In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses – beside the Hodge decomposition for one-forms – an analogous decomposition of symmetric tensor fields of second rank on Riemannian manifolds with constant curv...

This paper presents the novel approach for pre-coding in multiple input and multiple output systems using arithmetic mean decomposition. This proposed decomposition scheme has low complexity than popular geometric mean decomposition. CORDIC based Givens rotation is used for making the channel matrix as bi-diagonal matrix and then 2x2 singular value decomposition and 2x2 arithmetic mean decompos...

Abstract. Let nn(C) be the algebra of strictly upper-triangular n × n matrices and X2 = {u ∈ nn(C) : u2 = 0} the subset of matrices of nilpotent order 2. Let Bn(C) be the group of invertible upper-triangular matrices acting on nn by conjugation. Let Bu be the orbit of u ∈ X2 with respect to this action. Let S2n be the subset of involutions in the symmetric group Sn. We define a new partial orde...

The proposal lateral load pattern for pushover analysis is given in two forms for symmetric concrete buildings: 1-(X/H)0.5 for low-rise and mid-rise buildings, 2- Sin(ΠX/H) for high-rise buildings. These two forms give more realistic results as compared to conventional load patterns such as triangular and uniform load patterns. The assumed buildings of 4, 8, 12, 16, 20 and 30 story concrete bui...

Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution σ of G. We prove a polar decomposition G = KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of groups Ai which are the k-points of maximal (k, σ)-split tori, one for each H-conjugacy class. T...

We formulate the Hopf algebraic approach of Connes and Kreimer to renormalization in perturbative quantum field theory using triangular matrix representation. We give a Rota– Baxter anti-homomorphism from general regularized functionals on the Feynman graph Hopf algebra to triangular matrices with entries in a Rota–Baxter algebra. For characters mapping to the group of unipotent triangular matr...

A solution of the problem of calculating cartesian coordinates from a matrix of interpoint distances (the embedding problem) is reported. An efficient and numerically stable algorithm for the transformation of distances to coordinates is then obtained. It is shown that the embedding problem is intimately related to the theory of symmetric matrices, since every symmetric matrix is related to a g...

This paper proposes a hardware accelerator for Cholesky decomposition on FPGAs by designing a single triangular linear equation solver. Good performance is achieved by reordering the computation of Cholesky factorization algorithms and thus alleviating the data dependency. The dedicated hardware architecture for solving triangular linear equations is designed and implemented for different accur...

Given a set of symmetric/antisymmetric filter vectors containing only regular multiresolution filters, the method we present in this article can establish a balanced multiresolution scheme for images, allowing their balanced decomposition and subsequent perfect reconstruction without the use of any extraordinary boundary filters. We define balanced multiresolution such that it allows balanced d...

A new identification method is proposed for Hammerstein systems in presence of dead zone input nonlinearities. To describe and identify the nonlinear system, a new decomposition technique using the triangular basis functions is employed. Then a parameterized model is derived to represent the entire system. The approximation by Triangular basis functions for the description of the static nonline...