In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

We develop a new Approximate Dynamic Programming (ADP) method for infinite horizon discounted reward Markov Decision Processes (MDP) based on projection onto a subsemimodule. We approximate the value function in terms of a (min,+) linear combination of a set of basis functions whose (min,+) linear span constitutes a subsemimodule. The projection operator is closely related to the Fenchel transf...

Monte-Carlo evaluation consists in estimating a position by averaging the outcome of several random continuations, and can serve as an evaluation function at the leaves of a min-max tree. This paper presents a new framework to combine tree search with Monte-Carlo evaluation, that does not separate between a min-max phase and a MonteCarlo phase. Instead of backing-up the min-max value close to t...

in this paper, we find explicit solution to the operator equation$txs^* -sx^*t^*=a$ in the general setting of the adjointable operators between hilbert $c^*$-modules, when$t,s$ have closed ranges and $s$ is a self adjoint operator.

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

As a newly emerged distributed computing platform, the Gird aims at the implementation of resources sharing and collaborative computing on the internet. Research on grid resource scheduling algorithm is one of the core problems of grid technology, as well as an essential part of grid resource management. Resource scheduling in grid environment refers to the application of tasks scheduling algor...

In a longitudinal clinical trial the treatment times needed for the fabrication of veneer restorations (VRs) were recorded and analysed. Treatment times were determined for: (1) direct resin composite (DC), (2) indirect resin composite (IC) and (3) porcelain (P) veneer restorations and for two preparation designs, with and without incisal coverage. Significant effects on the treatment times wer...