Identities and exponential bounds for transfer matrices

The exponential functions of central-symmetric $X$-form matrices

It is well known that the matrix exponential function has practical applications in engineering and applied sciences. In this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric $X$-form. For instance, $e^{mathbf{A}t}$, $t^{mathbf{A}}$ and $a^{mathbf{A}t}$ will be evaluated by the new formulas in this par...

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

Capacity Bounds and High-SNR Capacity of the Additive Exponential Noise Channel With Additive Exponential Interference

Communication in the presence of a priori known interference at the encoder has gained great interest because of its many practical applications. In this paper, additive exponential noise channel with additive exponential interference (AENC-AEI) known non-causally at the transmitter is introduced as a new variant of such communication scenarios‎. First, it is shown that the additive Gaussian ch...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Generating Matrix Identities and Proof Complexity Lower Bounds

Motivated by the fundamental lower bounds questions in proof complexity, we investigate the complexity of generating identities of matrix rings, and related problems. Specifically, for a field F let A be a non-commutative (associative) F-algebra (e.g., the algebra Matd(F) of d × d matrices over F). We say that a non-commutative polynomial f(x1, . . . , xn) over F is an identity of A, if for all...