Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras

It is known that a generalized $q$-Schur algebra may be constructed as a quotient of a quantized enveloping algebra \UU or its modified form \dot{\UU}. On the other hand, we show here that both \UU and \dot{\UU} may be constructed within an inverse limit of a certain inverse system of generalized $q$-Schur algebras. Working within the inverse limit \hat{\UU} clarifies the relation between \dot{\UU} and \UU. This inverse limit is a $q$-analogue of the linear dual $R[G]^*$ of the coordinate algebra of a corresponding linear algebraic group $G$.Comment: 18 pages; to appear in J. Algebr

Caught in the Middle: Empowerment in Middle Managers

Citation: Doty, N. (2017) Caught in the Middle: Empowerment in Middle Managers. Unpublished manuscript, Kansas State University, Manhattan, KS.Kirmser Undergraduate Research Award - Individual Non-Freshman Category, grand prizePrevious studies on the topic of middle management focus on how these specific managers drive the organizations they are a part of, how they motivate their subordinates to work effectively and efficiently, how middle managers create excitement, and how their leadership style helps their followers find purpose in their work. And yet, little is done to flesh out how these strong MMs are created, what motivates them, and how they succeed in their position (Kominis & Emmanuel, 2007). These MMs are the “basis of strategic renewal” in bettering an ever-changing organizational environment and, conversely, can even “sabotage implementation efforts” in the changing strategy of the workplace (Mantere, 2008, p. 294). This paper aims to discover what factors influence the empowerment of middle managers for the purpose of better understanding and development of MMs in organizational and workplace structures. Motivation is the influence on a person’s “direction, vigor and persistence of action” (Rajhans, 2012, p. 82). The current literature on the subjects of management, motivation, and work performance focus on the topics of role expectations, and empowerment, and are typically viewed through the theoretical lenses of structural empowerment and psychological empowerment, which are outlined below

Dimension Extractors and Optimal Decompression

A *dimension extractor* is an algorithm designed to increase the effective dimension -- i.e., the amount of computational randomness -- of an infinite binary sequence, in order to turn a "partially random" sequence into a "more random" sequence. Extractors are exhibited for various effective dimensions, including constructive, computable, space-bounded, time-bounded, and finite-state dimension. Using similar techniques, the Kucera-Gacs theorem is examined from the perspective of decompression, by showing that every infinite sequence S is Turing reducible to a Martin-Loef random sequence R such that the asymptotic number of bits of R needed to compute n bits of S, divided by n, is precisely the constructive dimension of S, which is shown to be the optimal ratio of query bits to computed bits achievable with Turing reductions. The extractors and decompressors that are developed lead directly to new characterizations of some effective dimensions in terms of optimal decompression by Turing reductions.Comment: This report was combined with a different conference paper "Every Sequence is Decompressible from a Random One" (cs.IT/0511074, at http://dx.doi.org/10.1007/11780342_17), and both titles were changed, with the conference paper incorporated as section 5 of this new combined paper. The combined paper was accepted to the journal Theory of Computing Systems, as part of a special issue of invited papers from the second conference on Computability in Europe, 200

A System Appallingly out of Balance : Morgan v. State and the Rights of Defendants and Victims in Sexual Assault Prosecutions

In a series of three cases that culminate with Morgan v. State, Alaska\u27s courts established a unique protection for defendants in sexual assault cases. This protection, which allows such defendants to attack their victims in court with previous reports of sexual assault that did not result in prosecution, is not afforded to defendants in other cases and is based on a dubious general principle that the credibility of sexual assault victims has special relevance. The protection is problematic in several ways: it is grounded in erroneous stereotypes about the victims of sex crimes; it is detrimental to victims and the pursuit of truth; it is inconsistent with traditional rules of evidence; and it is unnecessary to protect the rights of defendants. For these reasons, this protection for defendants in sexual assault cases should be abrogated by legislative action as proposed herein

Effects of microgravity on rat bone, cartlage and connective tissues

The response to hypogravity by the skeletal system was originally thought to be the result of a reduction in weight bearing. Thus a reduced rate of new bone formation in the weight-bearing bones was accepted, when found, as an obvious result of hypogravity. However, data on non-weight-bearing tissues have begun to show that other physiological changes can be expected to occur to animals during spaceflight. This overview of the Cosmos 1887 data discusses these results as they pertain to individual bones or tissues because the response seems to depend on the architecture and metabolism of each tissue under study. Various effects were seen in different tissues from the rats flown on Cosmos 1887. The femur showed a reduced bone mineral content but only in the central region of the diaphysis. This same region in the tibia showed changes in the vascularity of bone as well as some osteocytic cell death. The humerus demonstrated reduced morphometric characteristics plus a decrease in mechanical stiffness. Bone mineral crystals did not mature normally as a result of flight, suggesting a defect in the matrix mineralization process. Note that these changes relate directly to the matrix portion of the bone or some function of bone which slowly responds to changes in the environment. However, most cellular functions of bone are rapid responders. The stimulation of osteoblast precursor cells, the osteoblast function in collagen synthesis, a change in the proliferation rate of cells in the epiphyseal growth plate, the synthesis and secretion of osteocalcin, and the movement of water into or out of tissues, are all processes which respond to environmental change. These rapidly responding events produced results from Cosmos 1887 which were frequently quite different from previous space flight data