Algorithms for nonlinear piecewise polynomial approximation: Theoretical aspects

In this article algorithms are developed for nonlinear -term Courant element approximation of functions in ( ) on bounded polygonal domains in . Redundant collections of Courant elements, which are generated by multilevel nested triangulations allowing arbitrarily sharp angles, are investigated. Scalable algorithms are derived for nonlinear approximation which both capture the rate of the best approximation and provide the basis for numerical implementation. Simple thresholding criteria enable approximation of a target function to optimally high asymptotic rates which are determined and automatically achieved by the inherent smoothness of . The algorithms provide direct approximation estimates and permit utilization of the general Jackson-Bernstein machinery to characterize -term Courant element approximation in terms of a scale of smoothness spaces (-spaces) which govern the approximation rates.

     

内孔缝位置对嵌套腔体微波耦合特性的影响

 利用时域有限差分（FDTD）方法计算了不同内孔缝位置情况下微波脉冲与带缝嵌套圆柱形腔体系统的耦合过程；分别分析了内孔缝位置对外部带缝腔体和内部带缝腔体耦合特性的影响。结果表明:除了内孔缝附近区域以外，内孔缝位置对外腔耦合特性的影响很小，可以忽略不计；但内孔缝位置对内腔耦合特性的影响较大，而且内腔的屏蔽性能由外腔内的耦合场分布以及内孔缝的位置共同决定。     

The vertex isoperimetric problem for the powers of the diamond graph

We introduce a new graph for all whose cartesian powers the vertex isoperimetric problem has nested solutions. This is the fourth kind of graphs with this property besides the well-studied graphs like hypercubes, grids, and tori. In contrast to the mentioned graphs, our graph is not bipartite. We present an exact solution to the vertex isoperimetric problem on our graph by introducing a new class of orders that unifies all known isoperimetric orders defined on the cartesian powers of graphs.     

First-order system least squares and the energetic variational approach for two-phase flow

This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen–Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques.     

A greedy algorithm for the two-level nested logit model

We consider the assortment optimization problem under the classical two-level nested logit model. We establish a necessary and sufficient condition for the optimal assortment and develop a simple and fast greedy algorithm that iteratively removes at most one product from each nest to compute an optimal solution.     

CUT ELIMINATION FOR PROPOSITIONAL DYNAMIC LOGIC WITHOUT

The aim of this paper is to extend the semantic analysis of tense logic in Rescher/Urquhart [3] to propositional dynamic logic without*. For this we develop a nested sequential calculus whose axioms and rules directly reflect the steps in the semantic analysis. It is shown that this calculus, with the cut rule omitted, is complete with respect to the standard semantics. It follows that cut elimination does hold for this nested sequential calculus. MSC: 03B45.     

可列集合套

[1]中给出模糊集的分解定理与表现定理，指出可利用集合套H＝{H（λ）|λ∈[0,1]}刻化模糊集。本文定义可列集合套H＝{H（a）|a∈Q}，Q是（0，1）的可列稠密子集。相应地给出新的分解定理与表现定理。指出可利用可列集合套刻化的模糊集。     

The non-Markovian nature of nested logit choice

Discrete choice models are widely used for understanding how customers choose between a variety of substitutable goods. We investigate the relationship between two well studied choice models, the Nested Logit (NL) model and the Markov choice model. Both models generalize the classic Multinomial Logit model and admit tractable algorithms for assortment optimization. Previous evidence indicates that the NL model may be well approximated by, or be a special case of, the Markov model. We establish that the Nested Logit model, in general, cannot be represented by a Markov model. Further, we show that there exists a family of instances of the NL model where the choice probabilities cannot be approximated to within a constant error by any Markov choice model.     

Molecular characterization and first report of Cryptosporidium genotypes in human population in the Slovak Republic

In our study, we examined 91 fecal samples from five different groups of people containing HIV patients, hemodialysis patients, kidney transplant recipients, immunocompetent humans without clinical signs, and humans with suspected cryptosporidiosis. The purpose of our study was to determine species and genotype composition of representatives of Cryptosporidium spp. using PCR analysis of small subunit ribosomal RNA gene and 60‐kDa glycoprotein gene and examine their phylogenetic relationship. In HIV‐positive/AIDS‐infected group of patients and in hemodialysis patients, no presence of Cryptosporidium species was detected. In two kidney transplant recipients, we detected species/genotypes Cryptosporidium parvum IIaA13G1T1R1 (KT355488) and Cryptosporidium hominis IaA11G2R8 (KT355489) and in two immunocompetent patients with clinical symptoms, we identified Cryptosporidium muris and C. hominis IbA10G2T1 (KT355490). In the group of healthy immunocompetent individuals without clinical signs, we identified species/genotype C. hominis IbA11G2 (KT355491) in one sample.