Abstract We consider two natural gradings on the space of symmetric functions: by degree and length. introduce a differential operator T that leaves components this double grading invariant exhibit basis bihomogeneous functions in which is triangular. This allows us to compute eigenvalues , turn out be nonnegative integers.

Genetic Algorithms (GAs) emulate the natural evolution process and maintain a population of potential solutions to a given problem. Through the population, GAs implicitly maintain the statistics about the search space. This implicit statistics can be used explicitly to enhance GA’s performance. Inspired by this idea, a statistics-based adaptive non-uniform crossover (SANUX) has been proposed. S...

We list several open problems concerning the enumeration of directed animals on two-dimensional lattices. We show that most of these problems are special cases of two central problems: calculating the position generating function and the perimeter and area generating function for square lattice animals. We propose a possible direction for solving these two problems: we extend Dhar's corresponde...

Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric operators like normals, curvatures, or LaplaceBeltrami eigenfunctions at large computational and memory costs. We avoid this bottleneck with a compression techni...

This study presents a comparative survey of direct methods for solving Variational Problems. Thisproblems can be used to solve various differential equations in physics and chemistry like RateEquation for a chemical reaction. There are procedures that any type of a differential equation isconvertible to a variational problem. Therefore finding the solution of a differential equation isequivalen...

According to classical results by M. G. Krein and L. de Branges, for every positive measure μ on the real line R such that ∫ R dμ(t) 1+t2 <∞ there exists a Hamiltonian H such that μ is the spectral measure for the corresponding canonical Hamiltonian system JX ′ = zHX. In the case where μ is an even measure from Steklov class on R, we show that the Hamiltonian H normalized by detH = 1 belongs to...

BLAS (Basic Linear Algebra Subprograms) plays a very important role in scientific computing and engineering applications. ATLAS is often recommended as a way to generate an optimized BLAS library. Based on ATLAS, this paper optimizes the algorithms of triangular matrix functions on 750 MHZ Loongson 2F processor-specific architecture. Using loop unrolling, instruction scheduling and data pre-fet...

We present a parallelization of Parlett s algorithm for computing arbitrary functions of upper triangular matrices The parallel algorithm preserves the numerical stability properties of the serial algorithm and is suitable for implementation on coarse grain parallel computers The algorithm ob tains a speedup of for matrices of size greater than as our analysis and actual implementation on a pro...