Quotient graphs for power graphs

In a previous paper of the first author a procedure was developed for counting the components of a graph through the knowledge of the components of its quotient graphs. We apply here that procedure to the proper power graph $\mathcal{P}_0(G)$ of a finite group $G$, finding a formula for the number $c(\mathcal{P}_0(G))$ of its components which is particularly illuminative when $G\leq S_n$ is a fusion controlled permutation group. We make use of the proper quotient power graph $\widetilde{\mathcal{P}}_0(G)$, the proper order graph $\mathcal{O}_0(G)$ and the proper type graph $\mathcal{T}_0(G)$. We show that all those graphs are quotient of $\mathcal{P}_0(G)$ and demonstrate a strong link between them dealing with $G=S_n$. We find simultaneously $c(\mathcal{P}_0(S_n))$ as well as the number of components of $\widetilde{\mathcal{P}}_0(S_n)$, $\mathcal{O}_0(S_n)$ and $\mathcal{T}_0(S_n)$

A wave-envelope of sound propagation in nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. The solution recovers the solution based on the method of multiple scales for slowly varying duct geometry. A computer program was developed based on the wave-envelope analysis for general mean flows. Results are presented for the reflection and transmission coefficients as well as the acoustic pressure distributions for a number of conditions: both straight and variable area ducts with and without liners and mean flows from very low to high subsonic speeds are considered

Transmission of sound through nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined, circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. Although the theory is described for circular ducts, it is applicable to other duct configurations - annular, two dimensional, and rectangular. The theory is described for the linear problem, but the technique is general and has the advantage of being applicable to the nonlinear case as well as the linear case. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave. A computer program was developed. The mean flow model consists of a one dimensional flow in the core and a quarter-sine profile in the boundary layer. Results are presented for the reflection and transmission coefficients in ducts with varying slopes and carrying different mean flows

A mechanical, thermal and electrical packaging design for a prototype power management and control system for the 30 cm mercury ion thruster

A prototype electric power management and thruster control system for a 30 cm ion thruster is described. The system meets all of the requirements necessary to operate a thruster in a fully automatic mode. Power input to the system can vary over a full two to one dynamic range (200 to 400 V) for the solar array or other power source. The power management and control system is designed to protect the thruster, the flight system and itself from arcs and is fully compatible with standard spacecraft electronics. The system is easily integrated into flight systems which can operate over a thermal environment ranging from 0.3 to 5 AU. The complete power management and control system measures 45.7 cm (18 in.) x 15.2 cm (6 in.) x 114.8 cm (45.2 in.) and weighs 36.2 kg (79.7 lb). At full power the overall efficiency of the system is estimated to be 87.4 percent. Three systems are currently being built and a full schedule of environmental and electrical testing is planned

Chronic intestinal inflammation: Inflammatory bowel disease and colitis-associated colon cancer

The inflammatory bowel diseases (IBD), including Crohn’s disease (CD) and ulcerative colitis (UC), are chronic inflammatory disorders of the intestine. The prevalence in the United States is greater than 200 cases per 100,000, with the total number of IBD patients between 1 and 1.5 million. CD may affect all parts of the gastrointestinal tract, from mouth to anus, but most commonly involves the distal part of the small intestine or ileum, and colon. UC results in colonic inflammation that can affect the rectum only, or can progress proximally to involve part of or the entire colon. Clinical symptoms include diarrhea, abdominal pain, gastrointestinal bleeding, and weight loss. A serious long-term complication of chronic inflammation is the development of colorectal cancer. A genetic basis for IBD had long been recognized based on the increased familial risk. However, significant discordance for CD in twins, and a much less robust phenotypic concordance for UC, suggested additional factors play a role in disease pathogenesis, including environmental factors. In the past several years, progress in understanding the molecular basis of IBD has accelerated, beginning with the generation of animal models of colitis and progressing to the identification of specific genetic markers from candidate gene, gene linkage, and genome-wide association analyses. Genetic studies have also resulted in the recognition of the importance of environmental factors, particularly the crucial role of the gut microbiota in CD and UC. Altered immune responses to the normal intestinal flora are key factors in IBD pathogenesis. In this research topic, the genetic basis of IBD, the genetic and cellular alterations associated with colitis-associated colon cancer, and the emerging role of the intestinal microbiota and other environmental factors will be reviewed

Free-vibration characteristics and correlation of a space station split-blanket solar array

Two methods for studying the free-vibration characteristics of a large split-blanket solar array in a zero-g cantilevered configuration are presented. The zero-g configuration corrresponds to an on-orbit configuration of the Space Station solar array. The first method applies the equations of continuum mechanics to determine the natural frequencies of the array; the second uses the finite element method program, MSC/NASTRAN. The stiffness matrix from the NASTRAN solution was found to be erroneously grounded. The results from the two methods are compared. It is concluded that the grounding does not seriously compromise the solution to the elastic modes of the solar array. However, the correct rigid body modes need to be included to obtain the correct dynamic model

Pharmacogenomics in cardiovascular disorders: Steps in approaching personalized medicine in cardiovascular medicine

Christopher Barone, Shaymaa S Mousa, Shaker A MousaThe Pharmaceutical Research Institute, Albany College of Pharmacy and Health Sciences, Albany, NY, USAAbstract: Some of the most commonly prescribed medications are those for cardiovascular maladies. The beneficial effects of these medications have been well documented. However, there can be substantial variation in response to these medications among patients, which may be due to genetic variation. For this reason pharmacogenomic studies are emerging across all aspects of cardiovascular medicine. The goal of pharmacogenomics is to tailor treatment to an individual’s genetic makeup in order to improve the benefit-to-risk ratio. This review examines the potential pharmacogenomic parameters which may lead to a future of personalized medicine. For example, it has been found that patients with CYP2C9 and VKORC1 gene variations have a different response to warfarin. Other studies looking at β-blockers, ACE inhibitors, ARBs, diuretics and statins have shown some results linking genetic variations to pharmacologic response. However these studies have not impacted clinical use yet, unlike warfarin findings, as the small retrospective studies need to be followed up by larger prospective studies for definitive results.Keywords: cardiovascular, pharmacogenomics, genetics, cardiovascular medicine, personalized medicine, polymorphis

HILLE-KNESER-TYPE CRITERIA FOR SECOND-ORDER DYNAMIC EQUATIONS ON TIME SCALES

We consider the pair of second-order dynamic equations, (r(t)(xΔ)γ)Δ + p(t)xγ(t) = 0 and (r(t)(xΔ)γ)Δ + p(t)xγσ (t) = 0, on a time scale T, where γ \u3e 0 is a quotient of odd positive integers. We establish some necessary and sufficient conditions for nonoscillation of Hille-Kneser type. Our results in the special case when T = R involve the well known Hille-Kneser-type criteria of second-order linear differential equations established by Hille. For the case of the second-order half-linear differential equation, our results extend and improve some earlier results of Li and Yeh and are related to some work of Dosly and Rehak and some results of Rehak for half-linear equations on time scales. Several examples are considered to illustrate the main results