We propose a new type of three-cluster equation which uses two-cluster resonating-groupmethod (RGM) kernels. In this equation, the orthogonality of the total wave-function to two-cluster Pauli-forbidden states is essential to eliminate redundant components admixed in the three-cluster systems. The explicit energy-dependence inherent in the exchange RGM kernel is self-consistently determined. Fo...

In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the orthogonality condition of the atoms, yielding overcomplete dictionaries with an extended number of atoms. More generally than the linear decomposition, overcomple...

In this paper we present two different results in the theory of Cauchy-Stieltjes Kernel (CSK) families. We firstly provide construction free Sheffer systems with CSK associate a additive convolution semigroup probability measures to any and prove that is only one leads an orthogonal systems. also show orthogonality occurs if associated generates families quadratic variance function. Secondly, a...

Abstract: In this paper, we use the mutual information between error/input as the cost function for adaptive filtering. For the finite-impulse response (FIR) filter, the connections between the minimum error/input information (MEII) criterion and traditional mean-square error (MSE) criterion are investigated. We show that, for Gaussian case, the MEII criterion is equivalent to the well-known or...

The spectral decomposition for an explicit second-order differential operator T is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one. The spectral analysis gives rise to a generalized Fourier transform with an explicit hypergeometric function as a kernel. Using Jacobi polynomial...

Dmitrii Karp Institute of Applied Mathematics 7 Radio Street, Vladivostok, 690041, Russia [email protected] Abstra t Let fk be the k-th Fourier oe ient of a fun tion f in terms of the orthonormal Hermite, Laguerre or Ja obi polynomials. We give ne essary and su ient onditions on f for the inequality k |fk|θ < ∞ to hold with θ > 1. As a by-produ t new orthogonality relations for the Hermite and La...

Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...

In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structur...