This paper addresses the positive semi-deffnite procrustes problem (PSDP). The PSDP corresponds to a least squares over set of symmetric and matrices. These kinds problems appear in many applications such as structure analysis, signal processing, among others. A non-monotone spectral projected gradient algorithm is proposed obtain numerical solution for PSDP. employs Zhang Hager's technique com...

D First, we present definite-clause set grammars (DCSG), a DCG-like formalism for free-word-order languages. The DCSG formalism is well suited for problem solving. By dealing with DCSG as a generalized parsing problem, we avoid a certain type of looping problem in backward chaining. Next, we extend DCSG by viewing grammar rules as definitions for set conversions. In order to realize inverse con...

We study the following question posed by Turán. Suppose Ω is a convex body in Euclidean space Rd which is symmetric in Ω and with value 1 at the origin; which one has the largest integral? It is probably the case that the extremal function is the indicator of the half-body convolved with itself and properly scaled, but this has been proved only for a small class of domains so far. We add to thi...

Let (A, B) be a definite pair of n × n Hermitian matrices. That is, |x∗Ax| + |x∗Bx| 6= 0 for all non-zero vectors x ∈ C. It is possible to find an n × n non-singular matrix X with unit columns such that X∗(A + iB)X = diag(α1 + iβ1, . . . , αn + iβn) where αj and βj are real numbers. We call the pairs (αj, βj) normalized generalized eigenvalues of the definite pair (A, B). These pairs have not b...

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudopositive definite functional (subject to some reasonable restrictions) there exists a representing pseudo-positive measure. The second main result is a characterization of determinacy in the class of equivalent pseudo-positive representation measures. Finally ...

[t]he analysis of the phrase " how many " unambiguously leads to a definite meaning for the question [ " How many different sets of integers do their exist? " ]: the problem is to find out which one of the ‫'א‬s is the number of points of a straight line… Cantor, after having proved that this number is greater than ‫א‬ 0 , conjectured that it is ‫א‬ 1. An equivalent proposition is this: any inf...