Groups with star free commuting graphs

Let $G$ be a group and $Z(G)$ be its center. We associate a commuting graph ${\Gamma}(G)$, whose vertex set is $G\setminus Z(G)$ and two distinct vertices are adjacent if they commute. We say that ${\Gamma}(G)$ is strong $k$ star free if the $k$ star graph is not a subgraph of ${\Gamma}(G)$. In this paper, we characterize all strong $5$ star free commuting graphs. As a byproduct, we classify all strong claw-free graphs. Also, we prove that the set of all non-abelian groups whose commuting graph is strong $k$ star free is finite.Comment: 12 pages, 4 figure

On the spectrum of generalized H-join operation constrained by indexing maps -- I

Fix $m \in \mathbb N$. A new generalization of the $H$-join operation of a family of graphs $\{G_1, G_2, \dots, G_k\}$ constrained by indexing maps $I_1,I_2,\dots,I_k$ is introduced as $H_m$-join of graphs, where the maps $I_i:V(G_i)$ to $[m]$. Various spectra, including adjacency, Laplacian, and signless Laplacian spectra, of any graph $G$, which is a $H_m$-join of graphs is obtained by introducing the concept of $E$-main eigenvalues. More precisely, we deduce that in the case of adjacency spectra, there is an associated matrix $E_i$ of the graph $G_i$ such that a $E_i$-non-main eigenvalue of multiplicity $m_i$ of $A(G_i)$ carry forward as an eigenvalue for $A(G)$ with the same multiplicity $m_i$, while an $E_i$-main eigenvalue of multiplicity $m_i$ carry forward as an eigenvalue of $G$ with multiplicity at least $m_i - m$. As a corollary, the universal adjacency spectra of some families of graphs is obtained by realizing them as $H_m$-joins of graphs. As an application, infinite families of cospectral families of graphs are found

A REVIEW ON NATURAL COMPOSITES

Natural fibers have attracted the interest to engineers, researchers, professionals and scientists all over the world as an alternative reinforcement, because of its superior properties such as high specific strength, low weight, low cost, fairly good mechanical properties, non abrasive, eco-friendly and bio-degradable characteristics. A brief review has been carried out to make use of the natural fibers (such as abaca, jute, cotton, coir, Glass fiber etc) abundantly available in India. This paper presents a review on the mechanical properties of Abaca, Jute, Glass fibre

A study on the efficacy and adverse effects of methotrexate in psoriasis patients in a tertiary care centre

Background: Psoriasis is a common, chronic and recurrent inflammatory disease of the skin. Methotrexate has been used in patient with psoriasis, a folic acid antagonist interfering with purine pathway and the mechanism of action in psoriasis is immune modulation and anti-inflammation. So, this study aims at monitoring the efficacy and adverse effects of methotrexate in south Indian patients with psoriasis attending a tertiary care hospital.Methods: It is a prospective, observational study conducted for a period of one year in subjects of either sex having psoriasis. Methotrexate was initiated in a single weekly oral dose of 5mg to 25mg. The efficacy was evaluated using psoriasis Area and Severity Index (PASI) score in all patients before starting methotrexate therapy and the end of first month, third month and sixth month of therapy. Adverse reaction was monitored.Results: All 40 psoriasis patients after treatment with methotrexate therapy showed improved  skin lesions by falling PASI scoring at the end of first, third and sixth month of treatment. None of the patients in our study had pulmonary toxicity, life threatening adverse effects which required hospitalization.Conclusions: Use of methotrexate in the treatment of psoriasis in this study was found to be safe and highly efficacious and caused minimal adverse effects and it was well tolerated

Source localization in shallow ocean using a vertical array of acoustic vector sensors

This paper introduces a new approach to 3D localisation of a narrowband acoustic source in a shallow ocean using acoustic vector sensors (AVS). Assuming a horizontally stratified and range-independent model of the ocean, it is shown that the azimuth of the source can be determined from the estimates of the horizontal components of the acoustic intensity vector obtained from the measurements of an AVS. The range and depth of the source could then be estimated through a 2D search to match the computed complex acoustic intensity vector expressed as a function of these parameters with its estimate obtained from the AVS measurements. However the search in range is computationally intensive as the range parameter is unbounded. We propose an alternative approach employing a vertical array of AVS, based on eigen-decomposition of the spatial correlation matrix of the data vector, leading to a closed form solution for the range parameter. The source depth is then estimated through a 1D search of this bounded parameter

Effectiveness of taichi exercises on stress among college students at selected colleges, Salem

A Study was conducted to Evaluate the Effectiveness of Taichi Exercises on stress among college students at Selected colleges, Salem. The design adopted was true-experimental pre-test post-test control group design. Setting of the study was Vinayaka Mission Kirubananda Variyar College of Engineering (Experimental group) and Sri Annapoorna College of Engineering (Control Group). The screening was done with the use of Perceived Stress Scale (PSS). Then the subjects were separated based on their stress level. 60 samples were drawn through simple random sampling technique (Lottery method without replacement).Level of stress was assessed by four point rating scale through structured self-administered questionnaire. Taichi Exercises was administered for 21 consecutive days. Then Post-test was done. The data gathered were analysed by descriptive and inferential statistical method. The findings revealed that during pre-test, all 30 (100%), of the samples had moderate stress in Experimental and control group. During post-test, in experimental group, 10(33.33%) and 20(66.67%) of the college students had mild and moderate stress, whereas in control group, all 30(100%) of the samples had moderate stress. The mean difference in the level of stress between pre test and post test of experimental group was 24.4 and the estimated paired ‘t’ value 18.29 was most significantly higher than table value 2.05 at p≤ 0.05 level. Hence H1 was retained. The post test mean difference in the level of stress between the experimental and control group was 23.1 and the estimated ‘t’ value 8.39 was most significantly higher than table value 2.06 at p≤ 0.05 level. Hence H2 was retained, which shows that the Taichi Exercises was effective in reducing the stress among college students. There was no significant association (p≤0.05) between the stress among college students in experimental group and control group. Hence H3 was rejected. The study concluded that Taichi Exercises was effective and innovative therapeutic approach, and a cost effective technique in establishing, maintaining and promoting a good sense of psychological wellbeing among students

Pyogenic Granuloma in a Patient of Sturge-Weber Syndrome with Bilateral Port Wine Stain- A Rare Case Report

Sturge-Weber syndrome (SWS) also known as encephalotrigeminal angiomatosis. It is a neurocutaneous syndrome, characterized by a facial vascular birthmark and neurological abnormalities. An ipsilateral or bilateral facial cutaneous vascular malformation Port Wine Stain (PWS) usually affects the upper face. Other clinical manifestations are seizures, glaucoma, hemiparesis, mental retardation and delayed developmental milestones. The main objective of this case report is to unravel such a rarest syndrome with bilateral port-wine stain, which has intraoral manifestation of pyogenic granuloma involving gingiva in an 11 year old boy