in this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. a numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. truncation errors are derived for both continuous and discontinuous problems. parameter uni...

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...

Using the discrete logarithm in [7] and [9] a large family of pseudorandom binary sequences was constructed. Here we extend this construction. An interesting feature of this extension is that in certain special cases we get sequences involving points on elliptic curves. 2000 AMS Mathematics Subject Classification: 11K45. List of keywords and phrases: pseudorandom, elliptic curve.

We consider the α-stable Ornstein-Uhlenbeck process in Rd with the generator L = ∆α/2 − λx · ∇x. We show that if 2 > α ≥ 1 or α < 1 = d the Harnack inequality holds. For α < 1 < d we construct a counterexample that shows that the Harnack inequality doesn’t hold. keywords: α-stable Ornstein-Uhlenbeck process, harmonic functions, Harnack inequality. AMS Subject Classification: 60J75 60J45

A function f bounds graphs from above if there exists an infinite family of graph G, such that if G ∈ G then f(|VG|) = |EG| and for all nonempty subgraphs H of G we have that F (|VH |) ≥ |EH |. This paper considers the question: which functions bound graphs? keywords graphs, extremal graph theory AMS subject classification 05C99

It was conjectured by Hoffmann-Ostenhof that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. In this paper, we show that this conjecture holds for traceable cubic graphs. keywords: Cubic graph, Hoffmann-Ostenhof’s Conjecture, Traceable AMS Subject Classification: 05C45, 05C70

In this paper nonparametric statistical technology is derived for estimating with confidence a 3D configuration of points from noncalibrated camera views of such a configuration. This is applied to pattern recognition of a spatial scene, from multiple views, in absence of occlusions. keywords scene reconstruction, pinhole camera views, image analysis, projective shape data analysis AMS subject ...

Ahlswede, Khachatrian, Mauduit and A. Sárközy introduced the notion family-complexity of families of binary sequences. They estimated the family-complexity of a large family related to Legendre symbol introduced by Goubin, Mauduit and Sárközy. Here their result is improved, and apart from the constant factor the best lower bound is given for the family-complexity. 2000 AMS Mathematics Subject C...

Let N be a positive integer and let A and B be dense subsets of {1, . . . , N}. The purpose of this paper is to establish a good lower bound for the greatest prime factor of ab+ 1 as a and b run over the elements of A and B respectively. 1991 AMS Mathematics Subject Classification. Primary 11N30, Secondary 11L05, keywords: greatest prime factor, Selberg’s sieve, Kloosterman sums.

A ?semigroup is a semigroup whose lattice of congruences is a chain with respect to inclusion. Schein 9] and Tamura 11] have investigated commutative ?semigroups, Trotter 13] exponential, Nagy 4] weakly exponential and Bonzini and Cherubini Spoletini 2] nite ?semigroups. The pupose of the present paper is to investigate archimedean weakly commutative and H?commutative ?semigroups. 1 Weakly comm...