Mathematics

Fatigue is a universally shared experience and a significant component of rheumatologic diseases. The fact that rheumatologic patients experience fatigue that negatively affects their quality of life has been well documented. What is less clearly understood are the multifactorial physical and emotional mechanisms that contribute to this fatigue and, as a result, limit effective treatment strategies, which to date still remain mostly empiric. Fatigue is often rated by patients with rheumatologic disease as one of the key factors leading to decreased quality of life. Fatigue is poorly correlated with the severity of disease. Despite the omnipresence of and the stress caused by fatigue, it is surprising how infrequently it is addressed by both patients and physicians. Rheumatologic patients often believe that fatigue is an expected part of the disease process or a side effect of medications. Physicians, however, either dismiss the fatigue as functional in origin or focus more on joint and muscle involvement or abnormal laboratory values. DEFINITION There are many definitions of fatigue offered in the medical literature. However, for the purpose of discussing rheumatologic disease, a more global, biopsychosocial orientation is applied. As quoted in the Physiologic Basis of Rehabilitation Medicine, 1 Dill offered the following definition: ''The various unmistakably disagreeable sensations commonly referred to the word fatigue are in fact the accompaniment of a great variety of physiologic conditions, which have in common only this, that the physiologic equilibrium of the body is breaking down.'' A distinction should also be made between

Molecular recognition sites on cell membranes serve as the main communication channels between the inside of a cell and its surroundings. Upon receptor binding, celular messages such as ion channel opening or activation of enzymes are triggered. In this report, we demonstrate that artificial cell membranes made from conjugated lipid polymers (poly(diacetylene)) can, on a simple level, mimic membrane processes of molecular recognition and signal transduction. The ganglioside GM1 was incorporated into poly(diacetylene) liposomes. Molecular recognition of cholera toxin at the interface of the liposome resulted in a change of the membrane color due to conformational changes in the conjugated (ene-yne) polymer backbone. The "colored liposomes" might be used as simple colorimetric sensors for drug screening or as new tools to study membrane-membrane or membrane-receptor interactions.

We examine some numerical iterative methods for computing the eigenvalues and eigenvectors of real matrices. The five methods examined here range from the simple power iteration method to the more complicated QR iteration method. The derivations, procedure, and advantages of each method are briefly discussed.

A beta expansion is the analogue of the base 10 representation of a real number, where the base may be a non-integer. Although the greedy beta expansion of 1 using a non-integer base is in general infinitely long and non-repeating, it is known that if the base is a Pisot number, then this expansion will always be finite or periodic. Some work has been done to learn more about these expansions, but in general these expansions were not explicitly known. In this paper, we present a complete list of the greedy beta expansions of 1 where the base is any regular Pisot number less than 2, revealing a variety of remarkable patterns. We also answer a conjecture of Boyd's regarding cyclotomic co-factors for greedy expansions.

Telecommunication companies, such as Internet and cellular service providers, are seeing rapid and uncertain growth of traffic routed through their networks. It has become a challenge for these companies to make optimal decisions for equipment purchase that simultaneously satisfy the uncertain future demand while minimizing investment cost.

Telecommunication companies, such as Internet and cellular service providers, are seeing rapid and uncertain growth of traffic routed through their networks. It has become a challenge for these companies to make optimal decisions for equipment purchase that simultaneously satisfy the uncertain future demand while minimizing investment cost. This paper

This study investigates and quantifies the impact of financial inclusion and digital payments on income and individual government tax revenues for countries around the world.  Of the almost two billion people in the world that are financially excluded, the World Bank and other stakeholders have committed to helping one billion people gain access to financial services and become involved in the formal economy by 2020.  This rapid pace of financial inclusion will bring vast amounts of income and tax revenues into the global economy that is important to understand as it creates different opportunities and challenges for developing and advanced countries that they will need to prepare for.

    Using various global datasets, a methodology was developed to forecast financial inclusion rates, digital payments rates, average income, and other factors up to the year 2020. The results suggest a sharp increase in financial inclusion rates and digital payment rates which translate to hundreds of millions of people entering the formal economy. Details of the most affected countries by dollar value, percent change, and the regional affects are provided for various indicators throughout the study.  With regards to capturing the most tax revenue, China and the United States gain the most in dollar terms while Turkmenistan gains the most in percentage terms. Between 2014 and 2020, a cumulative $12 trillion of income is projected to enter the formal economy worldwide resulting in $4.1 trillion in tax revenue.  Governments around the globe could take advantage of this significant opportunity.

Through its history German-speaking world has gone through many upheavals that shaped it into todays known Germany, Austria and Switzerland. Three major reformations happened in 15th century, 1920 and
1961 and were motivated respectively by Martin Luther, Nazi party, and Soviet Union.

This is the story of how efforts to solve a centuries-old problem originating
with Euclid led a Russian mathematician to discover a new geometry. You will learn about Nikolai Lobachevsky's life in 19th century Russia and what led him to the discovery of new Geometry. In addition, we will delve into the principles of Non-Euclidean Geometry. This paper is oriented for general public and does not require any particular mathematical background except knowledge of high school geometry.

SUMMARY: Research report evaluating the hazards/disasters-related work of an NGO Length: 3000 – 3500 words 1 ½ spaced 12 font (excluding maps, figures, tables and bibliography). This assignment requires you to form a small " team " (2-3 members) which will evaluate the work of an NGO (" non-governmental organization ") dealing with hazards and disasters. Such work may include: humanitarian responses (e.g. immediate disaster relief such as rescue/emergency housing/food/ water or longer-term reconstruction), disaster risk reduction, hazard awareness, community-based disaster management, disaster vulnerability reduction, disaster preparedness, disaster policy & advocacy, etc. Include in your paper: