Existence of solutions for k-dimensional system of multi-term fractional q-integro-differential equations under anti-periodic boundary conditions via quantum calculus

We prove the existence and uniqueness of solutions for a $k$-dimensional system of multi-term fractional $q$-integro-differential equations via anti-periodic boundary conditions by using some well-known tools of fixed point technique such as Arzelà–Ascoli theorem. We firstly give the corresponding Green function for the boundary value problem and some of its attributes. In addition to, we give a numeric method to verify the analysis for checking the existence of a solution of the system. Finally, an interesting example is presented to illustrate the results.     

A immunosuppressive triterpenoid saponin from the stems of Epigynum griffithianum

Abstract

Chemical investigation of the stems of Epigunum griffithianum led to the isolation and identification of a new triterpenoid saponin (1) and two known compounds (epigynosides A (2) and B (3)). These structures were elucidated by means of spectroscopic analysis (1D and 2D NMR, MS, UV, IR) as well as comparison with the reported data. Compound 1 was evaluated in vitro for the immunosuppressive activities on proliferation of mice splenocyte and displayed significant immunosuppressive activities compared to the positive control (dexamethasone) with the concentration at 25?μM.     

The Bergman kernel for the Vekua equation

The paper extends some well-known results for analytic functions onto solutions of the Vekua equation $\partial \overline{{}_z}W=aW+b\overline{W}$ regarding the existence and construction of the Bergman kernel and of the corresponding Bergman projection operator.     

Construction of a High‐Mannose‐Type Glycan Library by a Renewed Top‐Down Chemo‐Enzymatic Approach

A comprehensive method for the construction of a high‐mannose‐type glycan library by systematic chemo‐enzymatic trimming of a single Man9‐based precursor was developed. It consists of the chemical synthesis of a non‐natural tridecasaccharide precursor, the orthogonal demasking of the non‐reducing ends, and trimming by glycosidases, which enabled a comprehensive synthesis of high‐mannose‐type glycans in their mono‐ or non‐glucosylated forms. It employed glucose, isopropylidene, and N‐acetylglucosamine groups for blocking the A‐, B‐, and C‐arms, respectively. After systematic trimming of the precursor, thirty‐seven high‐mannose‐type glycans were obtained. The power of the methodology was demonstrated by the enzymatic activity of human recombinant N‐acetylglucosaminyltransferase‐I toward M7–M3 glycans, clarifying the substrate specificity in the context of high‐mannose‐type glycans.     

Strong Convergence Theorems for Mixed Typ e Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappin...     

Reliability analysis of a single warm-standby system subject to repairable and nonrepairable failures

An n-unit system provisioned with a single warm standby is investigated. The individual units are subject to repairable failures, while the entire system is subject to a nonrepairable failure at some finite but random time in the future. System performance measures for systems observed over a time interval of random duration are introduced. Two models to compute these system performance measures, one employing a policy of block replacement, and the other without a block replacement policy, are developed. Distributional assumptions involving distributions of phase type introduce matrix Laplace transformations into the calculations of the performance measures. It is shown that these measures are easily carried out on a laptop computer using Microsoft Excel. A simple economic model is used to illustrate how the performance measures may be used to determine optimal economic design specifications for the warm standby.     

Roe‐type Riemann solvers for general hyperbolic systems

We present a Roe‐type weak formulation Riemann solver where the average coefficient matrix is computed numerically. The novelty of this approach is that it is general enough that can be applied to any hyperbolic system while retaining the accuracy of the original Roe solver. We show applications to the compressible Euler equations with general equation of state. An alternative version of the method uses directly the eigenvectors in the averaging process, simplifying the algorithm. These new solvers are applied in conservative and path‐conservative schemes with high‐order accuracy and on unstructured meshes. Copyright © 2014 John Wiley & Sons, Ltd.