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...

Probit residuals need not sum to zero in general. However, if explanatory variables are qualitative the sum can be shown to be zero for many models. Indeed this remains true for binary dependent variable models other than Probit and Logit. Even if some explanatory variables are quantitative, residuals can sum to almost zero more often than might at first seem plausible.

We take a new perspective on the weighted sumrate maximization in multiple-input multiple-output (MIMO) interference networks, by formulating an equivalent max-min problem. This seemingly trivial reformulation has significant implications: the Lagrangian duality of the equivalent max-min problem provides an elegant way to establish the sum-rate duality between an interference network and its re...

We study the I-ultrafilters on ω, where I is a a collection of subsets of a set X , usually R or ω1. The I-ultrafilters usually contain the P -points, often as a small proper subset. We study relations between I-ultrafilters for various I, and closure of I-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether I-ultrafilters always exist.

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

The capacity region of the N -sender additive white Gaussian noise (AWGN) multiple access channel (MAC) with feedback is not known in general, despite significant contributions by Cover, Leung, Ozarow, Thomas, Pombra, Ordentlich, Kramer, and Gastpar. This paper studies the class of generalized linear feedback codes that includes (nonlinear) nonfeedback codes at one extreme and the linear feedba...

The clique vector c(G) of a graph G is the sequence (c1, c2, . . . , cd) in N, where ci is the number of cliques in G with i vertices and d is the largest cardinality of a clique in G. In this note, we use tools from commutative algebra to characterize all possible clique vectors of k-connected chordal graphs.