LIFTS OF G(α, β)(3, 2, 1)-STRUCTURES FROM MANIFOLDS TO TANGENT BUNDLES

The aim of the present paper is to explore the lifts of an f(\alpha,\beta)(3; 2; 1)-structure and obtain its partial integrability and integrability conditions on the tangent bundle. Also, the prolongation of an f(\alpha,\beta)(3; 2; 1)-structure on the third tangent bundle T3M is studied

TANGENT BUNDLE ENDOWED WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION ON AN ALMOST HERMITIAN MANIFOLD

In this paper, we have studied the tangent bundle endowed with quarter-symmetric non-metric connection obtained by vertical and complete lifts of a quarter-symmetric non-metric connection on the base manifold and, also, proposed the study of the tangent bundle of an almost Hermitian manifold and an almost Kaehler manifold. Finally, we obtained some theorems for Nijenhuis tensor on the tangent bundle of an almost Hermitian manifold and an almost Kaehler manifold.\

TANGENT BUNDLES ENDOWED WITH SEMI-SYMMETRIC NON-METRIC CONNECTION ON A RIEMANNIAN MANIFOLD

The differential geometry of the tangent bundle is an effective domain of differential geometry which reveals many new problems in the study of modern differential geometry. The generalization of connection on any manifold to its tangent bundle is an application of differential geometry. Recently a new type of semi-symmetric non-metric connection on a Riemannian manifold is studied and established a relationship between Levi-Civita connection and semi-symmetric non-metric connection. The various properties of a Riemannian manifold with relation to such connection are also discussed. The present paper aims to study the tangent bundle of a new type of semi-symmetric non-metric connection on a Riemannian manifold. The necessary and sufficient conditions for projectively invariant curvature tensors corresponding to such connection are proved and show many basic results on the Riemannian manifold in the tangent bundle. Furthermore, the properties of group manifolds of the Riemannian manifolds with respect to the semi-symmetric non-metric connection in the tangent bundle are studied.Moreover, theorems on the symmetry property of Ricci tensor and Ricci soliton in the tangent bundle are established

PARALLELISM OF DISTRIBUTIONS AND GEODESICS ON F(±a2; ±b2)-STRUCTURE LAGRANGIAN MANIFOLD

This paper deals with the Lagrange vertical structure on the vertical space TV (E) endowed with a non null (1,1) tensor field FV satisfying (Fv2-a2)(Fv2+a2)(Fv2 - b2)(Fv2 + b2) = 0. In this paper, the authors have proved that if an almost product structure P on the tangent space of a 2n-dimensional Lagrange manifold E is defined and the F(±a2; ±b2)-structure on the vertical tangent space TV (E) is given, then it is possible to define the similar structure on the horizontal subspace TH(E) and also on T(E). In the next section, we have proved some theorems and have obtained conditions under which the distribution L and M are r-parallel, r¯ anti half parallel when r = r¯ . The last section is devoted to proving theorems on geodesics on the Lagrange manifol

TANGENT BUNDLES OF LP-SASAKIAN MANIFOLD ENDOWED WITH GENERALIZED SYMMETRIC METRIC CONNECTION

The aim of the present work is to study and establish conditions for anLP-Sasakian manifold on the tangent bundle $TM$. An LP-Sasakian manifold with the generalized symmetric metric connection on $TM$ is investigated. Next, the curvature tensor and the Ricci tensor of an LP-Sasakian manifold with respect to the generalized symmetric metric connection on $TM$ are calculated. Moreover, the projective curvature tensor with respect to the generalized symmetric metric connection on $TM$ is studied and showed that $TM$ is not $\hat{\xi}^C$-projectively flat. In particular, if $\alpha=0$ and $\beta=1$ then $TM$ is $\hat{\xi}^C$-projectively flat

Cytotoxicity study of dimethylisatin and its heterocyclic derivatives

Isatin derivatives are bioactive molecules. To study the cytotoxicity and eventually the anticancer activities against cancer cell lines, a series of dimethyl-substitituted isatin derivatives (4-8) starting from isatin thiosemicarbazones (3) had been synthesized in high yields. Investigation of the cytotoxicity of these compounds was carried out against brine shrimp by lethality bioassay. The present study shows that compounds 4, 5, 6 and 8/ with heterocyclic moiety had pronounced cytotoxicity whereas 7, 7/ and 8 were moderately active. It is remarkable that the substituent, X = -OCH3 has greater activity than the bromine atom in this series.

Socio-demographic risk factors for severe malnutrition in children aged under five among various birth cohorts in Bangladesh

Tackling malnutrition is a major health priority for a developing country like Bangladesh. This study explored the differences in prevalence of having only one form, and multiple forms, of severe malnutrition (stunting, wasting and underweight) among under-5 children in Bangladesh, and aimed to identify the important factors affecting these. Data were extracted from the Bangladesh Demographic Health Surveys conducted in 2007, 2011 and 2014. The outcome measures were ‘only one form’ and ‘multiple forms’ of severe malnutrition in children aged under 5 years. A Chi-squared test was performed to find the association of outcome variables with selected socio-demographic factors and logistic regression models were applied to identify risk factors. A total of 19,874 children aged under 5 years were included in the analysis. The overall proportion with one form of severe child malnutrition was approximately 12%, and the proportion with multiple forms was 8%. Age, mother’s education, father’s occupation, mother currently working, watching television, source of water, solid waste used in cooking, intimate partner violence (IPV), wealth index, urban/rural place of residence and birth cohort were found to be significant factors for both having only one and having multiple forms of severe child malnutrition. Children with an uneducated mother of poor socioeconomic class had a higher risk of severe malnutrition. Children of fathers with a professional occupation were at lower risk of having multiple forms of severe malnutrition. The proportions of children aged under 5 years with one or multiple forms of severe malnutrition were shown to be high in Bangladesh. The prevention of malnutrition in the country should be seen as a significant public health issue and given top priority

Urban-rural differences in the associated factors of severe under-5 child undernutrition based on the composite index of severe anthropometric failure (CISAF) in Bangladesh

Introduction Severe undernutrition among under-5 children is usually assessed using single or conventional indicators (i.e., severe stunting, severe wasting, and/or severe underweight). But these conventional indicators partly overlap, thus not providing a comprehensive estimate of the proportion of malnourished children in the population. Incorporating all these conventional nutritional indicators, the Composite Index of Severe Anthropometric Failure (CSIAF) provides six different undernutrition measurements and estimates the overall burden of severe undernutrition with a more comprehensive view. This study applied the CISAF indicators to investigate the prevalence of severe under-5 child undernutrition in Bangladesh and its associated socioeconomic factors in the rural-urban context. Methods This study extracted the children dataset from the 2017–18 Bangladesh Demographic Health Survey (BDHS), and the data of 7661 children aged under-5 were used for further analyses. CISAF was used to define severe undernutrition by aggregating conventional nutritional indicators. Bivariate analysis was applied to examine the proportional differences of variables between non-severe undernutrition and severe undernutrition group. The potential associated socioeconomic factors for severe undernutrition were identified using the adjusted model of logistic regression analysis. Results The overall prevalence of severe undernutrition measured by CISAF among the children under-5 was 11.0% in Bangladesh (rural 11.5% vs urban 9.6%). The significant associated socioeconomic factors of severe undernutrition in rural areas were children born with small birth weight (AOR: 2.84), children from poorest households (AOR: 2.44), and children aged < 36 months, and children of uneducated mothers (AOR: 2.15). Similarly, in urban areas, factors like- children with small birth weight (AOR: 3.99), children of uneducated parents (AOR: 2.34), poorest households (APR: 2.40), underweight mothers (AOR: 1.58), mothers without postnatal care (AOR: 2.13), and children’s birth order ≥4 (AOR: 1.75), showed positive and significant association with severe under-5 undernutrition. Conclusion Severe undernutrition among the under-5 children dominates in Bangladesh, especially in rural areas and the poorest urban families. More research should be conducted using such composite indices (like- CISAF) to depict the comprehensive scenario of severe undernutrition among the under-5 children and to address multi-sectoral intervening programs for eradicating severe child undernutrition

Does household food insecurity influence nutritional practice of children age 6 to 23 months in Bangladesh?

To examine the prevalence of household food insecurity (HHFI) among children aged between 6-23 months in Bangladesh. This paper also aims to identify the individual, household and community levels determinants of HHFI and the association between nutritional behavior and HHFI. Bangladesh Demographic Health Survey (BDHS), 2011 was used for this research. A total of 2,344 children were selected for analysis. Statistical analysis and tests were guided by the nature of the variables. Finally, logistic regression analysis was used to find out the association between independent variables and outcome. The overall prevalence of HHFI was 36.3% (95% CI: 33.6-39.0) among the participants (children). The prevalence of HHFI was significantly higher among children who did not receive nutritional items. In contrast, HHFI was more prevalent among children who were breastfed (37.0%) as compared to non-breastfed. Binary logistic regression analysis showed that children of illiterate mothers (adjusted OR: 2.20, 95% CI: 1.17-4.10), illiterate fathers (adjusted OR: 2.27, 95% CI: 1.41-3.66) and socio-economically poor families (adjusted OR: 11.35, 95% CI: 7.20-17.91) were more at risk of experiencing HHFI, whereas, rural children (adjusted OR: 0.72, 95% CI: 0.57-0.93) were more protective. In the adjusted logistic regression model, children who did not receive juice (adjusted OR: 1.54, 95% CI: 1.09-2.16) had experienced HHFI. The prevalence of HHFI among children is still high in Bangladesh. Therefore, to achieve the Millennium Development Goals, the Government of Bangladesh should priorities HHFI as a major public health issue. Strong collaborations among various stakeholders are also crucial to improve the situation