三种类型汽车的能耗和使用成本的建模研究

本文对电动,传统,混合动力三种类型汽车的能耗和使用成本问题进行了建模、求解及分析．首先定义了电动汽车的能量利用率ηE。根据能量守恒将所有电量转换成汽油消耗量,而传统车型则直接反映到汽油的消耗上,混合动力汽车则综合电动汽车和传统汽车的能耗模型,从而统一能耗水平评价标准．这样,我们就得到了三种不同类型车的能耗模型再进行模型求解以此来分析比较三种类型车哪一种节能效果好．对电动汽车来说,使用成本主要包括驾驶维护成本、报废处理成本,而对传统汽车来说,使用成本主要包括驾驶维护成本、报废处理成本、环境成本和其他成本,混合动力汽车则结合二者使用成本．因此,根据不同车型使用成本类型建立相应的数学模型,按照建立的公式,可以得到电动汽车的使用成本LCC1、传统汽车的使用成本LCC2和混合动力汽车的使用成本LCC3,从而进行模型求解．     

A relaxation algorithm for the minimization of a quasiconcave function on a convex polyhedron

A study was made of the global minimization of a general quasiconcave function on a convex polyhedron. This nonconvex problem arises in economies of scale environments and in alternative formulations of other well-known problems, as in the case of bilinear programming.Although not very important in our final results, a local minimum can be easily obtained. However, a major aspect is the existence of two families of lower bounds on the optimal functional value: one is provided by non-linear programming duality, the other is derived from a lexicographic ordering of basic solutions which allows the use of relaxation concepts. These results were exploited in a finite algorithm for obtaining the global minimum whose initial implementation has had encouraging performance.     

Optimal dynamic investment with learning by doing in the adjustment cost function

In an optimal control model of a firm's dynamic investment policy, we analyze the effects of including learning by doing in the adjustment cost function (the larger the existing capital stock, the smaller the cost of installing an additional unit of capital stock).The authors wish to thank two anonymous reviewers for valuable comments. The research of the second author was sponsored by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

Analysis of generalized continued fraction algorithms over polynomials

We study and compare natural generalizations of Euclid's algorithm for polynomials with coefficients in a finite field. This leads to gcd algorithms together with their associated continued fraction maps. The gcd algorithms act on triples of polynomials and rely on two-dimensional versions of the Brun, Jacobi–Perron and fully subtractive continued fraction maps, respectively. We first provide a unified framework for these algorithms and their associated continued fraction maps. We then analyse various costs for the gcd algorithms, including the number of iterations and two versions of the bit-complexity, corresponding to two representations of polynomials (the usual and the sparse one). We also study the associated two-dimensional continued fraction maps and prove the invariance and the ergodicity of the Haar measure. We deduce corresponding estimates for the costs of truncated trajectories under the action of these continued fraction maps, obtained thanks to their transfer operators, and we compare the two models (gcd algorithms and their associated continued fraction maps). Proving that the generating functions appear as dominant eigenvalues of the transfer operator allows indeed a fine comparison between the models.     

A PDE approach to risk measures of derivatives

This paper proposes a partial differential equation (PDE) approach to calculate coherent risk measures for portfolios of derivatives under the Black-Scholes economy. It enables us to define the risk measures in a dynamic way and to deal with American options in a relatively effective way. Our risk measure is based on the representation form of coherent risk measures. Through the use of some earlier results the PDE satisfied by the risk measures are derived. The PDE resembles the standard Black-Scholes type PDE which can be solved using standard techniques from the mathematical finance literature. Indeed, these results reveal that the PDE approach can provide practitioners with a more applicable and flexible way to implement coherent risk measures for derivatives in the context of the Black-Scholes model.     

Exhaust gas analysers and optimised sampling, uncertainties and costs

Decision-making in the conformity assessment of exhaust gas analysers with due account of measurement uncertainty and limited sampling is considered. Risks of incorrect decisions where test results lie in the vicinity of a specification limit are assessed in terms of percentage probability and the costs of measurement and environmental consequences, with examples based on the metrological requirements on these analysers stipulated in the new EU Measurement Instrument Directive. An optimised uncertainty methodology is proposed for the first time in legal metrology based on quantitative testing of new instruments for type approval and initial verification, and gives valuable insight into traditional rules limiting uncertainty in conformity assessment in general. Further, an analysis of subsequent verification of exhaust gas analysers in use in society, leads to a new optimised uncertainty methodology based on attribute sampling.

有保证权益连结寿险合约的定价

本文在考虑买卖标的股票需支付比例交易成本的条件下,根据效用最大化原理,将效用无差别定价方法应用到有保证权益连结寿险合约的定价上,给出了合约保留卖价的表达式,并做了数值模拟,计算结果表明本文的方法是合理的.     

有交易费的折算资产优化可达性

针对所给出的有交易费的资产模型，引入了资产折算函数，并利用辅助鞅和凸分析方法，讨论了该模型下一种资产优化的可达性。     

Recent advances in oxygen electrocatalysts based on tunable structural polymers

Due to their high energy density, great safety and eco-friendliness, zinc-air batteries (ZABs) attract much attention. During the process of charging and discharging, the two key processes viz. oxygen evolution reaction (OER) and oxygen reduction reaction (ORR) limit their efficiency. In general, the noble metal-based electrocatalysts (ORR: platinum (Pt); OER: iridium (IV) oxide [IrO₂] and ruthenium oxide [RuO₂]) have long been used. Nonetheless, these noble metal electrocatalysts also have their limitations owing to high cost and poor stability. As alternatives, polymers are found to be most promising on account of their tunable structure, uniform network, high surface morphology and strong durability. Polymers are capable catalysts. In this review, recent advances as well as insight into the architecture of covalent organic polymers (COPs), metal coordination polymers (MCPs) and pyrolysis-free polymers (PFPs) are duly outlined.     

A hybrid method for pricing European options based on multiple assets with transaction costs

The problem of pricing European options based on multiple assets with transaction costs is considered. These options include, for example, quality options and options on the minimum of two or more risky assets. The value of these options is the solution of a nonlinear parabolic partial differential equation subject to a final condition given by the payoff function associated with the option. A computationally efficient method to solve this final-value problem is proposed. This method is based on an asymptotic expansion of the required solution with respect to the parameters related to the transaction costs followed by the numerical solution of the linear partial differential equations obtained at each order in perturbation theory. The numerical solution of these linear problems involves an implicit finite-difference scheme for the parabolic equation and the use of the fast Fourier sine transform to solve the resulting elliptic problems. Numerical results obtained on test problems with the method proposed here are shown and discussed.