Pure annihilation decay of strange beauty meson into two charm heavy mesons

In this study, the heavy to heavy decay of \begin{document}$ B^0_s\rightarrow D^{*+}D^- $\end{document} is evaluated through the factorization approach by using the final state interaction as an effective correction. Under the factorization approach, this decay mode occurs only through the annihilation process, so a small amount is produced. Feynman's rules state that six meson pairs can be assumed for the intermediate states before the final meson pairs are produced. By taking into account the effects of twelve final state interaction diagrams in the calculations, a significant correction is obtained. These effects correct the value of the branching ratio obtained by the pure factorization approach from \begin{document}$ (2.41\pm1.37)\times10^{-5} $\end{document} to \begin{document}$ (8.27\pm2.23)\times10^{-5} $\end{document}. The value obtained for the branching ratio of the \begin{document}$ B^0_s\rightarrow D^{*+}D^- $\end{document} decay is consistent with the experimental results.     

Factorizations of complete graphs into caterpillars of diameter 5

We examine factorizations of complete graphs K_2n into caterpillars of diameter 5. First we present a construction generalizing some previously known methods. Then we use the new method along with some previous partial results to give a complete characterization of caterpillars of diameter 5, which factorize the complete graph K_2n.     

Polynomial factorization over

We describe algorithms for polynomial factorization over the binary field , and their implementation. They allow polynomials of degree up to to be factored in about one day of CPU time, distributing the work on two processors.

     

A fluctuation theory for Markov chains

A fluctuation theory for Markov chains on an ordered countable state space is developed, using ladder processes. These are shown to be Markov renewal processes. Results are given for the joint distribution of the extremum (maximum or minimum) and the first time the extremum is achieved. Also a new classification of the states of a Markov chain is suggested. Two examples are given.     

Kp,q-factorization of complete bipartite graphs

Let K_(m,n) be a complete bipartite graph with two partite sets having m and nvertices, respectively. A K_(p,q)-factorization of K_(m,n) is a set of edge-disjoint K_(p,q)-factorsof K_(m,n) which partition the set of edges of K_(m,n). When p=i and q is a prime number,Wang, in his paper "On K_(1,k)-factorizations of a complete bipartite graph" (Discrete Math,1994, 126; 359-364), investigated the K_(1,q)-factorization of K_(m,n) and gave a sufficientcondition for such a factorization to exist. In the paper "K_(1,k)-factorizations of completebipartite graphs" (Discrete Math, 2002, 259: 301-306), Du and Wang extended Wang'sresult to the case that q is any positive integer In this paper, we give a sufficient conditionfor K_(m,n) to have a K_(p,q)-factorization. As a special case, it is shown that the Martin's BACconjecture is true when p: q=k: (k+1) for any positive integer k.     

Factorization in finite-codimensional ideals of group algebras

Let G be a -compact, locally compact group and I be a closed2-sided ideal with finite codimension in L¹(G). It is shownthat there are a closed left ideal L having a right boundedapproximate identity and a closed right ideal R having a leftbounded approximate identity such that I = L + R. The proofuses ideas from the theory of boundaries of random walks ongroups. 2000 Mathematics Subject Classification: primary 43A20;secondary 42A85, 43A07, 46H10, 46H40, 60B11.     

Factorization Systems and Adjunctions

Several results on the translation of factorization systems along adjunctions are proved. The first of these results is the answer to the question posed by G.Janelidze.     

A comparison of preconditioners for incompressible Navier–Stokes solvers

We consider solution methods for large systems of linear equations that arise from the finite element discretization of the incompressible Navier–Stokes equations. These systems are of the so‐called saddle point type, which means that there is a large block of zeros on the main diagonal. To solve these types of systems efficiently, several block preconditioners have been published. These types of preconditioners require adaptation of standard finite element packages. The alternative is to apply a standard ILU preconditioner in combination with a suitable renumbering of unknowns. We introduce a reordering technique for the degrees of freedom that makes the application of ILU relatively fast. We compare the performance of this technique with some block preconditioners. The performance appears to depend on grid size, Reynolds number and quality of the mesh. For medium‐sized problems, which are of practical interest, we show that the reordering technique is competitive with the block preconditioners. Its simple implementation makes it worthwhile to implement it in the standard finite element method software. Copyright © 2007 John Wiley & Sons, Ltd.     

Quantum Computation in a Ising Spin Chain Taking into Account Second Neighbor Couplings

We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms can be performed with the help of appropriate radio-frequency pulses. In addition to the standard nearest-neighbor Ising coupling, we also allow for a second neighbor coupling. It is shown, how to apply the 2π k method in this more general setting, where the additional coupling eventually allows to save a few pulses. We illustrate our results with two numerical simulations: the Shor prime factorization of the number 4 and the teleportation of a qubit along a chain of 3 qubits. In both cases, the optimal Rabi frequency (to suppress non-resonant effects) depends primarily on the strength of the second neighbor interaction.