Showing papers in "Journal of Linear and Topological Algebra in 2015"

s-Topological vector spaces

Abstract: In this paper, we have defined and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are defined by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is an s-topological vector space. A homomorphism between s-topological vector spaces is semi-continuous if it is s-continuous at the identity.

New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces

Abstract: In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hilbert fusion basis and obtain some character- izations of them. we study orthonormal fusion systems and Riesz fusion bases for Hilbert spaces. we consider the stability of fusion bases under small perturbations. We also general- ized a result of Paley-Wiener (16) to the situation of fusion basis.

On fuzzy soft connected topological spaces

Abstract: In this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. We also investigate effect to fuzzy soft connectedness. Moreover, $C_i$-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

An algorithm for determining common weights by concept of membership function

Abstract: Data envelopment analysis (DEA) is a method to evaluate the relative eciency of decision making units (DMUs). In this method, the issue has always been to determine a set of weights for each DMU which often caused many problems. Since the DEA models also have the multi-objective linear programming (MOLP) problems nature, a rational relationship can be established between MOLP and DEA problems to overcome the problem of determining weights. In this study, a membership function was dened

Bernoulli collocation method with residual correction for solving integral-algebraic equations

Abstract: The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when the exact solutions are polynomials. Also, an error analysis based on the use of the Bernoulli polynomials is provided under several mild conditions. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods.

Numerical solution of Fredholm integral-dierential equations on unbounded domain

Abstract: In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultilized to reduce the (FIDEs) to the solution of a system of linear algebraic equations with unknown generalized Laguerre coefficients. In addition, two examples are given to demonstrate the validity, efficiency and applicability of the technique.

A new Approximation to the solution of the linear matrix equation AXB = C

Abstract: It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB = C. Furthermore, the conditions will be explored to check the convergence of the homotopy series. Numerical examples are also adapted to illustrate the properties of the modified method. c ⃝ 2015 IAUCTB. All rights reserved.

Duals and approximate duals of g-frames in Hilbert spaces

Abstract: In this paper we get some results and applications for duals and approximate duals of g-frames in Hilbert spaces. In particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of Hilbert spaces. We also obtain some results for perturbations of approximate duals.

A numerical solution of mixed Volterra Fredholm integral equations of Urysohn type on non-rectangular regions using meshless methods

Abstract: In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radial basis functions (RBFs) constructed on a set of disordered data. The method is a meshless method, because it is independent of the geometry of the domain and it does not require any background interpolation or approximation cells. The error analysis of the method is provided. Numerical results are presented, which confirm the theoretical prediction of the convergence behavior of the proposed method.

Second order linear differential equations with generalized trapezoidal intuitionistic Fuzzy boundary value

Abstract: In this paper the solution of a second order linear dierential equations with intu- itionistic fuzzy boundary value is described. It is discussed for two dierent cases: coecient is positive crisp number and coecient is negative crisp number. Here fuzzy numbers are taken as generalized trapezoidal intutionistic fuzzy numbers (GTrIFNs). Further a numerical example is illustrated.

Application of triangular functions for solving the vasicek model

Abstract: This paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (TFs) in combination with the collocation method. The method is stated by using conversion the the vasicek model to a stochastic nonlinear system of 2m + 2 equations and 2m + 2 unknowns. Finally, the error analysis and some numerical examples are provided to demonstrate applicability and accuracy of this method. c

On duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules

Abstract: In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be again a g-Riesz basis. We find a situation for a g-Riesz basis to have unique dual g-Riesz basis. Also, we show that every modular g-Riesz basis is a g-Riesz basis in Hilbert C*-module but the opposite implication is not true. c ⃝ 2015 IAUCTB. All rights reserved.

Classical Wavelet Transforms over Finite Fields

Abstract: This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as a finite coherent sum of classical wavelet coefficients.

Some results on higher numerical ranges and radii of quaternion matrices

Abstract: Let n and k be two positive integers, k ⩽ n and A be an n−square quaternion matrix. In this paper, some results on the k−numerical range of A are investigated. Moreover, the notions of k-numerical radius, right k-spectral radius and k-norm of A are introduced, and some of their algebraic properties are studied. c ⃝ 2015 IAUCTB. All rights reserved.

On the girth of the annihilating-ideal graph of a commutative ring

Abstract: The annihilating-ideal graph of a commutative ring $R$ is denoted by $AG(R)$, whose vertices are all nonzero ideals of $R$ with nonzero annihilators and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this article, we completely characterize rings $R$ when $gr(AG(R))neq 3$.

Quotient Arens regularity of $L^1(G)$

Abstract: Let $mathcal{A}$ be a Banach algebra with BAI and $E$ be an introverted subspace of $mathcal{A}^prime$. In this paper we study the quotient Arens regularity of $mathcal{A}$ with respect to $E$ and prove that the group algebra $L^1(G)$ for a locally compact group $G$, is quotient Arens regular with respect to certain introverted subspace $E$ of $L^infty(G)$. Some related result are given as well.

Analytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations

Abstract: In this work, we conduct a comparative study among the combine Laplace trans- form and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro- dierential equations of the second kind. The nonlinear part of integro-dierenti al is approx- imated by Adomian polynomials, and the equation is reduced to a simple equations. The proper implementation of combine Laplace transform and modied Adomian decomposition method can extremely minimize the size of work if compared to existing traditional tech- niques. Moreover, three particular examples are discussed to show the reliability and the performance of method. c

Frames for compressed sensing using coherence

Abstract: We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satisfied. Moreover, we give better estimations then the ones given recently by Cai, Wang and Xu.

Fixed Point Theorems for semi lambda-subadmissible Contractions in b-Metric spaces

Abstract: Here, a new certain class of contractive mappings in the b metric spaces is intro- duced. Some xed point theorems are proved which generalize and modify the recent results in the literature. As an application, some results in the b metric spaces endowed with a partial ordered are proved. c

Lie higher derivations on B(X)

Abstract: Let X be a Banach space of dimX > 2 and B(X) be the space of bounded linear operators on X. If L : B(X) ! B(X) be a Lie higher derivation on B(X), then there exists an additive higher derivation D and a linear map : B(X) ! FI vanishing at commutators (A;B) for all A;B 2 B(X) such that L = D + .

The solutions to some operator equations in Hilbert $C^*$-module

Abstract: In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we find explicit solution of the operator equation $TXS^*-SX^*T^*= A$.

On the boundedness of almost multipliers on certain Banach algebras

Abstract: Almost multiplier is rather a new concept in the theory of almost functions. In this paper we discuss on the boundedness of almost multipliers on some special Banach algebras, namely stable algebras. We also define an adjoint and extension for almost multiplier. c ⃝ 2015 IAUCTB. All rights reserved.

On dual shearlet frames

Abstract: In This paper, we give a necessary condition for function in L 2 with its dual to generate a dual shearlet tight frame with respect to admissibility.

Characterization of G2(q), where 2 < q = 1(mod3) by order components

Abstract: In this paper we will prove that the simple group $G_2(q)$, where $2 < q equiv 1(mod3)$ is recognizable by the set of its order components, also other word we prove that if $G$ is a fi nite group with $OC(G)=OC(G_2(q))$, then $G$ is isomorphic to $G_2(q)$.

On the convergence of the homotopy analysis method to solve the system of partial differential equations

Abstract: One of the efficient and powerful schemes to solve linear and nonlinear equations is homotopy analysis method (HAM). In this work, we obtain the approximate solution of a system of partial differential equations (PDEs) by means of HAM. For this purpose, we develop the concept of HAM for a system of PDEs as a matrix form. Then, we prove the convergence theorem and apply the proposed method to defined the approximate solution of some systems of PDEs. Also, we show the region of convergence by plotting the H-surface.

Stochastic averaging for SDEs with Hopf Drift and polynomial diffusion coefficients

Abstract: It is known that a stochastic dierential equation (SDE) induces two probabilistic objects, namely a diusion