Local monotonicity structure of Calderón-Lozanovskiǐ spaces

We first prove that if x is an element on the unit sphere of arbitrary Köthe space E, x is strickly positive μ-a.e. and x is an LM-point, then x is an UM-point. Criteria for lower and upper monotone points in Calderón-Lozanovskiǐ spaces E_? are presented. Points of lower local uniform monotonicity and upper local uniform monotonicity in E_? are also considered. Some sufficient conditions and necessary conditions for these properties of a given point x in S(E_?⁺) are given.     

Limit relations for three simple hyperbolic systems of conservation laws

This paper is concerned with the limit relations from the Euler equations of one‐dimensional compressible fluid flow and the magnetohydrodynamics equations to the simplified transport equations, where the δ‐shock waves occur in their Riemann solutions of the latter two equations. The objective is to prove that the Riemann solutions of the perturbed equations coming from the one‐dimensional simplified Euler equations and the magnetohydrodynamics equations converge to the corresponding Riemann solutions of the simplified transport equations as the perturbation parameterx ε tends to zero. Furthermore, the result can also be generalized to more general situations. Copyright © 2009 John Wiley & Sons, Ltd.     

原子荧光光谱法研究贝壳堤岛贝壳沙中As的空间分布特征

用原子荧光光谱法测定了贝壳沙中As元素含量,研究了As在黄河三角洲贝壳堤岛贝壳沙中的空间分布规律,分析了贝壳沙中As与其他营养元素的相关性,并对影响其含量与空间分布的因素进行探讨。结果表明：贝壳沙样品中As的含量范围为0.78～8.76 mg·kg-1,平均值为3.11 mg·kg-1,整体上处于清洁的水平。贝壳沙中As含量有随剖面深度增加而增大的趋势,贝壳沙粒径大小也影响贝壳沙中As的含量,贝壳沙粒径越小,As含量越高,且不同粒径贝壳沙中As含量差异显著(p≤0.05)。贝壳沙中As与全磷(total phosphor,TP)和全钾(total potassium,TK)以及Cu, Zn, Mn均具有极显著的正相关关系,与全氮(total nitrogen,TN)和Fe的相关性不显著。综合分析认为,贝壳沙中As主要来自于风化后的贝壳沙对环境中As元素的吸附与固定而非贝壳形成过程中对该元素的富集作用。     

On the credibility of insurance claim frequency: Generalized count models and parametric estimators

We analyze the concept of credibility in claim frequency in two generalized count models–Mittag-Leffler and Weibull count models–which can handle both underdispersion and overdispersion in count data and nest the commonly used Poisson model as a special case. We find evidence, using data from a Danish insurance company, that the simple Poisson model can set the credibility weight to one even when there are only three years of individual experience data resulting from large heterogeneity among policyholders, and in doing so, it can thus break down the credibility model. The generalized count models, on the other hand, allow the weight to adjust according to the number of years of experience available. We propose parametric estimators for the structural parameters in the credibility formula using the mean and variance of the assumed distributions and a maximum likelihood estimation over a collective data. As an example, we show that the proposed parameters from Mittag-Leffler provide weights that are consistent with the idea of credibility. A simulation study is carried out investigating the stability of the maximum likelihood estimates from the Weibull count model. Finally, we extend the analyses to multidimensional lines and explain how our approach can be used in selecting profitable customers in cross-selling; customers can now be selected by estimating a function of their unknown risk profiles, which is the mean of the assumed distribution on their number of claims.     

Nonparametric estimation and adaptive control in a class of finite Markov decision chains

We consider a class of Markov decision processes withfinite state and action spaces which, essentially, is determined by the following condition: The state space isirreducible under the action of any stationary policy. However, except by this restriction, the transition law iscompletely unknown to the controller. In this context, we find a set of policies under which thefrequency estimators of the transition law are strongly consistent and then, this result is applied to constructadaptive asymptotically discount-optimal policies.Dedicated to Professor Truman O. Lewis, on the occasion of his sixtieth birthdayThis research was supported in part by the Third World Academy of Sciences (TWAS) under Grant TWAS RG MP 898-152, and in part by the Consejo Nacional de Ciencia y Tecnología (CONACYT) under Grant A128CCOEO550 (MT-2).     

On a hierarchical error estimator combined with a stabilized method for the Navier–Stokes equations

This work combines two complementary strategies for solving the steady incompressible Navier–Stokes model with a zeroth‐order term, namely, a stabilized finite element method and a mesh–refinement approach based on an error estimator. First, equal order interpolation spaces are adopted to approximate both the velocity and the pressure while stability is recovered within the stabilization approach. Also designed to handle advection dominated flows under zeroth‐order term influence, the stabilized method incorporates a new parameter with a threefold asymptotic behavior. Mesh adaptivity driven by a new hierarchical error estimator and built on the stabilized method is the second ingredient. The estimator construction process circumvents the saturation assumption by using an enhancing space strategy which is shown to be equivalent to the error. Several numerical tests validate the methodology. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Some estimation theory on the sphere

Summary We consider distributions with densities of the formf(μ′x) andf(‖x _v ‖) where μ andx are unit vectors inR ^q and ‖x _v ‖ is the norm of the part ofx in somes dimensional subspaceV ofR ^q . For several loss functions, optimal Bayesian and Pitman estimators of μ andV are given. When uniform priors are used, these estimators are identical. Then the infinitesimal robustness characteristics of several special cases of these estimators are calculated.     

Generalizations of Perfect, Semiperfect, and Semiregular Rings

For a ring R and a right R-module M, a submodule N of M is said to be -small in M if, whenever N + X = M with M/X singular, we have X = M. If there exists an epimorphism p: P M such that P is projective and Ker(p) is -small in P, then we say that P is a projective -cover of M. A ring R is called -perfect (resp., -semiperfect, -semiregular) if every R-module (resp., simple R-module, cyclically presented R-module) has a projective -cover. The class of all -perfect (resp., -semiperfect, -semiregular) rings contains properly the class of all right perfect (resp., semiperfect, semiregular) rings. This paper is devoted to various properties and characterizations of -perfect, -semiperfect, and -semiregular rings. We define (R) by (R)/Soc(R_R) = Jac(R/Soc(R_R)) and show, among others, the following results:

D-admissible hybrid control of a class of singular systems

This paper mainly studies the problem of designing a hybrid state feedback D-admissible controller for a class of linear and nonlinear singular systems. Based on the relationship between singular discrete systems and singular delta operator systems, several necessary and sufficient conditions for a linear singular delta operator system to be D-admissible (i.e. regular, causal and all finite poles lie in a prescribed circular region) with different representations are derived. Then, the existence conditions and explicit expressions of a desirable D-admissible controller are given by means of matrix inequalities and strict linear matrix inequalities, respectively. We further extend the obtained results to singular delta operator systems with Lipschitz nonlinear perturbations, and the design methods of hybrid controller are presented for the nonlinear case as well. Finally, numerical examples as well as simulations are provided to illustrate the effectiveness of the theoretical outcomes obtained in the paper.