Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...

This work is based on the Euler-Seidel matrix method [11] which is related to algorithms, combinatorics and generating functions. This method is quite useful to investigate properties of some special numbers and polynomials. In this paper we consider the Euler-Seidel matrix method for some combinatorial numbers and polynomials. This method is relatively easier than the most of combinatorial met...

The purpose of this note is to investigate the close relationship that exists between the Euler-Seidel matrix [3, 4, 5, 6, 10] of an integer sequence, and the Hankel matrix [9] of that sequence. We do so in the context of sequences that have integral moment representations, though many of the results are valid in a more general context. While partly expository in nature, the note assumes a cert...

Rotating beams have been considerably appealing to engineers and designers of complex structures i.e. aircraft’s propeller and windmill turbines. In this paper, a new flexibility-based method is proposed for the dynamic analysis of rotating non-prismatic Euler-Bernoulli beams. The flexibility basis of the method ensures the true satisfaction of equilibrium equations at any interior point of the...

The present study investigates buckling characteristics of both nonlinear symmetric power and sigmoid functionally graded (FG) beams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by the sigmoid-law distribution (S-FGM), and the symmetric power function (SP-FGM). These functions have smooth variation of properties across the boundary rather tha...

In this paper, vibration analysis of multiple-stepped Bernoulli-Euler and Timoshenko beams carrying point masses is presented analytically for various boundary conditions. Each attached element is considered to have both translational and rotational inertias. The method of solution is “transfer matrix method” which is based on the changes in the vibration modes at the vicinity of any discontinu...

This note provides explicit techniques to compute the exponentials of a variety of anti-Hermitian matrices in dimension four. Many of these formulae can be written down directly from the entries of the matrix. Whenever any spectral calculations are required, these can be done in closed form. In many instances only 2 × 2 spectral calculations are required. These formulae cover a wide variety of ...

We’ll follow the notational conventions of Shoemake’s “Euler Angle Conversion”, Graphics Gems IV, pp. 222-9, with the exception that our vectors are row vectors instead of column vectors. Thus, all our matrices are transposed relative to Shoemake’s, and a sequence of rotations will be written from left to right. We’ll simplify the discussion by ignoring the various possible axis permutations, a...

Abstract: This paper gives some sufficient conditions for a given polyhedral set which is represented as a set of linear inequalities to be positive D-invariant for uncertain linear discrete-time systems in the case such that the systems matrices depend linearly on uncertain parameters whose ranges are given intervals. Further, the results will be applied to uncertain linear continuous systems ...

In this paper, we construct a hierarchy of hybrid numerical methods for multi-scale kinetic equations based on moment realizability matrices, a concept introduced by Levermore, Morokoff and Nadiga in [15]. Following such a criterion, one can consider hybrid scheme where the hydrodynamic part is given either by the compressible Euler or Navier-Stokes equations, or even with more general models, ...