In this paper we prove some new results concerning multi-dimensional Hardy type integral inequalities and also some corresponding limit Pólya–Knopp type inequalities.

A large number of practical applications rely on effective algorithms for propositional model enumeration and counting. Examples include knowledge compilation, model checking and hybrid solvers. Besides practical applications, the problem of counting propositional models is of key relevancy in computational complexity. In recent years a number of algorithms have been proposed for propositional ...

We do computational studies concerning the enumeration of isolated cliques in graphs. Isolation, as recently introduced, measures the degree of connectedness of the cliques to the rest of the graph. Isolation helps both in getting faster algorithms than for the enumeration of maximal general cliques and in filtering out cliques with special semantics. We compare three isolation concepts and the...

Lattice enumeration is a linear-space algorithm for solving the shortest lattice vector problem (SVP). Extreme pruning practical technique accelerating enumeration, which has mature theoretical analysis and implementation. However, these works have yet to be applied discrete pruning. In this paper, we improve pruned (DP enumeration) provide solution proposed by Léo Ducas Damien Stehlé regarding...

Definition 2.2 (Enumeration Order Reducibility on Listings and sets) 1. For listings , : we say is “Enumeration order reducible” to and write , if and only if, , ( . 2. For r.e. sets , , we say is “Enumeration order reducible” to and write , if and only if, for any listing of there exist some computable function (from the listings of to the listings of ) such that . 3. For two listings , (r.e. ...

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent to enumeration of certain vector subspaces in finite fields. In particular, we present enumeration results for quasi-cyclic subcodes of the si...

We used a haptic enumeration task to investigate whether enumeration can be facilitated by perceptual grouping in the haptic modality. Eight participants were asked to count tangible dots as quickly and accurately as possible, while moving their finger pad over a tactile display. In Experiment 1, we manipulated the number and organization of the dots, while keeping the total exploration area co...

This paper develops an analytic theory for the study of some Pólya urns with random rules. The idea is to extend the isomorphism theorem in Flajolet et al. (2006), which connects deterministic balanced urns to a differential system for the generating function. The methodology is based upon adaptation of operators and use of a weighted probability generating function. Systems of differential equ...

In this paper we study a generalized Pólya urn with balls of two colors and a random triangular replacement matrix. We extend some results of Janson (2004), (2005) to the case where the largest eigenvalue of the mean of the replacement matrix is not in the dominant class. Using some useful martingales and the embedding method introduced in Athreya and Karlin (1968), we describe the asymptotic c...