Locally torsion-free quasi-coherent sheaves

Let X   be an arbitrary scheme. It is known that the category Qcoh(X)$\mathfrak{Qcoh}(X)$ of quasi-coherent sheaves admits arbitrary products. However its structure seems to be rather mysterious. In the present paper we will describe the structure of the product object of a family of locally torsion-free objects in Qcoh(X)$\mathfrak{Qcoh}(X)$, for X an integral scheme. Several applications are provided. For instance it is shown that the class of flat quasi-coherent sheaves on a Dedekind scheme X   is closed under arbitrary direct products, and that the class of all locally torsion-free quasi-coherent sheaves induces a hereditary torsion theory on Qcoh(X)$\mathfrak{Qcoh}(X)$. Finally torsion-free covers are shown to exist in Qcoh(X)$\mathfrak{Qcoh}(X)$.     

On the bondage number of middle graphs

Let G = (V (G),E(G)) be a simple graph. A subset S of V (G) is a dominating set of G if, for any vertex v ∈ V (G) — S, there exists some vertex u ∈ S such that uv ∈ E(G). The domination number, denoted by γ(G), is the cardinality of a minimal dominating set of G. There are several types of domination parameters depending upon the nature of domination and the nature of dominating set. These parameters are bondage, reinforcement, strong-weak domination, strong-weak bondage numbers. In this paper, we first investigate the strong-weak domination number of middle graphs of a graph. Then several results for the bondage, strong-weak bondage number of middle graphs are obtained.     

Numerical solution of the Bagley–Torvik equation by the Bessel collocation method

In this article, a numerical technique is presented for the approximate solution of the Bagley–Torvik equation, which is a class of fractional differential equations. The basic idea of this method is to obtain the approximate solution in a generalized form of the Bessel functions of the first kind. For this purpose, by using the collocation points, the matrix operations and a generalization of the Bessel functions of the first kind, this technique transforms the Bagley–Torvik equation into a system of the linear algebraic equations. Hence, by solving this system, the unknown Bessel coefficients are computed. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples. Copyright © 2012 John Wiley & Sons, Ltd.     

The effect of high hydrostatic pressure on the muscle proteins of rainbow trout (Oncorhynchus mykiss Walbaum) fillets wrapped with chitosan-based edible film during cold storage (4±1°C)

This study was to determine the effects of changes that occurred in the muscle proteins of fresh rainbow trout (Oncorhynchus mykiss) fillets during storage at 4±1°C as a result of packaging in vacuum (C), subject to high pressure after packaging in vacuum high hydrostatic pressue (HHP), packaged in vacuum after wrapping with chitosan film (CFW) and subject to high pressure after wrapping with chitosan-based film and packaged in vacuum (HHP+CFW ). Samples were subjected to SDS-PAGE in four-day intervals and the densitometric analyses of the gels were carried out. According to the results, minor changes were determined in the major bands of the sarcoplasmic and myofibrillar muscle fractions of trouts as a result of HHP application and CFW. The most important change occurred in the myofibrillar muscle fraction as a decrease in the densities of the bands at 200 and 31.4 kDa after HHP application. Similarly, the sarcoplasmic muscle fraction of trout fillet decreased in the densities of the bands at 39.3, 26.6 and 23.3 kDa after HHP application. In addition, it is thought that the bands that occur at 30 kDa in the myofibrillar muscle fraction and at 20.7 kDa at the sarcoplasmic muscle fraction may be related with the degradation of trouts during cold storage.     

Entanglement of a Single Spin-1 Object: An Example of Ubiquitous Entanglement

Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. [A.A. Klyachko and A.S. Shumovsky, J. Phys: Conf. Series 36, 87 (2006), E-print quant-ph/0512213]. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states with maximal amount of uncertainty of all basic observables. The approach gives purely physical picture of entanglement. In particular, it separates principle physical properties of entanglement from inessential. Within the model example under consideration, we show relativity of entanglement with respect to dynamic symmetry and argue existence of single-particle entanglement. A number of physical examples are considered.      

Vacancy‐induced minority‐spin states in half‐metallic Heusler alloys

Ferromagnetic full Heusler alloys containing Co are amongst the most studied half‐metallic systems. Several studies recently have been concentrated on the effect of defects and impurities. We focus in this Letter on the case of vacancies in these alloys. We show that the occurrence of vacancies at the sites occupied by Co atoms can destroy half‐metallicity and alters the Slater–Pauling rule. Such defects are likely to occur since they result to the C1_b lattice structure of the semi‐Heusler alloys. Contrary, the appearance of vacancies at the other sites keeps the half‐metallic character of the parent alloys. Thus for realistic devices it is important to prevent the appearance of vacancies during the growth of thin films. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convergence,stability, and numerical solution of unsteady free convection magnetohydrodynamical flow between two slipping plates

In this study, the unsteady free convection magnetohydrodynamical flow of a viscous, incompressible, and electrically conducting fluid between two horizontally directed slipping plates is considered. The external magnetic filed is applied uniformly in the y-direction and the fluid is assumed to be of low conductivity so that the induced magnetic field is negligible. So the relevant variables, that is, the velocity and the temperature, depend only on one coordinate, the y-axis. The governing equations of velocity and temperature fields are obtained from the continuity, momentum, and energy equations. The boundary conditions for the velocity are taken in the most general form as Robins type which contain slipping parameter. Moreover, the upper plate is heated exponentially and the lower plate is adiabatic. Finite difference method (FDM) is used to simulate the numerical solutions of the problem in which the explicit forward difference in time variable t and central difference in space variable y is used. Hartmann number, Prandtl number, decay factor, and slipping parameter influences on the flow and temperature are shown graphically. It is seen that as the Hartmann number increases, the velocity magnitude drops, which is the well-known flattening tendency of the MHD flow. Also, the increase in decay factor causes an increase in both the velocity and temperature magnitudes at increasing time levels, but it does not change further close to the steady-state. Furthermore, the convergence and stability conditions of the considered scheme are obtained in terms of Hartmann number, Prandtl number, and the slip length.     

Spectral studies of safranin-O in different surfactant solutions

The interaction of Safranin-O (SO), a cationic dye, with various surfactants viz., anionics; Sodiumdodecylsulfate (SDS) and Sodiumdodecylsulfonate (SDSo), nonionics; polyoxyethylenesorbitanmonolaurate (Tween 20) and polyoxyethylenedodecylether (Brij 35), cationic; Dodecyltrimethylammoniumbromide (DTAB) and zwitterionic; Laurylsulfobetaine (LSB) was studied spectrophotometrically as a function of surfactant concentration ranging from premicellar to postmicellar region in aqueous media in the absence and presence of cosolvents. The binding constants (K(b)) and fraction of bound SO to micelles (f), were calculated by means of Benesi-Hildebrand Equation. The binding tendency of SO to micelles followed the order as; Tween 20>Brij 35>SDS>SDSo>LSB. The presence of cosolvents, such as Methanol, Dimethylformamide (DMFA) and 1,4 Dioxan (DX) at various volume percentages, increased the CMC of both SDS and Tween 20 and at a certain concentration totally inhibited the micellization. The binding of SO to micelles decreased as the concentration of the cosolvents increased. This inhibitory effect of cosolvents on binding of SO to micelles followed the order as; Methanol>DMFA>DX.