Determining if a symmetric function is Schur-positive is a prevalent and, in general, a notoriously difficult problem. In this paper we study the Schur-positivity of a family of symmetric functions. Given a partition ν, we denote by νc its complement in a square partition (mm). We conjecture a Schur-positivity criterion for symmetric functions of the form sμ′sμc − sν′sνc , where ν is a partitio...

In this paper, the relationship between the (P,Q)-orthogonal symmetric and symmetric matrices is derived. By applying the generalized singular value decomposition, the general expression of the least square (P,Q)-orthogonal symmetric solutions for the matrix equation AXB = C is provided. Based on the projection theorem in inner space, and by using the canonical correlation decomposition, an ana...

Abstract Recently, Taneja [7] studied two one parameter generalizations of J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric divergence. These two generalizations in particular contain measures like: Hellinger discrimination, symmetric chi-square divergence, and triangular discrimination. These measures are well known in the literature of Statistics and Information theory. In thi...

In the context of Synthetic Differential Geometry, we describe the square volume of a “second-infinitesimal simplex”, in terms of square-distance between its vertices. The square-volume function thus described is symmetric in the vertices. The square-volume gives rise to a characterization of the volume form in the top dimension.

A symmetric space analogue of Casselman’s criterion for square integrability of representations of a p-adic group is established. It is described in terms of exponents of Jacquet modules along parabolic subgroups associated to the symmetric space.

We consider symmetric powers of a graph. In particular, we show that the spectra of the symmetric square of strongly regular graphs with the same parameters are equal. We also provide some bounds on the spectra of the symmetric squares of more general graphs. The connection with generic exchange Hamiltonians in quantum mechanics is discussed in an appendix.

DOI: http://dx.doi.org/10.1090/noti1454 best explained in the framework of complex symmetric operators, a surprisingly large class of tractable and well-behaved operators. Let H be a complex Hilbert space. Examples include Cn, the Lebesgue spaces L2(X,μ) of square-integrable functions on X with respect to a measure μ, the spaces l2(N) and l2(Z) of square integrable sequences indexed byN andZ, a...