条件风险下的两基金分离定理

鉴于条件风险价值CVaR具有风险度量的合理性以及两基金分离定理对证券投资的重要意义,以CVaR作为风险度量研究两基金分离定理.在组合收益率服从正态分布的假设下,分别就投资组合含有或没有无风险资产的情形提出并证明了两基金分离定理;放开方差-协方差矩阵为非奇异这一通常假设,证明了CVaR风险度量下的两基金分离定理依然成立.     

A Complete Solution to Spectrum Problem for Five‐Vertex Graphs with Application to Traffic Grooming in Optical Networks

A G‐design of order n is a decomposition of the complete graph on n vertices into edge‐disjoint subgraphs isomorphic to G. Grooming uniform all‐to‐all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph on n vertices into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The existence spectrum problem of G‐designs for five‐vertex graphs is a long standing problem posed by Bermond, Huang, Rosa and Sotteau in 1980, which is closely related to traffic groomings in optical networks. Although considerable progress has been made over the past 30 years, the existence problems for such G‐designs and their related traffic groomings in optical networks are far from complete. In this paper, we first give a complete solution to this spectrum problem for five‐vertex graphs by eliminating all the undetermined possible exceptions. Then, we determine almost completely the minimum drop cost of 8‐groomings for all orders n by reducing the 37 possible exceptions to 8. Finally, we show the minimum possible drop cost of 9‐groomings for all orders n is realizable with 14 exceptions and 12 possible exceptions.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

An explicit counter-example for the shephard problem of convex bodies in ℝ n

Comparing the volume of the projection body of a double cone and that of the projection body of a ball, we give an explicit counter-example for the Shephard problem of convex bodies in Rⁿ (n ≥ 3) and an affirmative answer to the question of Zhang.     

Order acceptance and scheduling on two identical parallel machines

We study the order acceptance and scheduling problem on two identical parallel machines. At the beginning of the planning horizon, a firm receives a set of customer orders, each of which has a revenue value, processing time, due date, and tardiness weight. The firm needs to select orders to accept and schedule the accepted orders on two identical parallel machines so as to maximize the total profit. The problem is intractable, so we develop two heuristics and an exact algorithm based on some optimal properties and the Lagrangian relaxation technique. We evaluate the performance of the proposed solution methods via computational experiments. The computational results show that the heuristics are efficient and effective in approximately solving large-sized instances of the problem, while the exact algorithm can only solve small-sized instances.     

Comparison of microbiological loads and physicochemical properties of raw milk treated with single-/multiple-cycle high hydrostatic pressure and ultraviolet-C light

The effects of ultraviolet-C radiation (UV-C, 11.8?W/m²), single-cycle and multiple-cycle high hydrostatic pressure (HHP at 200, 400 or 600?MPa) on microbial load and physicochemical quality of raw milk were evaluated. Reductions of aerobic plate count (APC) and coliform count (CC) by HHP were more than 99.9% and 98.7%, respectively. Inactivation efficiency of microorganisms increased with pressure level. At the same pressure level, two-cycle treatments caused lower APC, but did not show CC differences compared with single-cycle treatments. Reductions of APC and CC by UV-C were somewhere between 200?MPa and 400/600?MPa. Both HHP and UV-C significantly decreased lightness and increased pH, but did not change soluble solids content and thiobarbituric acid-reactive substances’ values. Two 2.5?min cycles of HHP at 600?MPa caused minimum APC and CC, and maximum conductivity. Compared with HHP, UV-C markedly increased protein oxidation and reduced darkening.     

Facile and surfactant-free synthesis of SnO<Subscript>2</Subscript>-graphene hybrids as high performance anode for lithium-ion batteries

A facile microwave-assisted ethylene glycol method is developed to synthesize the SnO₂ nanoparticles dispersed on or encapsulated in reduced graphene oxide (SnO₂-rGO) hybrids. The morphology, structure, and composition of SnO₂-rGO are investigated by scanning electron microscopy, transmission electron microscope, thermo-gravimetric analyzer, X-ray diffraction, Raman spectroscopy, and X-ray photoelectron spectroscopy. The electrochemical performance of SnO₂-rGO as anode materials for lithium-ion batteries was tested by cyclic voltammetry, galvanostatic charge–discharge cycling, and rate capability test. It is found that the SnO₂ nanoparticles with a uniform distribution have p-type doping effect with rGO nanosheets. The as-prepared SnO₂-rGO hybrids exhibit remarkable lithium storage capacity and cycling stability, and the possible mechanism involved is also discussed. Their capacity is 1222 mAhg^?1 in the first cycle and maintains at 700 mAhg^?1 after 100 cycles. This good performance can be mainly attributed to the unique nanostructure, good structure stability, more space for volume expansion of SnO₂, and mass transfer of Li⁺ during cycling.