基于可替代资源的稀缺资源利用问题研究

在线性规划资源利用问题模型基础上,研究了减少一种稀缺程度相对较高的资源限量,同时增加一定比例的另一种可替代该资源的稀缺程度相对较低的资源限量,而使企业原有最优生产目标值不减的问题.通过对不同情况的分类讨论,得到相应的资源改变量及其比例的取值决定和取值范围,对稀缺资源的节省利用具有一定意义.     

国民经济最优规划中的共轭问题研究

本论文针对稀缺资源提出国民经济最优化的共轭问题．由共轭定理得到了共轭问题解一致的可能性及其成立的条件，共轭定理为检验国民经济协调发展提供了理论依据和方法．论文着重讨论了以劳动资源为稀缺资源的国民经济规划共轭问题，给出其约束条件的影子价格的经济意义，证明了同一约束条件的影子价格是成比例的，劳动资源的影子价格是国民财富的影子价格的倒数．同时指出产品与资源等价替代系数与其影子价格有关，影子价格是产品与资源的短缺性、产品与资源的平衡的度量．最后讨论了影子价格与生产活动的消耗、劳动消耗与效益的关系．     

用边际法求解一类设备的最优分配问题

本文针对一类设备的最优分配问题，将利润表转化为边际利润表，并建立了相应的寻优方程，通过实例说明，在一定情况下，用改进后的算法比常规算法节省一定的计算工作量。     

线性规划在饲料配方中的应用

本文应用线性规划方法，以计算机为工具，对哈尔滨国营红旗农场养鸡场饲料传统配方进行了优化设计，经过 ３个周期的使用，证明每年可节省饲料费 ２８万元，经济效益十分显著。     

用边际法求解－类设备的最优分配问题

本文针对一类设备的最优分配问题，将利润表转化为边际利润表，并建立了相应的寻优方程，通过实例说明，在一定情况下，用改进后的算法比常规算法节省一定的计算工作量．     

东西部能源经济系统可持续发展博弈分析

引入经济可持续发展能源可承受度概念,建立中央和东西部地区兼顾经济增长及能源可持续发展的博弈模型,分析西部大开发战略中中央、东部和西部能源开发的战略选择,得到能源作为稀缺资源在地区及全国范围内最优配置的相关结论.     

弹性圆板在一侧受均载而四周固定的条件下不用Kirchhoff—Love假设的一...

本文在前文［１］所得的微分方程和有关边界条件的基础上，求得一这些方程在有关边界条件下的解析解。当然，为了节省计算工作量，我们进一步简化了一级近似理论，使它在保持合理的基础上，更加简单化了。     

正交试验设计在麦白霉素高产菌株选育中的应用

本文应用正交试验设计改进了麦白霉素的生产工艺，在四个关键环节上选出了比对照组高出７００μ／ｍｌ以上的高产稳定菌株。该法使试验次数减少，选育周期缩短，既节省了人力物力和降低了生产成本，又增加了麦白霉素药粉的产量，取得了可观的经济效益。     

基于双层规划的集群式供应链供应商激励机制研究

对存在多级供应商的集群式供应链中稀缺资源供应的激励问题进行了研究。在假设市场某种零部件稀缺,制造商的产量直接与零部件供应量链相关,而零部件供应量直接与一级供应商努力程度相关的情况下,建立了相应的单多双层规划模型,分别研究了制造商针对供应商结盟与不结盟的情况下的最优激励机制。最后进行了仿真,结果表明本文的激励机制能较好激励供应商并能有效防范其结盟。     

求最短路问题的改进算法

本对图论中含有负权的最短路问题的算法进行了讨论，给出了一个具有“可节省存储空间、提高运算速度、易编程实现”等优点的改进算法（算法三），并通过例题进一步验证了该改进算法的优越性，具有一定的现实意义。     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Effects of permeability and viscosity in linear polymeric gels

We propose and analyze a mathematical model of the mechanics of gels, consisting of the laws of balance of mass and linear momentum of the polymer and liquid components of the gel. We consider a gel to be an immiscible and incompressible mixture of a nonlinearly elastic polymer and a fluid. The problems that we study are motivated by predictions of the life cycle of body‐implantable medical devices. Scaling arguments suggest neglecting inertia terms, and therefore, we consider the quasi‐static approximation to the dynamics. We focus on the linearized system about stress‐free states, uniform expansions, and compressions and derive sufficient conditions for the solvability of the time‐dependent problems. These turn out to be conditions that guarantee local stability of the equilibrium solutions. We also consider non‐stress free equilibria and states with residual stress and derive an energy law for the corresponding time‐dependent system. The conditions that guarantee stability of solutions provide a selection criteria of the material parameters of devices. The boundary conditions that we consider are of two types, displacement‐traction and permeability of the gel surface to the fluid. We address the cases of viscous and inviscid solvent, assume Newtonian dissipation for the polymer component, and establish existence of weak solutions for the different boundary permeability conditions and viscosity assumptions. We present two‐dimensional, finite element numerical simulations to study stress concentration on edges, this being the precursor to debonding of the gel from its substrate. Copyright © 2015 John Wiley & Sons, Ltd.     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

Boundary-Value Problems of the Theory of Thin and Nonthin Orthotropic Shells with Account of Nonlinearly Elastic Properties and Low Shear Rigidity of Composite Materials

The basic geometric and physical relations and resolving equations of the theory of thin and nonthin orthotropic composite shells with account of nonlinear properties and low shear rigidity of their materials are presented. They are derived based on two theories, namely the theory of anisotropic shells employing the Timoshenko or Kirchhoff-Love hypothesis and the nonlinear theory of elasticity and plasticity of anisotropic media in combination with the Lagrange variational principle. The procedure and algorithm for the numerical solution of nonlinear (linear) problems are based on the method of successive approximations, the difference-variational method, and the Lagrange multiplier method. Calculations of the stress-strain state for a spherical shell with a circular opening loaded with internal pressure are presented. The effect of transverse shear strains and physical nonlinearity of the material on the distribution of maximum deflections and circumferential stresses in the shell, obtained according to two variants of the shell theories, is studied. A comparison of the results of the problem solution in linear and nonlinear statements with and without account of the shell shear strains is given. The numerical data obtained for thin and nonthin (medium thick) composite shells are analyzed.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

Unsteady motion of a spherical bubble in a complex fluid: Mathematical modelling and simulation

The nonlinear response of an oscillatory bubble in a complex fluid is studied. The bubble is immersed in a Newtonian liquid, which may have a dilute volume fraction of anisotropic additives such as fibers or few ppm of macromolecules. The constitutive equation for the fluid is based on a Maxwell model with an extensional viscosity for the viscous contribution. The model is considered new in the study of bubble dynamics in complex fluids. The numerical computation solves a system of three first order ordinary differential equations, including the one associated with the solution of the convolution integral, using a fifth order Runge–Kutta scheme with appropriated time steps. Asymptotic solutions of governing equation are developed for small values of the pressure forcing amplitude and for small values of the elastic parameter. A study of the bubble collapse radius is also presented. We compare the results predicted by our model with other model in the literature and a good agreement is observed. The calculated asymptotic solutions are also used to test the results of the numerical simulations. In addition, the orientation of the additives is considered. The angular probability density function is assumed to be a normal distribution. The results show that the model based on the fully aligned additives with the radial direction overestimates the tendency of the additives to stabilize the bubble motion, since the effect of extensional viscosity occurs due to the particle resistance to the movement throughout its longitudinal direction.     

基于NSGA-Ⅱ的应急储备库多目标

应急物资储备库选址问题是在近年世界灾害多发的现实背景下产生的,根据具体选址问题特点建立了多目标选址决策模型。该模型综合考虑了两种灾害风险下储备库的成本费用、覆盖效率以及对重点地区的备用覆盖,以使模型更加符合实际目标及约束情况。算法设计上,首次采用带精英策略的非支配排序遗传算法(Fast and elitist Non-dominated Sorting Genetic Algorithm Ⅱ,NSGA-Ⅱ)解决储备库多目标选址问题,得到了Pareto非劣解分布并同不带精英策略的常规NSGA算法下的仿真结果进行对比分析。验证了模型的可行性以及NSGA-Ⅱ在解决储备库多目标选址问题的有效性。     

拍卖机制设计在区块链中的应用与挑战

区块链是新一代信息技术的重要组成部分,是分布式网络、加密技术、智能合约等多种技术集成的新型数据库软件。过去的十多年,区块链技术在全球范围内产生广泛影响。如今的区块链技术,已从最初的关注于解决货币和支付的去中心化问题,转入到解决市场的去中心化问题。智能合约的出现使得基于区块链技术的去中心化金融进入高速发展状态,也涌现出区块链环境下的各类拍卖场景。本文首次从机制设计角度,以区块链交易费机制,非同质化代币(Non-Fungible Token,NFT)拍卖和矿工可提取价值(Miner-Extractable Value,MEV)交易位置拍卖为主要对象,总结和剖析近些年来区块链上特有的拍卖机制;并针对区块链特性,提出区块链上拍卖机制设计所面临的挑战和未来亟待解决的问题。     

On the hyperbolicity of the period-doubling fixed point

We give a new proof of the hyperbolicity of the fixed point for the period-doubling renormalization operator using the local dynamics near a semi-attractive fixed point (in a Banach space) and the theory of holomorphic motions. We also give a new proof of the exponential contraction of the Feigenbaum renormalization operator in the hybrid class of the period-doubling fixed point: our proof uses the non-existence of invariant line fields in the period-doubling tower (C. McMullen), the topological convergence (D. Sullivan), and a new infinitesimal argument.

     

Mathematical modeling of time fractional reaction–diffusion systems

We study a fractional reaction–diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives. It is shown that by combining the fractional derivatives index with the ratio of characteristic times, it is possible to find the marginal value of the index where the oscillatory instability arises. The increase of the value of fractional derivative index leads to the time periodic solutions. The domains of existing periodic solutions for different parameters of the problem are obtained. A computer simulation of the corresponding nonlinear fractional ordinary differential equations is presented. For the fractional reaction–diffusion systems it is established that there exists a set of stable spatio-temporal structures of the one-dimensional system under the Neumann and periodic boundary conditions. The characteristic features of these solutions consist of the transformation of the steady-state dissipative structures to homogeneous oscillations or space temporary structures at a certain value of fractional index and the ratio of characteristic times of system.