Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lamé potentials ma(a+ 1) sn(x,m) are computed for integer values a = 1, 2, 3, .... For all cases (except a = 1), we show that the partner potential is distinctly differ...

We study geometric variations of the discriminating code problem. In discrete version problem, a finite set points P and objects S are given in $$\mathbb {R}^d$$ . The objective is to choose subset $$S^* \subseteq S$$ minimum cardinality such that for each point $$p_i \in P$$ , $$S_i^* S^*$$ covering $$p_i$$ satisfies $$S_i^*\ne \emptyset $$ pair $$p_i,p_j $$i \ne j$$ we have S_j^*$$ continuous...

A group is subdirectly reducible if it has two non-trivial normal subgroups with trivial intersection. Such groups may be an easy case in certain inductive arguments. We prove that every solvable finite group can be generated by at most one subdirectly reducible subgroup together with two subgroups of prime-power order and one element. We also prove that every group of prime-power order can be ...

Abstract. A case of the matrix Kummer relation of Herz (1955) based on the Pearson VII type matrix model is derived in this paper. As a con- sequence, the polynomial Pearson VII configuration density is obtained and this sets the corresponding exact inference as a solvable aspect in shape theory. An application in postcode recognition, including a nu- merical comparison between the exact poly...

In the literature two notions of the word problem for a variety occur. A variety has a decidable word problem if every finitely presented algebra in the variety has a decidable word problem. It has a uniformly decidable word problem if there is an algorithm which given a finite presentation produces an algorithm for solving the word problem of the algebra so presented. A variety is given with f...

Given a set of trees with leaves labelled from a set L, is there a tree T with leaves labelled by L such that each of the given trees is homeomorphic to a subtree of T ? This question is known to be NP-complete in general, but solvable in polynomial time if all the given trees have one label in common (equivalently, if the given trees are rooted). Here we show that this problem is NP-complete e...

In this paper, we first study the problem of rounding a real-valued matrix into an integer-valued matrix to minimize an Lp-discrepancy measure between them. To define the Lp-discrepancy measure, we introduce a family F of regions (rigid submatrices) of the matrix, and consider a hypergraph defined by the family. The difficulty of the problem depends on the choice of the region family F. We firs...

We prove that in a locally finite variety that has definable principal congruences (DPC), solvable congruences are nilpotent, and strongly solvable congruences are strongly abelian. As a corollary of the arguments we obtain that in a congruence modular variety with DPC, every solvable algebra can be decomposed as a direct product of nilpotent algebras of prime power size.

Let Γ be a finitely generated linear group over a field of characteristic 0. Suppose that every solvable subgroup of Γ is polycyclic. Then any solvable subgroup of Γ is separable. This conclusion is false without the hypothesis that every solvable subgroup of Γ is polycyclic.

Given an alphabet , a (directed) graph G whose edges are weighted and -labeled, and a formal language L , we consider the problem of finding a shortest (simple) path p in G complying with the additional constraint that l(p) 2 L. Here l(p) denotes the unique word given by concatenating the -labels of the edges along the path p. The main contributions of this paper include the following: 1. We sh...