An integer linear programming approach for a class of bilinear integer programs

We propose an Integer Linear Programming (ILP) approach for solving integer programs with bilinear objectives and linear constraints. Our approach is based on finding upper and lower bounds for the integer ensembles in the bilinear objective function, and using the bounds to obtain a tight ILP reformulation of the original problem, which can then be solved efficiently. Numerical experiments suggest that the proposed approach outperforms a latest iterative ILP approach, with notable reductions in the average solution time.     

超Li系统的Bargmann对称约束和双非线性化

给出超Li系统的一个显式对称约束和关于其Lax对的双非线性化.在此对称约束下,超Li系统的时间部分和空间部分分别被约化为有限维Liouville可积超Li系统.     

特殊集上素变数方程的解

令n=e_0+e_12+…+e_k2~k,其中e_j=0,1(j=0,…,k)表示自然数n的二进制展开式,N_0表示二进制展开式中项数为偶数的自然数的集合.分别给出了这个特殊集上素变数方程p_1+p_2+p_3~k=N和p_1+p_2~2+p_3~2+p_4~2=N解的个数的渐近公式.     

弱碱性和强碱性阴离子交换树脂的离子交换平衡的比较SO_4~(2-)-Cl~--NO_3~-体系

本文详细地比较了在弱碱性和强碱性阴离子交换树脂上,SO_4~(2-)-Cl~-、NO_3~--Cl~-及NO_3~--SO_4~(2-)二元交换的等温线和修正选择系数。实验测定及理论计算了上述三种二元交换反应的标准自由能的改变量。测得了在弱碱性树脂上的SO_4~(2-)-Cl~--NO_3~-三元交换的等温线。适用于强酸性和强碱性树脂的从二元交换平衡数据推算三元交换平衡数据的方法推广应用于弱碱性树脂。     

Molecular dynamics comparative study of methane–nitrogen and methane–nitrogen–ethane systems

This work concerns the site–site interaction study of 256 particles using the Buckingham potential model. We have calculated the new parameters of the Buckingham potential using an iterative algorithm with a mean square method. This adapted model allows determining the characteristics for each state point. We have applied this model to study the liquefied natural gas LNG properties for methane-nitrogen and methane–nitrogen–ethane mixtures by molecular dynamics. We have calculated the thermodynamic, dynamic and structural properties for both the microcanonical NVT and the isothermal-isobaric NPT ensembles of binary and ternary systems from the SP₁ to SP₉ points. Then, we have compared the results between binary and ternary systems. We have obtained a good prediction on transport properties. From the calculated values of self-diffusion coefficient and viscosity, we have confirmed the liquid state of the liquefied natural gas LNG system.     

Multistability of impact, utility and threshold concepts of binary choice models

The decision making problem in the context of binary choice is considered by means of impact function, utility function and threshold model approaches. The properties of generalized impact function and utility function are examined; it is shown that these two approaches are equivalent. Their relation to the threshold model is studied and the correspondence between respective cumulative distribution functions is displayed. The stationary state corresponding to the thermodynamic equilibrium is determined within mean field approximation. Multistability of the stationary state is expressed in terms of the distribution function of the random variable of impact/utility function. The correspondence with statistical physics predictions for Ising model is discussed: logistic distribution leads to the mean-field result, i.e. Curie-Weiss approximation. Variations of the distribution functions and/or other model parameters, of social character, self-support, nonlinearity of social interactions, etc., would break the direct correspondence to statistical physics of Ising model, leading in particular cases to richer structure of the multistability.     

Binary functions,degeneracy, and alternating dimaps

This paper continues the study of combinatorial properties of binary functions — that is, functions $f:2^E\to ?$ such that $f(0?)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.     

二元液态金属Cu-Ni和Ag-Cu凝固过程的分子动力学模拟研究

用Quantum Sutton-Chen多体势对Ag6Cu4和CuNi液态金属凝固过程进行了分子动力学模拟研究.在冷却速率2×1012到2×1014K/s范围内,CuNi总是形成fcc晶体结构,而Ag6Cu4总是形成非晶态结构.考虑到CuNi及AgCu中原子半径之比分别为1.025和1.13,那么模拟结果证实了原子的尺寸差别是非晶态合金形成的一个主要影响因素.此外采用键对及原子多面体类型指数法对凝固过程中微观结构组态变化的分析,不但能说明二十面体结构在非晶态合金形成和稳定性中所起的关键作用,又有助于对液态金属的凝固过程、非晶态结构特征的深入理解.