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

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

Polycystic ovary syndrome and its impact on women’s quality of life: More than just an endocrine disorder

In the past, polycystic ovary syndrome has been looked at primarily as an endocrine disorder. Studies now show that polycystic ovary syndrome is a metabolic, hormonal, and psychosocial disorder that impacts a patient’s quality of life. It is extremely important to holistically treat these patients early on to help them deal with the emotional stress that is often overlooked with polycystic ovary syndrome. Early diagnosis and long term management can help control polycystic ovary syndrome so that women can still live a healthy active life and avoid long-term complications such as metabolic syndrome and cardiovascular diseases

Preparation and study of the Structural, Morphological and Optical properties of pure Tin Oxide Nanoparticle doped with Cu

             في هذه الدراسة، تم تصنيع جزيئاتSnO2  النانويه النقيه والمشوبة بالنحاس بواسطة طريقه الترسيب الكيميائي . تم استخدام SnCl2.2H2O , CuCl2.2H2O  كمواد خام . تم تلدين المواد عند°C 550 لمدة 3ساعات من اجل تحسين التبلور. اظهرت نتائج حيود الاشعه السينية ان العينات تبلورت في طورمن نوع  رباعي الروتيل , SnO2  نظرا ان متوسط الحجم البلوري لSnO2 النقي 9 نانومتر ويختلف مع تغير منشطات النحاس (0.5%, 1%, 1.5%, 2%, 2.5%, 3%) , ، ( 8.35 ,8.36 ,8.67 , 9,7 ,8.86) نانومتر على التوالي والتركيب البلوريSnO2  لا يتغير مع ادخال النحاس , أكدت نتائج SEM للنقاوة والمخدر أن حجم الجسيمات يقع في نطاق (25-56) نانومتر داخل الحجم النانوي .كانت دراسات UV-ViS  حيث كشف التحليل الطيفي للانعكاس ان طاقه فجوة النطاق تزداد مع زيادة نسب المنشطات (4.18,4.33 ,4.21 , 4.21 4.35,4.23 ) الكترون فولت للنقي والمشوب بالنحاس ( (0.5%, 1%, 1.5%, 2%, 2.5%, 3%) على توالي . واظهرت نتائج AFM معدل الخشونة، SPMوحجم الحبوب للعينات النقيه والمشوبة وان معدل الخشونة نانومتر و (3.04, 25,27,16,41.8,23.6,25.2) ومعدل القطر (98.9, 72.56,92.91, 88.38, 76.79, 70.94, 71.21) نانومتر للنقي والمشوب على التوالي.                   In this study, pure SnO2 Nanoparticles doped with Cu were synthesized by a chemical precipitation method. Using SnCl2.2H2O, CuCl2.2H2O as raw materials, the materials were annealed at 550°C for 3 hours in order to improve crystallization. The XRD results showed that the samples crystallized in the tetragonal rutile type SnO2 stage. As the average SnO2 crystal size is pure 9nm and varies with the change of Cu doping (0.5%, 1%, 1.5%, 2%, 2.5%, 3%),( 8.35, 8.36, 8.67, 9 ,7, 8.86)nm respectively an increase in crystal size to 2.5% decreases at this rate and that the crystal of SnO2 does not change with the introduction of Cu, and SEM results of the pure and doped confirmed that the particle size is within the range (25-56)nm within the nanosize. UV-Vis studies of reflection spectroscopy revealed that energy of band gap increased with increasing doping ratios (4.33,4.18 ,4.21, 4.21 4.23,4.35) ev For pure and doped with Cu (0.5%, 1%, 1.5%, 2%, 2.5%, 3%) respectively. Results of AFM show roughness rate, SPM and grain size of pure samples doped with Cu where the roughness rate of SnO2 is (3.04, 25,27,16,41.8,23.6,25.2) nm and average diameter is (98.9, 72.56 ,92.91, 88.38, 76.79, 70.94, 71.21) nm for pure and doped with Copper (0.5%, 1%, 1.5%, 2%, 2.5%, 3%) respectively

Properties of Flow through and over Gravel Basket Weir

يؤدي إنشاء هدارات من سلال الحصى في المجاري المائية إلى تراكم المياه أمام هذه المشأت المسامية، ويكون فيها منسوب المياه أقل من تلك التي تتجمع مقدمة الهدارات الصلبة. تتضمن هذه الدراسة، تقديرعمق الماء المتجمع امام هذه الهدارات مع قياس شكل السطح الحر للجريان والتنبؤ بقيمة معامل التصريف من خلال التجارب المختبرية. كما تمت دراسة أربعة أطوال مختلفة من الهدارات (15 ، 20 ، 25 و 30 سم) وأربع خشونات مختلفة من الحصى (1.13 ، 1.58 ، 2.19 و 2.27). وفقًا لذلك، فقد تم اختبارستة عشر نموذجاً في ظروف مختلفة من التدفق الحر. أظهرتحليل نتائج نظام الجريان "التدفق النافذ" أن الزيادة في عرض السد تسبب في زيادة عمق الماء المتجمع امام الهدارات ولجميع درجات الخشونة بنسبة 30٪ بينما تقلل الخشونة من العمق بنسبة 28٪. وفي "التدفق الانتقالي"، يؤدي مضاعفة الطول إلى زيادة عمق التدفق بنسبة 7٪، بينما تؤدي زيادة الخشونة من 1.13 إلى 2.72 سم في انخفاض عمق الجريان بنسبة 7٪. يبدأ نظام "التدفق الفائض" بالظهورعندما تساوي نسبة عمق الماء إلى عرض السد حوالي 0.75 للعرض الكبير و1.54 للعرض القليل. تشير المقارنة بين هدارات سلال الحصى والهدارات الصلبة إلى أن متوسط تقليل عمق الماء هو 7.5٪ للصلابة البالغة 1.13 سم و9٪  للصلابة البالغة 2.72 سم. تم اقتراح نماذج رياضية للتنبؤ بعمق المياه لأنظمة التدفق الثلاثة، أما بالنسبة لنظام "التدفق الفائض"، فقد اقتُرِحَت صيغة تجريبية لتقدير معامل التصريف بدقة مقبولة.Construction of gravel basket weir in waterways causes water accumulation in front of this porous structure less than solid weir. In the present study the upstream flow depth, water surface profile and discharge coefficient are investigated through laboratory experiments. Four different weir lengths (15, 20, 25 and 30 cm) and four different degrees of gravel coarseness (1.13, 1.58, 2.19 and 2.27) are studied. Accordingly, sixteen models are tested under different free flow conditions. Analysis of the results show that in "through flow" regime the increase in weir length raises the generated upstream depth for all coarseness degrees by 30% while coarseness lowers the depth by 28%. In "transition flow", however, doubling the length increases the flow depth by 7%, but increasing coarseness from 1.13 to 2.72 cm mean diameter causes 7% reduction in flow depth. The "overflow" regime begins to appear when the depth to length ratio equals 0.75 for long weir, and about 1.54 for shortest weir. A comparison between gravel basket weir and corresponding solid weir indicates that average depth reduction is 7.5% for coarseness of 1.13 cm and 9% for coarseness of 2.72 cm. Mathematical models for water depth prediction for the three flow regimes are presented. For "overflow" an empirical formula is proposed to estimate the coefficient of discharge with acceptable accuracy