Precise synthesis of a series of poly(4‐n‐alkylstyrene)s and their glass transition temperatures

Poly(4‐n‐alkylstyrene)s with six kinds of n‐alkyl groups such as methyl, ethyl, propyl, butyl, hexyl, and octyl groups covering wide molecular weight range from around 5 k to over 100 k were precisely synthesized by living anionic polymerizations. It was confirmed that all the polymers obtained have narrow molecular weight distribution, that is, M_w/M_n is all less than 1.1, by SEC. T_gs of all the polymers were estimated by DSC measurements and it turned out to be clear that their molecular weight dependence was well described by the Fox–Flory equations. Furthermore, it is evident that T_g monotonically decreases as a number of carbon atoms of n‐alkyl group is increased, though T_g values are all 20 K or more higher than those reported previously for the same polymer series. This is because backbone mobility increases by introducing longer n‐alkyl side groups with high mobility, while T_g difference in between this work and the previous one may due to the experimental conditions and also to the molecular weight range adopted. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 757–763     

First-order phase transitions: equivalence between bimodalities and the Yang–Lee theorem

First-order phase transitions in finite systems can be defined through the bimodality of the distribution of the order parameter. This definition is equivalent to the one based on the inverted curvature of the thermodynamic potential. Moreover we show that it is in a one-to-one correspondence with the Yang–Lee theorem in the thermodynamic limit. Bimodality is a necessary and sufficient condition for zeroes of the partition sum in the control intensive variable complex plane to be distributed on a line perpendicular to the real axis with a uniform density, scaling like the number of particles.     

Measuring the performance of manufacturing firms with super slacks based model of data envelopment analysis: An application of 500 major industrial enterprises in Turkey

Data envelopment analysis (DEA) is a mathematical programming technique which has a wide application area. There are many applications of DEA to measure firms’ performance. Balance sheet data is frequently used in order to measure performance of firms through DEA. So it is the characteristic of balance sheets that assets and liabilities amount to the same value. When the data for inputs and outputs are selected from both assets and liabilities sections of the balance sheet, it is important that more attention be paid to the analysis since values assigned to inputs and outputs could be included in assets and liabilities at the same time. Such a situation could create problems concerning the conclusions drawn as a result of analysis.     

Optimal Operations Management and Network Planning of a District Heating System with a Combined Heat and Power Plant

District heating plants are becoming more common in European cities. These systems make it possible to furnish users with warm water while locating the production plants in the outskirts having the double benefit of lowering the impact of pollution on the center of the city and achieving better conversion performances. In order to amortize the costs throughout the year, the system often includes a combined heat and power (CHP) plant, to exploit the energy during the summer as well, when the demand for warm water decreases. A linear programming model for the optimal resource management of such a plant is presented and some results for a real case are reported. A distribution network design problem is also addressed and solved by means of mixed integer linear programming.     

LIQUID-LIQUID PHASE EQUILIBRIUM OF POLYMER SOLUTIONS AND POLYMER BLENDS UNDER POSITIVE AND NEGATIVE PRESSURE

In this paper we would like to give a brief review about the extensibility of the liquid-liquid locus into the negativepressure region. Negative pressure states are hardly explored; most researchers believe that the pressure scale ends at p = 0.We would like to show that this is not true, the p = 0 point is not a special point for liquids, it can be "easily" crossed. We aregoing to give a few example, where the extension of liquid-liquid locus for polymer blends and solutions below p = 0 givesus some interesting results, like the merging of UCST and LCST branches in weakly interacting polymer solutions or thereason why most UCST blends exhibit pressure induced immiscibility. Also, we will see what happens with the immiscibilityisland of aqueous polymer solutions when -- reaching the critical molar mass -- it "disappears".     

集合风险模型的可分解性

本文讨论了集合风险模型中 ,在复合二项分布和复合负二项分布两种情况下的可分解性问题 ,得到了同复合泊松分布情况下类似的结果     

A different construction of Gaussian fields from Markov chains: Dirichlet covariances

We study a class of Gaussian random fields with negative correlations. These fields are easy to simulate. They are defined in a natural way from a Markov chain that has the index space of the Gaussian field as its state space. In parallel with Dynkin's investigation of Gaussian fields having covariance given by the Green's function of a Markov process, we develop connections between the occupation times of the Markov chain and the prediction properties of the Gaussian field. Our interest in such fields was initiated by their appearance in random matrix theory.     

从几何光学研究负折射率透镜的有限尺寸效应

从几何光学理论证明了,在左手系材料(负折率材料)透镜中存在完善聚焦的概念。当该透镜的尺寸可以认为是无穷大时,该透镜是无几何像差透镜。进一步考虑了有限透镜孔径对成像面上成像质量的影响,模拟结果表明:成像面上亮度对比度分布不均匀;且随着透镜孔径大小与厚度的比值减小,像的对比度将会增加。     

二维三温热传导方程组的分数步隐式差分格式

本文给出一个解二维三温热传导方程组的分数步隐式有限差分格式，利用离散变分形式及能量方法，给出差分格式的最优阶离散H^1范数先验误差及稳定性估计。     

NA序列重对数律的几个极限定理

设{X_n;n≥1}均值为零、方差有限的NA平稳序列。记S_n=∑_(k=1)~n X_k,M_n=maxk≤n|S_k|,n≥1.假设σ~2=EX_1~2+2∑_(k=2)~∞EX_1X_k>0。本文讨论了:当ε 0时,P{M_n≥εσ(2nloglogn)~(1/2)的一类加权级数的精确渐近性质,以及当ε∞时,P{M_n≤εσ(π~2n/(8loglogn))~(1/2)}的一类加权级数的精确渐近性质。这些性质与重对数律和Chung重对数律的速度有关。