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...

Since Heubner's (1985) pioneering study, there have been many studies on (mis) use/ non-use of articles by L2 learners from article-less and article languages. The present study investigated how Persian L2 learners of English produce and interpret English definite descriptions and demonstrative descriptions. It was assumed that definite and demonstrative descriptions share the same central sema...

The multiple load structural topology design problem is modeled as a minimization of the weight of the structure subject to equilibrium constraints and restrictions on the local stresses and nodal displacements. The problem involves a large number of discrete design variables and is modeled as a non-convex mixed 0–1 program. For this problem, several convex and mildly non-convex continuous rela...

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...

For arbitrary real matrices F and G, the positive semi-deenite Procrustes problem is minimization of the Frr obenius norm of F ? PG with respect to positive semi-deenite symmetric P. Existing solution algorithms are based on a convex programming approach. Here an unconstrained non-convex approach is taken, namely writing P = E 0 E and optimizing with respect to E. The main result is that all lo...