Splitting‐characterizations of the Papangelou process

For point processes we establish a link between integration‐by‐parts‐ and splitting‐formulas which can also be considered as integration‐by‐parts‐formulas of a new type. First we characterize finite Papangelou processes in terms of their splitting kernels. The main part then consists in extending these results to the case of infinitely extended Papangelou and, in particular, Pólya and Gibbs processes.     

Homo- and heteronuclear 2D NMR approaches to analyse a mixture of deuterated unlike/like stereoisomers using weakly ordering chiral liquid crystals

We describe several homo- and heteronuclear 2D NMR strategies dedicated to the analysis of anisotropic (2)H spectra of a mixture of dideuterated unlike/like stereoisomers with two remote stereogenic centers, using weakly orienting chiral liquid crystals. To this end, we propose various 2D correlation experiments, denoted "D(H)(n)D" or "D(H)(n)C" (with n=1, 2), that involve two heteronuclear polarization transfers of INEPT-type with one or two proton relays. The analytical expressions of correlation signals for four pulse sequences reported here were calculated using the product-operators formalism for spin I=1 and S=1/2. The features and advantages of each scheme are presented and discussed. The efficiency of these 2D sequences is illustrated using various deuterated model molecules, dissolved in organic solutions of polypeptides made of poly-gamma-benzyl-L-glutamate (PBLG) or poly-epsilon-carbobenzyloxy-L-lysine (PCBLL) and NMR numerical simulations.     

Splittings of Mapping Tori of Free Group Automorphisms

We present necessary and sufficient conditions for the existence of a splitting over of the mapping torus of a free group automorphism .     

Canonical splittings of groups and 3-manifolds

We introduce the notion of a `canonical' splitting over or for a finitely generated group . We show that when happens to be the fundamental group of an orientable Haken manifold with incompressible boundary, then the decomposition of the group naturally obtained from canonical splittings is closely related to the one given by the standard JSJ-decomposition of . This leads to a new proof of Johannson's Deformation Theorem.

     

Three-bridge links with infinitely many three-bridge spheres

We construct infinitely many three-bridge links each of which admits infinitely many three-bridge spheres up to isotopy.     

Minimal rambling sets with codimension one dominated splittings

In this paper,we study the dynamics of minimal rambling sets with codimension one dominatedsplittings     

A numerical technique based on B-spline for a class of time-fractional diffusion equation

This paper presents an efficient numerical technique for solving a class of time-fractional diffusion equation. The time-fractional derivative is described in the Caputo form. The L1 scheme is used for discretization of Caputo fractional derivative and a collocation approach based on sextic B-spline basis function is employed for discretization of space variable. The unconditional stability of the fully-discrete scheme is analyzed. Two numerical examples are considered to demonstrate the accuracy and applicability of our scheme. The proposed scheme is shown to be sixth order accuracy with respect to space variable and (2 − α)-th order accuracy with respect to time variable, where α is the order of temporal fractional derivative. The numerical results obtained are compared with other existing numerical methods to justify the advantage of present method. The CPU time for the proposed scheme is provided.     

Strong contribution to octet baryon mass splittings

We calculate the _md−_mu$m_d-m_u$ contribution to the mass splittings in baryonic isospin multiplets using SU(3) chiral perturbation theory and lattice QCD. Fitting isospin-averaged perturbation theory functions to PACS-CS and QCDSF-UKQCD Collaboration lattice simulations of octet baryon masses, and using the physical light-quark mass ratio _mu/_md$m_u/m_d$ as input, allows _Mn−_Mp$M_n-M_p$, _MΣ−−_MΣ+$M_{{\Sigma }^{-}}-M_{{\Sigma }^{+}}$ and _MΞ−−_MΞ0$M_{{\Xi }^{-}}-M_{{\Xi }^0}$ to be evaluated from the full SU(3) theory. The resulting values for each mass splitting are consistent with the experimental values after allowing for electromagnetic corrections. In the case of the nucleon, we find _Mn−_Mp=2.9±0.4 MeV$M_n-M_p=2.9\pm 0.4\text{MeV}$, with the dominant uncertainty arising from the error in _mu/_md$m_u/m_d$.     

Characterization of 3-bridge links with infinitely many 3-bridge spheres

In an earlier paper, the author constructed an infinite family of 3-bridge links each of which admits infinitely many 3-bridge spheres up to isotopy. In this paper, we prove that if a prime, unsplittable link L in S³ admits infinitely many 3-bridge spheres up to isotopy then L belongs to the family.     

On the convergence of general stationary iterative methods for range‐Hermitian singular linear systems

General stationary iterative methods with a singular matrix M for solving range‐Hermitian singular linear systems are presented, some convergence conditions and the representation of the solution are also given. It can be verified that the general Ortega–Plemmons theorem and Keller theorem for the singular matrix M still hold. Furthermore, the singular matrix M can act as a good preconditioner for solving range‐Hermitian linear systems. Numerical results have demonstrated the effectiveness of the general stationary iterations and the singular preconditioner M. Copyright © 2009 John Wiley & Sons, Ltd.