Fractals and the Cantor Set :: Fractal Cantor Essays

Fractals and the Cantor Set Fractals are remarkable designs noted for their infinite self-similarity. This means that small parts of the fractal contain all of the information of the entire fractal, no matter how small the viewing window on the fractal is. This contrasts for example, with most functions, which tend to look like straight lines when examined closely. The Cantor Set is an intriguing example of a fractal. The Cantor set is formed by removing the middle third of a line segment. Then the middle third of the new line segments are removed. This is repeated an infinite number of times. In the end, we are left with a set of scattered points. These points have some very curious properties. First, there are an infinite number of them. In fact, there are so many points that no matter what list we create or what rule we apply, not all of the points will appear, even if our list is infinite. In other words, the set belongs to aleph-one. This is demonstrated through diagonalization. Here’s how—first one endpoint of the original line segment is labeled zero. The other endpoint becomes one. All the points in between are assigned fractional values. We can calculate more easily if we assign the values in tertiary, the base-three system. Unlike the common decimal system, the natural numbers are labeled 1, 2, 10, 11, 12, 20, 21, 22, 100, and so forth. Notice that the places of the digits represent the powers of three rather than the powers of ten. The â€Å"decimal places† represent 1/3, 1/9, 1/27, and so forth. The first removal takes out all points between .1 and .2. The second removal takes out all points between .01 and .02 as well as the values from .21 and .22. By continuing these specifications, all numbers that contain a â€Å"1† are removed, (except numbers ending in a one, such as .220021) and number containing merely twos and zeros are kept. The numbers ending in 1 are re-written by replacing the final 1 with 02222222222222†¦. because this is equal to 1 in tertiary. Suppose that we could somehow count all Cantor Set elements in one list. Then we could write out that list in order, one above the other. However, if we took the first decimal of the

Penn Foster English Essay

I. Introduction 1. Albert Einstein said, â€Å"Learning is not a product of schooling but the lifelong attempt to acquire it. † 2. Penn Foster is one route that helps motivated independent learners acquire the knowledge and certification they need. 3. Students' lives may change due to the decision to further their education. 4. I plan to use the following method balance work, family, and Penn Foster. II. Step 1: Figure Out What Really Matters in Life 1. Spending introspective time thinking about my life is the first step to achieving a balanced life. 2. I use an exercise for figuring out what matters most,† Laura Berman Fortgang (a personal coach) tells WebMD. She has her clients take a couple days off from work to contemplate the following series of questions: 1. If my life could focus on one thing and one thing only, what would that be? 2. If I could add a second thing, what would that be? † and so on. (WebMD) 3. After the list is compiled, then the plan is to de partmentalize my life. 4. When I'm at home with the family, I will focus and concern myself with them. 5. However, when I'm working on Penn Foster, I will only be thinking about learning and completing assignments. . This will help me to spend quality time in the areas that are most important. III. Step 2: Figure Out â€Å"Musts† vs â€Å"Shoulds† 1. The next step will be to figure out the difference between â€Å"Musts† vs â€Å"Shoulds. † 2. â€Å"We always manage to find time for those things that we decide we must do and its the things we think we should do that get left by the way side. † (Caroline) 3. To do this, I need to take my list from Step 1 and decide which activities on the list must I do. 4. Then, I need to take activities that I would like to do and put them in the should category. 5. While I do this, I need to be careful not to put too many commitments into the must column. 6. The reason is to not overwhelm myself and over commit my time. 7. Some of my musts will be family, work, and Penn Foster. 8. Right now, everything else in my life I consider a â€Å"should† until school is finished. IV. Step 3: Take Daily â€Å"Time-Outs† 1. The last step to ensure that I can balance my life is to take daily â€Å"time-outs. † 2. â€Å"Take a nap, a walk, or a mini-meditation break with a few minutes of silence. Maintain daily rituals, such as teatime, meditation, prayer, exercise. †(Womensnet) 3. By doing this, I can adapt myself to my new hectic schedule. 4. I will be able to maintain my energy throughout the day. 5. Keeping daily â€Å"time-outs† will ensure that I keep my sanity and they will give me something to look forward to throughout the day. V. Conclusion 1. Maintaining a balance between work, life, and Penn Foster can be accomplished using these three steps. 2. The first step is to figure out what really matters in life. 3. Then, I will create a must and should list. 4. After that, I will ensure I take â€Å"time-outs† to give myself a routine to look forward to during my day. . By doing these three steps, I can balance it all. Works Cited â€Å"Easy Steps to Work-Life Balance | Grants For Women in Business | Loans and Credit for Women Business Owners | Grants For Small Business. † Grants For Women in Business | Loans and Credit for Women Business Owners | Grants For Small Business. 24 Mar. 2009 . discover, you may. â€Å"5 Tips for Better Wor k-Life Balance. † WebMD – Better information. Better health.. 24 Mar. 2009 . way, the, and I wouldn&. â€Å"How to Find the Right Work-Life Balance: 6 Steps | Caroline Middlebrook. † Caroline Middlebrook. 24 Mar. 2009 .

Biopure Case Study Essay

Oxyglobin and Hemopure are two blood substitutes that Biopure Corporation was developing. Oxyglobin was recently approved by the FDA for veterinary use while Hemapure is estimated to be approved in two years for human use. If Oxyglobin is launched it will be the first blood substitute for the veterinary market a small and price sensitive market. There is a perceived risk by Ted Jacobs, the VP of Human Clinical Trials at Biopure, that if Oxuglobin, the vet product, is launched before Hemopure and at the low price of $150/unit, that it will become very challenging to sell Hemopure once launched at $800/unit. B. Market Analysis a)Human 14 million units of RBCs were donated in the United States in 1995, 12. 9 Million from volunteer donors and 1. 1 million from autologous donors (donate to self, few weeks prior to surgery). 50% of the blood supplies are handled by the American Red Cross. Of the 14 million units donated 2. 7 million are discarded due to expiration or contamination, 3. 2 million transfused into anemia patients and the remaining 8. 1 million transfused into surgery and trauma patients. Blood Collection is a struggle as post AIDS blood contamination paying for donation of blood units is prohibited by the law; it should be done on volunteer basis. Due to low rates of donation and short shelf-life, shortage of RBC units in medical facilities in not uncommon and therefore the need for blood substitutes in the human market is high. b)Veterinary The veterinary market is smaller than the humans as in 1995 2. 5% of 800 dogs/vet GP suffering from acute blood loss were deemed critical and received transfusion, for a total of 300,000 dogs (800Ãâ€"15,000 vet GPx 0.  025), although there is a potential to cover 30% of these pets or about or 3. 6 million dogs. These veterinary GP lack adequate supply of canine blood units lack of animal blood banks. Vets rely on housed donor animals which 84% of them are dissatisfied with the current available blood transfusion alternatives. This constitutes a big opportunity for Oxyglobin. C. Competition Biopure has two competitors for the human product, Baxter and Northfield both of whom are pursuing a Hemoglobin purified from outdated RBC at unit cost ranging from $8-$26 vs. Biopure’s hemoglobin purified from cattle at unit cost of $1. 50. Both Northfield’s and Baxter’s products are expected to launch 2 years after Oxyglobin and same year as Hemopure. Oxyglobin’s only competition is the blood collected from in-house animal donors. One important difference between Hemopure/Oxyglobin and competition is that Biopure’s products do not require storage at 4 °C and can be stored at room temperature; this is a significant difference because there is no added cost attributed to refrigeration. D. Pricing Hemopure as Baxter’s Hem Assist and Northfield is expected to be priced between $600-$800/unit and I suggest that it prices at the highest range of the spectrum because it does not require refrigeration and there will be perceived savings by pharmacists and hospital managers. On the other hand Oxyglobin and because of the â€Å"doubling rule† used by the vets meaning they charge pets owners double the price of the manufacturers ask price), it is arguable and to keep the drug affordable that the price ranges from $80-$100 per unit. Others argued that the price should be set at $200/unit because of all the advantages, added business and cost savings it brings to the practice and pet owners as well. II. Problem/Decision statement Two related issues need to be addressed by the CEO. †¢Should Oxyglobin be launched before Hemopure? Although Oxyglobin was granted approval by the FDA, few challenges remain to be sorted, such as: 1. Reluctance of veterinarians to use the product instead of blood from animal donors 2. Setting the price of the product at a rate that won’t affect the future sales of Hemopure 3. Devise a good distribution strategy for the product (manufacturer direct vs. distributor) On the other hand Hemopure needs to overcome the following obstacles: 1. FDA approval 2. Price of hemoglobin vs. blood transfusion ($600 vs. $125) 3. Fierce competition from Human hemoglobin by Baxter and Northfield 4. Uptake by physicians Biopure needs to launch its first product to start generating revenue, take the company public, raise more funds to support Hemopure’s Phase 3 trial and launch. Before deciding on launching Oxyglobin ahead of Hemopure, all the challenges mentioned above need to be addressed. III. Strategies for Improvement To overcome Oxyglobin’s challenges listed above, the following criteria need to be met: 1. Target Emergency care vet practices 2. Target large Vet practices (3+) 3. Set the price at $200 (see Appendix 1 for analysis) 4. Focus Marketing efforts on non-critical dogs Biopure should start by targeting emergency care vet practices as blood transfusion are more common there, 150 transfusion/year as compared to 17 at vet GP, penetration to this market will measured by unit sold per care center and lower reliance on animal donors. To increase the market share further large vet practices with 3+ doctors as according to exhibit 7 pg 17 of the case, these practices have the highest â€Å"average monthly case load† of about 450 dogs per month, it’s imperative to measure a rapid incline in uptake of our product by these practices. Based on the analysis in Appendix 1, it is clear that setting the price at $100 is more lucrative but we have to plan for the launch of Hemopure and therefore we should consider setting the price at $200 to justify its launch at $600 to $800 in 2 years. We should monitor the sales of Oxyglobin at this price and monitor if the uptake from vets is increasing from the 5% predicted by the market analysis (table A). Finally, focusing the marketing effort on non-critical dogs is crucial as they are a sizeable market and because although veterinarians can justify using this product to critical dogs, it’s hard to justify that for non-critical dogs (pricing and efficacy should help support that). The cease of using animal donors in these clinics will show that Oxyglobin is successfully replacing this old practice. Alternatively it is important to think about the possibility of setting the price of Oxyglobin at $100 to reap as much benefit from being the first and only vet blood-substitute, in the event that Hemopure doesn’t get approval from the FDA. It’s highly probable that Hemopure won’t be successful in the clinic because it’s of cattle origin, they changed the formulation to be stable at room temperature (excipients could be toxic) and the concentrations used are much higher than their human counterparts. In this case and to mitigate this risk, lowering the price to a $100 will help the sales and uptake of the product by a larger market. The market research conducted prior to launch (Table A and B) shows that a high number of veterinarians and pet owners will use the product at the $100/$200(x2) price. Based on the calculations in Appendix 1, it is clear that setting the price at $100 is more lucrative to Biopure than pricing it at $150 or 200$ because of the double price rule which affects the uptake by both pet owners and vets. To be cognizant and not to jeopardize the future Hemopure launch, I recommend that we set the price at $200, because there is a need for a blood substitute as 84% of the vets are reporting overall dissatisfaction with the blood transfusion alternatives available in the marketplace. Secondly, Oxyglobin provides an alternative for animal blood donated by other animals which incurs the risk of matching and potential transfer of diseases. The storage at room temperature adds value as this will reduce the need to buy expensive refrigerators that need calibration, validation and maintenance. Finally, there no assurance that vets will automatically double the price of the product especially if they foresee a high demand by pet owners, a practice that we should encourage and help the vets appreciate the upside. Although blood transfusions in the veterinary market are infrequent and the market scope is limited, Oxyglobin has the potential to become a lucrative investment for Biopure. It is possible that Hemopure will not be licensed by the FDA, that humans will resist buying a product of cattle origin especially that human hemoglobins will be available around the same time by competitors and that physicians will not prescribe it for the reasons described above. To minimize these risks and to start generating revenue that will help the company grow, become public and raise more funding, I therefore recommend that we sell Oxyglobin first before the launch of Hemopure.

AntiWar Movement

The antiwar movement against Vietnam in the US from 1965-1971 was the most significant movement of its kind in the nation’s history. After evaluating different social theories such as: Functionalism, Conflict and Interactionism, I have decided to classify the Anti-War movement during the Vietnam War as a Conflict Theory. I feel the Anti-War Movement’s has characteristics of Neo-Marxism. Though the first American protests against U. S. intervention in Vietnam took place in 1963, the antiwar movement did not begin in diligence until two years later, when President Lyndon B. Johnson ordered massive U. S. military intervention and the sustained bombing of North Vietnam. Chambers) 2000. In the spring of 1965, â€Å"teach? ins† against the war were held on many college campuses. The Anti-War Movement was centered on America’s higher-education system, the students, playing leading roles. Teach-ins were extreme, massive public protests. By 1968 Protesters numbered close to seven million and over half of them were Caucasian college students. The teach-ins were primarily peaceful, but effective. They were successful in capturing the attention of the public as well as those in government. The motivation behind teach-ins were just that, with the hopes of further escalation in Vietnam to slow down or come to a halt. In April 1965, President Johnson gave a major Vietnam address at John Hopkins University, in response to the growing campus protest activity. This speech marked the political impact of campus demonstrations. (Electric Library) This is an example of Neo-Marxism. The protestors were getting a partial system change. They had the attention of the public, and most importantly the government. However, by 1967 a lot of anti-war activists began to think peaceful protests were not going to be enough to influence war policy, so they began using civil disobediences, strikes, public disruption, shouting at government speakers and guerilla theatre to get their message heard loud and clear. In March 1967, a national organization of draft resisters was formed. In April 1967, more than 300,000 people demonstrated against the war in New York. Six months later, 50,000 surrounded the Pentagon, sparking nearly 700 arrests. By this time it became typical for, senior Johnson administration officials to encounter demonstrators when speaking in public, forcing them to restrict their outside appearances. Many also had sons, daughters, or wives who opposed the war, fueling the sense of attack. Prominent participants in the antiwar movement included Dr. Benjamin Spock, Robert Lowell, Harry Belafonte, and Rev. Martin Luther King, Jr. With prominent leaders extending their support in the movement it gave the activist a great deal of motivation and validation. The social theory of Neo-Marxism was in full effect. By 1968, the Johnson administration realized the impact of widespread public opposition to the war and the troubling prospects in Vietnam, causing them to put a halt on the bombing of North Vietnam and to stabilize the ground war. This policy reversal was the major turning point. U. S. troop strength in Vietnam would climax at 543,000 (Chambers) 2000. The antiwar movement reached its peak under President Richard M. Nixon. In October 1969, more than 2 million people participated in Vietnam Moratorium protests across the country. The following month, over 500,000 demonstrated in Washington and 150,000 in San 4 Francisco. Militant protest, continued to spread, leading many Americans to wonder whether the war was worth a split society. And other forms of antiwar activity lingered on. The Nixon administration took a host of measures to dull the movement, mainly mobilizing supporters, smearing the movement, tracking it, withdrawing U. S. troops from Vietnam, instituting a draft lottery, and eventually ending draft calls. Once U. S. troops began coming home, the antiwar movement gradually declined between 1971 and 1975 (Chambers) 2000. The American movement against the Vietnam War was the most successful antiwar movement in U. S. history. The Neo-Marxism social theory is easily applied to the Anti-War Movement. The characteristics of the conflict were disorder, boycotts, intense conflict, commitment, and emotional involvement all of which resulted in system change. The activists involved in the Anti-War movement of this time were passionate and dedicated to seek change. They sought out peace and love for our Country and did not lose sight of their objective. They went to great lengths to achieve what seemed like the impossible. References http://www.encyclopedia.com/doc/1O126-VietnamAntiwarMovement.html AntiWar Movement The antiwar movement against Vietnam in the US from 1965-1971 was the most significant movement of its kind in the nation’s history. After evaluating different social theories such as: Functionalism, Conflict and Interactionism, I have decided to classify the Anti-War movement during the Vietnam War as a Conflict Theory. I feel the Anti-War Movement’s has characteristics of Neo-Marxism. Though the first American protests against U. S. intervention in Vietnam took place in 1963, the antiwar movement did not begin in diligence until two years later, when President Lyndon B. Johnson ordered massive U. S. military intervention and the sustained bombing of North Vietnam. Chambers) 2000. In the spring of 1965, â€Å"teach? ins† against the war were held on many college campuses. The Anti-War Movement was centered on America’s higher-education system, the students, playing leading roles. Teach-ins were extreme, massive public protests. By 1968 Protesters numbered close to seven million and over half of them were Caucasian college students. The teach-ins were primarily peaceful, but effective. They were successful in capturing the attention of the public as well as those in government. The motivation behind teach-ins were just that, with the hopes of further escalation in Vietnam to slow down or come to a halt. In April 1965, President Johnson gave a major Vietnam address at John Hopkins University, in response to the growing campus protest activity. This speech marked the political impact of campus demonstrations. (Electric Library) This is an example of Neo-Marxism. The protestors were getting a partial system change. They had the attention of the public, and most importantly the government. However, by 1967 a lot of anti-war activists began to think peaceful protests were not going to be enough to influence war policy, so they began using civil disobediences, strikes, public disruption, shouting at government speakers and guerilla theatre to get their message heard loud and clear. In March 1967, a national organization of draft resisters was formed. In April 1967, more than 300,000 people demonstrated against the war in New York. Six months later, 50,000 surrounded the Pentagon, sparking nearly 700 arrests. By this time it became typical for, senior Johnson administration officials to encounter demonstrators when speaking in public, forcing them to restrict their outside appearances. Many also had sons, daughters, or wives who opposed the war, fueling the sense of attack. Prominent participants in the antiwar movement included Dr. Benjamin Spock, Robert Lowell, Harry Belafonte, and Rev. Martin Luther King, Jr. With prominent leaders extending their support in the movement it gave the activist a great deal of motivation and validation. The social theory of Neo-Marxism was in full effect. By 1968, the Johnson administration realized the impact of widespread public opposition to the war and the troubling prospects in Vietnam, causing them to put a halt on the bombing of North Vietnam and to stabilize the ground war. This policy reversal was the major turning point. U. S. troop strength in Vietnam would climax at 543,000 (Chambers) 2000. The antiwar movement reached its peak under President Richard M. Nixon. In October 1969, more than 2 million people participated in Vietnam Moratorium protests across the country. The following month, over 500,000 demonstrated in Washington and 150,000 in San 4 Francisco. Militant protest, continued to spread, leading many Americans to wonder whether the war was worth a split society. And other forms of antiwar activity lingered on. The Nixon administration took a host of measures to dull the movement, mainly mobilizing supporters, smearing the movement, tracking it, withdrawing U. S. troops from Vietnam, instituting a draft lottery, and eventually ending draft calls. Once U. S. troops began coming home, the antiwar movement gradually declined between 1971 and 1975 (Chambers) 2000. The American movement against the Vietnam War was the most successful antiwar movement in U. S. history. The Neo-Marxism social theory is easily applied to the Anti-War Movement. The characteristics of the conflict were disorder, boycotts, intense conflict, commitment, and emotional involvement all of which resulted in system change. The activists involved in the Anti-War movement of this time were passionate and dedicated to seek change. They sought out peace and love for our Country and did not lose sight of their objective. They went to great lengths to achieve what seemed like the impossible. References http://www.encyclopedia.com/doc/1O126-VietnamAntiwarMovement.html

Financial Management Essay Example | Topics and Well Written Essays - 500 words - 6

Financial Management - Essay Example The company continues to be on the rise according to the FIA report of 2010. The report that was published on March 2011 reveals that contracted traded in NYSE Euronext experienced a rise of 24.6% in the FY2010 to reach 2.155 contracts (Heckman, 2009) The NYSE is the world’s largest company in terms of cash equities exchange. It has been in operation for about 215 years, and its dealings are in capital formation, whereby the company serves institutional and individual investors, the trading movement and its listed companies. By the end of 2006, over 2700 users (operating companies, exchange traded funds and closed end funds) were listed in the corporation. These listed companies represented the global market capitalization of over b$25 trillion. Ever since, the company has enhanced its reputation in cash equities exchange. As compared to the rest, Euronext is an extremely new financial entity, which was formed in 2000 (Brigham, 2009). The governance of NYSE Euronext is by a board of directors that is elected manually. A majority of these directors are independent while the rest of the team comprises of a CEO, deputy CEO, non executive chairman and deputy chairman. The markets of the company are regulated according to local requirements. When the merger was done, it was agreed that there would be no additional requirements for all the listed companies. This was to guard the company from American Law especially, the Sarbanes-Oxley Act. The Sarbanes-Oxley Act of 2002, also known as the Public Company Accounting Reform and Investor Protection Act is an enactment of 2002 is a federal law that governs corporate finance. The law was enacted after many high ranking companies including WorldCom and Enron were implicated in corporate accounting scandals. The Act brought reform into American business and enhanced criminal penalties for any company that destroys, falsifies,

Portfolio Assessment Assignment Example | Topics and Well Written Essays - 1000 words

Portfolio Assessment - Assignment Example It first involves determining the actual existent state of a company of business. External and internal audits should be carried out to clearly bring out an understanding of an organization’s actual competency and the existing competitive environment. It will then become necessary to determine the most important goals for the company (Porter 2008, p. 89). Priorities should be set at this stage and it should be ensured that the strategic plan focuses on these priorities. Objectives should then be set in order to address any priority issues that may be existent. Accountabilities should then set so that communication becomes easier and the objectives are addressed at individual levels. The plan should then be reviewed over and over again due to the dynamic nature of the market. Strategic tools are the essential and most applied business solution tools that companies apply so as to achieve sustainable competitive advantage. Innovations and new developments only become successful if the resulting products and services can sell well. These tools are instrumental in analyzing the existing market, be it a niche, so as to create opportunities for serving clients with a wide variety of products that are more competitive and adapted to a dynamic market development as compared to the other competitors. Some of these tools include Porter’s 5 forces Model, The BCG Matrix, The SWOT Matrix, and The 4 P’s of the Marketing mix, Life Cycle Analysis, Ansoff Matrix, Maslow’s Pyramid and the 7-S McKinsey method. All these strategies are aimed at analyzing different aspects and levels of existence in an organization (Simerson 2011, p. 123). As such, not all these tools are applicable to any situations, thereby their effectiveness is limited to specific si tuations. The political factors of analysis involve government controls and rules in the effort of the company to keep up with the Environmental and Corporate Social

Dominican Republic Essay Example | Topics and Well Written Essays - 1000 words

Dominican Republic - Essay Example Many local people, knowing there destiny fled fearing the Europeans and later on formed there own colonies, called the Maroon colonies. The colonizers brought in another change, they imported the black people and slavery was one of the most predominant features at that time. But all this changed because of the Haitian Liberation, this made sure that slavery was completely abolished from the country, as a result of which, the blacks having no where to go settled on in the country. This is the history of the country, which saw many a change taking place. The people of Dominican Republic are masters when it comes to indirect communication, they firmly believe in maintaining a good relationship with as many people as they possibly can. The people of the Dominican Republic consider themselves to be more Latin American than Caribbean. The situation of the country as of now is quite bad; the people are struggling to fight against the corrupt people, who are currently in power. Spanish is spoken in the country and the people are very proud of the purity of Spanish they speak in the country. The flag of the country is designed in such a manner that it shows national pride and patriotism. The flag consists of the colors red and blue which indicate the blood of the people who gave up their lives and liberty respectively. The Dominican coat of arms can be found in the centre of the flag. "A recent national symbol, constructed in 1992, is the Columbus Lighthouse. It was a work project conceived of by President Joaqun Balaguer when he was 85 ye ars old and blind. It is an enormous cross, flat on the ground, facing the sky and bursting with lights, and was built as a tourist attraction." (Every Culture, 14 August, 2008). The light house is in an area where there is utter poverty; people live in despair, without any electricity and without many more basic necessities. The light house is a very big attraction and can even be seen burning brightly from Puerto Rico. The native people are called the Tianos; Columbus was well greeted when he first arrived in the country. These Tianos were peace loving people and lived in the tropical forest. These Tianos lives in make shift homes and many families lived under the same roof. The villages were further subdivided into districts, each district had a chief, who took care if that particular district. During this time there was no slavery in the country and it was free from all other evils too. The Tianos were very good at growing crops, specially the root crops. They also dug and used it as ornaments. Columbus kept a close eye on the gold digging skills of the Tianos and thought that he had a good chance of paying his debts to the king and queen of Spain. The culture of the Tianos is not very clearly presented because nearly all the Tianos died after three decades of Columbus's visit to the country. Columbus is known the world over for his navigating skills but he failed in dominating these Tainos, inst ead of farming he made them dig in pursuit of gold. The natives died, as there were torturous condition, food was not available in plenty and the population decreased. The country also saw the invasion of the United States of America from 1916 to 1924. The dominance of the United States brought many changes, for instance during the rule many new classes of land owners emerged and the country also sa