On Lattices of Uniformities

We study lattice theoretical properties of lattices of uniformities such as modularity, distributive laws and the existence of (relative) complements. For this the concepts of permutable uniformities (see Definition 3.1) and independent uniformities (see Definition 4.1) are important. Moreover, we show that e.g. the lattice of all lattice uniformities on a lattice L is a closed sublattice of the lattice of all uniformities on L.     

Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.     

A dynamic scorecard for monitoring baseline performance with application to tracking a mortgage portfolio

A principled technique for monitoring the performance of a consumer credit scorecard through time is derived from Kalman filtering. Standard approaches sporadically compare certain characteristics of the new applicants with those predicted from the scorecard. The new approach systematically updates the scorecard combining new applicant information with the previous best estimate. The dynamically updated scorecard is tracked through time and compared to limits calculated by sequential simulation from the baseline scorecard. The observation equation of the Kalman filter is tailored to take the results of fitting local scorecards by logistic regression to batches of new clients that arrive in the current time interval. The states in the Kalman filter represent the true or underlying score for each attribute in the card: the parameters of the logistic regression. Their progress in time is modelled by a random walk and the filter provides the best estimate of the scores using past and present information. We illustrate the technique using a commercial mortgage portfolio and the results indicate significant emerging deficiencies in the baseline scorecard.     

Group-valued measures on coarse-grained quantum logics

In [3] it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later ([9]) this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms of cyclic coarse-grained quantum logics.     

Mixed Elastico-Plasticity Problems with Partially Unknown Boundaries

In this paper,we study mixed elastico-plasticity problems in which part of the boundary is known,while the other part of the boundary is unknown and is a free boundary.Under certain conditions,this problemcan be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundaryvalue problem for complex equations.Using the theory of generalized analytic functions,the solvability of theproblem is discussed.     

对光电效应实验装置的剖析

光电效应是物理学中一个重要课问题，也是近代物理学几个重大的实验之一．一般物理学教材均要介绍光电效应．但是，在众多的教材中，对光电效应实验装置图的引入存在差异，有些有失科学性，因而引起广大物理学教育工作者的关注．     

In situ hybridization to chitosan/magnetite nanocomposite induced by the magnetic field

Chitosan/magnetite nanocomposite was synthesized induced by magnetic field via in situ hybridization in ambient condition. Results of XRD patterns and TEM micrographs indicated that magnetite particles with 10–20 nm were dispersed in chitosan homogeneously. An interesting result is that magnetite nanoparticles were assembled to form chain-like structures under the influence of the external magnetic field, which mimics the magnetite chains inside of magnetotatic bacteria. The saturated magnetization (Ms) of nano-magnetite in chitosan was 50.54 emu/g, which is as high as 54% of bulk magnetite. The remanence (Mr) and coercivity (Hc) were 4 emu/g and14.8 Oe, respectively, which indicated that magnetite nanoparticles were superparamagnetic. The key of route is that a pre-precipitated chitosan hydrogel membrane, used as chemical reactor, which controlled the precipitation of chitosan precipitation and in situ transformation of magnetite from the precursor simultaneously in the magnetic field environment.     

Property (<Emphasis Type="Italic">T</Emphasis>) and rigidity for actions on Banach spaces

We study property (T) and the fixed-point property for actions on L ^p and other Banach spaces. We show that property (T) holds when L ² is replaced by L ^p (and even a subspace/quotient of L ^p ), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L ^p follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L ^p holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive spaces. Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US).     

Risk and quality control in a supply chain: competitive and collaborative approaches

This paper provides a quantitative and comparative economic and risk approach to strategic quality control in a supply chain, consisting of one supplier and one producer, using a random payoff game. Such a game is first solved in a risk-neutral framework by assuming that both parties are competing with each other. We show in this case that there may be an interior solution to the inspection game. A similar analysis under a collaborative framework is shown to be trivial and not practical, with a solution to the inspection game being an ‘all or nothing’ solution to one or both the parties involved. For these reasons, the sampling random payoff game is transformed into a Neyman–Pearson risk constraints game, where the parties minimize the expected costs subject to a set of Neyman–Pearson risk (type I and type II) constraints. In this case, the number of potential equilibria can be large. A number of such solutions are developed and a practical (convex) approach is suggested by providing an interior (partial sampling) solution for the collaborative case. Numerical examples are developed to demonstrate the procedure used. Thus, unlike theoretical approaches to the solution of strategic quality control random payoff games, the approach we construct is both practical and consistent with the statistical risk Neyman–Pearson approach.     

Properties of<Emphasis Type="Italic">B</Emphasis><Subscript>c</Subscript> meson

The mass spectrum ofcb meson is investigated with an effective quark-antiquark potential of the form -α_c/r +Ar ^νwith ν varying from 0.5 to 2.0. TheS andP-wave masses, pseudoscalar decay constant, weak decay partial widths in spectator model and the lifetime ofB _cmeson are computed. The properties calculated here are found to be in good agreement with other theoretical and experimental values at potential index,ν = 1