In this paper, firstly we find the best constant for a convolution problem on the unit circle via a variational method. Then we apply the best constant on a nonlinear rod equation to give sufficient conditions on the initial data, which guarantee finite time singularity formation for the corresponding solutions. Mathematics Subject Classification(2000): 30C70, 37L05, 35Q58, 58E35

In this article, we prove the existence of a best proximity point for F contractive nonself mappings and state some results in the complete metric spaces. Also we define two kinds of F proximal contraction and extend some best proximity theorems and improve the recent results. 2010 Mathematics Subject Classification: 46N40; 47H10; 54H25; 46T99

In a generalization of the classical Hilbert inequality by Hardy, Littlewood and Pólya, the best constant for an inequality is determined provided that the generating function for the corresponding matrix satisfies certain monotonicity condition. In this paper, we determine the best constant for a class of inequalities when the monotonicity condition is no longer satisfied. Mathematics subject ...

We establish some common best proximity point results for generalized α−ψ-proximal contractive non-self mappings. We provide some concrete examples. We also derive some consequences on some best proximity results on a metric space endowed with a graph. 2000 Mathematics Subject Classification: 47H10, 54H25.

Using the methods of differential subordination and superordination, sufficient conditions are determined on the Liu-Srivastava linear operator of meromorphic functions in the punctured unit disk to obtain respectively the best dominant and the best subordinant. New sandwich-type results are also obtained. 2000 Mathematics Subject Classification: Primary 30C80; Secondary 30C45

We study the sojourn time of customers in an M/M/1 queue with processor sharing service discipline and service interruptions. The lengths of the service interruptions have a general distribution, whereas the periods of service availability are assumed to have an exponential distribution. A branching process approach is shown to lead to a decomposition of the sojourn time into independent contri...

We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worstcase” ones. So we exhibit the relation between hard functions a...

Working in Bishop’s constructive mathematics, we first show that minima can be defined as best approximations, in such a way as to preserve the compactness of the underlying metric space when the function is uniformly continuous. Results about finding minima can therefore be carried over to the setting of finding best approximations. In particular, the implication from having at most one best a...

We study the average performance of online greedy matching algorithms on G(n, n, p), the random bipartite graph with n vertices on each side and edges occurring independently with probability p = p(n). In the online model, vertices on one side of the graph are given up front while vertices on the other side arrive sequentially; when a vertex arrives its edges are revealed and it must be immedia...