t-clique ideal and t-independence ideal of a graph

In this paper, we introduce and study families of squarefree monomial ideals called clique ideals and independence ideals that can be associated to a finite graph. A family of clique ideals with linear resolutions has been characterized. Moreover, some families of graphs for which the quotient ring of their clique ideal is Cohen–Macaulay are introduced and some homological invariants of the clique ideal of a graph G, which is the complement of a path graph or a cycle graph, are obtained. Also some algebraic properties of the independence ideal of path graphs, cycle graphs and chordal graphs are studied.     

Design,synthesis, biological evaluation,and docking study of new acridine-9-carboxamide linked to 1,2,3-triazole derivatives as antidiabetic agents targeting α-glucosidase

A new series of acridine-9-carboxamide-1,2,3-triazole derivatives 7a-m were designed, synthesized, and evaluated as novel α-glucosidase inhibitors. Acridine-9-carboxamide-1,2,3-triazole scaffold has been designed by combination of effective moieties from potent α-glucosidase inhibitors. Most of the synthesized compounds were more potent than standard inhibitor acarbose. Among the title compounds, the most potent compounds were compounds 7j , 7k , and 7a with IC₅₀ values of 120.2 ± 1.0, 151.1 ± 1.4, and 157.6 ± 1.6 μM, respectively (IC₅₀ value of acarbose = 750.0 ± 10.0 μM). Docking study of the most potent compounds demonstrated that these compounds formed stable complexes with α-glucosidase active site. Anti-α-amylase assay of compounds 7j , 7k , and 7a was performed and no activity was observed. in vitro cytotoxicity assay of the latter compounds revealed that these compounds were not cytotoxic toward human normal (HDF) and cancer (MCF-7) cell lines. ADME and toxicity prediction of compounds 7j , 7k , and 7a were also performed.     

Immobilization of cerium (IV) and erbium (III) in mesoporous MCM‐41: Two novel and highly active heterogeneous catalysts for the synthesis of 5‐substituted tetrazoles,and chemo‐ and homoselective oxidation of sulfides

Two well‐ordered 2D ‐ hexagonal cerium (IV) and erbium (III) embedded functionalized mesoporous MCM ‐ 41(MCM‐41@Serine/Ce and MCM ‐ 41@Serine/Er) have been developed via functionalization of mesoporous MCM ‐ 41. The surface modification method has been used in the preparation of serine‐grafted MCM ‐ 41 and led to the development of MCM‐41@Serine. The reaction of MCM‐41@Serine with Ce (NH₄)₂(NO₃)₆·2H₂O or ErCl₃·6H₂O in ethanol under reflux led to the organization of MCM‐41@Serine/Ce and MCM‐41@Serine/Er catalysts. The structures of these catalysts were determined using scanning electron microscopy, mapping, energy‐dispersive X‐ray spectroscopy, Fourier transform‐infrared, thermogravimetric analysis, X‐ray diffraction, inductively coupled plasma, and Brunauer–Emmett–Teller analysis. These MCM‐41@Serine/Ce and MCM‐41@Serine/Er catalysts show outstanding catalytic performance in sulfides oxidation and synthesis of 5‐substituted tetrazoles. These catalysts can be recycled for seven repeated reaction runs without showing a considerable decrease in catalytic performance.     

Exact Solutions of Five Complex Nonlinear Schr¨odinger Equations by Semi-Inverse Variational Principle

In this paper, we establish exact solutions for five complex nonlinear Schr¨odinger equations. The semiinverse variational principle(SVP) is used to construct exact soliton solutions of five complex nonlinear Schr¨odinger equations. Many new families of exact soliton solutions of five complex nonlinear Schr¨odinger equations are successfully obtained.     

First principles study of electronic properties,interband transitions and electron energy loss of <Emphasis Type="Italic">α</Emphasis>-graphyne

The electronic and optical properties of α-graphyne sheet are investigated by using densityfunctional theory. The results confirm that α-graphyne sheet is a zero-gap semimetal. Theoptical properties of the α-graphyne sheet such as dielectric function,refraction index, electron energy loss function, reflectivity, absorption coefficient andextinction index are calculated for both parallel and perpendicular electric fieldpolarizations. The optical spectra are strongly anisotropic along these two polarizations.For (E ∥x), absorption edge is at 0 eV, while there is noabsorption below 8 eV for (E ∥z).     

Preparation,Characterization and Electrochemical Application of ZnS/ZnAl2S4 Nanocomposite for Voltammetric Determination of Methionine and Tryptophan Using Modified Carbon Paste Electrode

ZnS/ZnAl₂S₄ nanocomposite and 2‐chlorobenzoyl ferrocene, were synthesized and used to construct a modified carbon paste electrode. The electrooxidation of methionine at the surface of the modified electrode was studied. Under the optimized conditions, the square wave voltammetric (SWV) peak current of methionine increased linearly with methionine concentration in the range of 5.0×10^?8 to 8.0×10^?4 M and detection limit of 10.0 nM was obtained for methionine. The prepared modified electrode exhibits a very good resolution between the voltammetric peaks of methionine and tryptophan which makes it suitable for the detection of methionine in the presence of tryptophan in real samples.     

Investigation of polycarbonate/acrylonitrile butadiene styrene/multiwall carbon nanotube nanocomposites under impact loading

In this study, the effect of polycarbonate (PC)/acrylonitrile butadiene styrene (ABS)‐reinforced multiwall carbon nanotube (MWCNT) nanocomposites under a high‐velocity impact was investigated. PC/ABS (70/30 w/w)/MWCNT nanocomposites containing 1, 2, and 4 wt% were used to manufacture samples for this study. The samples were fabricated in sheet form with 100 × 100 mm dimensions and tested by gas gun for high‐velocity impact tests. The experimental results indicate that the energy absorption, limit velocity, and tensile modulus of the nanocomposite samples increased by approximately 121%, 52%, and 103% for the PC/ABS (70/30 w/w)/2 wt% MWCNT samples respectively. These results were confirmed by a transmission electron microscopy analysis test that was conducted for the state of dispersion of MWCNTs in the nanocomposite samples. The transmission electron microscopy results show that the best morphological structure of carbon nanotube at the interface of PC and ABS is that for the nanocomposite containing 2 wt% MWCNTs, which led to improved interface of the nanocomposites and higher mechanical properties. Copyright © 2016 John Wiley & Sons, Ltd.     

Absolute Value Equations with Tensor Product Structure: Unique Solvability and Numerical Solution

Applications of Mathematics - We consider the absolute value equations (AVEs) with a certain tensor product structure. Two aspects of this kind of AVEs are discussed in detail: the solvability and...     

Joint Reliability Function of Coherent Systems with Shared Heterogeneous Components

In this paper, we consider two coherent systems having shared components. We assume that in the two systems there are three different types of components; components of type one that just belong to the first system, components of type two that lie only in the second system and components of type three that are shared by the two systems. We use the concept of joint survival signature to assess the joint reliability function of the two systems. Using this concept, some representations for the joint reliability function of the system lifetimes are obtained under two different scenarios of component failures. In the first scenario, we assume that the components of the systems fail according to different counting processes such as non-homogeneous Poisson processes. In the second scenario, it is assumed that the component lifetimes of each type are exchangeable while the three types of component lifetimes can be independent or dependent. To illustrate the theoretical results, two systems with shared components are studied numerically and graphically.