Are there an infinite number of twin prime pairs?

Field: Number Theory

We call a pair of prime numbers that have a difference of two “twin primes”.

Examples of twin primes include

(3, 5), (5, 7), (11, 13), (17, 19), .  . .                                                                                                            (2)

Are there an infinite number of twin prime pairs?

Writing this out in a mathy way. Define the set of twin primes to be

T = {(p, p + 2)|p, p + 2 are prime}.                                                                                                        (3)

Is |T | infinite?

For this problem I would like you to write

1. A background section detailing in simple terms the field and necessary information to understand your results
2. A results section detailing in simple terms the prior proofs/experiments performed in the past
3. A summary section detailing potential consequences of a proof of this problem, and how it could impact a sector of computer science

These sections do not need to be long, as they are just so that I can sufficiently understand the following section. I do not have a minimum required length, however note that if you have each of these sections as one single sentence such that it appears you have only a surface level understanding on the material, I will grade accordingly.  These three sections will be worth 50% of your final exam grade, and will be graded on how well you describe the material to me, as well as how well I believe you understand the material.

Next, I ask that you take the results and document the process of you “playing” with the results. Most research is gained through insight into other’s cut- ting edge research, and through new perspectives that the original researchers did not consider. Playing with the results can be, but are not limited to, any of the following

• Expanding on the results of a paper (better error bounds, considering different cases, )
• Applying new research to a problem
• Using your class knowledge to look at a problem in a new way
• Applying techniques from another field to a problem

Numerically computing large amounts of examples will not be good enough this semester. For example if you are working on Twin Primes you cannot ust calculate the first 100 twin primes.

This section will be also 50% of your final exam grade, and will consist of how well you articulate your thought process while attempting to expand on the results of the paper. You can get negative results (ie the stuff you came up with failed / is uninteresting) but so long as I can tell you made a clear attempt to attack the problem in a way you found interesting, and legitimately tried, I will consider that sufficient.

How have the different cultural groups shaped historical developments in your country?

• Women and abortion in Colombia

-1500 words about 6 pages.

1. Introduction/Thesis ( a good argument)
2. Issue/Topics about women and abortion in colombia
3. Background (Where is your country located? How has geography affected the people who live in the area? What are the predominant cultural groups in your country? What language(s) do they speak? What religion(s) do they follow? Are there any major conflicts or tensions within or among the major populations? How has geography shaped and impacted culture in the region? How have the different cultural groups shaped historical developments in your country? )
4. Analysis/Conclusion
5. 8 sources

Outline some of the advantages and disadvantages of your selected company using the cloud.

Improving Data Governance (80 points).

Corporations are increasingly moving their data to the cloud. Select an organization, national or international, that has used or should consider using cloud technology. Then, address the following requirements:

• Explain details (e.g., mission, vision, values, industry) about the organization that you selected.
• Outline some of the advantages and disadvantages of your selected company using the cloud.
• Explain industry practices. Do other organizations in your selected organization’s industry use the cloud? Why or why not?
• What are some of the factors that must be considered before any organization uses the cloud?

Your well-written report should be 4-5 pages in length, not including the title and reference pages. To make it easier to read and therefore grade, make sure you clearly delineate each section of your answer so it can be matched with the relevant question. Use APA style guidelines, citing at least four references in support of your work, in addition to your text and assigned readings. Review the grading rubric to see how you will be graded for this assignment.

Use assay form introduction which has a thesis, body and conclusion

Discuss how Ca2+ affects each of the body systems below

16. **EXTRA CREDIT** Several electrolytes have significant roles and/or effects in the body and have functions in multiple organ systems. One example of an electrolyte that has important roles and/or effects in every organ system within our bodies is Ca²⁺. Discuss how Ca²⁺ affects each of the body systems below:
    1. Nervous system
    2. Muscular system
    3. Skeletal system
    4. Hematological system
    5. Cardiovascular system
    6. Immune system
    7. Respiratory system
    8. Gastrointestinal system
    9. Urinary system
    10. Reproductive system
    11. Integumentary system
    12. Endocrine system
    13. Lymphatic system

How does chronic alcoholism impact the cardiovascular system?

15 [28 POINTS + 8 POINTS BONUS]

5. A 38yo caucasian male presents to the ER after a 2 week bender of heavy alcohol consumption. He admits to drinking 5 handles of whiskey in the past 2 days. He claims that he has started to vomit up blood and has lost 15 pounds in the last 2 weeks due to not having an appetite. He eats mainly Ho-Hos and Twinkies. He is experiencing epigastric abdominal pain and has significant melena. He also has ataxic gait, poor muscle coordination, and significant confusion. His skin and sclera have a yellow hue, he has moderate hepatomegaly, pitting edema in his legs, and significant abdominal ascites.
   1. The patient is significantly dehydrated. Explain the physiological reason for this based on his history of heavy alcohol consumption. Alcohol specifically causes profound diuresis because causes what condition of the endocrine system? Which hormone is affected? Explain your answer. [4 POINTS]

1. Describe effects of chronic alcoholism on the GI system. What are THREE conditions that this patient needs to be evaluated for based on his history? Support your answers with supporting items from patient’s history. [6 POINTS]

1. The patient’s lab values are shown below. Interpret his lab values and vitals. Which values are high, low, and normal. For each result that is not within normal range, explain why it is high or low in this patient. [12 POINTS]

• BP: 105/69 mmHg, HR: 118 bpm, Temperature: 38.9 °C
• O₂ saturation: 92% on room air, Respirations: 8 breaths/min and shallow

1. Is there an acid-base disorder present? If so, what is the disturbance? Show your work and explain your answer clearly (HINT: use the step-wise method that I demonstrated during class for determining an acid-base disorder). Is there compensation? Explain? What is the likely cause of the acid-base disturbance, if present? Explain your answer. [6 POINTS]

1. **EXTRA CREDIT** Describe the nutritional deficiencies that chronic alcoholism has caused in this patient. Why is he displaying ataxic gait, lack of coordination, and confusion? What vitamin or mineral deficiency would these symptoms likely result from? What is this condition called? What other nutritional deficiencies would this patient be at increased risk for? Why? [5 POINTS]

1. **EXTRA CREDIT** How does chronic alcoholism impact the cardiovascular system? What type of cardiomyopathy is likely to be caused by chronic alcoholism? Explain your answer. [3 POINTS]

Describe the differences between alpha-1, alpha-2, beta-1, and beta-2 adrenergic receptors.

Describe the differences between alpha-1, alpha-2, beta-1, and beta-2 adrenergic receptors. What are the effects of stimulation of each type of receptor? Describe why certain beta-blockers, beta-agonists, alpha-blockers, and alpha-agonists are specifically chosen as a treatment for patients. For example: certain medications are not used in a patient with asthma or COPD when trying to treat heart failure and hypertension. Explain why this is the case. Be concise but specific in your responses . [8 POINTS]

Describe how failure of the heart to pump efficiently will impact the respiratory, urinary, cardiovascular, as well as endocrine systems?

1. In left-sided systolic congestive heart failure, the heart fails to contract sufficiently enough to pump blood throughout the body. Describe how failure of the heart to pump efficiently will impact the respiratory, urinary, cardiovascular, as well as endocrine systems? I want you to think about how everything fits together physiologically. [12 POINTS]

Do these results signify an obstructive process or a restrictive process? How do you know?

Theodore (“Teddy”) is sitting in his athletic training suite feeling sorry for himself.  He moved from Southern California to play soccer at Michigan State University (MSU) as a highly recruited player.  All was well until he got sick with a miserable cold.  He soon recovered, but now he finds himself with a lingering dry cough and difficulty catching his breath any time he exerts himself.  He also notices it has gotten worse as the weather has become colder. To make things worse, Teddy feels, and looks, like he’s out of shape, so his coach has been criticizing him for “dogging it.”

A few days later, Teddy relays his story to Al, the head athletic trainer at MSU.  “I’m thinking my cold is coming back, or something else is wrong with me. When I’m just hanging out, like now, I feel fine. But as soon as I start to run, I get winded and can’t stop coughing.”  Al listens to Teddy’s breathing sounds with his stethoscope but hears nothing abnormal. He tells Teddy to come back as soon as the symptoms return during soccer practice.  Twenty minutes later, Teddy is back in the athletic training suite, audibly wheezing, coughing, and short of breath.  The team physician, Dr. Gibson, happens to be there and performs a complete physical exam.  He also does pulmonary function tests with Teddy using spirometry, including a forced vital capacity (FVC) and forced expiratory volume in one second (FEV1).  He instructs Teddy to take a maximal inhalation and then exhale as forcefully and maximally as possible into the spirometer.

Based on his findings, Dr. Gibson tells Teddy he thinks he is experiencing cold-induced bronchoconstriction, or cold-induced asthma, which is made worse by exertion. The doctor explains to Teddy that his recent upper respiratory infection probably inflamed his airways, making them hypersensitive and reactive to irritants, such as cold and physical exertion.  When Teddy exercises in the cold, autumn afternoons of Michigan, his sensitive airways temporarily bronchoconstrict, causing the symptoms he is experiencing.  Dr. Gibson prescribes two puffs of an albuterol inhaler, to be used 10 minutes before a bout of exercise in the cold.

1. When Teddy is experiencing an asthmatic attack, his forced vital capacity (FVC) is 53% of normal, and his FEV₁ (Forced expiratory volume in 1 second) is 45% of normal. Explain these test results and what they represent in Teddy’s case. Do these results signify an obstructive process or a restrictive process? How do you know?. [4 POINTS]

2. Spirometry testing is routinely performed on patients with lung disease. Describe how the various lung volumes and respiratory capacities would be predicted to change (from normal) in a patient with a restrictive lung process (i.e pulmonary fibrosis) as well as a patient with an obstructive lung process (i.e asthma or COPD). Using the pathophysiology underlying restrictive and obstructive lung diseases, explain why you predicted each volume and/or capacity to increase, decrease, or stay the same in each type of lung disease. [16 points]

Describe the three processes involved in urine formation.

Part 4: Questions 10-11 [38 POINTS]

5. Describe the three processes involved in urine formation. Be detailed about each process, where each process occurs, and the role each process plays in overall urine formation. [6 POINTS]

6. 1. Describe BOTH the anatomy AND physiology of the nephron (i.e discuss all five (5) main parts of the nephron/collecting system). Be specific. [10 POINTS]

1. Describe how the two limbs of the loop of Henle differ in function and permeability (i.e ascending vs. descending limbs). Be specific. Explain how this contributes to urine formation. [4 POINTS]

1. What is meant by “renal multiplier” and “renal countercurrent” exchanger?” Be specific about what each one represents. [4 POINTS]

1. Discuss TWO major hormones involved in urine formation. Describe the effects of each hormone, the portion of nephron/collection system that each acts, and how both are regulated. [6 POINTS]

1. Discuss the Renin-angiotensin-aldosterone system (R-A-A-S). How does this pathway work and how are the various body systems that we learned about this semester (i.e endocrine, cardiovascular, respiratory, GI, and urinary) involved in this pathway? [8 POINTS]

How would each of these abnormalities affect his cardiac function? Explain.

One evening during a recent trip to Indonesia, Dr. Fugu Spork sat down to a meal of puffer fish and rice, also called “Fugu.” Because Dr, Spork and this dish share a name, he couldn’t resist ordering it. Within an hour of returning to his hotel room, Dr. Spork felt numbness in his lips and tongue, which quickly spread to his face and neck. Before he could call the front desk, he began to feel pains in his stomach, throat, and mouth. He then developed feelings of severe nausea and eventually severe vomiting. The vomit was positive for blood as well.

Fearing that he had eaten some “bad fish” for dinner, Dr. Spork called the local hospital to describe his condition.  The numbness in his lips and face made it almost impossible to communicate, but the ER nurse was able to get part of the address written down and an ambulance was dispatched. As Dr. Fugu Spork was rushed to the ER, his breathing became increasingly labored and he was showing signs that he could not protect his airway.

Part 2 – Numb, sweaty, and short of Breath…not love at first bite

Upon presenting to the ER, he was diaphoretic, exhibited significant motor dysfunction, paresthesias, nausea, an ascending paralysis starting in his legs and spreading to upper body, arms, face, and head. He also had problems with his breathing and was cyanotic and hypoventilating. Within 30 minutes of presenting in the ER, Dr. Spork developed bradycardia with hypotension. Atropine was administered in response to the bradycardia. Intravenous hydration, gastric lavage, and activated charcoal followed a presumptive diagnosis of tetrodotoxin poisoning. Five hours after treatment, the following vital signs were noted:

• BP: 125/79 mmHg with HR: 78 bpm
• Oxygen saturation: 97% with Respiration rate: 12 on ventilator in ICU

After discussing Dr. Spork’s case with his physician, you learned that he had probably been the victim of pufferfish poisoning. Normal lab values are listed below.

Questions

5. Interpret Dr. Spork’s ABG findings. What is the presenting acid-base disturbance? Is there any compensation? Do these lab findings make sense in light of the clinical picture in the Emergency Department? [5 POINTS]

6. Describe the relevance of an elevated Na⁺ level in this patient. What does the serum sodium tell you about his water balance within the body? Explain your answer. [4 POINTS]

7. It is noted that the patient has an elevated K⁺ level as well as a low Ca²⁺ level in his blood. How would each of these abnormalities affect his cardiac function? Explain. [4 POINTS]

8. How would the endocrine system respond to low Ca²⁺ levels in the blood? What hormone would be secreted and how would that hormone raise blood Ca²⁺ levels? Be specific. [4 POINTS]

9. Explain how tetrodotoxin causes this patient’s hypotension and hypoventilation. [4 POINTS]