Resumo em Inglês:

This paper studies the stability and boundedness of solutions of certain nonlinear third-order delay differential equations. Sufficient conditions for the stability and boundedness of solutions for the equations considered are obtained by constructing a Lyapunov functional. Mathematical subject classification: 34K20.

Resumo em Inglês:

In the present work the inverse problem of identification of radiative properties, the total extinction and scattering coefficients, is analyzed and explicitly formulated based in an elementary semi-group theory. The Chandrasekhar discrete ordinates finite dimensional approximation of the angular variables is used for the direct problem representation with the stationary Linear Transport (Boltzmann) Equation in absorbing and scattering media in matrix form. For the inverse problem we suppose known the albedo operator from measured intensities at the boundaries of the medium. Here we analize the inverse problem for an N-dimensional medium and from the solution of the transmission problem we present an explicit form for the matrix that contains the total extinction and scattering coefficients. Mathematical subject classification: 80A23, 15A29.

Resumo em Inglês:

The steady state inverse radiative transfer problem in one-dimensional participating media is studied as an example of application of the new methodology presented in a accompanying paper by the authors [2]. Spectral methods are used for the appropriate analysis of the direct transport problem. For the inverse problem, we present a matrix that involves only values of the flux intensities at the boundary of the medium. Its columns are built with a set of linearly independent solutions for the system, which is formed when angular half-range prescribed boundary values and the complementary measured half-range boundary values are coupled. The final inverse albedo problem is treated as a full range two point boundary value problem. Test cases results are presented. Mathematical subject classification: 80A23, 15A29.

Resumo em Inglês:

In this paper, we produce shuffle relations from multiple zeta values of the form ζ ({ 1 }m-1, n+1). Here { 1 }k is k repetitions of 1, and for a string of positive integers α1, α2, ...,αr with αr > 2 . ζ (α1, α1, ..., α1) = Σ n1-α1n2-α2... n r-αr 1 < n1 < n2 < ... < n r As applications of the sum formula and a newly developed weighted sum formula, we shall prove for even integers k, r > 0 that k r Σ Σ (-1)ℓ Σ ζ (α0, α1, ..., αj + βj, βj+1, ..., βk, βk+1 + 1) j = 0 ℓ = 0 |α| = j + r - ℓ + 1 |β| = k - j + ℓ + 2 + Σ Σ ζ (α0, α1, ..., αk r - ℓ + 3) = ζ (k + r + 4). 0 < ℓ < r |α| = k + ℓ + 1 ℓ : even Mathematical subject classification: Primary: 40A25, 40B05; Secondary: 11M99, 33E99.

Resumo em Inglês:

An iterative algorithm is considered for variational inequalities, generalized equilibrium problems and fixed point problems. Strong convergence of the proposed iterative algorithm is obtained in the framework Hilbert spaces. Mathematical subject classification: 47H05, 47H09, 47J25, 47N10.

Resumo em Inglês:

Zeros of orthogonal polynomials associated with two different Sobolev inner products involving the Jacobi measure are studied. In particular, each of these Sobolev inner products involves a pair of closely related Jacobi measures. The measures of the inner products considered are beyond the concept of coherent pairs of measures. Existence, real character, location and interlacing properties for the zeros of these Jacobi-Sobolev orthogonal polynomials are deduced. MATHEMATICAL SUBJECT CLASSIFICATION: 33C45, 33C47, 26C10.

Resumo em Inglês:

We are concerning with two analytical methods; the classical method of successive approximations (Picard method) [14] which consists the construction of a sequence of functions such that the limit of this sequence of functions in the sense of uniform convergence is the solution of a quadratic integral equation, and Adomian method which gives the solution as a series see ([1-6], [12] and [13]). The existence and uniqueness of the solution and the convergence will be discussed for each method. Mathematical subject classification: Primary: 39B82; Secondary: 44B20, 46C05.

Resumo em Inglês:

A method of successive Lagrangian formulation of linear approximation for solving boundary value problems of large deformation in finite elasticity is proposed. Instead of solving the nonlinear problem, by assuming time steps small enough and the reference configuration updated at every step, we can linearize the constitutive equation and reduce it to linear boundary value problems to be solved successively with incremental boundary data. Moreover, nearly incompressible elastic body is considered as an approximation to account for the condition of incompressibility. For the proposed method, numerical computations of pure shear of a square block for Mooney-Rivlin material are considered and the results are compared with the exact solutions. Mathematical subject classification: Primary: 65C20; Secondary: 74B20.

Resumo em Inglês:

The aim of this paper is to introduce a new family of sequences which faster converge to the Euler-Mascheroni constant. Finally, numerical computations are given. Mathematical subject classification: 41A60, 41A25, 57Q55.

Resumo em Inglês:

In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, 20H10.

Resumo em Inglês:

We develop the impulsive inequality and the classical lower and upper solutions, and establish the comparison principles. By using these results and the monotone iterative technique, we obtain the existence of solutions of periodic boundary value problems for a class of impulsive neutral differential equations with multi-deviation arguments. An example is given to demonstrate our main results. Mathematical subject classification: Primary: 34A37; Secondary: 34k10.

Resumo em Inglês:

In this paper, we present a method and associated theory for solving the multi-input Sylvester-Observer equation arising in the construction of the Luenberger observer in control theory. The proposed method is a particular generalization of the algorithm described by Datta and Saad in 1991 to the multi-output. We give some theoretical results and present some numerical experiments to show the accuracy of the proposed algorithm. Mathematical subject classification: 65F10, 65F30.