Abstract:
This paper deals with Bianchi type VI0 anisotropic cosmological models filled with a bulk viscous cosmic fluid in the presence of time-varying gravitational and cosmological constant. Physically realistic solutions of Einstein's field equations are obtained by assuming the conditions 1) the expansion scalar is proportional to shear scalar 2) the coefficient of the bulk viscosity is a power function of the energy density and 3) the cosmic fluid obeys the barotropic equation of state. We observe that the corresponding models retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Physical behaviours of the cosmological models are also discussed.

Abstract:
Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of bulk viscous fluid for the totally anisotropic Bianchi type II space-time in such a way as to preserve the energy momentum tensor. We have presented solutions of field equations which represent expanding, shearing and non-rotating cosmological models of the universe. The physical behaviours of the models are discussed .We observe that the results obtained match with recent observations of SNIa.

Abstract:
Quantitative safety assessment of safety systems plays an important role in decision making at all stages of system lifecycle, i.e.,design,deployment and phase out.Most safety assessment methods consider only system parameters,such as configuration,hazard rate,coverage,repair rate,etc.along with periodic proof-tests (or inspection).Not considering demand rate will give a pessimistic safety estimate for an application with low demand rate such as nuclear power plants,chemical plants,etc.In this paper,a basic model of IEC 61508 is used.The basic model is extended to incorporate process demand and behavior of electronic- and/or computer-based system following diagnosis or proof-test.A new safety index,probability of failure on actual demand (PFAD) based on extended model and demand rate is proposed.Periodic proof-test makes the model semi-Markovian,so a piece-wise continuous time Markov chain (CTMC) based method is used to derive mean state probabilities of elementary or aggregated state.Method to determine probability of failure on demand (PFD) (IEC 61508) and PFAD based on these state probabilities are described.In example,safety indices of PFD and PFAD are compared.

Abstract:
In this paper, we have adapted Gupta and Shabbir (2008) estimator in systematicsampling using auxiliary information. For the family of estimators, under systematic sampling theexpression of mean square error (MSE) up to the first order approximations is derived. Thefamily of estimators in its optimum case is discussed. Also, an empirical study is carried out toshow the properties of the proposed estimators.

Abstract:
Bertrand's Postulate is the statement that there is a prime between $n$ and $2n$ for $n>1.$ It was proved first by Chebyshev in 1850 and a simple elementary proof not requiring even calculus was given by Erd\H{o}s in 1932. We make some changes to obtain a proof that, in addition, does not require the binomial theorem, knowing about logarithms or $e$ or any infinite series, or a prime number beyond 29 to verify the postulate by hand for small n.

Abstract:
For $k\geq 2$, we derive an asymptotic formula for the number of zeros of the forms $\prod_{i=1}^{k}(x_{2i-1}^2+x_{2i}^2)+\prod_{i=1}^{k}(x_{2k+2i-1}^2+x_{2k+2i}^2)-x_{4k+1}^{2k}$ and $x_1\prod_{i=1}^{k}(x_{2i}^2+x_{2i+1}^2)+x_{2k+2}\prod_{i=1}^{k}(x_{2k+2i+1}^2+x_{2k+2i+2}^2)-x_{4k+3}^{2k+1}$ in the box $1\leq x_i\leq P$ using the circle method.

Abstract:
In an earlier paper [4], we derived asymptotic formulas for the number of representations of zero and of large positive integers by the cubic forms in seven variables which can be written as $L_1(x_1,x_2,x_3) Q_1(x_1,x_2,x_3)+ L_2(x_4,x_5,x_6) Q_2(x_4,x_5,x_6) + a_7 x_7^3$ where $L_1$ and $L_2$ are linear forms, $Q_1$ and $Q_2$ are quadratic forms and $a_7$ is a non-zero integer and for which certain quantities related to $L_1Q_1$ and $L_2Q_2$ were non-zero. In this paper, we consider the case when one or both of these quantities is zero but $L_1Q_1$ and $L_2Q_2$ are still nondegenerate cubic forms in three variables.

Abstract:
ABSTRACT: Diabetes mellitus is one of the most common metabolic disorders that cause micro and macro vascular complications. Because of additive effects of hyperglycaemia and hyperlipidaemia for cardiovascular disease, serum lipid and glucose level should be closely monitored in diabetes. Chronic Hyperglycaemia resulting from diabetes has profound effects on nearly every system of the body. The toxic effects of hyperglycaemia may result from accumulation of nonenzymatically glycosylated products, increased sorbitol production in tissue, formation of diacylglycerol leading to activation of protein kinase C or by free radical generation. Since type 2 DM is a major public health problem, accounting for significant premature mortality and morbidity, every possible effort should be made to minimize its complications. Studies have shown that diabetes is accompa nied by an increased oxidative damage to all the bimolecules. Enhanced oxidative stress contributes to the development of the diabetic complications. Over the last 5 years, a number of large observational studies have suggested an association between the onset of type 2 diabetes and Vitamin deficiencies. As vitamins have important effects on insulin action, serum lipid and glucose and may have impact on a number of pathways which may be of importance in the development of type 2 diabetes. This article reviews the evidence linking role of Vitamins in the prevention of risk factors associated with type 2 diabetes, and suggests current recommendations for supplementation and the most pertinent research on the use of key vitamins in diabetes management.

Abstract:
These analytes were separated on a reverse phase C18 column by using a mobile phase of acetonitrile: 5% acetonitrile in water with 0.07% acetic acid (75:25 v/v), flow rate of 100 muL/min was maintained. The qTOF-MS was operated under multiple reaction monitoring (MRM) mode using electro-spray ionization (ESI) technique with positive ion polarity. The major product ions in the positive mode for curcuminoids were at m/z 369.1066, 339.1023 and 309.0214 respectively. The recovery of the analytes from mouse plasma was optimized using solid phase extraction technique.The total run time was 5 min and the peaks of the compounds, bisdemethoxycurcumin, demethoxycurcumin and curcumin occurred at 2.06, 2.23 and 2.40 min respectively. The calibration curves of bisdemethoxycurcumin, demethoxycurcumin and curcumin were linear over the concentration range of 2--1000 ng/mL (r2, 0.9951), 2--1000 ng/mL (r2, 0.9970) and 2-1000 ng/mL (r2, 0.9906) respectively.Intra-assay and inter-assay accuracy in terms of% bias for curcumin was in between -7.95to +6.21, and -7.03 to + 6.34; for demethoxycurcumin was -6.72 to +6.34, and -7.86 to +6.74 and for bisdesmetoxycurcumin was -8.23 to +6.37 and -8.47 to +7.81. The lower limit of quantitation for curcumin, demethoxycurcumin and bisdemethoxycurcumin was 2.0 ng/mL. Analytes were stable under various conditions (in autosampler, during freeze-thaw, at room temperature, and under deep-freeze conditions). This validated method was used during pharmacokinetic studies of curcumin in the mouse plasma.A specific, accurate and precise UPLC-qTOF-MS/MS method for the determination of curcumin, demethoxycurcumin and bisdemethoxycurcumin both individually and simultaneously was optimized.

Abstract:
Drugs are traditionally been identified on basis of
chromatographic-spectroscopic hyphenated techniques in instrumental analysis.
Gas chromatography (GC) and Liquid chromatography (LC) hyphenated with mass
spectroscopy (MS) i.e. GC-MS and
LC-MS give reliable and confirmatory results in drugs identification. In the
present work the novel hyphenated technique High Performance Thin Layer Chromatography-Mass
Spectroscopy (HPTLC-MS) has been used. This technique provides efficient, quick
and simple method for identification and separation of Narcotic drugs and psychotropic
substances. The drugs under study are Papaverine, Methadone, Cocaine, Ketamine,
Caffeine, Codeine, Diazepam, Thebaine, Heroin, Methamphetamine, Carbamazepine,
Morphine, Narcotine and Ephedrine. The present study comprising of sixteen
drugs has been carried out on CAMAG HPTLC instrument with automatic sampling.
Thin layer chromatography (TLC) plates were developed in various solvent
systems, scanned under TLC scanner and the results in terms of Retention Factor
(R_{f} value) and UV spectrum (λmax)
are presented in the manuscript. Using hyphenated technique of HPTLC-MS (MS
2020 SHIMADZU) spots of these drugs from TLC plate was lifted
with CAMAG TLC-MS interface and confirmed by the mass spectrum of the
individual drugs by their m/z values
thus delivering fast and accurate confirmatory result on the TLC plate.