A basic class of symmetric orthogonal functions with six free parameters

In a previous paper, we introduced a basic class of symmetric orthogonal functions (BCSOF) by an extended theorem for Sturm-Liouville problems with symmetric solutions. We showed that the foresaid class satisfies the differential equation

     

Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces

The similarity solution for the unsteady laminar incompressible boundary layer flow of a viscous electrically conducting fluid in stagnation point region of an impulsively rotating and translating sphere with a magnetic field and a buoyancy force gives a system of non-linear partial differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the homotopy analysis method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the magnetic parameter, buoyancy parameter and rotation parameter on the surface shear stresses and surface heat transfer. It is noted that the behavior of the HAM solution for the surface shear stresses and surface heat transfer is in good agreement with the numerical solution given in reference [H. S. Takhar, A. J. Chamkha, G. Nath, Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces, Heat Mass Transfer 37 (2001) 397].     

Solution algorithms for a class of continuous linear programs with fuzzy valued objective functions

This paper discusses a class of continuous linear programs with fuzzy valued objective functions. A member of this class is called a fuzzy separated continuous linear program (FSCLP). Such problems have applications in a number of domains, including, production and inventory systems, communication networks, and pipeline systems for transportation. The discretization approach is used to construct two ordinary fuzzy linear programming problems, which give a lower and an upper bound on the optimal value of FSCLP. It is then shown how to construct an improved feasible solution for FSCLP starting from a nonoptimal one. This leads to the development of a class of algorithms based on a sequence of discrete approximations to FSCLP. Numerical examples in the context of continuous-time networks are presented to show the applicability of the proposed method.     

An arithmetical view to first-order logic

A value space is a topological algebra B equipped with a non-empty family of continuous quantifiers :B^∗→B. We will describe first-order logic on the basis of B. Operations of B are used as connectives and its relations are used to define statements. We prove under some normality conditions on the value space that any theory in the new setting can be represented by a classical first-order theory.     

On the stability of the first-order linear recurrence in topological vector spaces

Suppose that X is a sequentially complete Hausdorff locally convex space over a scalar field K, V is a bounded subset of X, (a_n)_n≥0 is a sequence in K?{0} with the property lim inf_n→∞|a_n|>1, and (b_n)_n≥0 is a sequence in X. We show that for every sequence (x_n)_n≥0 in X satisfying

     

Analytical Holographic Superconductor with Backreaction Using AdS 3/CFT 2

The holographic model for a two-dimensional superconductor has been investigated by considering the three-dimensional gravity in the bulk. To find the critical temperature, we used the Sturm–Liouville variational method. Where as the same method is applied for calculating the condensation of the dual operators on the boundary. We included the back reactions on the metric by a combination of the perturbation method of the fields with respect to the small parameter and then applying the variational integrals on the resulting equations of the motion. The critical temperature has been successfully obtained on the backreaction effects, and we showed that it dropped with a rise in the backreaction of the fields, and it makes the condensation harder. We can use our analytical results to support the numerical data which was reported previously.     

Rheological Studies of Silica-Tragacanth Suspensions

Formation of a concentrated solid/liquid suspension, as an industrial intermediate, is often necessary in many industrial manufacturing processes, particularly for paints, paper coating, ceramics, catalysts, etc. Polysaccharides have been widely used for the control of the stability of suspensions. In this paper, various rheological parameters; such as viscosity—shear rate, shear stress—shear rate, storage and loss modulus frequency at various temperatures, and strain stress; have been measured for different compositions of silica powder in water with 0.3 wt% tragacanth gum as a phase stabilizer.     

An Exact Family of Einstein–Maxwell Wyman–Adler Solution in General Relativity

This paper presents a family of two-parametric interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with particular choice of charge distribution and the metric component g ₀₀. This family gives us wide range of parameters, n and K, for which the solutions are regular and acceptable on physical grounds and hence suitable for modeling of charged compact star. The maximum allowable mass and corresponding radius, for this family of solutions with the particular form of charge distribution, is determined to be 2.48M _⊙ and 10.56 km respectively by assuming the stellar “surface” density equal to strange (quark) matter density at zero pressure. It is hoped that our investigation may be of some importance in connection with the study of internal structure of electrically charged strange (quark) star.