Remarks on the tensor degree of finite groups

The present paper is a note on the tensor degree of finite groups, introduced recently in literature. This numerical invariant generalizes the commutativity degree through the notion of nonabelian tensor square. We show two inequalities, which correlate the tensor and the commutativity degree of finite groups, and, indirectly, structural properties will be discussed.Comment: 5 pages; to appear with revisions in Filoma

Incidence rate of non-Hodgkin's lymphomas among males in Saudi Arabia: an observational descriptive epidemiological analysis of data from the Saudi cancer registry, 2001-2008

Background: This study describes epidemiological data of non-Hodgkin's lymphoma (NHL) diagnosed from 2001 to 2008 among Saudi men. Materials and methods: Retrospective data from all NHL cancer cases among Saudi men recorded in the Saudi Cancer Registry (SCR) between January 2001 and December 2008 were used. Descriptive statistics, analysis of variance, Poisson regression, and simple linear regression were also used. Results: In total, 2,555 new cases of NHL were recorded between January 2001 and December 2008. The region of Riyadh, Saudi Arabia had the highest overall age-standardized incidence rate (ASIR) at 7.8, followed by the Eastern region at 6.8, and Makkah at 6.1 per 100,000 men; however, Jazan, Hail, and Baha had the lowest average ASIRs at 2.5, 3.7, and 3.9 per 100,000 men, respectively. The incidence-rate ratio for the number of NHL cases was significantly higher in Riyadh (4.68, 95 confidence interval CI 4.11-5.32), followed by Makkah (4.47, 95% CI 3.94-5.07), and the Eastern region of Saudi Arabia (3.27, 95% CI 2.90-3.69) than that in the reference region of Jazan. Jouf had the highest changes in the ASIRs of NHL among Saudi men from 2001 and 2008 (5.0 per 100,000 men). Conclusion: A significant increase in the crude incidence rate and ASIR for NHL in Saudi Arabia between 2001 and 2008 was found. Riyadh, the Eastern region, and Makkah had the highest overall ASIR in Saudi Arabia. Jazan, Hail, and Baha had the lowest rates. Additionally, Riyadh, Makkah, and the Eastern region had the highest incidence-rate ratio for the number of NHL cases. Finally, Jouf had the highest changes in crude incidence rate and ASIR from 2001 to 2008. Further analytical studies are needed to determine the potential risk factors of NHL among Saudi men. © 2014 Alghamidi et al

Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations

A shifted Jacobi Galerkin method is introduced to get a direct solution technique for solving the third- and fifth-order differential equations with constant coefficients subject to initial conditions. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. A quadrature Galerkin method is introduced for the numerical solution of these problems with variable coefficients. A new shifted Jacobi collocation method based on basis functions satisfying the initial conditions is presented for solving nonlinear initial value problems. Through several numerical examples, we evaluate the accuracy and performance of the proposed algorithms. The algorithms are easy to implement and yield very accurate results

Global Stability of Humoral Immunity HIV Infection Models with Chronically Infected Cells and Discrete Delays

We study the global stability of three HIV infection models with humoral immune response. We consider two types of infected cells: the first type is the short-lived infected cells and the second one is the long-lived chronically infected cells. In the three HIV infection models, we modeled the incidence rate by bilinear, saturation, and general forms. The models take into account two types of discrete-time delays to describe the time between the virus entering into an uninfected CD4+ T cell and the emission of new active viruses. The existence and stability of all equilibria are completely established by two bifurcation parameters, R0 and R1. The global asymptotic stability of the steady states has been proven using Lyapunov method. In case of the general incidence rate, we have presented a set of sufficient conditions which guarantee the global stability of model. We have presented an example and performed numerical simulations to confirm our theoretical results

A Shifted Jacobi-Gauss Collocation Scheme for Solving Fractional Neutral Functional-Differential Equations

The shifted Jacobi-Gauss collocation (SJGC) scheme is proposed and implemented to solve the fractional neutral functional-differential equations with proportional delays. The technique we have proposed is based upon shifted Jacobi polynomials with the Gauss quadrature integration technique. The main advantage of the shifted Jacobi-Gauss scheme is to reduce solving the generalized fractional neutral functional-differential equations to a system of algebraic equations in the unknown expansion. Reasonable numerical results are achieved by choosing few shifted Jacobi-Gauss collocation nodes. Numerical results demonstrate the accuracy, and versatility of the proposed algorithm

A comparative study of the effects of different low-level lasers on the proliferation, viability, and migration of human melanocytes in vitro.

The aim of this study was to investigate the effects of different low-level laser therapies (LLLTs) of various wavelengths and energies on normal cultured human melanocytes. Various studies have shown the effects of LLLs on various types of cultured cells. Presently, little is known about the biological effects of LLLTs on melanocytes. Melanocytes were exposed to LLLT at 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, or 5.0 J/cm(2) using a blue (457 nm), red (635 nm), or ultraviolet (UV) (355 nm) laser. Melanocyte viability, proliferation, and migration were monitored at 72 h after irradiation. The blue (P < 0.001) and red (P < 0.001 and P < 0.01) lasers significantly enhanced viability at 0.5 to 2.0 J/cm(2), whereas the UV laser (P < 0.001) could significantly enhance viability only at 0.5 and 1.0 J/cm(2) compared with controls. The blue and red lasers also significantly enhanced the proliferation of the melanocytes at 0.5 to 2.0 J/cm(2) (P < 0.001), and the UV laser significantly enhanced proliferation at 0.5 to 1.5 J/cm(2) (P < 0.001 and P < 0.01) compared with controls. The blue laser significantly enhanced melanocyte migration at 0.5 to 4.0 J/cm(2) (P < 0.001 to P < 0.05), but the red (P < 0.001 and P < 0.01) and UV (P < 0.001 to P < 0.05) lasers could significantly enhance such migration at 0.5 to 1.0 J/cm(2) and 0.5 to 2.0 J/cm(2), respectively, compared with controls. LLLT at low energy densities is able to significantly increase melanocyte viability, proliferation, and migration in vitro, and at higher energy densities, it gives non-stimulatory results. Additionally, the blue laser was the best among the three lasers. These findings might have potential application in vitiligo treatment in future

23. Epidemiological aspects and clinical outcomes of mitral valve prolapse in Saudi adults over a 10 year period

Mitral valve prolapse (MVP) is a well recognized clinical entity that is associated with significant morbidity. Epidemiology, echocardiographic (echo) characteristics and clinical outcome of MVP in Saudi Arabia have not been studied. To determine the prevalence, echo features and clinical outcome of MVP among the adult Saudi patients who underwent echo evaluation over a 10-year period.Retrospective review of consecutive cases of MVP or any of its components as diagnose by echocardiogram. Study was conducted in King Abdulaziz Cardiac Center, Riyadh and included 121,419 adult echo studies done between January 2003 and December 2012. Study population consisted of 77,176 patients after removing duplicate studies. Echo parameters for all Saudi nationals ⩾14y of age were collected from the Xcelera database. Mitral valve disease due to non-myxomatous prolapse were excluded. Among the study population (n=77,176) 600 patients were labled as having MVP or any of its echo features (0.7%). Mean age was 64 years and 62% were males. Majority of patients (54.4%) had mild MVP, while moderate and severe prolapse were present in 21.1% and 24.5% respectively. Severe mitral regurgitation was present in 16.5% and chordal rupture was noted in 9%. Left ventricular size was moderately dilated in 7.6% and severely dilated in 1.3%.Prevalence of MVP in Saudi nationals at a referral cardiac center is less than the reported international figure of 1-3%. In contrary to published literature MVP in Saudi population seems to be more common in males and seems to be diagnosed at a later age

Supporting Low-achieving EFL Learners: Expectations, Procedure and Significance of Remedial Sessions at a Saudi University

This study reports on and investigates an institutionalized remedial approach held by an English language institute (ELI) at a Saudi University in order to support foundation year struggling students who often achieve low grades or fail to pass a certain level of the English language program. The study utilizes semi-structured interviews to address three issues: (1) Screening for low-achieving learners; (2) Remedial sessions’ procedure and significance; (3) Learners’ attitudes and conduct during remedial sessions. Thematic analysis of interviews with teachers shows that time limitation and lack of logistical structure lower the effectiveness of remedial sessions in terms of numbers of supported learners and the remedial procedure itself. It was also found that class teachers’ role is often lacking in this case-study. Low-achieving learners are rarely referred by their teachers, but instead come on their own to seek support. However, this optional nature of the process resulted in remedial sessions receiving learners who are self-motivated, have positive attitude, and exhibit different classroom conduct than students in the mainstream classes. Furthermore, the analysis yields other findings related to the usefulness and significance of remedial intervention. Learners were found to seek remedial support for two main reasons: supportive environment and simplified instruction. Much of this can be addressed in regular classrooms. The study concludes with other implications for remedial sessions’ logistics and practices, as well as for the teaching/learning process of low-achievers

Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms

Since the collocation method approximates ordinary differential equations, partial differential equations, and integral equations in physical space, it is very easy to implement and adapt to various problems, including variable coefficient and nonlinear differential equations. In this paper, we derive a Jacobi-Gauss-Lobatto collocation method (J-GL-C) to solve numerically nonlinear time-delayed Burgers-type equations. The proposed technique is implemented in two successive steps. In the first one, we apply nodes of the Jacobi-Gauss-Lobatto quadrature which depend upon the two general parameters , and the resulting equations together with the two-point boundary conditions constitute a system of ordinary differential equations (ODEs) in time. In the second step, the implicit Runge-Kutta method of fourth order is applied to solve a system of ODEs of second order in time. We present numerical results which illustrate the accuracy and flexibility of these algorithms