Configurational Effects in Statistical Theory of Branched Non-Random Polycondensation

The statistical theory of gelation in the simplest process of the non-random polycondensation (S. I. Kuchanov, T. V. Zharnikov, J. Stat. Phys., 111(5/6), 1273 (2003)) has been refined as to be able to take into account the effect of a monomer configuration on topological characteristics of the polymer network of the gel. Proceeding from the kinetic analysis of such a polycondensation, we rigorously prove that it can be described in terms of some stochastic branching process. The parameters of the process depend on the overall number of functional groups in the monomer as well as on the pattern of their mutual arrangement. Examples of some model systems illustrate the effect of kinetic and configurational factors on the topology of a polymer network formed in the course of non-random polycondensation.     

金融数学的发展及其在证券投资组合中的应用

论述了金融科学中一种新兴的数学工具和数学技术——倒向随机微分方程，通过运用倒向随机微分方程，研究当投资者以将来某一时刻获取一定数额的适应性收益为投资目标时，如何确定当前证券投资组合中各证券的投资比例．     

A mathematical programming model and solution for scheduling production orders in Shanghai Baoshan Iron and Steel Complex

In this paper, we investigate the production order scheduling problem derived from the production of steel sheets in Shanghai Baoshan Iron and Steel Complex (Baosteel). A deterministic mixed integer programming (MIP) model for scheduling production orders on some critical and bottleneck operations in Baosteel is presented in which practical technological constraints have been considered. The objective is to determine the starting and ending times of production orders on corresponding operations under capacity constraints for minimizing the sum of weighted completion times of all orders. Due to large numbers of variables and constraints in the model, a decomposition solution methodology based on a synergistic combination of Lagrangian relaxation, linear programming and heuristics is developed. Unlike the commonly used method of relaxing capacity constraints, this methodology alternatively relaxes constraints coupling integer variables with continuous variables which are introduced to the objective function by Lagrangian multipliers. The Lagrangian relaxed problem can be decomposed into two sub-problems by separating continuous variables from integer ones. The sub-problem that relates to continuous variables is a linear programming problem which can be solved using standard software package OSL, while the other sub-problem is an integer programming problem which can be solved optimally by further decomposition. The subgradient optimization method is used to update Lagrangian multipliers. A production order scheduling simulation system for Baosteel is developed by embedding the above Lagrangian heuristics. Computational results for problems with up to 100 orders show that the proposed Lagrangian relaxation method is stable and can find good solutions within a reasonable time.     

Calorimetry in nonstandard conditions: The noncrystalline phases of linear polyethylene

A linear Union Carbide PE (UC) has been analyzed by nonstandard calorimetry with a common DSC calorimeter and a Setaram C80 calorimeter. Nonstandard calorimetry entails using a low rate of heating (0.5–1 K/min), a small mass (0.5–1.5 mg), and an open cell (O‐cell) instead of the standard C‐cell. Events in O‐cells overlap less and occur with a faster kinetics than in C‐cells. PE crystals are nascent, solution‐grown (S‐grown), press‐grown (P‐grown), and strained by extrusion. In Part A, the traces show that the phase‐changes in the melt, previously observed in a C80 calorimeter (slow T‐ramp) and characterized by ΔH_network, can be observed with a common DSC in nonstandard conditions. In Part B, the difference between the C‐ and O‐cells and the changes in the main peak enthalpy (ΔH_ortho) are of interest. The main result is that, in O‐cells, the value of ΔH_ortho around T_ortho, exceeds unambiguously in certain conditions ΔH_ortho found for perfect orthorhombic crystals. The main endotherm contains then another contribution, namely ΔH_network. Crystal reorganization during the slow T‐ramp is followed in the C‐ and O‐cells on S‐grown crystals. In O‐cells, lamellar thickening observed in the slow‐ramp is more extensive. The ease of phase‐change depends on the sample history. It is as follows: strained‐part extruded > nascent > S‐grown > P‐grown. Co‐operative chain motions are more hindered in the standard C‐cells than in the O‐cells. In Part C, lower values of m succeed in bringing phase‐changes in P‐grown (O‐cells) samples. The origin of the events is discussed: three processes are thought to contribute to the phase‐changes namely, melting of strained short‐range order, activation of vibrations in the CH₂ groups, and fast decay of chain orientation which occurs simultaneously with melting. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1932–1949, 2007     

Collective Directional Transport in Symmetric Periodic Potentials by Breaking the Coupling Symmetry

Collective unidirectional motion of an asymmetrically coupled array of oscillators in symmetric periodic potentials is studied. A directed current is observed when the drift coupling is presented, while no external biased force is applied. Negative directed current is found when varying system parameters. An addition of a periodic rocking force may enhance the efficiency of directed transport. Resonant steps of the current are found and interpreted as the mode locking between the array and the ac force. Noise-assisted transport is observed, and an optimal noise intensity can give rise to a most efficient transport. The directed transport thus can be optimized and furthermore controlled by suitably adjusting the parameters of the system.     

A study of shear-stress relaxation anomalies in binary mixtures of monodisperse polystyrenes

We report measurements of the nonlinear relaxation moduli after a step-shear strain of polystyrene solutions with nearly monodisperse and with bidisperse distributions of molecular weight. We find, as have others, that for monodisperse solutions with M/M_e > 60, there are anomalies, such as an unusually low nonlinear modulus and a kink in a plot of shear stress versus time after the step strain. Here M is the polymer molecular weight and M_e is the entanglement molecular weight. We find that in the bidisperse solutions the anomalies persist as long as M_w/M_e > 60, where M_w is the weight-averaged molecular weight of the bidisperse solution. The persistence of the anomalies in bidisperse solutions disagrees with a theory of Marrucci and Grizzuti that attributes the anomalies to strain inhomogeneities similar to shear banding. The Marrucci-Grizzuti theory predicts that as little as 10% short chains in the bidisperse mix should eliminate the anomalies, whereas in the experiments reported here at least 30% is required. Nevertheless the way in which the anomalies disappear at high strains when one increases the fraction of low-molecular-weight component is qualitatively similar to the theoretical predictions and supports the notion that strain inhomogeneities occur in these systems. © 1992 John Wiley & Sons, Inc.     

两指标随机积分方程解的唯一性

在正交增量的随机积分基础上，利用Ｌｉｐｓｃｈｉｔｚ条件，讨论了下面一类两参数随机积分方程解的唯一性。Ｘ（ｓ，ｔ）＝Ｚ（ｓ，０）＋Ｚ（０，ｔ）－Ｚ（０，０）＋∫Ｒｓｔα（ｕ，ｖ，Ｘ）ｄＭｕｖ＋∫Ｒｓｔβ（ｕ，ｖ，Ｘ）ｄｍｕｖ＋∫Ｒ＾ｓｔγ１（ｕ，ｖ，ｕ＇，ｖ＇，Ｘ）ｄＭｕｖｄＭｕ＇ｖ＇＋∫Ｒ＾２ｓｔγ２（ｕ，ｖ，ｕ＇，ｖ＇，Ｘ）ｄＭｕｖｄｍｕ＇ｖ＇＋∫Ｒ＾２ｓｔγ３（ｕ，ｖ，ｕ＇，ｖ＇，Ｘ）ｄｍｕｖ     

An Iterative Procedure for Evaluating Digraph Competitions

A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. After describing the resulting procedure of redistributing the initial weights, an iterative process is described that repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights. Existence and uniqueness of the limit is established for arbitrary digraphs. Applications to the evaluation of, e.g., sport competitions and paired comparison experiments are discussed.     

The Likelihood of the Parameters of a Continuous Time Vector Autoregressive Model

This paper provides a method of constructing the likelihood function of the parameters of a continuous time vector autoregressive model on the basis of discrete data without requiring the restrictions extant methods impose on the data that are capable of being rejected by a statistical test. In particular, the method does not rely on a steady-state assumption that can rule out unit root processes; it allows for weak assumptions on the innovations; and it allows for a mixture of skip-sampled and temporally-aggregated data. This revised version was published online in August 2006 with corrections to the Cover Date.     

倒向随机微分方程及其应用

本文将介绍一类新的议程：倒向随机微分方程，为了便于理解，我们将首先通过与常微分方程和经典的随机微分方程的对比，并通过数理经济和数学金融学中的一个典型的例子来引入倒向随机微分方程。