Classification of finite groups with toroidal or projective-planar permutability graphs

Let $G$ be a group. The permutability graph of subgroups of $G$, denoted by $\Gamma(G)$, is a graph having all the proper subgroups of $G$ as its vertices, and two subgroups are adjacent in $\Gamma(G)$ if and only if they permute. In this paper, we classify the finite groups whose permutability graphs are toroidal or projective-planar. In addition, we classify the finite groups whose permutability graph does not contain one of $K_{3,3}$, $K_{1,5}$, $C_6$, $P_5$, or $P_6$ as a subgraph.Comment: 30 pages, 8 figure

Permutability graphs of subgroups of some finite non-abelian groups

In this paper, we study the structure of the permutability graphs of subgroups, and the permutability graphs of non-normal subgroups of the following groups: the dihedral groups $D_n$, the generalized quaternion groups $Q_n$, the quasi-dihedral groups $QD_{2^n}$ and the modular groups $M_{p^n}$. Further, we investigate the number of edges, degrees of the vertices, independence number, dominating number, clique number, chromatic number, weakly perfectness, Eulerianness, Hamiltonicity of these graphs.Comment: 35 pages, 1 figur

Resistivity and Thermopower of Ni2.19Mn0.81Ga

In this paper, we report results of the first studies on the thermoelectric power (TEP) of the magnetic heusler alloy Ni$_{2.19}$Mn$_{0.81}$Ga. We explain the observed temperature dependence of the TEP in terms of the crystal field (CF) splitting and compare the observed behavior to that of the stoichiometric system Ni$_2$MnGa. The resistivity as a function of temperature of the two systems serves to define the structural transition temperature, T$_M$, which is the transition from the high temperature austenitic phase to low temperatures the martensitic phase. Occurrence of magnetic (Curie-Weiss) and the martensitic transition at almost the same temperature in Ni$_{2.19}$Mn$_{0.81}$Ga has been explained from TEP to be due to changes in the density of states (DOS) at the Fermi level.Comment: 12 pages, 4 figures, Accepted in Physical Review B vol 70, Issue 1

Is low self-esteem a risk factor for depression among adolescents? an analytical study with interventional component

Background: Self – esteem is an important factor for helping persons deal with life stressors. It is an important determinant of psychological well-being that is particularly problematic during an adolescent life stage. Low self-esteem might contribute to depression through both interpersonal and intrapersonal pathways. Many theories of depression postulate that low self esteem is a defining feature of depression. Aims: Self-esteem in adolescents has been associated with a number of risk and protective factors in previous studies. This study examined the relationship between low self esteem and depression among adolescents. Methods: This study used a case control (retrospective) design. Samples of 1120 adolescents, aged 14-17 years were selected for the study. Screening was done by using MINI-KID and the level of depression was assessed by using Beck depression inventory. Self esteem was measured by Rosenberg self esteem scale. Odds Ratio and Multivariate logistic regression were used to examine the relation between self-esteem and socio-demographic variables. Results: The odds ratio analysis revealed that adolescents who had low self esteem found to have 3.7 times (95% CI=1.9-6.9 and p- value 0.001) more risk of developing depression than the adolescents who had high self esteem. Conclusions: The findings implied that low self-esteem is a risk factor for depression among adolescents. Adolescents with low self esteem have to be identified earlier and prompt interventions will prevent future psychiatric illnesses. As an intervention towards the educational component pamphlet was distributed to the adolescents, parents and teachers. A concept programme called “Self Esteem Education & Development – SEED” programme, is planned for, from High school level

Floral Ecology and Reproductive Biology of Pterospermum Reticulatum Wight and Arn. (sterculiaceae): A Vulnerable Tree Species of Western Ghats of India

Pterospermum reticulatum Wight and Arn is a vulnerable according to IUCN red list category (1998). In the present study observations were made on floral ecology and reproductive biology of Pterospermum reticulatum at Pilikula reserve forest, Mangalore, Karnataka during 2012-2013. The peak flowering was observed during February to April and anthesis occurred in the even ing between 18:30 -22:30hrs. Inflorescences in terminal or axillary fascicles, Flowers are white colour and 5 petals and 5 linear sepals. Stamens are 15, in group of five. Fruits are capsule, brown, 5-angled and 5-valved, development of fruit to dehiscence was observed. Pollen production per flower was counted 3, 93499.9 and pollen ovule ratio was 1: 393500. Floral biology including the stigma receptivity, pollen viability, pollen germination and pollen tube growth were recorded during the flowering period. Macro and Micro nutrients of the soil collected from the rhizosphere were analyzed. The factors responsible for declining of the population of Pterospermum reticulatum are discussed