The classical Kronecker limit formula describes the constant term in Laurent expansion at first order pole of non-holomorphic Eisenstein series associated to cusp infinity modular group. Recently, meromorphic continuation and type formulas were investigated for hyperbolic elliptic elements a Fuchsian group kind by Jorgenson, Kramer named author. In present work, we realize averaged versions all...

In this paper a wide family of identifying codes over regular Cayley graphs of degree four which are built over finite Abelian groups is presented. Some of the codes in this construction are also perfect. The graphs considered include some well-known graphs such as tori, twisted tori and Kronecker products of two cycles. Therefore, the codes can be used for identification in these graphs. Final...

The large neutrino mixing angles have generated interest in finite subgroups of SU(3), as clues towards understanding the flavor structure of the Standard Model. In this work, we study the mathematical structure of the simplest non-Abelian subgroup, ∆(3n2). Using simple mathematical techniques, we derive its conjugacy classes, character table, build its irreducible representations, their Kronec...

This paper presents an exact minimization algorithm for fixed polarity Reed-Muller expressions (FPRMs) for incompletely specified functions. For an n-variable function with unspecified minterms there are 2 distinct FPRMs. A minimum FPRM is one with the fewest products. The minimization algorithm is based on the multi-terminal binary decision diagrams. Experimental results for a set of functions...

We define multidimensional Vandermonde matrices (MV) to be certain submatrices of Kronecker products of standard Vandermonde matrices. These MV matrices appear naturally in multidimensional problems of polynomial interpolation. An explicit algorithm is produced to solve systems of linear equations with MV matrices of coefficients. This is an extension of work of Stenger for the two-dimensional ...

We introduce a framework and early results for massively scalable Gaussian processes (MSGP), significantly extending the KISS-GP approach of Wilson and Nickisch (2015). The MSGP framework enables the use of Gaussian processes (GPs) on billions of datapoints, without requiring distributed inference, or severe assumptions. In particular, MSGP reduces the standard O(n) complexity of GP learning an...

In this work, we present a computational method for solving Poisson equations and biharmonic equations which are based on the use of Haar wavelets. The first transform the spectral coefficients into the nodal variable values. The second use Kronecker products to construct the approximations for derivatives over a tensor product grid of the horizontal and vertical blocks. Finally, solve the obta...

A common assumption in the design and analysis of many MIMO transmission schemes is the so-called Kronecker model. This model is often a crucial step to obtain mathematically tractable solutions, but has also been criticized for being unrealistic. In this paper, we present a numerical approach to determine a channel whose statistics is as far from being Kronecker as possible, keeping only an as...

Recently, quaternion orthogonal designs (QODs) were introduced as a mathematical construct with the potential for applications in wireless communications. The potential applications require new methods for constructing QODs, as most of the known methods of construction do not produce QODs with the exact properties required for implementation in wireless systems. This paper uses real amicable or...