高校实验室开放教学的探讨

从实验室建制、师资队伍建设、实验教学体系构建和实验室开放保障措施等4个方面进行了探讨．以求加快实施实验室开放的步伐．     

Free product actions with relative property (T) and trivial outer automorphism groups

We show that every non-amenable free product of groups admits free ergodic probability measure preserving actions which have relative property (T) in the sense of S. Popa (2006) [Pop06, Def. 4.1]. There are continuum many such actions up to orbit equivalence and von Neumann equivalence, and they may be chosen to be conjugate to any prescribed action when restricted to the free factors. We exhibit also, for every non-amenable free product of groups, free ergodic probability measure preserving actions whose associated equivalence relation has trivial outer automorphisms group. This gives, in particular, the first examples of such actions for the free group on 2 generators.     

Construction of Gel Type Reference and Combination Ion-Selective Electrodes

Abstract

A simple and an inexpensive procedure for the construction of the reference electrodes and of the conversion of ion-selective electrodes to the “combination” types is described. It allows the manipulation of the reference electrode filling solution according to the needs of a particular measurement. The electrodes have good reproducibility and stable inter-comparison potentials of ± 0.2 mV. The performance characteristics of these electrodes are satisfactory for potentiometric measurements.     

The benefits of differential variance-based constraints in portfolio optimization

The main problem of portfolio optimization is parameter estimation error. Various methods have been suggested to mitigate this problem, among which are shrinkage, resampling, Bayesian updating, naïve diversification, and imposing constraints on the portfolio weights. This study suggests two substantial extensions of the constrained optimization approach: the Variance-Based Constraints (VBC), and the Global Variance-Based Constraints (GVBC) methods. By the VBC method the constraint imposed on the weight of a given stock is inversely proportional to its standard deviation: the higher a stock’s sample standard deviation, the higher the potential estimation error of its parameters, and therefore the tighter the constraint imposed on its weight. GVBC employs a similar idea, but instead of imposing a sharp boundary constraint on each stock, a quadratic “cost” is assigned to deviations from the naive 1/N weight, and a single global constraint is imposed on the total cost of all deviations. Comparing ten optimization methods we find that the two new suggested methods typically yield the best performance, as measured by the Sharpe ratio. GVBC ranks first. These results are obtained for two different datasets, and are also robust to the number of assets under consideration.     

Stochastic Differential Games with Multiple Modes and Applications to Portfolio Optimization

Abstract

We study a zero-sum stochastic differential game with multiple modes. The state of the system is governed by “controlled switching” diffusion processes. Under certain conditions, we show that the value functions of this game are unique viscosity solutions of the appropriate Hamilton–Jacobi–Isaac' system of equations. We apply our results to the analysis of a portfolio optimization problem where the investor is playing against the market and wishes to maximize his terminal utility. We show that the maximum terminal utility functions are unique viscosity solutions of the corresponding Hamilton–Jacobi–Isaac' system of equations.     

Existence of good large sets of Steiner triple systems

The concept of good large set of Steiner triple systems (or GLS in short) was introduced by Lu in his paper “on large sets of disjoint Steiner triple systems”, [J. Lu, On large sets of disjoint Steiner triple systems, I-III, J. Combin. Theory (A) 34 (1983) 140-182]. In this paper a doubling construction for GLSs is displayed and some existence results are obtained.     

Collapsing Construction with Nilpotent Structures

A fundamental result concerning collapsed manifolds with bounded sectional curvature is the existence of compatible local nilpotent symmetry structures whose orbits capture all collapsed directions of the local geometry [CFG]. The underlying topological structure is called an N-structure of positive rank. We show that if a manifold M admits such an N-structure , then M admits a one-parameter family of metrics g _∈ with curvature bounded in absolute value while injectivity radii and the diameters of -orbits away from the singular set of uniformly converge to zero as . Moreover, g _∈ is -invariant away from the singular set. This result extends collapsing results in [CG1], [Fu3] and [G]. Q.C. supported partially by a Jingshi research fund from Beijing Normal University. X.R. supported partially by NSF Grant DMS 0504534 and by a Jingshi research fund from Beijing Normal University.     

Constructions for rotational Steiner quadruple systems

A direct construction for rotational Steiner quadruple systems of order p+ 1 having a nontrivial multiplier automorphism is presented, where p≡13 (mod24) is a prime. We also give two improved product constructions. By these constructions, the known existence results of rotational Steiner quadruple systems are extended. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 353–368, 2009     

Markowitz’s model with Euclidean vector spaces

In this paper a new approach of the Markowitz’s model is presented. Indeed, using an inner product, a quantitative and explicit solution for optimal portfolio selection is given. To do this, a scalar product is defined in Rⁿ${\mathfrak{R}}^n$ which allows us to calculate the composition of the optimal portfolio and the variance for a given expected return by means of the distance between the subspace of feasible solutions and the origin of the affine space.