Warm Inflation in f(R,T)f(R,T) gravity

In this work, we explored warm inflation in the background of $f(R,T)$ gravity in the strong dissipation regime. Considering scalar field for FLRW universe, we derived modified field equations. We then deduced slow-roll parameters under slow-roll approximations followed by power spectrum for scalar and tensor perturbations and their corresponding spectral indices. We have considered Chaotic and Natural potentials and estimated scalar spectral index and tensor-to-scalar ratio for constant as well as variable dissipation factor $\Gamma$. We found that both the rejected potentials can be revived under the context of $f(R,T)$ gravity with suitable choice of the model parameters. Further, it is seen that within the warm inflationary scenario both the potentials are consistent with Planck 2018 bounds at the Planckian and sub Planckian energy scales.Comment: 19 pages, 5 figure

Assessment of serum nitrate-nitrite ratio vis-a-vis insulin sensitivity and resistance in type 2 diabetics in a tertiary hospital in Eastern India

Background: Insulin Resistance is of paramount importance in the pathophysiology of Type 2 Diabetes Mellitus along with endothelial dysfunction is mediated by Nitric Oxide (NO). Central to this endothelial dysfunction is the action of Insulin on the Nitric oxide synthase enzyme. Since NO cannot be measured because of its short half-life, metabolites of NO (namely nitrite and nitrate) are measured towards assessing their relationship along with different direct and surrogate markers of insulin resistance in patients of Diabetes Mellitus attending a tertiary care hospital in Eastern India. Aim of the study was to assess the level of Insulin resistance with the direct and surrogate markers of insulin resistance in patients of Diabetes Mellitus attending a tertiary care hospital in Eastern India.Methods: Blood samples from newly diagnosed Type 2 Diabetic patients were assayed for fasting and postprandial sugar and insulin, lipid profile and serum nitrate and nitrite and different anthropological parameters were measured. After that, HOMA-IR and QUICKI’ index were measured.Results: Values of anthropological parameters and the direct and surrogate markers of insulin resistance showed statistically significant difference between cases and controls. Bivariate analysis of post-prandial blood glucose showed strong co-relation with HOMA-IR while serum total nitrate-nitrite ratio showed a strong co-relation with QUICKI.Conclusions: Serum nitrate-nitrite ratio showed a strong co-relation with HOMA-IR and QUICKI. The significance of this study lies in the fact that measurement of the serum nitrate-nitrite may give an idea of the level of insulin resistance of a diabetic patient

Synthesis, molecular and crystal structure of a new dicarbonylruthenium(II) complex containing a xantphos dioxide chelating ligand

The reaction of xantphos dioxide (O\O) with the polynuclear precursor [Ru(CO)2Cl2]n to give the mononuclear complex [Ru(CO)2Cl2(O\O)](1) is reported together with single crystal X-ray structure analyses of both the free ligand and the ruthenium complex. The synthesized compounds have also been characterized by elemental analyses, IR and NMR (1H, 31P and 13C) spectroscopy. The ligand O\O crystallizes with lattice water molecules in a triclinic system with space group P�1 whereas the complex 1 crystallizes in an orthorhombic system with space group P212121. Each mononuclear unit of O\O and 1 is stabilized in their solid state through non-covalent (C–H���O, C–H���Cl and C–H���p) interactions to develop an extended three-dimensional network structure. The complex 1 exhibits an interesting intramolecular O���O interaction between one of the P@O groups and backbone O leading to different electron donacity of two P@O groups to the metal centre

Dicarbonylruthenium(II) complexes of diphosphine ligands and their catalytic activity

The hexa-coordinated chelate complexes of the type [Ru(CO)2Cl2(P-P)](1a,b) [where P-P = 9,9-dimethyl- 4,5-bis(diphenylphosphino)xanthene(a) and [bis(2-diphenylphosphinophenyl)ether(b)] have been synthesized by reacting the polymeric precursor [Ru(CO)2Cl2]n with the ligands in 1:1 molar ratio. The complexes 1a,b are characterized by elemental analyses, Mass, IR and NMR spectroscopy together with the single crystal X-ray structure determination of 1a. The compound 1a crystallizes in a monoclinic system with space group C2/c showing a slightly distorted octahedral geometry around the Ru centre. The complexes 1a and 1b are thermally stable up to 300 �C and exhibit high catalytic activity in transfer hydrogenation of aldehyde and ketones to corresponding alcohols. The complexes 1a and 1b show much higher catalytic activity for the hydrogenation of aldehyde than ketones. In general, the catalytic efficiency of 1b is higher compared with 1a

On the first and second Zagreb indices of some products of signed graphs

AbstractSome of the most comprehensively studied degree-based topological indices are the Zagreb indices. In this article, the pair of Zagreb indices have been determined for five product graphs namely tensor product, Cartesian product, lexicographic product, strong product, symmetric difference of G1 and G2 in terms of the Zagreb indices of the signed graphs of the factor graphs G1 and G2 and their orders and sizes

Motion planning in cartesian product graphs

Let G be an undirected graph with n vertices. Assume that a robot is placed on a vertex and n − 2 obstacles are placed on the other vertices. A vertex on which neither a robot nor an obstacle is placed is said to have a hole. Consider a single player game in which a robot or obstacle can be moved to adjacent vertex if it has a hole. The objective is to take the robot to a fixed destination vertex using minimum number of moves. In general, it is not necessary that the robot will take a shortest path between the source and destination vertices in graph G. In this article we show that the path traced by the robot coincides with a shortest path in case of Cartesian product graphs. We give the minimum number of moves required for the motion planning problem in Cartesian product of two graphs having girth 6 or more. A result that we prove in the context of Cartesian product of Pn with itself has been used earlier to develop an approximation algorithm for (n2 − 1)-puzzl

Inflation in f(R,T) gravity with Double-Well potential

In this piece of work, we studied the inflation in the context of f(R,T) theory of gravity. We assumed the functional form of f(R,T) to be $R+ \lambda T$, where R is the Ricci scalar, T is the trace of the Energy-Momentum tensor and $\lambda$ is the model parameter. The cosmological observable parameters like scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ are estimated for Double-Well potential. We found that for $\lambda = 115$, $n_s$ and $r$ are in good agreement with PLANCK 2018 data. Further, considering the vacuum expectation value in Double-Well potential to be Planckian, we observed the admissible range of model parameter to be $101 < \lambda < 130$ for which this model remains consistent with PLANCK 2018 data.Comment: 9 pages, 2 figure