Some Quantitative Characterizations of Certain Symplectic Groups

Given a finite group $G$, denote by ${\rm D}(G)$ the degree pattern of $G$ and by ${\rm OC}(G)$ the set of all order components of $G$. Denote by $h_{{\rm OD}}(G)$ (resp. $h_{{\rm OC}}(G)$) the number of isomorphism classes of finite groups $H$ satisfying conditions $|H|=|G|$ and ${\rm D}(H)={\rm D}(G)$ (resp. ${\rm OC}(H)={\rm OC}(G)$). A finite group $G$ is called OD-characterizable (resp. OC-characterizable) if $h_{\rm OD}(G)=1$ (resp. $h_{\rm OC}(G)=1$). Let $C=C_p(2)$ be a symplectic group over binary field, for which $2^p-1>7$ is a Mersenne prime. The aim of this article is to prove that $h_{\rm OD}(C)=1=h_{\rm OC}(C)$

On the Unit Graph of a Noncommutative Ring

Let $R$ be a ring (not necessary commutative) with non-zero identity. The unit graph of $R$, denoted by $G(R)$, is a graph with elements of $R$ as its vertices and two distinct vertices $a$ and $b$ are adjacent if and only if $a+b$ is a unit element of $R$. It was proved that if $R$ is a commutative ring and \fm is a maximal ideal of $R$ such that |R/\fm|=2, then $G(R)$ is a complete bipartite graph if and only if (R, \fm) is a local ring. In this paper we generalize this result by showing that if $R$ is a ring (not necessary commutative), then $G(R)$ is a complete $r$-partite graph if and only if (R, \fm) is a local ring and $r=|R/m|=2^n$, for some $n \in \N$ or $R$ is a finite field. Among other results we show that if $R$ is a left Artinian ring, $2 \in U(R)$ and the clique number of $G(R)$ is finite, then $R$ is a finite ring.Comment: 6 pages. To appear in Algebra Colloquiu

Global limits on kinetic Alfv\'{e}non speed in quasineutral plasmas

Large amplitude kinetic Alfv\'{e}non (exact Alfv\'{e}n soliton) matching condition is investigated in quasineutral electron-ion and electron-positron-ion plasmas immersed in a uniform magnetic field. Using the standard pseudopotential method, the magnetohydrodynamics (MHD) equations are exactly solved and a global allowed matching condition for propagation of kinetic solitary waves is derived. It is remarked that, depending on the plasma parameters, the kinetic solitons can be sub- or super-Alfv\'{e}nic, in general. It is further revealed that, either upper or lower soliton speed-limit is independent of fractional plasma parameters. Furthermore, the soliton propagation angle with respect to that of the uniform magnetic field is found to play a fundamental role in controlling the soliton matching speed-range.Comment: To be published in Physics of Plasma

Percolation in Networks with Voids and Bottlenecks

A general method is proposed for predicting the asymptotic percolation threshold of networks with bottlenecks, in the limit that the sub-net mesh size goes to zero. The validity of this method is tested for bond percolation on filled checkerboard and "stack-of-triangle" lattices. Thresholds for the checkerboard lattices of different mesh sizes are estimated using the gradient percolation method, while for the triangular system they are found exactly using the triangle-triangle transformation. The values of the thresholds approach the asymptotic values of 0.64222 and 0.53993 respectively as the mesh is made finer, consistent with a direct determination based upon the predicted critical corner-connection probability.Comment: to appear, Physical Review E. Small changes from first versio

Influence of Hydroxypropyl Methylcellulose Molecular Weight Grade on Water Uptake, Erosion and Drug Release Properties of Diclofenac Sodium Matrix Tablets

Purpose: To comparatively evaluate the effect of two hydroxylpropyl methylcellulose (HPMC) molecular weight grades (K4M and K15M) on drug release from diclofenac sodium matrix tablets.Methods: Tablets containing diclofenac sodium were prepared by direct compression method at various drug/HPMC ratios and evaluated in vitro for their water uptake, erosion and dissolution characteristics over a period of 8 h. Their release data were analyzed according to various release kinetic models.Results: The release rate of diclofenac decreased with increase in polymer content and was dependent on the HPMC type used, with the lower release rate observed in formulations containing the higher molecular weight grade HPMC K15M. Formulations containing the higher molecular weight HPMC (F4, F5 and F6) showed higher water uptake than those containing the lower molecular weight polymer (F1, F2 and F3) (p < 0. 001). The formulations incorporating the lower molecular weight HPMC K4M (F1, F2 and F3) showed higher erosion than those that contained HPMC K15M (F4, F5 and F6) (p < 0.001). Kinetic data based on the release exponent, n, in Peppas model, showed that n values were between 0.14 and 0.55, indicating that drug release from HPMC matrices was predominantly by diffusion.Conclusion: This study demonstrates that the molecular weight (MW) of HPMC does affect the water uptake and erosion as well as the rate of drug release from of HPMC matrices.Keywords: Matrix, Diclofenac sodium, HPMC, Erosion, Water uptake

Development and Evaluation of Mucoadhesive Chlorhexidine Tablet Formulations

Purpose: To formulate mucoadhesive chlorhexidine tablets and evaluate their drug release characteristics and mechanism.Methods: Chlorhexidine buccal adhesive tablets were prepared by direct compression using a blend of hydroxypropyl methylcellulose (HPMC) and chitosan as the bioadhesive polymers. Their dissolutionproperties were assessed according to USP 24 (paddle method). In order to determine the mode of drug release from the tablets, the release data were subjected to various release kinetic models. Thebioadhesive strength of the tablets was also evaluated. Results: The results showed that as the proportion of HPMC in the blend increased, drug release rate decreased, with the lowest release rate observed when HPMC alone was used as the bioadhesive polymer (p < 0.001). Both the type and ratio of the polymers used influenced release kinetics. Also,bioadhesion force increased with increasing proportion of HPMC in the tablets, with the highest adhesion force shown when HPMC was the only polymer used, and lowest when chitosan was used alone (p < 0.01). Conclusion: The chlorhexidine formulations developed showed promise as a bioadhesive delivery system for the drug.Keywords:  Mucoadhesive tablets; Chlorhexidine; HPMC; Chitosan; Release properties; Bioadhesive strength

High prevalence of vitamin d deficiency among iranian population: A systematic review and meta-analysis

Background: The prevention and correction of vitamin D deficiency requires a precise depiction of the current situation and identification of risk factors in each region. The present study attempted to determine these entities using a systematic review and meta-analysis in Iran. Methods: Articles published online in Persian and English between 2000 and November 1, 2016, were reviewed. This was carried out using national databases such as SID, IranMedex, Magiran, and IranDoc and international databases such as PubMed, Google Scholar, and Scopus. The heterogeneity index among the studies was determined using the Cochran (Q) and I2 test. Based on the heterogeneity results, the random-effect model was applied to estimate the prevalence of vitamin D deficiency. In addition, meta-regression analysis was used to determine heterogeneity-suspected factors, and the Egger test was applied to identify publication bias. Results: The meta-analysis of 48 studies identified 18531 individuals with vitamin D deficiency. According to the random-effect model, the prevalence of vitamin D deficiency among male, female, and pregnant women was estimated to be 45.64% (95% CI: 29.63 to 61.65), 61.90% (95% CI: 48.85 to 74.96), and 60.45% (95% CI: 23.73 to 97.16), respectively. The results of the meta-regression analysis indicated that the prevalence of vitamin D deficiency was significantly different in various geographical regions (β=4.4; P=0.023). Conclusion: The results obtained showed a significant prevalence of vitamin D deficiency among the Iranian population, a condition to be addressed by appropriate planning. © 2018, Shiraz University of Medical Sciences. All rights reserved