Some <Emphasis Type="Italic">I</Emphasis>-convergent sequence spaces defined by Orlicz functions

In this article we introduce the sequence spaces cI(M),c0I(M),mI(M) and m0I(M) using the Orlicz function M.We study some of the properties like solid,symmetric,sequence algebra,etc and prove some inclusion relations.     

Estimates for eigenvalues of stochastic matrices

It is well-known that the eigenvalues of stochastic matrices lie in the unit circle and at least one of them has the value one. Let {1, r 2 , ··· , r N } be the eigenvalues of stochastic matrix X of size N × N . We will present in this paper a simple necessary and sufficient condition for X such that |r j | < 1, j = 2, ··· , N . Moreover, such condition can be very quickly examined by using some search algorithms from graph theory.     

UNIVERSAL INTERPOLATING SEQUENCES ON SPACES OF ANALYTIC FUNCTIONS

This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk.     

The rotational dimension of a graph

Given a connected graph G = (N, E) with node weights s∈? and nonnegative edge lengths, we study the following embedding problem related to an eigenvalue optimization problem over the second smallest eigenvalue of the (scaled) Laplacian of G: Find v_i∈?^|N|, i∈N so that distances between adjacent nodes do not exceed prescribed edge lengths, the weighted barycenter of all points is at the origin, and is maximized. In the case of a two‐dimensional optimal solution this corresponds to the equilibrium position of a quickly rotating net consisting of weighted mass points that are linked by massless cables of given lengths. We define the rotational dimension of G to be the minimal dimension k so that for all choices of lengths and weights an optimal solution can be found in ?^k and show that this is a minor monotone graph parameter. We give forbidden minor characterizations up to rotational dimension 2 and prove that the rotational dimension is always bounded above by the tree‐width of G plus one. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:283‐302, 2011     

Fast iterative solver for convection‐diffusion systems with spectral elements

We introduce a solver and preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection–diffusion equation. The method is based on a Robin–Robin interface preconditioner coupled to a fast diagonalization solver which is used to efficiently eliminate the interior degrees of freedom and perform subsidiary subdomain solves. Using a spectral element discretization, we first apply our technique to constant wind problems, and then propose a means for applying the technique as a preconditioner for variable wind problems. We demonstrate that iteration counts are mildly dependent on changes in mesh size and convection strength. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Reproducing Kernel method for the solution of nonlinear hyperbolic telegraph equation with an integral condition

In this article, an iterative method is proposed for solving nonlinear hyperbolic telegraph equation with an integral condition. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n‐term approximation u_n(x, t) of the exact solution u(x, t) is obtained and is proved to converge to the exact solution. Moreover, the partial derivatives of u_n(x, t) are also convergent to the partial derivatives of u(x, t). Some numerical examples have been studied to demonstrate the accuracy of the present method. Results obtained by the method have been compared with the exact solution of each example and are found to be in good agreement with each other. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 867–886, 2011     

Excited-state hydrogen bonding and deprotonation of esculetin in solution: a DFT/TDDFT study

The combined density functional theory (DFT) and time-dependent density functional theory (TDDFT) method was used to study the electronic spectral properties of different deprotonated forms of esculetin. By comparing the experimental absorption and fluorescence bands with the calculated electronic spectra, it is evidently demonstrated that the minor absorption and fluorescence bands observed at slightly longer wavelengths than the principal bands in experiments are predominantly from the de-H3 form of the esculetin monomer. Furthermore, we clarified the relationship between electronic spectral shifts and electronic excited-state intramolecular hydrogen bonding changes: the strengthening of intramolecular hydrogen bond can induce an electronic spectral blueshift while the intramolecular hydrogen bond weakening can result in an electronic spectral redshift.     

Coquet-type formulas for the rarefied weighted Thue–Morse sequence

Newman proved for the classical Thue–Morse sequence, ((−1)^s(n))_n≥0, that for all N∈N with real constants satisfying c₂>c₁>0 and λ=log3/log4. Coquet improved this result and deduced , where F(x) is a nowhere-differentiable, continuous function with period 1 and η(N)∈{−1,0,1}. In this paper we obtain for the weighted version of the Thue–Morse sequence that for the sum a Coquet-type formula exists for every r∈{0,1,2} if and only if the sequence of weights is eventually periodic. From the specific Coquet-type formulas we derive parts of the weak Newman-type results that were recently obtained by Larcher and Zellinger.