The conjugate traceand traceof a planepartition aredefined,and thegenerating function for the number of plane partitions TT of n with <r rows and largest part <m, with conjugate trace t (or trace I, when m = co), is found. Various properties of this generating function are studied. One consequence of these properties is a formula which can be regarded as a q-analog of a well-known result arisin...

In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the ...

Abstract: The conjugate gradient method is an algorithm for the numerical solution of systems of linear equations whose matrices are positive-definite and symmetric. It is an iterative method that can even be applied to solve a sparse system of equations. In this paper, we applied the conjugate gradient method of higher order to wave propagation control problems. The algorithm of this method wa...

UltraWideband (UWB) systems use Multi-Band OFDM (MB-OFDM) techniques for transmission. UWB based systems are power limited by the regulation of Federal Communications Commission (FCC). CP introduces correlation in the transmitted data sequence and hence introduces ripples in the power spectral density (PSD) of the transmitted data. This in turn reduces the range of data transmission. The overla...

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesics connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional spacetimes and to GRW spacetimes satisfying the timelike convergence conditi...

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesics connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional spacetimes and to GRW spacetimes satisfying the timelike convergence conditi...

This paper is concerned with proving theoretical results related to the convergence of the Conjugate Gradient method for solving positive definite symmetric linear systems. New relations for ratios of the A-norm of the error and the norm of the residual are provided starting from some earlier results of Sadok [13]. These results use the well-known correspondence between the Conjugate Gradient m...

In this paper we define the Evans function for Sturm-Liouville problems. We show that the Evans function is analytic in the spectral parameter, has zeros in one-to-one correspondence with the eigenvalues, and is under certain conditions what we call conjugate symmetric. We conclude by showing that the Evans function can be used to track the movement of the eigenvalues as the coefficients in the...

In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such system where is an XXZ Richardson-Gaudin integrable model and detail its exact Bethe ansatz solution. While no longer Hermitian, Hamiltonian pseudo-Hermitian/PT-symmetric, as strength of coupling environment increased spectrum in fixed symmetry sector changes ...