On solution sequences of the singular Liouville equations with an integral constraint

In this paper,we analyze the blow-up behavior of sequences{uk}satisfying the following conditionsΔuk=|x|2αk V k eukinΩ,(0.1)whereΩR2,V k→V in C1,|Vk|≤A,0a≤Vk≤b,0≤αk→α∈(0,∞),andΩ|x|2αkeuk dx≤Λ1.(0.2)Furthermore,we assume that there exists someq∈(1,2)such that rq 2Br(p)|uk|qdx≤Λ2(0.3)for anyB r(p)Ω.As a result,we give a new proof of the concentration-compactness theorem for the mean feld equation.     

Lie algebroid modules and representations up to homotopy

We establish a relationship between two different generalizations of Lie algebroid representations: representation up to homotopy and Vaĭntrob’s Lie algebroid modules. Specifically, we show that there is a noncanonical way to obtain a representation up to homotopy from a given Lie algebroid module, and that any two representations up to homotopy obtained in this way are equivalent in a natural sense. We therefore obtain a one-to-one correspondence, up to equivalence.     

Soluble polybenzimidazoles with intrinsic porosity: Synthesis,structure, properties and processability

We have explored two novel comonomers, namely, 4,16‐dicarboxyl[2.2]paracyclophane and 5,5′,6,6′‐tetraamino‐3,3,3′,3′‐tetramethyl‐1,1′‐spirobi[indane], for the synthesis of co‐polybenzimidazoles (co‐PBIs) with intrinsic porosity. Both these monomers possess twisted structures that can lead to “awkward” macromolecular shapes that cannot pack efficiently. The consequences of introducing these two monomers on the structure and properties of PBIs are reported. The random copolymers synthesized are amorphous and possess glass transition temperatures (T_gs) greater than 400 °C. T_g decreases with increasing comonomer content indicating an increase in fractional free volume. The copolymers have low surface area. TEM and BET measurements show evidence of mesopore formation. The copolymers show significant carbon dioxide adsorption. Single chain molecular dynamics simulation of 24‐mer repeat units shows intramolecular void spaces arising as a result of distorted polymer chain with reduced conformational mobility. These studies define a new synthetic strategy for “bottoms‐up” synthesis of PBIs with intrinsic porosity. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 1046–1057     

Numerical solution of the heat equation with nonlinear boundary conditions in unbounded domains

The numerical solution of the heat equation in unbounded domains (for a 1D problem‐semi‐infinite line and for a 2D one semi‐infinite strip) is considered. The artificial boundaries are introduced and the exact artificial boundary conditions are derived. The original problems are transformed into problems on finite domains. The space semi‐discretization by finite element method and the full approximation by the implicit‐explicit Euler's method are presented. The solvability of the full discretization schemes is analyzed. Computational examples demonstrate the accuracy and the efficiency of the algorithms. Also, the behavior of blowing up solutions is examined numerically. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 379–399, 2007     

A real options approach for entering the Internet securities trading businesses with start‐up time

This paper uses a real options approach to establish a new evaluation model under uncertainty of both the volume of Internet securities transactions and the total transaction volume of a securities firm. The proposed approach can assist securities firms in evaluating the optimal thresholds for entering the Internet securities trading business and withdrawing from the conventional securities trading business. This paper assumes that the annual number of Internet securities transactions and the total annual number of securities transactions both follow a geometric Brownian motion. Besides, this model considers a start‐up time to complete the entry project's procedure. Accordingly, a decision model based on the real options approach is introduced, and the closed form solutions for the optimal threshold values of the entry or withdrawal models are determined. The conclusions provide some valuable references to help strategic managers of securities firms in making decisions on entering the Internet securities trading business or withdrawing from the conventional trading business. Copyright © 2003 John Wiley & Sons, Ltd.     

真值表查询式光学符号替换

本文提出了一种新的符号替换光学处理方法.采用互补编码和地点寻址的真值表查询,构造了一种可进行返回运算的全加数字处理器.利用由液晶光阀构成的行逻辑器件对这一符号替换系统进行了实验验证并给出了实验结果.     

Improvements in Silo Design for Moist and Cohesive Bulk Solids by Using a Silo Centrifuge

The Jenike‐method is state of the art in silo design for trouble‐free flow, even for cohesive bulk solids. However, for some bulk solids, especially very cohesive and moist bulk solids, even the correct application of the Jenike‐method can lead to an over‐design of the silo outlet. If a reliable estimation of the critical outlet dimension is possible the dimension as well as the machinery costs can be reduced. Model testing can help to reduce the over‐design but reasonable test equipment and flexibility are only possible with silo centrifuge testing. Results, regarding the state of stress and the critical outlet dimensions, from experiments using a silo centrifuge with cohesive and moist bulk solids are presented. The influence of creeping effects on silo design is investigated using the silo centrifuge with moist gypsum.     

近垒能区6Li+208Pb熔合激发函数测量

测量了6Li+208Pb熔合反应近垒能区全熔合截面,并与考虑非弹道耦合和不考虑耦合的CCFUS程序计算做了比较. 结果表明在垒上能区,破裂使熔合截面减小,在垒下能区,破裂对熔合截面的影响基本上可以忽略.