三维问题的局部块分解预条件

利用块三对角矩阵的嵌套局部块分解构造了一个不完全分解预条件子,并考虑了其修正型变种,分析了两者的存在性及若干性质.针对标准七点差分矩阵,给出了预条件后的实际条件数.结果表明,采用局部块分解预条件时条件数与矩阵阶数的2/3次幂成正比,而采用修正型预条件时条件数与矩阵阶数的立方根成正比.最后考虑了预条件的高效实现并在主频为550MHz、内存为256M的微机上作了若干数值实验,并与其它较有效的预条件方法进行了比较.     

The Dattoli-Srivastava conjectures concerning generating functions involving the harmonic numbers

In a recent paper Dattoli and Srivastava [3], by resorting to umbral calculus, conjectured several generating functions involving harmonic numbers. In this sequel to their work our aim is to rigorously demonstrate the truth of the Dattoli-Srivastava conjectures by making use of simple analytical arguments. In addition, one of these conjectures is stated and proved in more general form.     

The design of a Tort law to control accidents

In this paper we analyse a two-stage game involving the government and n agents who engage in a single activity (driving). The government establishes the legal policy setting and the agents proceed to play a non-cooperative game of incomplete information with a risk of accident in which their behavioral strategy is their level of care. We examine the Nash-equilibrium conditions for single-activity accidents between heterogeneous agents, ‘good’ drivers or ‘bad’ drivers allowing a variable damage function and a liability rule defined on the cube. The relative desirability for society of alternative equilibria and the conditions under which they can obtain are discussed. The constraints which circumscribe the ability of the government to induce an equilibrium involving careful driving are demonstrated. It transpires that when the proportion of good drivers increases, it becomes more difficult to sustain a careful equilibrium whereas an equilibrium of reckless behavior becomes easier to sustain. Various extensions of the models are also presented.     

Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints

In this paper, we present an interior-point algorithm for large and sparse convex quadratic programming problems with bound constraints. The algorithm is based on the potential reduction method and the use of iterative techniques to solve the linear system arising at each iteration. The global convergence properties of the potential reduction method are reassessed in order to take into account the inexact solution of the inner system. We describe the iterative solver, based on the conjugate gradient method with a limited-memory incomplete Cholesky factorization as preconditioner. Furthermore, we discuss some adaptive strategies for the fill-in and accuracy requirements that we use in solving the linear systems in order to avoid unnecessary inner iterations when the iterates are far from the solution. Finally, we present the results of numerical experiments carried out to verify the effectiveness of the proposed strategies. We consider randomly generated sparse problems without a special structure. Also, we compare the proposed algorithm with the MOSEK solver. Research partially supported by the MIUR FIRB Project RBNE01WBBB “Large-Scale Nonlinear Optimization.”     

Generation of anti-trenbolone monoclonal antibody and establishment of an indirect competitive enzyme-linked immunosorbent assay for detection of trenbolone in animal tissues, feed and urine

Trenbolone (TRE) is a steroid used by veterinarians on livestock to increase appetite and body weight. The use of TRE has been restricted because of its harmful side effect for consumers. To effectively control TRE residue in food and food product, a rapid and convenient immunoassay was developed by preparing an anti-TRE monoclonal antibody. The immunogen and coating antigen were prepared by coupling TRE hapten with carrier proteins via 1-ethyl-3-(dimethylaminopropyl)carbodiimide hydrochloride (EDC) method. The optimized method gave an average IC₅₀ value of 0.323 ng mL⁻¹ towards TRE and an average detection limit (LOD) of 0.06 ng mL⁻¹, which is much lower than the maximum residue levels (2.0 ng g⁻¹) accepted by the Joint FAO/WHO Expert Committee on Food Additives (JECFA). The specificity of the antibody was evaluated by measuring cross-reactivity of six structurally related compounds, including 19-nortestosterone (9.7%), testosterone (0.13%), methyltestosterone (<0.01%), methandrostenolone (<0.01%), (+)-dehydroisoandrosterone (<0.001%) and β-estradiol (<0.001%). The recovery rates of the test in detection of TRE-fortified animal tissue, urine and animal feed samples were in the range of 81.3-89.4%, while the intra- and inter-assay coefficients of variation were less than 12.0%.     

非完全汽化气相色谱法测定溶剂型涂料中的微量苯、甲苯、二甲苯

用乙酸乙酯稀释溶剂型涂料样品，在较低的汽化温度下直接进样，溶剂型涂料中未汽化的组分留在汽化室里，而苯、甲苯和二甲苯汽化后进入毛细管，用气相色谱法氢火焰离子化检测器进行检测，与国家标准分析方法进行比较，该法具有操作简单、精密度高等优点。     

Evaluation of Orbital- and Ground State Energies of Some Open- and Closed-Shell Atoms over Integer and Noninteger Slater Type Orbitals

Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two-electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.     

The circular chemistry conceptual framework: A way forward to sustainability in industry 4.0

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基于乘性一致性残缺互补判断矩阵的决策方法

对于满足乘性一致性的残缺互补判断矩阵的决策问题,提出了一种决策方法。首先把互补判断矩阵的乘性一致性定义进行了简化,得到了互补判断矩阵乘性一致性的另外几种表达形式;进一步得到了在已知n-1个特殊元素的条件下,残缺互补判断矩阵中缺失元素的补全方法;然后给出了残缺互补判断矩阵可接受的条件,以及矩阵的一致性检验及调整方法;基于残缺互补判断矩阵,给出了以下决策步骤:残缺互补判断矩阵的一致性检验及调整过程,补全缺失元素的迭代过程和最优方案择优过程。最后给出了一个实例,通过该实例的计算以及本文方法与已有方法的比较,证明了本文方法是简便和有效的。     

基于变分不等式的生态工业链网络均衡问题研究

以变分不等式为基础提出生态工业链网络均衡模型。生态工业链是通过仿照自然生态系统中的物质循环方式与生物群体之间的竞争与共生模式,使不同企业之间形成共享资源和互换副产品从而实现园区各企业经济与环境效益的最大化。针对生态工业链网络的多产品(主副产品和废弃物)多层次的网络结构,模仿自然生态系统中的生产者、消费者和分解者,分别对各层决策者的独立优化决策行为及其相互作用进行分析,利用变分不等式分析各层均衡条件进而构建生态工业链网络均衡模型,得到系统达到均衡的条件并给出相应的经济解释。在证明系统变分不等式的解存在的基础上,通过数值算例验证模型的合理性与有效性。