Continuity argument revisited: geometry of root clustering via symmetric products

We study the spaces of polynomials stratified into the sets of polynomial with fixed number of roots inside certain semialgebraic region $\Omega$, on its border, and at the complement to its closure. Presented approach is a generalisation, unification and development of several classical approaches to stability problems in control theory: root clustering ($D$-stability) developed by R.E. Kalman, B.R. Barmish, S. Gutman et al., $D$-decomposition(Yu.I. Neimark, B.T. Polyak, E.N. Gryazina) and universal parameter space method(A. Fam, J. Meditch, J.Ackermann). Our approach is based on the interpretation of correspondence between roots and coefficients of a polynomial as a symmetric product morphism. We describe the topology of strata up to homotopy equivalence and, for many important cases, up to homeomorphism. Adjacencies between strata are also described. Moreover, we provide an explanation for the special position of classical stability problems: Hurwitz stability, Schur stability, hyperbolicity.Comment: 45 pages, 4 figure

Understanding the Implications of a Global Village

Whether the world is shrinking, expanding, or remaining the same metaphorical size, it is clear that how we communicate across physical and cultural boundaries is changing at an accelerated rate. With these changes comes a responsibility, as humans, to consider the implications of our shifting realities. Without an objective and inclusive analysis of these issues, we will be unprepared for the rollercoaster of cultural mayhem that could inevitably ensue. If we are in fact becoming a global village, we will be able to reach some sort of consensus as a global village about how these issues should be addressed in order to benefit all members of our village equally

Gentian violet for pyoderma gangrenosum: a retrospective chart review

Pyoderma gangrenosum is a rare autoinflammatory skin disease. Treatment is multifactorial, addressing inflammation, pain, underlying disease, if present, and the wound. Gentian violet has been used for hundreds of years in a variety of dermatologic conditions for its anti-inflammatory properties. This study aims to evaluate gentian violet in wound healing for pyoderma gangrenosum. We conducted a retrospective chart review of patients with pyoderma gangrenosum treated with gentian violet at the Wake Forest School of Medicine Department of Dermatology in the last 10 years. The primary outcome was clinical improvement. Of the 34 cases that met inclusion criteria, 70% improved with gentian violet, 24% had no documented change, 3% initially improved then worsened, and 3% had unclear results. Gentian violet is a safe and cheap treatment that may improve resolution of pyoderma gangrenosum lesions in addition to systemic therapy

An Examination Of Accounting Majors\u27 Ethical Decisions Before And After An Ethics Course Requirement

The increased focus on ethical decision making in the accounting profession has resulted in greater attention being paid to the education of future accountants. Texas is one of the states that requires a State Board approved university course in Accounting Ethics to be on the transcript of prospective CPA candidates. This study reports on research using senior/graduate level accounting majors at a Texas state university before the university course requirement and after the requirement. The survey presented four vignettes for the students to consider (i.e., 2 describe an ethical decision and 2 describe an unethical decision). Students were requested to indicate (1) how ethical/unethical they believed the actions described were and (2) the probability that they would take the same action as the actor. The results of the analysis indicate no significant differences in the responses of the students whenever the vignette describes a situation in which the accountant makes an ethical decision. However, significant differences were indicated in both decisions whenever the students were dealing with a vignette describing an accountant making an unethical decision

When Management Override Negates Common Sense

Write OK per big boss across the invoice and everything is fine! Or is it? This paper analyzes the human factor link related to the Debra Valice Case. The human factor is the weakest link of any internal control system. Understanding the human factors that cause people to not follow the rules, is key to strengthening this link. This research will utilize the human factors adapted from the Independence Education Program to analyze the DebraValice Case. Valice was responsible for ensuring a secure internal control system. The Chief Executive Officer was able to manipulate this system and unauthorized payments were made to him or on his behalf. Valices lack of good judgment allowed this to happen. The human factors allowing this breach were professional character, business culture and environment, the ability to recognize there is an issue and the quality of the decision-making process as outlined by the Independence Education Program

Efficient magneto-optical trapping of Yb atoms with a violet laser diode

We report the first efficient trapping of rare-earth Yb atoms with a high-power violet laser diode (LD). An injection-locked violet LD with a 25 mW frequency-stabilized output was used for the magneto-optical trapping (MOT) of fermionic as well as bosonic Yb isotopes. A typical number of $4\times 10^6$ atoms for $^{174}$Yb with a trap density of $\sim 1\times10^8/$cm$^3$ was obtained. A 10 mW violet external-cavity LD (ECLD) was used for the one-dimensional (1D) slowing of an effusive Yb atomic beam without a Zeeman slower resulting in a 35-fold increase in the number of trapped atoms. The overall characteristics of our compact violet MOT, e.g., the loss time of 1 s, the loading time of 400 ms, and the cloud temperature of 0.7 mK, are comparable to those in previously reported violet Yb MOTs, yet with a greatly reduced cost and complexity of the experiment.Comment: 5 pages, 3 figures, 1 table, Phys. Rev. A (to be published

About the barotropic compressible quantum Navier-Stokes equations

In this paper we consider the barotropic compressible quantum Navier-Stokes equations with a linear density dependent viscosity and its limit when the scaled Planck constant vanish. Following recent works on degenerate compressible Navier-Stokes equations, we prove the global existence of weak solutions by the use of a singular pressure close to vacuum. With such singular pressure, we can use the standard definition of global weak solutions which also allows to justify the limit when the scaled Planck constant denoted by $\epsilon$ tends to 0