This paper presents a novel approach for analyzing the free vibration response of variable-stiffness panels. A method is proposed herein, which relies upon combination R-functions and Ritz method. powerful peculiar aspect this consists in possibility handling any complex geometry with reduced modeling effort few degrees freedom to be handled. The so-obtained formulation particular interest earl...

Many inequality relations between real vector quantities can be succinctly expressed as “weak (sub)majorization” relations using the symbol ≺w. We explain these ideas and apply them in several areas: angles between subspaces, Ritz values, and graph Laplacian spectra, which we show are all surprisingly related. Let Θ(X ,Y) be the vector of principal angles in nondecreasing order between subspace...

The Rayleigh–Ritz method is widely used for eigenvalue approximation. Given a matrix X with columns that form an orthonormal basis for a subspace X , and a Hermitian matrix A, the eigenvalues of XHAX are called Ritz values of A with respect to X . If the subspace X is A-invariant, then the Ritz values are some of the eigenvalues of A. If the A-invariant subspace X is perturbed to give rise to a...

We describe the construction of trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of two irreducible representations of a quantum algebra Uq(G). Our method is a generalization of the tensor product graph method to the case of two different representations. It yields the decomposition of the R-matrix into projection operators. Many new examples of trigonometric R-m...

In this note, we describe a method for establishing trigonometric inequalities that involve symmetric functions in the cosines of the angles of a triangle. The method is based on finding a complete set of relations that define the cosines of such angles.

In this paper is presented a new approach in fractal image coding based on trigonometric approximation. The least square approximation method is used for approximation of blocks in standard fractal image compression algorithm. In the paper is shown that it is possible to use also trigonometric approximation for describing of blocks in fractal image coding. This approximation was implemented and...

A C1 piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of deve...