In this paper, we study the equation -Au = K ( x ) u 5 in R3 and provide a large class of positive functions K ( x ) for which we obtain infinitely many positive solutions which decay at infinity at the rate of Ix(-'.

This paper presents some solvability criteria for the second order nonlinear equation (p(t)u′(t))′ − q(t)u(t) = f ( t, ∫ t 0 u(s)ds, u′(t) ) , t ∈ (0, 1), with one of the following boundary conditions au(0)− bp(0)u′(0) = 0, cu(1) + dp(1)u′(1) = μ1u(ξ), au(0)− bp(0)u′(0) = μ2u(ξ), cu(1) + dp(1)u′(1) = 0, au(0)− bp(0)u′(0) = μ1u(ξ), cu(1) + dp(1)u′(1) = μ2u(ξ). Under the appropriate nonlinear res...

We simulate the fragmentation processes in the α + Au collisions at the bombarding energy 5 GeV/u using the simplified RQMD approach. The statistical decay calculation is connected to obtain the final state. From the simulation we find that the residual nucleus created by this collision has a annular eclipse shape, and then expands more strongly to the transverse direction than to the beam-dire...

We classify the compact quantum groups Au(Q) and Bu(Q) up to isomorphism and analyze their structures. Structures et classifications isomorphiques des groupes quantiques compacts Au(Q) et Bu(Q) Résumé. Nous classifions les groupes quantiques compacts Au(Q) et Bu(Q) à isomorphisme près et analysons leur structures. Version française abrégée Rappelons [5, 4, 3] que pour chaque Q ∈ GL(n,C), le gro...

In this paper, all graphs are simple and connected, but they are not necessarily finite. As is well known, a (connected) graph G comes equipped with a natural metric on its vertex set V (G), given by defining the distance xy between any pair of vertices x, y ∈ V (G) to be the length of some shortest path or geodesic between x and y. Given a quartet x, y, u, v ∈ V (G), define δ(x, y, u, v) to be...

‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...

In this article we propose a new method, which we name ‘quartet neighbor joining’, or ‘quartet-NJ’, to infer an unrooted species tree on a given set of taxa T from empirical distributions of unrooted quartet gene trees on all four-taxon subsets of T . In particular, quartet-NJ can be used to estimate a species tree on T from distributions of gene trees on T . The quartet-NJ algorithm is concept...