A CELL-CENTERED ALE METHOD WITH HLLC-2D RIEMANN SOLVER IN 2D CYLINDRICAL GEOMETRY

This paper presents a second-order direct arbitrary Lagrangian Eulerian (ALE) method for compressible flow in two-dimensional cylindrical geometry.This algorithm has half-face fluxes and a nodal velocity solver,which can ensure the compatibility between edge fluxes and the nodal flow intrinsically.In two-dimensional cylindrical geometry,the control vol-ume scheme and the area-weighted scheme are used respectively,which are distinguished by the discretizations for the source term in the momentum equation.The two-dimensional second-order extensions of these schemes are constructed by employing the monotone up-wind scheme of conservation law (MUSCL) on unstructured meshes.Numerical results are provided to assess the robustness and accuracy of these new schemes.     

环$F_2 uF_2 u^2F_2$上的循环码及自对偶码

We give the structures of a cyclic code over ring
R = F2 ＋ uF2 ＋ u^2F2 = {0, 1,u, u^2,v, v^2,uv, v^3},
where u^3 = 0, of odd length and its dual code. For the cyclic code, necessary and sufficient conditions for the existence of self-dual code are provided.     

不定方程x~2+y~2=z~2的若干推广与统一解法

本文对不定方程x2+y2=z2给出了四个推广,并用一种统一的解法对这四个推广给出了解答.     

2×2算子矩阵的逆

设H和K为复的无限维可分Hilbert空间．本文利用算子的几何结构着重研究了Hilbert空间H(?)K上的2×2算子矩阵的逆,给出了一些有意义的结果．     

Characterizations on 2-isometries

We consider 2-isometries, weak 2-isometries and 2-continuous mappings and investigate the relation between three mappings in linear 2-normed spaces. Also we prove that the Riesz theorem holds when X is a linear 2-normed spaces.     

Linear optimal control problem for discrete 2-D systems with constraints

Optimal control problem for linear two-dimensional (2-D) discrete systems with mixed constraints is investigated. The problem under consideration is reduced to a linear programming problem in appropriate Hubert space. The main duality relations for this problem is derived such that the optimality conditions for the control problem are specified by using methods of the linear operator theory. Optimality conditions are expressed in terms of solutions for conjugate system.     

Minimal 2-matching-covered graphs

A perfect 2-matching M of a graph G is a spanning subgraph of G such that each component of M is either an edge or a cycle. A graph G is said to be 2-matching-covered if every edge of G lies in some perfect 2-matching of G. A 2-matching-covered graph is equivalent to a “regularizable” graph, which was introduced and studied by Berge. A Tutte-type characterization for 2-matching-covered graph was given by Berge. A 2-matching-covered graph is minimal if G−e is not 2-matching-covered for all edges e of G. We use Berge’s theorem to prove that the minimum degree of a minimal 2-matching-covered graph other than K₂ and K₄ is 2 and to prove that a minimal 2-matching-covered graph other than K₄ cannot contain a complete subgraph with at least 4 vertices.     

Pseudo-commutativity of KZ 2-monads

In this paper we prove that KZ 2-monads (also known as lax-idempotent 2-monads) are pseudo-commutative. The main examples of KZ 2-monads for us will be 2-monads whose algebras are V-categories with chosen colimits of a given class; this provides a large family of examples of pseudo-commutative 2-monads. In order to achieve this we characterise pseudo-commutativities on a 2-monad in terms of extra structure on its 2-category of algebras and pseudomorphisms. We also consider tensor products associated to pseudo-closed structures and show some results on preservation of colimits. To cover the general case of V-enriched categories and not only ordinary categories we are led to consider monads enriched in a 2-category, and some of the associated two-dimensional monad theory.     

Partially-2-Homogeneous Monounary Algebras

This paper is a continuation of [5], where k-homogeneous and k-set-homogeneous algebras were defined. The definitions are analogous to those introduced by Fraïssé [2] and Droste, Giraudet, Macpherson, Sauer [1] for relational structures. In [5] we found all 2-homogeneous and all 2-set-homogeneous monounary algebras when the homogenity is considered with respect to subalgebras, to connected subalgebras and with respect to connected partial subalgebras, respectively. The results of [3], where all homogeneous monounary algebras were characterized, were applied in [4] for 1-homogeneity.The aim of the present paper is to describe all monounary algebras which are 2-homogeneous and 2-set-homogeneous with respect to partial subalgebras, respectively; we will say that they are partially-2-homogeneous and partially-2-set-homogeneous.     

Numerical modeling of the transmission dynamics of drug-sensitive and drug-resistant HSV-2

IntroductionThe prevalence of genital herpes infection (caused by HSV-2) in the United States is approximately 22% II]. In developing nations, the infection rate is between 40%A10% I2' 3]. Althoughthere is currently no cure for genital herpes, drug treatment with agents such as acyclovir isknown to significantly relieve symptoms and reduce viral shedding['1. Most cases of HSV-2infections remain untreated in developing nations, and even in the USA only 5%--10% aretreated[4]. Whilst incre…     

Representation theory of 2-groups on Kapranov and Voevodsky's 2-vector spaces

In this paper the representation theory of 2-groups in 2-categories is considered, focusing the attention on the 2-category Rep2MatK(G) of representations of a 2-group G in (a version of) Kapranov and Voevodsky's 2-category of 2-vector spaces over a field K. The set of equivalence classes of such representations is computed in terms of the invariants π₀(G), π₁(G) and [α]∈H³(π₀(G),π₁(G)) classifying G, and the categories of intertwiners are described in terms of categories of vector bundles endowed with a projective action. In particular, it is shown that the monoidal category of finite dimensional linear representations (more generally, the category of [z]-projective representations, for any given cohomology class [z]∈H²(π₀(G),K^∗)) of the first homotopy group π₀(G) as well as its category of representations on finite sets both live in Rep2MatK(G), the first as the monoidal category of endomorphisms of the trivial representation (more generally, as the category of intertwiners between suitable 1-dimensional representations) and the second as a non-full subcategory of the homotopy category of Rep2MatK(G).     

新的基于Type-2模糊系统的直接自适应模糊控制

在Type-1模糊系统的直接自适应控制基础上,将规则前件、后件改为Type-2模糊集合,建立Type-2模糊系统的直接自适应模糊控制器,给出了直接自适应控制器的设计方法,讨论了直接自适应控制系统的稳定性,研究了直接自适应控制系统的收敛性,针对一类非线性系统给出了仿真。     

非定常Oseen方程最优控制问题的一种新型L~2投影稳定化方法

对非定常Oseen方程最优控制问题分析了一种新型L~2投影稳定化方法.空间采用工程上好用的多项式有限元P_l/P_l(l≥1)逼近,时间采用中心差分离散.该稳定化方法对速度和压力分别采用全局或局部L~2投影,不仅绕开了inf-sup条件对等阶元的束缚,而且克服了雷诺数较大,对流占优造成的解的震荡.该方法特点是,所有计算只需要在同一套网格上执行,不需要嵌套的网格或将速度和压力的梯度投影到粗网格上进行计算.给出了详细的误差分析,误差结果与雷诺数一致,且数值解的L~2误差与雷诺数无关.     

2-Coherent and 2-convex conditional lower previsions

In this paper we explore relaxations of (Williams) coherent and convex conditional previsions that form the families of n-coherent and n-convex conditional previsions, at the varying of n. We investigate which such previsions are the most general one may reasonably consider, suggesting (centered) 2-convex or, if positive homogeneity and conjugacy is needed, 2-coherent lower previsions. Basic properties of these previsions are studied. In particular, we prove that they satisfy the Generalised Bayes Rule and always have a 2-convex or, respectively, 2-coherent natural extension. The role of these extensions is analogous to that of the natural extension for coherent lower previsions. On the contrary, n-convex and n-coherent previsions with $n\ge 3$ either are convex or coherent themselves or have no extension of the same type on large enough sets. Among the uncertainty concepts that can be modelled by 2-convexity, we discuss generalisations of capacities and niveloids to a conditional framework and show that the well-known risk measure Value-at-Risk only guarantees to be centered 2-convex. In the final part, we determine the rationality requirements of 2-convexity and 2-coherence from a desirability perspective, emphasising how they weaken those of (Williams) coherence.     

基于样本广义方差的改进|S|~(1/2)控制图

以常用的广义方差为基础,利用矩估计的方法,从一组样本推广到多组独立样本,得出具有无偏控制限的改进|S|~(1/2)控制图,并对比说明了矩估计方法的简洁性和准确性.与标准|S|~(1/2)控制图相比,其具有更小的平均运行链长(ARL).结合实例,采用数值模拟的方法说明该控制图对过程中方差的漂移有较强的检测能力.     

Explicit formulas for 2-characters

Ganter and Kapranov associated a 2-character to 2-representations of a finite group. Elgueta classified 2-representations in the category of 2-vector spaces 2Vectk in terms of cohomological data. We give an explicit formula for the 2-character in terms of this cohomological data and derive some consequences.     

两指标双F统计过程控制图

当产品质量指标服从二元正态分时,可用T2控制图与Λ控制图联合判断产品生产的过程是否处于受控状态。本文利用T2统计量与F统计量、Λ统计量与F统计量之间的关系,得到了两指标情形下两类基于F分布统计量的统计过程控制图,简称双F统计过程控制图,并给出了控制图应用实例。