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The main aim of this paper is to define and study of the Chebyshev matrix polynomials. An explicit representation, a three-term matrix recurrence relations for the Chebyshev matrix polynomials are given. These polynomials appear as finite series solutions of second order matrix differential equations. The expansion Chebyshev matrix polynomials in series of Hermite matrix polynomials and the Christoffel formula of summation are established.

The principal object of this work is to define and study of a new kummer’s matrix function, namely, composite l(m, n)-Kummer’s matrix functionof two complex variables. The radius of regularity and matrix recurrence relationson this function are obtained. The effect of differential operator (D) on thisfunction is investigated and a solution of a certain partial differential equation is established.

An analysis has been carried out to study a problem of the natural convective boundary-layer flow of a nanofluid past a non-linear stretching surface with convective boundary condition in the presence of yield stress in porous media. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The local similarity solutions are obtained by using an efficient numerical shooting technique with a fourth-order Runge–Kutta scheme (MATLAB package). The results corresponding to the dimensionless temperature profiles and the reduced Nusselt number, Sherwood number and skin friction coefficient are displayed graphically for various pertinent parameters. It was found that Nusselt number ( Re − 1 = 2 x Nu x ) and Sherwood number ( Re − 1 = 2 x Sh x ) is a decreasing function of the yield stress parameter Ω and the porous media parameter ξ , while the skin friction coefficient ( Re 1 = 2 x C f ) is an increasing function of the yield stress parameter Ω and the porous media parameter ξ

The aim of this paper is to calculate the analytical form of the equation of state for dilute relativistic plasma. We obtained the excess free energy and pressure in the form of a convergent series expansion in terms of the thermal parameter μ where μ = mc^2/KT, m is the mass of charge, c is the speed of light, K is the Boltzmann’s constant, and T is the absolute temperature. The results are discussed and compared with previous work of other authors.

The aim of this article is to calculate the thermodynamic functions of a neutron star in curved space. We obtained equation of state (EOS) and the excess free energy for a neutron star in curved space up to order n^4, where n is the density of particles.

We report here the structural and superconducting properties of Bi2Sr2CaYxCu2Oy superconductors with various x values (0.00 ≤ x ≤ 0.50) by using the resistivity and ac susceptibility measurements. It is found that addition of Y3+ does not influence the phase purity of Bi:2212, while c-parameter and orthorhombic distortion are affected. Furthermore, the critical temperatures Tc(R = 0) are increased from 92 K for Y = 0 up to 106 K by 0.15 of Y, followed by a decrease with increasing Y up to 0.50. It is interesting to note the resistivity of the samples with Y = 0.075 and 0.15 reaching to true zero value only at low dc currents up to 2 mA. Interestingly, the onset temperature of diamagnetism obtained from susceptibility data remains nearly unchanged at 94 K up to Y= 0.30, flowed by a decrease to 86 K at Y = 0.50. The superconducting volume fraction and critical currents are improved by Y addition up to 0.15, followed by a decrease with increasing Y up to 0.50. These results are explained in terms of the effects of excess oxygen, secondary phases, and carrier concentration per Cu ions which are produced by Y addition in Bi:2212 system.

BACKGROUND: Non-alcoholic fatty liver disease (NAFLD) is a multifactorial disease with a complex pathophysiology. The clinical features of NAFLD include obesity, insulin resistance (IR) and dyslipidemia. Consumption of a diet high in saturated fats and sucrose is an important factor in the increasing occurrence of these metabolic disorders, primarily NAFLD and IR. We sought to assess the role of a high-fat, high-sucrose (HFS) diet in the promotion of NAFLD and to evaluate the effects of quercetin (Q), berberine (BB) and o-coumaric acid (CA) on modulation of these disorders. METHODS: Fifty male rats were divided into 2 main groups as follows: group 1 comprised 10 rats fed a standard diet (SD), and group 2 comprised 40 rats fed an HFS diet for 6 weeks and then subdivided equally into 4 groups; one of these groups served as the HFS diet and each of the other three groups received daily supplementation with either Q, CA or BB for 6 weeks. RESULTS: In the present study, several metabolic disorders were induced in our laboratory animal model, as evidenced by histological and biochemical changes. These alterations included serum and hepatic dyslipidemia (i.e., increased triglyceride, total cholesterol and low-density lipoprotein levels and decreased high-density lipoprotein levels), alterations in metabolic enzyme activities (lipase, glycerol-3-phosphate dehydrogenase, and glucose-6-phosphate dehydrogenase), histological changes in the liver (micro- and macrovesicular steatosis) and the downregulation of peroxisome proliferator-activated receptor γ (PPARγ) in adipose tissue and the liver. Daily oral supplementation with Q, CA or BB for 6 weeks after NAFLD induction had a hypolipidemic action and modulated metabolic markers. CONCLUSION: We showed that an HFS diet is able to promote NAFLD, and our results suggest that CA and BB are promising complementary supplements that can ameliorate the metabolic disorders associated with an HFS diet; however, Q requires further investigation.

BACKGROUND: Non-alcoholic fatty liver disease (NAFLD) is a multifactorial disease with a complex pathophysiology. The clinical features of NAFLD include obesity, insulin resistance (IR) and dyslipidemia. Consumption of a diet high in saturated fats and sucrose is an important factor in the increasing occurrence of these metabolic disorders, primarily NAFLD and IR. We sought to assess the role of a high-fat, high-sucrose (HFS) diet in the promotion of NAFLD and to evaluate the effects of quercetin (Q), berberine (BB) and o-coumaric acid (CA) on modulation of these disorders. METHODS: Fifty male rats were divided into 2 main groups as follows: group 1 comprised 10 rats fed a standard diet (SD), and group 2 comprised 40 rats fed an HFS diet for 6 weeks and then subdivided equally into 4 groups; one of these groups served as the HFS diet and each of the other three groups received daily supplementation with either Q, CA or BB for 6 weeks. RESULTS: In the present study, several metabolic disorders were induced in our laboratory animal model, as evidenced by histological and biochemical changes. These alterations included serum and hepatic dyslipidemia (i.e., increased triglyceride, total cholesterol and low-density lipoprotein levels and decreased high-density lipoprotein levels), alterations in metabolic enzyme activities (lipase, glycerol-3-phosphate dehydrogenase, and glucose-6-phosphate dehydrogenase), histological changes in the liver (micro- and macrovesicular steatosis) and the downregulation of peroxisome proliferator-activated receptor γ (PPARγ) in adipose tissue and the liver. Daily oral supplementation with Q, CA or BB for 6 weeks after NAFLD induction had a hypolipidemic action and modulated metabolic markers. CONCLUSION: We showed that an HFS diet is able to promote NAFLD, and our results suggest that CA and BB are promising complementary supplements that can ameliorate the metabolic disorders associated with an HFS diet; however, Q requires further investigation.

Hepatitis C virus (HCV) infection is a worldwide healthcare problem; however, traditional treatment methods have failed to cure all patients, and HCV has developed resistance to new drugs. Systems biology-based analyses could play an important role holistic analysis of the impact of HCV on hepatocellular metabolism. Here, we integrated HCV assembly reactions with a genome-scale hepatocyte metabolic model to identify the metabolic targets for HCV assembly and the metabolic alterations that occur between different HCV progression states (cirrhosis, dysplastic nodule, and early and advanced hepatocellular carcinoma (HCC)) and healthy liver tissue. We found that diacylglycerolipids were essential for HCV assembly. In addition, the metabolism of keratan sulfate and chondroitin sulfate was significantly changed in the cirrhosis stage, whereas the metabolism of acyl-carnitine was significantly changed in the dysplastic nodule and early HCC stages. Our results explained the role of the upregulated expression of BCAT1, PLOD3 and six other methyltransferase genes involved in carnitine biosynthesis and S-adenosylmethionine metabolism in the early and advanced HCC stages. Moreover, GNPAT and BCAP31 expression was upregulated in the early and advanced HCC stages and could lead to increased acyl-CoA consumption. By integrating our results with copy number variation analyses, we observed that GNPAT, PPOX and five of the methyltransferase genes (ASH1L, METTL13, SMYD2, TARBP1 and SMYD3), which are all located on chromosome 1q, had increased copy numbers in the cancer samples relative to the normal samples. Finally, we confirmed our predictions with the results of metabolomics studies and proposed that inhibiting the identified targets has the potential to provide an effective treatment strategy for HCV-associated liver disorders.