The Gini index in the representation theory of the general linear group

The Gini index is a function that attempts to measure the amount of inequality in the distribution of a finite resource throughout a population. It is commonly used in economics as a measure of inequality of income or wealth. We define a discrete Gini index on the set of integer partitions with at most $n$ parts and show how this function emerges in the representation theory of the complex general linear group.Comment: 13 pages, 4 figure

Finite element convection models: comparison of shallow and deep mantle convection, and temperatures in the mantle

A Finite Element Method for solving the convection problem in a fluid with position-dependent Newtonian viscosity is developed, using bicubic and biquadratic spline functions on a rectangular grid. Introducing weak (less viscous) zones at the active margins of the lithosphere, dynamical mantle convection models are established which have a nearly uniform surface (plate) velocity and a satisfactory heat flux profile. A comparison of upper and deep mantle convection shows:— a moderate increase of viscosity with depth cannot confine the flow to the upper mantle;— in shallow depth convection models the temperature is too low inside the cell, but deep mantle convection models yield satisfactory temperatures for the upper mantle.For that reason deep (or whole) mantle convection should be the favored hypothesis.           ARK: https://n2t.net/ark:/88439/y025744 Permalink: https://geophysicsjournal.com/article/202 &nbsp

Realizing an Opportunity: Limiting the Power of the Executive in the Iraqi Constitution

In the summer of 2015, Iraqi citizens took to the streets in protest. After going without essential services, such as electricity, in the sweltering heat and after enduring corruption that undermined Iraqi forces battling the Islamic State, these citizens called for meaningful changes in the management of the Iraqi government and for the fulfillment of “democratic aspirations” enshrined in the Iraqi Constitution. In response to these protests, Iraqi Prime Minister, Haider al-Abadi, proposed sweeping reform measures to combat the decisive divides in the current administration. These reforms called for drastic change—including the elimination of the vice-president and deputy prime minister positions, the removal of a large percentage of cabinet members, and the cessation of sectarian and party quotas for state positions. After his reform package received unanimous approval from the Iraqi Parliament and from the Grand Ayatollah, Ali Al-Sistani, Abadi took immediate action to remove the vice presidents and deputy prime ministers from office. However, after the current vice-presidents brought challenges to the reforms, the Supreme Court of Iraq ruled that the removal of these positions was unconstitutional. The Parliament, therefore, withdrew its support for the package and accused Abadi of overstepping his authority. Outside the government, the Islamic State still controls large swaths of land, including, for the time being, twenty-five percent of the city of Ramadi—the provincial capital of Anbar, and Iraqi forces have only been able to claim back roughly six percent of government territory in the pastyear. Moreover, there is evidence that the Kurdish Government may be taking advantage of the war with the Islamic State to grab land and disputed oil resources, refueling the “long-running land dispute that has pitted Iraqi Kurdistan against the central government in Baghdad.” Additionally, Iraq is still facing an outbreak of cholera that has infected over 2,000 people. These internal and external factors paint an unattractive picture of the situation in Iraq, but combined, they might indicate a window of opportunity. After examining the current state of affairs in Iraq, this paper argues that there is a potential opening for constitutional reform. I contend that this potential opportunity should be taken advantage of with specific and narrowly tailored amendments to the Iraqi Constitution that limit the power of the executive branch. In Part One, I will provide a broad overview of the situation in Iraq, including the attitudes of government officials, the desires and needs of Iraqi citizens, and the significant internal and external factors pressing on top decision makers, culminating in a potential opportunity for constitutional reform. I argue that the internal and external factors—such as the severe security threat from the Islamic State, the economic crises, and recent actions taken by the Prime Minister—can be figuratively plotted out as exogenous shocks rising to a peak today whereby the opportunity for constitutional reform is potentially ripe. In Part Two, I will discuss the possible adjustments to the Constitution that could be introduced. I incorporate commentary from leading academics in this arena on why changes to the executive should be pushed. In short, this paper should be seen as a snapshot on the present situation in Iraq and as a brief source that can be used for further, more extensive, research on the current prospect of constitutional reform

An Optical-Fiber Based Sensor Array for the Simultaneous Analysis of Zinc and Copper in Aqueous Environments

Copper and zinc are elements commonly used in industrial applications, with many of these processes using these elements in aqueous environments. Before the solutions can be discharged into civil or native waterways, waste treatment processes must be undertaken to ensure compliance with federal, state and local guidelines restricting the concentration of ions discharged in solution. While there are methods of analysis currently available to monitor these solutions, each method has disadvantages, be it that they are cost prohibitive, inaccurate, and/or time-consuming. In this work, a new optical fiber-based platform capable of providing fast and accurate results when performing solution analysis for these metals is described. Using fluorescent compounds that exhibit a high sensitivity and selectivity for either zinc or copper have been employed for fabricating the sensors. These sensors demonstrated sub-part-per-million detection limits, 30-second response times, and the ability to analyze samples with an average error of under 10%. The inclusion of a fluorescent compound acting as a reference material to compensate for fluctuations from pulsed excitation sources has further increased the reliability and accuracy of each sensor. Finally, after developing sensors capable of monitoring zinc and copper individually, these sensors can be combined to form a single optical fiber sensor array capable of simultaneously monitoring concentration changes in zinc and copper in aqueous environments

Test of a Multidisciplinary Health Behavior Model of Medicare Elders\u27 Antihypertensive Acquisitions

This study examined the relative utility of the enhanced Health Belief Model as compared to the proposed Pharmaceutical Acquisition Model for Medicare Elders (PAMME) in describing antihypertensive acquisition with usage intentions for Medicare elders (65 years or older) in Southeastern Virginia. Data collection included record reviews to identify hypertensive Medicare elders. Consenting Medicare elders were randomly selected for invitation, with consenting Medicare elders contacted by telephone or in-person interviews. The survey instrument utilized open and closed ended questions. The target population for this study is Southeastern Virginia Medicare elders enrolled in a Part D plan and prescribed at least one antihypertensive. This study employed a quasi-experimental, retrospective, mixed methods design. Acombination of primary and secondary data was obtained through telephone, face-to-face interviews and administrative record review. This study retrospectively examined antihypertensive acquisition experiences of Southeastern Virginia\u27s Medicare elders, to explore how the Medicare Modernization Act of 2003 affected out-of-pocket costs and antihypertensive acquisitions. Analyses employed aggregate-based information to test the research hypotheses. Statistical analysis was conducted with SPSS Version 16. The majority (94 percent) of Medicare elders were able to legally acquire their antihypertensives. When comparing the enhanced Health Belief Model (HBM) with the Pharmaceutical Acquisition Model for Medicare Elderly (PAMME) the HBM has 95.5 while 96.2 indicating slightly increased prediction with the added constructs of Medication Adherence and Consumer Choice Theory. This study confirms other research findings regarding Medicare elders\u27 beliefs about generics with the majority (71.6 percent) who believe that the generic works just as well as the name brand. The complexity of antihypertensive acquisition decisions and beliefs about hypertension continue to provide a challenge for researchers. While this study has furthered our understanding of what factors influence legal antihypertensive acquisitions, much research remains to be conducted to fully comprehend the multidimensional constructs of hypertension and antihypertensives

Literal Imagery in Music: A Thesis to Accompany Constellation Suite

The relationship between music and its sources of inspiration probably has been debated for as long as people have created instrumental music. Baroque tone painting is a documented early correlation of musical theme to subject. Subsequent musical imagery and mood creation for the later programmatic music could be an outgrowth from this Baroque practice. Composers used several approaches to create each music-to-subject connection. One compositional device was using music that had become a cliché for its most common use to evoke a reference to that setting. Another device created music that “sounds like” its meaning—musical onomatopoeia—instrumental mimicry of extra-musical sounds. Stories are suggested by the mood of the music; sometimes the only connection between music and subject is a theme that evokes the mood. Musical moods that change with the story can produce musical forms. Pictorial literal imagery may be found by study of the score with imagination. One can find correlation between the contours of notation passages and shapes in a visual representation of the subject. Pictorial correlation can be found in shapes created by paths of movement. Size and spatial relationships can be described by corresponding motifs and harmonies. Constellation Suite is a symphony in four movements that uses all of the aforementioned pre-compositional constructs and subject relationships. The symphony\u27s four movements derive titles and thematic material from the star groupings Andromeda, Crux, Pleiades, and Orion. Superimposing a star chart on a staff created a primary motif in each movement, and Greek legends star-related stories inspired their moods, order of themes, and shapes. However, the symphony uses traditional or almost traditional forms—a modified sonata, an extended modified rondo, a modified da capo form, and an arch form. The movements also capitalize on interrelated thematic material that creates a cyclical effect. Because of these techniques, Constellation Suite would not require any non-musical interpretations or stories to be musically valid. This thesis will demonstrate that, regardless of this symphony\u27s tone poems\u27 intended meanings, it joins the work of other composers who have turned stories and literal imagery into music

The Gini Index in Algebraic Combinatorics and Representation Theory

The Gini index is a number that attempts to measure how equitably a resource is distributed throughout a population, and is commonly used in economics as a measurement of inequality of wealth or income. The Gini index is often defined as the area between the Lorenz curve of a distribution and the line of equality, normalized to be between zero and one. In this fashion, we will define a Gini index on the set of integer partitions and prove some combinatorial results related to it; culminating in the proof of an identity for the expected value of the Gini index. These results comprise the principle contributions of the author. We will then discuss symmetric polynomials, and show that the Gini index can be understood as the degrees of certain Kostka-foulkes polynomials. This identification yields a generalization whereby we may define a Gini index on the irreducible representations of a finite group generated by reflections, or a connected reductive linear algebraic group

Synthesis of 3-Vinylthiophene as a Precursor for Use in Solar-Cell Applications

The goal of our proposed research is to develop a high-yielding single-step synthesis from 4-bromotrifluoromethylbenzene. A relatively low cost, high yielding synthetic route to 4-trifluoromethylstyrene is desired in this experiment. The palladium catalyzed coupling of 4-bromotrifluoromethylbenzene with vinyltrimethoxysilane is the synthetic method used. Synthetic precursors to 4-pentafluorosulfurylstyrene are quite expensive, therefore developing a high yielding single step route using cheaper precursors and catalysts are desirable. The main goal is to attempt and develop a successful single step synthetic route to 4-bromotrifluroromethylbenzene using these less expensive trifluoromethyl group precursors. The first steps of the project turned out to be successful, with high yields of the ligands, and then obtaining high yields of the precursor. The last experiment involved a 100% yield of 4-bromotrifluoromethylbenzene after several failed attempts