A Note On Transversals

Let $G$ be a finite group and $H$ a core-free subgroup of $G$. We will show that if there exists a solvable, generating transversal of $H$ in $G$, then $G$ is a solvable group. Further, if $S$ is a generating transversal of $H$ in $G$ and $S$ has order 2 invariant sub right loop $T$ such that the quotient $S/T$ is a group. Then $H$ is an elementary abelian 2-group.Comment: 7 page

Solvable and Nilpotent Right Loops

In this paper the notion of nilpotent right transversal and solvable right transversal has been defined. Further, it is proved that if a core-free subgroup has a generating solvable transversal or a generating nilpotent transversal, then the whole group is solvable.Comment: arXiv admin note: substantial text overlap with arXiv:1307.539

On The Isomorphism Classes Of Transversals III

Let $G$ be a finite group and $H$ a subgroup of $G$. Each left transversal (with identity) of $H$ in $G$ has a left loop (left quasigroup with identity) structure induced by the binary operation of $G$. We say two left transversals are isomorphic if they are isomorphic with respect to the induced left loop structures. In this paper, we develop a method to calculate the number of isomorphism classes of transversals of $H$ in $G$. Also with the help of this we calculate the number of non-isomorphic left loops of a given order.Comment: 19 page

Estimation of extracellular lipase enzyme produced by thermophilic bacillus sp. isolated from arid and semi-arid region of Rajasthan, India

Thermophilic organisms can be defined as microorganisms which are adapted to live at high temperatures. The enzymes produce by thermophilic bacteria are capable of catalyzing biochemical reactions at high temperatures. Thermophilic bacteria are able to produce thermostable lipase enzymes capable of degradation of lipid at temperatures higher than those of mesophilic bacteria. Therefore, the isolation of thermophilic bacteria from natural sources and their identification are quite useful in terms of discovering thermophilic lipase enzymes. Due to great temperature fluctuation in hot arid and semi-arid regions of Rajasthan, this area could serve as a good source for new thermophilic lipase producing bacteria with novel industrially important properties. The main objective of this research is the isolation and estimation of industrially important thermophilic lipase enzyme produced by thermophilic bacteria, isolated from arid and semi-arid region of Rajasthan. For this research purpose, soil samples were collected from Churu, Sikar and Jhunjunu regions of Rajasthan. A total of 16 bacterial strains were isolated, and among these bacterial isolates only two thermophilic lipase producing bacteria were identified. The thermophilic lipase enzyme was estimated by qualitative and quantitative experiments. The isolate was identified as Bacillus sp. by microscopic, biochemical and molecular characterization. The optimum enzyme activity was observed at pH 8, temperature 60°C and 5% salt concentration at 24 hrs time duration. Lipases are useful in a variety of biotechnological fields such as food and dairy (cheese ripening, flavour development), detergent, pharmaceutical (naproxen, ibuprofen), agrochemical (insecticide, pesticide) and oleochemical (fat and oil hydrolysis, biosurfactant synthesis) industries. Lipases can be further used in many newer areas where they can serve as potential biocatalysts. 
&#xa

A Characterization of Group Through Isomorphism Classes of Transversals

Let G be a group and H a subgroup of G of finite index. In this article, it is proved that if the number of isomorphism classes of right transversals of H in G is 5, then the index of H in G is 6 and the permutation representation of G on right cosets of H in G is isomorphic to the alternating group on four symbols.Comment: 20 pages, 1 tabl

Study of Numerical Schemes for the CFD Simulation of Human Airways

Computational fluid dynamics (CFD) is increasingly used nowadays to capture air and particle transport in human respiratory tract model. In the present study, computer tomography (CT) scan based respiratory tract model is used for the CFD simulation. The main objective of the present study is to compare different pressure-velocity schemes (SIMPLE, SIMPLEC, PISO and COUPLED schemes) in terms of convergence and computational time. Numerical simulation is done for three inhalation flow rates, namely 20, 40 and 60 liters per minute for predictions of flow phenomena inside the sixth generation human airways and also to predict the effects of flow parameters; pressures and velocity on the sixth generation Human Airways. Low Reynolds Number (LNR) k-ω model is used to capture the turbulence effect. The findings will be useful for medical practitioner to understand complex airflow patterns in the human airways. Also, pressure distribution and velocity distribution help to define the medical phenomena in core engineering terms

HPLC Method Development and Validation for the Estimation of Esomeprazole in Bulk and Pharmaceutical Dosage Form

A reversed-phase high performance liquid chromatography (RP-HPLC) method was developed and validated for the estimation of esomeprazole in bulk and tablet dosage forms. The separation was achieved on Thermo C18 analytical column (250 mm × 4.6 mm i.d., 5.0 μm) using acetonitrile and methanol in the ratio 50:50 v/v as mobile phase and at a flow rate of 1.0 ml/min. Detection was carried out using a UV detector at 300nm. The total chromatographic analysis time per sample was about 8.0min with esomeprazole eluting at retention time of about 6.863±0.3 min. The method was validated for accuracy, precision, specificity, linearity and sensitivity. Validation studies demonstrated that this HPLC method is simple, specific, rapid, reliable and reproducible. The standard curve was linear over the concentration range of 5-25μg/ml with r2 close to one (0.999). The limit of detection (LOD) and limit of quantitation (LOQ) obtained for esomeprazole were 0.100μg/ml and 0.314μg/ml respectively. The developed and validated method was successfully applied for the quantitative analysis of ESOMZ 20 Tablet. The high recovery and low relative standard deviation confirm the suitability of the proposed method for the determination of esomeprazole in tablets dosage form. Keywords: Analytical method development, Reversed phase HPLC method, ICH guidelines, Tablet dosage forms, Accuracy and precisio