Mixed ligand complexes of AEE hexafluoroacetylacetonates with diglyme: Synthesis,crystal structure and thermal behavior

The novel mixed ligand complexes [Ca(hfa)₂(diglyme)(H₂O)] (I), [Sr(hfa)₂(diglyme)(H₂O)] (II) and [Ba(hfa)₂(diglyme)₂] (III) (Hhfa = 1,1,1,5,5,5-hexafluoropentane-2,4-dione, diglyme = 2,5,8-trioxanonane) were synthesized by the reactions of the alkaline earth element (AEE) carbonates in n-hexane with a mixture of Hhfa and diglyme, and they were characterized by elemental analysis, ¹H and ¹³C NMR, and FTIR spectroscopy. The crystal structures of I–III, consisting of mononuclear isolated molecules, have been determined. The thermal behavior and composition of the vapor phase have been studied for I–III by thermal analysis at low pressure and mass spectrometry using a Knudsen cell. The stability of the mixed ligand complexes [M(hfa)₂(diglyme)_n] to the removal of diglyme molecules under heating decreases in the row I > II ≈ III, and only I evaporates as the mixed ligand complex after water removal.     

混合染料荧光选择性增强受激拉曼散射Stokes波

报道用不同混合比的罗丹明6G(R6G)和罗丹明B(RB)混合染料荧光选择性放大CCl₄和苯的受激拉曼散射不同阶次Stokes波。CCl₄二至五阶Stokes波分别被混合摩尔比为20∶2,20∶13及20∶40(R6g∶RB)的R6G和RB的混合染料荧光放大;一阶Stokes波强度被混合溶液削弱。这是由于到二至五阶Stokes波分别位于以上三种混合溶液荧光峰附近,并且都远离了R6G和RB的吸收峰,混合溶液的荧光增强作用大于吸收作用,因此这几阶Stokes被混合溶液荧光放大。而CCl₄的一阶Stokes位于RB吸收峰附近,又远离各混合溶液荧光峰,溶液的吸收作用大于荧光增强作用,导致一阶Stokes被混合溶液削弱。文章还报道了苯的一、二和三阶Stokes波分别被不同混合比的R6G和DCM的混合乙醇溶液放大,并预测了该方法应用前景。     

Discrete optimization in public rail transport

Many problems arising in traffic planning can be modelled and solved using discrete optimization. We will focus on recent developments which were applied to large scale real world instances. Most railroad companies apply a hierarchically structured planning process. Starting with the definition of the underlying network used for transport one has to decide which infrastructural improvements are necessary. Usually, the rail system is periodically scheduled. A fundamental base of the schedule are the lines connecting several stations with a fixed frequency. Possible objectives for the construction of the line plan may be the minimization of the total cost or the maximization of the passengers’s comfort satisfying certain regulations. After the lines of the system are fixed, the train schedule can be determined. A criterion for the quality of a schedule is the total transit time of the passengers including the waiting time which should be minimized satisfying some operational constraints. For each trip of the schedule a train consisting of a locomotive and some carriages is needed for service. The assignment of rolling stock to schedule trips has to satisfy operational requirements. A comprehensible objective is to minimize the total cost. After all strategic and tactical planning the schedule has to be realized. Several external influences, for example delayed trains, force the dispatcher to recompute parts of the schedule on-line. A Web page with examples quoted in this survey can be found at http://www.math.tu-bs.de/mo/ismp.html.     

Classification of Dantzig–Wolfe reformulations for binary mixed integer programming problems

In this note, we provide a classification of Dantzig–Wolfe reformulations for Binary Mixed Integer Programming Problems. We specifically focus on modeling the binary conditions in the convexification approach to the Dantzig–Wolfe decomposition. For a general Binary Mixed Integer Programming problem, an extreme point of the overall problem does not necessarily correspond to an extreme point of the subproblem. Therefore, the binary conditions cannot in general be imposed on the new master problem variables but must be imposed on the original binary variables. In some cases, however, it is possible to impose the binary restrictions directly on the new master problem variables. The issue of imposing binary conditions on the original variables versus the master problem variables has not been discussed systematically for MIP problems in general in the literature and most of the research has been focused on the pure binary case. The classification indicates in which cases you can, and cannot, impose binary conditions on the new master problem variables.     

On the use of edge cracked short bend beam specimen for PMMA fracture toughness testing under mixed-mode I/II

In this paper an inclined edge cracked short beam specimen subjected to symmetric three-point bend loading was designed and examined for conducting mixed-mode I/II fracture toughness experiments. The aspect ratio (i.e. length to width ratio) and the loading span distance are considered much lower than the other conventional cracked bend beam samples. Crack tip parameters such as stress intensity factors and T-stress were computed numerically for this specimen by several finite element analyses and it was demonstrated that the specimen is able to produce full combinations of mode I and II including pure mode II. The practical capability of the short bend beam specimen was studied experimentally by conducting a set of mixed-mode fracture tests on PolymethylMethacrylate (PMMA) as a well-known model brittle material. The critical stress intensity factors, the direction of fracture kinking and the path of fracture trajectory were investigated both experimentally and theoretically using two stress and strain-based fracture criteria. The fracture toughness of tested PMMA was decreased by moving towards mode II case due to the effect of T-stress on the fracture mechanism of the short bend beam specimen.     

A TWO-LEVEL FINITE ELEMENT GALERKIN METHOD FOR THE NONSTATIONARY NAVIER-STOKES EQUATIONS I： SPATIAL DISCRETIZATION

In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a $H^1$-optimal velocity approximation and a $L_2$-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small, nonlinear Navier-Stokes problem on the coarse mesh with mesh size $H$, one linear Stokes problem on the fine mesh with mesh size $h << H$. The algorithm we study produces an approximate solution with the optimal, asymptotic in $h$, accuracy.     

Mixed integer programming for a special logic constrained optimal control problem

Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L² norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a complicated one, difficulties arise when integrating the additional logical constraints. First, we will present two different ways of modeling the problem, both of them leading us to Mixed Integer Problems. Furthermore, algorithms (Generalized Outer Approximation, Benders Decomposition and Branch and Cut) are applied on each model and results analyzed. We also present a Benders Decomposition algorithm variant that is adapted to our problem (taking into account its particular form) and we will conclude by looking at the optimal solutions obtained in an interesting physical example: the harmonic spring.     

An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static-dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time.     

基于Lagrange乘子法的一种二阶椭圆问题混合元格式

本文利用Lagrange乘子法的思想,修改了传统的混合变分形式,将二阶椭圆问题转化为与其等价的新的变分形工,给出了针对该新形式进行离散求解的一种混合元格式,与现在已知格式相比,用较少的自由度获得了较高的逼近阶。     

一个包含Euler函数及k阶Smarandache ceil函数的方程及其正整数解

设k≥2为给定的整数．对任意正整数n,k阶Smarandache ceil函数Sk（n）定义为Sk（n）=min{x：x∈N,n｜x^k}．本文的主要目的是利用初等方法研究函数方程Sk（n）=Ф（n）的可解性,并给出该方程的所有正整数解,其中Ф（n）为Euler函数．