We study the Case sum rules, especially C0, for general Jacobi matrices. We establish situations where the sum rule is valid. Applications include an extension of Shohat’s theorem to cases with an infinite point spectrum and a proof that if lim n(an− 1) = α and lim nbn = β exist and 2α < |β|, then the Szegő condition fails.

We study the interaction between two interfering Gaussian 2-user multiple access channels. The capacity region is characterized under mixed strong–extremely strong interference and individually very strong interference. Furthermore, the sum capacity is derived under a less restricting definition of very strong interference. Finally, a general upper bound on the sum capacity is provided, which i...

A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation properties of the form sum extension are observed.

We present decay bounds for a broad class of Hermitian matrix functions where the matrix argument is banded or a Kronecker sum of banded matrices. Besides being significantly tighter than previous estimates, the new bounds closely capture the actual (non-monotonic) decay behavior of the entries of functions of matrices with Kronecker sum structure. We also discuss extensions to more general spa...

The sum capacity of a multiuser synchronous CDMA system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed in [7] which had solved the equal power constraint case. We identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them.

We present decay bounds for a broad class of Hermitian matrix functions where the matrix argument is banded or a Kronecker sum of banded matrices. Besides being significantly tighter than previous estimates, the new bounds closely capture the actual (non-monotonic) decay behavior of the entries of functions of matrices with Kronecker sum structure. We also discuss extensions to more general spa...

The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

We study continuity properties of stochastic game problems with respect to various topologies on information structures, defined as probability measures characterizing a game. will establish the value function under total variation, setwise, and weak convergence structures. Our analysis reveals that for bounded is continuous variation structures in both zero-sum games team problems. Continuity ...

We study the problem of finding zero-sum blocks in bounded-sum sequences, which was introduced by Caro, Hansberg, and Montejano. Caro et al. determine minimum $\{-1,1\}$-sequence length for when there exist $k$ consecutive terms that sum to zero. corresponding sequence set $\{-1,1\}$ is replaced $\{-r,s\}$ arbitrary positive integers $r$ $s.$ This confirms a conjecture theirs. also construct $\...

in this paper, some results of singh, gopalakrishna and kulkarni (1970s) have been extended to higher order derivatives. it has been shown that, if $sumlimits_{a}theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $t(r, f)sim t(r, f^{(k)}), rrightarrowinfty$ if $theta(infty, f)=1$ and $t(r, f)sim (k+1)t(r, f^{(k)}), rrightarrowinfty$ if $th...