MATHEMATICAL SCIENCES
Year:2012 | Volume:6 | Issue:-|Papers Count:8

Purpose: This paper proposes the use of different analytical methods in obtaining approximate solutions for nonlinear differential equations with oscillations.Methods: Three methods are considered in this paper: Lindstedt-Poincare method, the Krylov-Bogoliubov first approximate method, and the differential transform method.Results: Figures that are given in this paper give a strong evidence that the proposed methods are effective in handling nonlinear differential equations with oscillations.Conclusions: This study reveals that the differential transform method provides a remarkable precision compared with other perturbation methods.

Purpose: The purpose of this paper is to study the multilinear commutator in weighted Morrey space.Methods: We divide the multilinear commutator into four parts and apply with the methods of weighted Lebesgue space and Perez and Trujillo-Gonzalez.Results: Let b®= (b1, …, bm), bj ∈ BMO (Rn), 1£j£ m; we show that T[1]b is bounded on weighted Morrey spaces Lp,κ (w), 1<p<¥, 0<k<1, w∈Ap. When p=1, it is shown that T®b is weak type bounded on weighted Morrey space.Conclusions: We extend the results of the commutator in weighted Morrey space. In particular, for m=1, this result is also new in the classical commutator.

Please click on PDF to view the abstract.

Purpose: In this paper, we investigate a class of Sturm-Liouville operators with eigenparameter-dependent boundary conditions and transmission conditions at finite interior points.Methods: By modifying the inner product in a suitable Krein space K associated with the problem, we generate a new self-adjoint operator A such that the eigenvalues of such a problem coincide with those of A.Results: We construct its fundamental solutions, get the asymptotic formulae for its eigenvalues and fundamental solutions, discuss some properties of its spectrum, and obtain its Green function and the resolvent operator.Conclusions: Three important conclusions can be drawn: (1) the new operator A is self-adjoint in the Krein space K; (2) if θi>0, i=1, m-, and ρj>0, j=1, 2, then, the eigenvalues of the problem (Equations 1 to 5) are analytically simple; (3) the residual spectrum of the operator A is empty, i.e., σr (A)=∅.

Purpose: Flux-switching permanent magnet (FSPM) machines are double salient machines with a high energy density suitable for e-mobility. For a fast design process, machine specialists need easy-to-use motor models. For the FSPM model, analytical methods cost high efforts to create and to improve them. Numerical methods such as the finite element method (FEM) have been extensively studied in the literature with little emphasis given to their alternatives.Methods: This research shows the implementation of the Schwarz-Christoffel (SC) mapping for the FSPM. With this numerical method, the double salient motor geometry is transformed into a simpler geometry to reduce the model complexity. For the electromagnetic analysis, SC mapping is implemented both as a stand-alone method and as an integrated method with the tooth contour method and the orthogonal field diagram method.Results: Findings are presented in a comparative analysis for all created models including the finite element method.Results show a very good agreement among the presented models.Conclusions: The results obtained in this paper show that SC mapping is a good alternative to the FEM. With the provided step-by-step explanation on how to implement SC mapping, the method can be expanded to other electrical machine classes.

Purpose: In this paper, we extend the concept of covering dimension of general topological spaces to L-topological spaces using a-Q-covers and quasi-coincidence relation.Methods: Dimension theory is a branch of topology devoted to the definition and study of the notion of dimension in certain classes of topological spaces. The dimension of a general topological space X can be defined in three different ways: the small inductive dimension indX, the large inductive dimension IndX, and the covering dimension dimX. The covering dimension dim behaves somewhat better than the other two dimensions, i.e., that for the dimension dim, a large number of theorems of the classical theory can be extended to general topological spaces. Also, there is a substantial theory of covering dimension for normal spaces.Results: A characterization of covering dimension in the weakly induced L-topological spaces is obtained. Moreover, a characterization of covering dimension for fuzzy normal spaces is also obtained.Conclusions: Finally, This paper provides some brief sketches regarding the topics covering dimension in L-topological spaces and covering dimension for fuzzy normal spaces. The neighborhood structure used for the investigations is the quasi-coincident neighborhood structure.

Purpose: The purpose of the present paper is to study the product (N, pn) (C, 1) summability of a sequence of Fourier coefficients which extends a theorem of Prasad.Methods: We use Np. C1 summability methods with dropping monotonicity on the generating sequence {pn−k} (that is, by weakening the conditions on the filter, we improve the quality of digital filter).Results: Let Bn(x) denote the nth term of conjugate series of a Fourier series. Mohanty and Nanda were the first to establish a result for C1 summability of the sequence {n Bn(x)}. Varshney improved the result for H1. C1 summability which was generalized by various investigators using different summability methods with different sets of conditions. In this paper, we extend a result of Prasad by dropping the monotonicity on the sequence {pn−k}.Conclusions: Various results pertaining to the C1 and H1. C1 summabilities of the sequence {n B n (x)} have been reviewed and the condition of monotonicity on the means generating the sequence {pn−k} has been relaxed. Moreover, a proper set of conditions have been discussed to rectify the errors pointed out in Remark 3.2 (1) and (2).

Purpose: The purpose of this work is to present an approximation for singular integrals of Cauchy type kernel on a smooth-oriented contour.Methods: For the method, we use a small modification of the spline functions in order to eliminate the singularity. Noting that this approximation is due to the idea of Sanikidze’s Approximate solution of singular integral equations in the case of closed contours of integrations.Results: This approximation represents a good approach for any singular integral given on the curve in the sense of Cauchy principal value.Conclusions: This approximation is destined to solve numerically the singular integral equations with Cauchy type kernel on a smooth-oriented contour.