: als een geheel getal n > 5 is dan kan dit geschreven worden als de som van drie priemgetallen. Dit vermoeden wordt ook wel het oneven vermoeden van Goldbach genoemd. Dit oneven vermoeden is eigenlijk een zwakkere vorm van het eigenlijke vermoeden. Want we kunnen bij n > 2 telkens het priemgetal toevoegen zodat we elk oneven getal n > 5 bekomen maar het oorspronkelijke vermoeden volgt niet uit het oneven vermoeden van Goldbach. Het oneven vermoeden staat al veel dichter bij het bewijs dan het oorspronkelijke want in 1937 bewees Vinogradov dat dit vermoeden geldt voor alle voldoende grote oneven getallen. Het probleem was wel dat Vinogradov niet wist hoe groot voldoende groot nu juist was. In 1956 kon men uiteindelijk op voldoende groot een getal plakken, namelijk groter dan 3315. De waarde die gelijk is aan voldoende groot is het getal n > 1043000 bewezen door Wang. De exacte waarde zal men pas kunnen vinden als men computers kan ontwikkelen die dit soort berekeningen aankunnen. Nog meer vermoedens We zullen vlug nog even enkele vermoedens vermelden: Voor ieder even getal 2n bestaan er oneindig veel priemgetalkoppels waarvoor het verschil tussen beide priemgetallen gelijk is aan 2n. Maar indien n = 1 dan hebben we te maken met een priemtweeling en bij n = 3 dan moet het verschil 6 zijn en is het priemgetalkoppel een koppel sexy priemgetallen. (zie 3.7.2) Ieder even nummer is een verschil van 2 priemgetallen. Priemgaten Opvallend bij priemgetallen is dat er geen logische volgorde zit in de opeenvolging. Hoe verder we gaan zoeken naar grote priemgetallen hoe moeilijkere deze te vinden zijn, want ze komen dan steeds minder voor. De gaten tussen twee priemgetallen worden steeds groter hoe verder je gaat. Deze gaten oftewel priemgaten zijn de ruimtes tussen 2 opeenvolgende priemgetallen. De grootte van deze gaten wordt dus bepaald door het verschil van de 2 opeenvolgende priemgetallen. Al een gehele tijd hebben wiskundigen een patroon proberen te ontdekken bij de opeenvolging van priemgetallen door de priemgaten te bestuderen. Priemgaten hebben geen beperking in grootte want als n ≠¥ 2 de minimale grootte is dan zijn de volgende gatallen allemaal samengesteld: (n + 1)! + 2, (n + 1)! + 3, (n + 1)! + 4, , (n+ 1)! + (n + 1) Vb. n = 2 dan zijn de eerste 3 getallen van het priemgat 8,9,10 Deze formule is niet alleen nuttig om het priemgat met grootte n te geven maar ook om het priemgat te geven met minimale grootte n. Hierdoor is de aanwezigheid van minimum n ontbindbare getallen verzekerd. Wat wel nog een probleem vormt is de mannier om de grootte van een priemgat te berekenen. Want men gebruikt het eerste priemgetal a en het tweede priemgetal b om de priemgaten te berekenen door priemgetal a af te trekken van priemgetal b. Het probleem is dat men oftewel bij de uitkomst 1 moet optellen of niet, want zonder 1 toe te voegen wordt het priemgetal a ook meegerekend met het priemgat. Illegale priemgetallen In 2001 ontdekte Phil Carmody dat de gezipte broncode C, wat men op computers gebruikt om DVDs te decoderen, overeenkomt met een priemgetal. Hij ging als volgt te werk: Eerst comprimeerde hij de C-Code met het computerprogramma Gzip. Het getal wat nu weergeven werd in het verkleinde bestand was priem. Er bestaan dus heel wat illegale priemgetallen. Hieronder volgt het allereerste illegale priemgetal, gevonden door Phil Carmody. Later zette Joerg Dietrich het priemgetal om zodat deze kon worden weergegeven in baseparen. Hij kwam een Dna-sequentie uit die 43016 basen telt. Hij kwam ook tot volgende vaststelling: het zinloos zou zijn om een wet te maken tegen het gebruik van het priemgetal want als men ooit het priemgetal in ons DNA mocht vinden dan zouden 6 miljard mensen de wet overtreden. Hier is een klein deeltje van de Dna-sequentie: Merkwaardige priemgetallen Congruente priemgetallen Een priemgetal dat een regelmatige figuur vormt noemt men een congruent priemgetal. Een regelmatige figuur oftewel een regelmatige n-hoek zoals een vierkant of een gelijkzijdige driehoek. Het middelste getal of centrum vormt dan het priemgetal omgeven door cijfers van binnen naar buiten toe. Als voorbeeld geven we volgende regelmatige figuren gevormd door een priemgetal. Vb. 1 met priemgetallen Palindroompriemgetallen Priemgetallen die je zowel naar voor als naar achter hetzelfde leest noemt men palindroompriemgetallen. Als voorbeeld kunnen we volgende priemgetallen gebruiken: 2, 11, 101, Maar ook gigantische priemgetallen zoals 14 ·10^6343-4199. Dit priemgetal telt 6343 cijfers en dit is gewoon heel de tijd 1 en 4 afgewisseld: 14 ·10^6343-4199 = 1414141414141414141 Zo heb je ook het grootste palindroompriemgetal van 3 cijfers namelijk 717. Er zijn ook priemgetallen die de decimale loop van p weergeven: 3, 31, 314159, Het 4de palindroompriemgetal bevat al 38 cijfers en het 5de al 500. Nog een zeer mooi palindroompriemgetal is het volgende: 923032900000000 00000000000006660000000000 00000000000000009230329 Het bestaan uit 666 en wordt omgeven door 32 nullen en 9230329 aan elke kant. En nog wat eigenschappen van dit palindroompriemgetal: 9230329 is exact het 666ste palindroompriemgetal 666.32 = 21312 wat een palindroompriemgetal is. 666.64 = 42624 wat ook een palindroompriemgetal is. De palindroompriemgetallen zijn nog verder ingedeeld zo heb je: De Titanic-palindroompriemgetallen gevonden door Samuel Yates: deze bevatten minimum 1000 cijfers. Samuel Yates zei dat dit een zeer lage grens is en later bleek waarom. Doordat men nu verder kon rekenen met machines werd de onderverdeling Gigantische palindroompriemgetallen gemaakt: dit zijn palindroompriemgetallen met ten minste 10 000 cijfers. De Megapalindroonpriemgetallen: deze bevatten ten minste 1 000 000 getallen en er waren er in 2003 slechts 4 gekend. Een pandigitaal palindroompriemgetal: bijvoorbeeld 1023456987896543201 Als we het getal in 2 verdelen in het midden en links en rechts het midden meetellen dan hebben we elk getal 1 keer. Een zeer bijzondere eigenschap van de palindroompriemgetallen is dat ze allen oneven zijn buiten 11 want moest men een palindroomgetal vinden dat even is dan is dit misschien wel palindroom maar zeker niet priem. Nog een palindroompriemgetaleigenschap is de palindroompriempiramide: Hier begin je met een priemgetal bij de volgende rij plak je aan beide kanten deze

Sjogren Syndrome Support Group Plan

Sjogren Syndrome Support Group Plan Punit Dave TABLE OF CONTENT (JUMP TO) INTRODUCTION Overview Challenges PROPOSED PLAN Leverage Points Effectiveness Success Metrics Future Planning Schedule Staff Budget CONCLUSION REFERENCES INTRODUCTION OVERVIEW In partnership with University of Houston Medicine and Technology department and American Association of Rheumatologist we are the only national nonprofit support group to provide education, awareness, regular checkup, and research for Sjogren syndrome. In autoimmune disease the immune system attack and destroys the monsieur producing glans throughout the person’s body. Sjogren is the second most common autoimmune disease in United States; which effecting estimated 5 million people in United State. The Sjogren is three times more common than related disease like, Lupus, Multiple sclerosis and it is more common among women then breast cancer. The nine out of the ten Sjogren patients are women. The Sjogren syndrome patients suffer from verity of symptoms that range from dry eye and dry mouth to chronic fatigue and muscling joint pain. This disease also effect internal organs and internal nerve systems. In anticipation of people become familiar with disease and its symptoms; it w ill remain difficult to diagnose everyone who suffering from Sjogren syndrome. That’s why our community continues to fight for patients who aren’t able to explain their diseases or confused by the many facets of the diseases. Our community dedicated to raising awareness, so some day the patient diagnoses with Sjogren then he or she will have heard of it and will know where to turn for support and guidance. CHALLENGES With Sjogren the correct diagnosed is often difficult to obtain. It will take around 4.7 years to correctly diagnose the Sjogren, because the Sjogren’s symptoms often mimic other condition and diseases. Sjogren is often overlooked or misdiagnosed. Patients will discuss dry eye with optometrist, dry mouth with their dentist or joint pain with their primary doctors. Each symptom alone wouldn’t suggest an autoimmune disease but couple symptoms together will lead physicians to suspect Sjogren. This is why increasing awareness among the general public is very important. We strongly recommend Sjogren’s patients get treatment form one doctor. Changing the doctors won’t cure Sjogren but it often creates confusions among the doctors and patients. Getting treatment from multiple doctors’ also lead to wrong medications, diagnostic and it will hurt patients financially and medically. With a help from university of Houston medicine department and AAR we provide many medical checkup, medical guideline and nutrition plans to our members so, they always get right advice and treatments. PROPOSED PLAN LEVERAGE POINTS Sjogren Syndrome support Group is the leading advocate for Sjogren’s patients. We have dynamic volunteers, medical, scientific advisory board and researchers who work in Sjogren’s and recognized nationwide. Together with this volunteers and healthcare professionals, our group has been able to implement programs such as the first ever clinical practice guidelines for Sjogren’s. This guideline gives Sjogren’s physicians a road map for how to treat, monitor and manage sjogren in their patients. This is just one example of our support group on how we achieving our mission and changing the life of sjogren patients. EFFECTIVENESS Sjogren Syndrome Support Group stands on our founding principal of putting the patients first. From our 10 plus patients run support groups to our hundreds technical volunteers we serve our members with an ability to connect with others who have Sjogren’s. Our programs of educations always involve our volunteers to help review our educational materials, conference topics and Sjogren’s content. Our research grants from our sponsors are also awarded based on innovations. It we will help us to change the field of Sjogren’s the fastest to estimate the greatest gain for sjogren patients. I believe our group is effective because of patient voice is never forgotten. SUCCESS METRICS What are the metrics of success for our group? The Sjogren Syndrome Support Group measures the impact and success by many variables. For example our support group manages over 50 support groups in Houston area. Prints many newsletters and distribute hundreds of brochures each year. The American association of rheumatologist distributes important guidelines to each patient and provides the advice to join our support group. It will give patients an opportunity to share their thoughts with others and help others to overcome from this situation. Most importantly our support group always uses metrics to gage the success of every campaign, every program and every project. We set goals, we set objectives and then we evaluate them against the simple questions of how do these impacts on life of Sjogren’s patients. FUTURE PLANNING Additional support from CCHP would help us expand our education and awareness programs. This support would enable us to attended more professional conferences to educate healthcare professionals. Additional reassures would also allowed our support group to distribute materials to more specialist which would ultimately assist us to reaching patients who may be suffering from particular symptoms, but didn’t realize the cause could be a systemic diseases such as Sjogren. Finally, for support the patient and cure of Sjogren, more funding needed that way our support group can produce national awareness campaign and reach the 3million penitents there are not yet diagnosed. SCHEDULE (May 10 2014 – August 30 2014) STAFF We excited about future of Sjogren and we really around pace for great discoveries, but in order to make Sjogren a household name we need everyone’s support and help for more awareness, raise funds and volunteers. We have hundreds of volunteers and volunteers board of directors to help and support our group. Along with that we have healthcare professionals from Medical and Scientific Advisory Board (MSAB) and American Association of Rheumatologist (AAR) to stands for the wide range of specialties involved in Sjogren’s diagnose treatment and research. BUDGET CONCLUSION It is a proud moment for us that, we are premier organization in Sjogren research and support group funding. However more funding is needed as more talented researchers are taking interest in Sjogren. Our support group’s goal is to finding an additional funding to support these groundbreaking projects. Without increase support from research we cannot fund this projects and thus thing must be turn away. Our hope is one day all Sjogrens research and support group adequately funded so patients can have the answers for their disease. Being a Sjogren’s patient is challenging, but neither having a therapy to treat your disease nor understating what causing it is heartbreaking. REFERENCES Autoimmune Disease Coordinating Committee. (n.d.).. Retrieved April 25, 2014, from http://autoimmune.pathology.jhmi.edu/adrp.pdf American Collage of Rheumatology. (n.d.).. Retrieved April 30, 2014, from http://www.rheumatology.org/ Grant Writing. (n.d.).Sample Budget and Narrative -. Retrieved May 1, 2014, from http://www.netplaces.com/grant-writing/developing-a-budget-and-budget-narrative/sample-budget-and-narrative.htm Sjà ¶grens Syndrome Foundation Scientific Initiatives. (n.d.).Sjà ¶grens Syndrome Foundation Scientific Initiatives. Retrieved April 28, 2014, from http://www.Sjogrens.org/home/research-programs/scientific-initiatives Sjogrens syndrome. (n.d.).Definition. Retrieved May 1, 2014, from http://www.mayoclinic.org/diseases-conditions/Sjogrens-syndrome/basics/definition/con-20020275 When an Autoimmune Disorder Forces You to Alter Your Life Plans Autoimmune Disorders Center Everyday Health. (n.d.).EverydayHealth.com. Retrieved April 28, 2014, from http://www.everydayhealth.com/autoimmune-disorders/when-an-autoimmune-disorder-alters-your-life-plans.aspx

GOA Essay -- Ecoturism, Konkan

GOA Goa is also known internationally in various names like: "Rome of the East", "Tourist Paradise" and "Pearl of the Orient" the state of Goa is located on the western coast of India in the coastal belt known as Konkan. Goa has a unique history, natural beauty and rich culture that have attracted tourists from around the world, over the past. Churches, museums, old streets and homes, beaches, and wildlife are the main tourist attractions of this place. (Goa tourism, 2011) Goa is the smallest state in India by area and population. Most of Goa is a part of the coastal country known as the Konkan, which is an escarpment rising up to the Western Ghats range of mountains, which separate it from the Deccan Plateau, and has 103 kilometres of coastline. The nearness to Arabian Sea and being a tropical zone, Goa has a hot and humid climate for most of the year. The vast green expanse of the Sahyadri mountain range ensures that Goa has an abundance of water. The sea and rivers abound in seafood - prawns, mackerels, sardines, crabs and lobsters are the most popular with the locals and the visitors. Along with English which is widely spoken all over Goa, Konkani and Marathi are the other recognized languages. Goan cuisine is a blend of different influences the Goans had to endure during the centuries. The staple food in Goa is fish and rice, both among the Hindus and the Catholics. The long period of Portuguese rule has strongly influenced the Goan cuisine. (Goa tourism, 2008) Traces of former Portuguese domination can be seen throughout when travelling through Goa; this creates an exotic ambience. Beaches, which are Goa’s greatest assets are illuminated with high mast lights allowing the tourist to roam around, even in the nights, safel... ...h wood furnishing and tiled floors inside. Guests get the chance to enjoy nature walks, bonfires, folk dances, and village excursions. This resort also rated as one of the beast eco resort of India by MSN Green (MSN, 2010). The Nature Conservation Facility has established at Chorla Ghats to help researchers and ecologist who monitoring and studying about the Western Ghats. They organize range of programs like making aware to the others about the importance of conservation and also support activities related to conservation of natural and cultural heritage, the Nature Conservation Facility is also being recognized as a hub of activity for volunteers and students who train here under researchers of international repute and carry forward the torch of nature conservation. Now the nature conservation facility is in the process of documenting about the local community.

Phonics and Whole language methods Essay -- essays papers

Phonics and Whole language methods Phonics is a technique that teaches beginning readers to associate a particular sound with each letter of the alphabet or letter combination (Unger, 1996). Students receive explicit instruction in the mechanics of reading before they begin the actual process. Once students know what sounds correspond with each letter or letter combination, they move on to sounding out words. The English language has only about forty-four sounds, so when students begin to read, they move along in strict order so that he or she only sees words whose letter sounds they have already learned (Flesch, 1983). An example from Rudolf Flesch‘s book Why Johnny Still Can‘t Read is that students would have learned the sounds of n, d, m, p, short a, and short I before trying to read the sentence: â€Å"Ann and Dan pin up the map,† (1983). Students continue learning to read in such a way, using basal (beginning) readers. The sentences get progressively harder as students learn more letter and letter combination sounds. Phonics instruction also emphasizes the memorization of rules that help the student sound out words. Some of these rules include that of the â€Å"silent e† and double vowels. The â€Å"silent e† rule is used in words such as like, make, and use. In each of these words, the e does not make a sound, but it makes the preceding vowel â€Å"say its name.† In other words, the vowel preceding the e is long. The double vowel rule includes such letter combinations as oa, ai, ea, and ee. These pairs make the sound of the first letter (Wilber, 2002). Some students are taught a short poem to help them remember this rule: â€Å"When two vowels go walking, the first one does the talking.† Other rules that phonics instructors teach... ...ics and whole language, dean says. Retrieved October 9, 2002, from Purdue University News Website: http://www.purdue.edu/UNS/html4ever/9804.Haring.literacy.html Moats, L. C. (2000, October). The illusion of balanced reading instruction. Retrieved November 17, 2002, from the Thomas B. Fordham Foundation website: http://www.edexcellence.net/library/wholelang/moats.html Reading/literacy. (2002). Retrieved November 19, 2002, from the Education Commission of the States web site: http://www.ecs.org/html/issue.asp?issueid=97 Schlafly, P. (1996, July). Phonics vs. whole language. The Phyllis Schlafly Report, 29(12). Retrieved on October 9, 2002, from http://www.eagleforum.org/psr/1996/july96/psrjul96.html Wilber, P. M. (2002, April). Phonics vs. whole language. Teach a child to read. Retrieved on October 23, 2002, from http://www.succeedtoread.com/phonics.html Phonics and Whole language methods Essay -- essays papers Phonics and Whole language methods Phonics is a technique that teaches beginning readers to associate a particular sound with each letter of the alphabet or letter combination (Unger, 1996). Students receive explicit instruction in the mechanics of reading before they begin the actual process. Once students know what sounds correspond with each letter or letter combination, they move on to sounding out words. The English language has only about forty-four sounds, so when students begin to read, they move along in strict order so that he or she only sees words whose letter sounds they have already learned (Flesch, 1983). An example from Rudolf Flesch‘s book Why Johnny Still Can‘t Read is that students would have learned the sounds of n, d, m, p, short a, and short I before trying to read the sentence: â€Å"Ann and Dan pin up the map,† (1983). Students continue learning to read in such a way, using basal (beginning) readers. The sentences get progressively harder as students learn more letter and letter combination sounds. Phonics instruction also emphasizes the memorization of rules that help the student sound out words. Some of these rules include that of the â€Å"silent e† and double vowels. The â€Å"silent e† rule is used in words such as like, make, and use. In each of these words, the e does not make a sound, but it makes the preceding vowel â€Å"say its name.† In other words, the vowel preceding the e is long. The double vowel rule includes such letter combinations as oa, ai, ea, and ee. These pairs make the sound of the first letter (Wilber, 2002). Some students are taught a short poem to help them remember this rule: â€Å"When two vowels go walking, the first one does the talking.† Other rules that phonics instructors teach... ...ics and whole language, dean says. Retrieved October 9, 2002, from Purdue University News Website: http://www.purdue.edu/UNS/html4ever/9804.Haring.literacy.html Moats, L. C. (2000, October). The illusion of balanced reading instruction. Retrieved November 17, 2002, from the Thomas B. Fordham Foundation website: http://www.edexcellence.net/library/wholelang/moats.html Reading/literacy. (2002). Retrieved November 19, 2002, from the Education Commission of the States web site: http://www.ecs.org/html/issue.asp?issueid=97 Schlafly, P. (1996, July). Phonics vs. whole language. The Phyllis Schlafly Report, 29(12). Retrieved on October 9, 2002, from http://www.eagleforum.org/psr/1996/july96/psrjul96.html Wilber, P. M. (2002, April). Phonics vs. whole language. Teach a child to read. Retrieved on October 23, 2002, from http://www.succeedtoread.com/phonics.html