Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of SSP explicit 3-stage Hermite-Birkhoff methods of orders 3 to 7 with nonnegative coefficients are constructed as k-step analogues of third-order Runge-Kutta methods, incorporating a function evaluation at two off-step points. Generally, these new methods have larger effective CFL coefficients than the hybrid methods of Huang with the same step number k. They have larger maximum scaled step sizes than hybrid methods on Burgers' equations.     

Sequential optimizing strategy in multi-dimensional bounded forecasting games

We propose a sequential optimizing betting strategy in the multi-dimensional bounded forecasting game in the framework of game-theoretic probability of Shafer and Vovk (2001) [10]. By studying the asymptotic behavior of its capital process, we prove a generalization of the strong law of large numbers, where the convergence rate of the sample mean vector depends on the growth rate of the quadratic variation process. The growth rate of the quadratic variation process may be slower than the number of rounds or may even be zero. We also introduce an information criterion for selecting efficient betting items. These results are then applied to multiple asset trading strategies in discrete-time and continuous-time games. In the case of a continuous-time game we present a measure of the jaggedness of a vector-valued continuous process. Our results are examined by several numerical examples.     

Analysis of nonsmooth vector-valued functions associated with infinite-dimensional second-order cones

Given a Hilbert space H, the infinite-dimensional Lorentz/second-order cone K is introduced. For any x∈H, a spectral decomposition is introduced, and for any function f:R→R, we define a corresponding vector-valued function f^H(x) on Hilbert space H by applying f to the spectral values of the spectral decomposition of x∈H with respect to K. We show that this vector-valued function inherits from f the properties of continuity, Lipschitz continuity, differentiability, smoothness, as well as s-semismoothness. These results can be helpful for designing and analyzing solution methods for solving infinite-dimensional second-order cone programs and complementarity problems.     

一类带有非牛顿位势的可压缩Navier-Stokes方程整体强解的存在性

主要研究了一类带有非牛顿位势的可压缩Navier-Stokes方程:其中粘性系数μ依赖于密度ρ,Φ是非牛顿位势.证明了上述问题的强解的存在性.在相容性条件下,得到了强解的唯一性.     

Ring-opening metathesis polymerization-derived monolithic strong anion exchangers for the separation of 5'-phosphorylated oligodeoxythymidylic acids fragments

Ring-opening metathesis polymerization (ROMP) derived monoliths were prepared from 5-norborn-2-enemethyl bromide (NBE-CH(2)Br) and tris(5-norborn-2-enemethoxy)methylsilane ((NBE-CH(2)O)(3)SiCH(3)) within the confines of surface-silanized borosilicate columns (100 mm × 3 mm I.D.), applying Grubbs' first generation benzylidene-type catalyst [RuCl(2)(PCy(3))(2)(CHPh)]. Two monoliths of the same recipe were converted into strong anion-exchangers applying two different approaches. Monolith I was prepared by a two-step reaction of the poly(NBE-CH(2)-Br) moieties with diethyl amine forming a weak-anion exchanger followed by reaction (quaternization) with ethyl iodide. Monolith II was prepared via a single-step reaction of the poly(NBE-CH(2)-Br) moieties with triethyl amine. The resulting monolithic anion-exchangers prepared demonstrated a good aptitude for the anion-exchange separation of single-stranded nucleic acids (ss-DNA). However, monolith II showed superior separation efficiency compared to monolith I indicated by sharper analyte peaks and better resolution values for the 5'-phosphorylated oligodeoxythymidylic acids fragments. On monolith II, the seven fragments of [d(pT)(12-18)] were baseline separated in less than 9 min. The influence of the buffer pH on the separation efficiency was studied applying a phosphate (0.05 mol/L, pH 7 and 8) and Tris-HCl buffer (0.05 mol/L, pH 9), respectively.     

On optimizing edge connectivity of product graphs

This work studies the super edge connectivity and super restricted edge connectivity of direct product graphs, Cartesian product graphs, strong product graphs and lexicographic product graphs. As a result, sufficient conditions for optimizing the edge connectivity and restricted edge connectivity of these graphs are presented.     

Strong competition model with non-uniform dispersal in a heterogeneous environment

In this study, a strong competition model was considered between two species in a heterogeneous environment. For a system with two different constant diffusion rates for each competitor, the fast diffuser can be selected evolutionally under suitable assumptions if the competing interaction between the species is strong. We also claim that a strongly interacting competition leads to a more evolutionary selection than that with the same population dynamics if a species moves with a certain non-uniform dispersal. Furthermore, species with a certain non-uniform dispersal have a competitive advantage over linear random diffusers. In addition, a species with highly sensitive dispersal response to the environment may survive. These strongly competitive advantages were demonstrated by investigating the stability of semi-trivial solutions of the system with non-uniform dispersal and comparing it to the conditions of the model with constant diffusion.     

On differential–algebraic equations in infinite dimensions

We consider a class of differential–algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the associated DAE. Moreover, we show that for arbitrary initial values we obtain mild solutions for the associated problem. We discuss the asymptotic behaviour of solutions for both problems. In particular, we provide a characterisation for exponential stability and exponential dichotomies in terms of the spectrum of the associated operator pencil.     

Subtractive manufacturing with geminal powers:making good use of a bad wave function

The cluster Jastrow antisymmetric geminal power ansatz was recently introduced as a promising approach for treating weak and strong electron correlations simultaneously. One crucial aspect of this ansatz is that the Jastrow operator allows the geminal power to achieve size consistency through the deletion of unphysical ionic terms. Here, we present data suggesting that the effects of such deletions go much deeper, causing the geminal to ‘intentionally’ take on a highly unphysical form that, in the presence of the Jastrow's deletions, nonetheless results in an accurate final wave function, a process that we note is similar to the variation-after-projection approach of projected Hartree–Fock theory. Indeed, in both LiF and N₂, we show that the optimal geminal is quite unphysical if considered on its own, but in ways that the Jastrow easily corrects to yield a highly accurate final wave function.     

Lower and upper orientable strong radius and strong diameter of complete k-partite graphs

For two vertices u and v in a strong digraph D, the strong distance sd(u,v) between u and v is the minimum size (the number of arcs) of a strong sub-digraph of D containing u and v. For a vertex v of D, the strong eccentricity se(v) is the strong distance between v and a vertex farthest from v. The strong radius srad(D) (resp. strong diameter sdiam(D)) is the minimum (resp. maximum) strong eccentricity among the vertices of D. The lower (resp. upper) orientable strong radius srad(G) (resp. SRAD(G)) of a graph G is the minimum (resp. maximum) strong radius over all strong orientations of G. The lower (resp. upper) orientable strong diameter sdiam(G) (resp. SDIAM(G)) of a graph G is the minimum (resp. maximum) strong diameter over all strong orientations of G. In this paper, we determine the lower orientable strong radius and diameter of complete k-partite graphs, and give the upper orientable strong diameter and the bounds on the upper orientable strong radius of complete k-partite graphs. We also find an error about the lower orientable strong diameter of complete bipartite graph K_m,n given in [Y.-L. Lai, F.-H. Chiang, C.-H. Lin, T.-C. Yu, Strong distance of complete bipartite graphs, The 19th Workshop on Combinatorial Mathematics and Computation Theory, 2002, pp. 12-16], and give a rigorous proof of a revised conclusion about sdiam(K_m,n).