A multifractal decomposition according to rate of returns

For one‐dimensional simple symmetric random walk, the Hausdorff and packing dimensions of sets of sample paths with prescribed rate of returns to the origin are determined. This gives a multifractal decomposition of the underlying sample space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ginzburg－Landau－Newell模型的动力学行为

木文对Ｇｉｎｚｂｕｒｇ－Ｌａｎｄａｕ－Ｎｅｗｅｄ模型的动力学行为进行了讨论，得到了该模型的整体吸引子的存在性，同时得到了此吸引子维数的下界估计和该吸引子的Ｈａｕｓｄｏｒｆｆ维数和Ｗａｃｔａｌ（分形）维数的上界估计．     

一类二维非线性Schrodinger方程的吸引子及其维数

本文研究了一类二维非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程解的有限维行为，我们得到了此方程存在吸引子，并得到了此吸引子维数的上界估计     

Finite dimensional semisimple Q-algebras

A Q-algebra can be represented as an operator algebra on an infinite dimensional Hilbert space. However we don’t know whether a finite n-dimensional Q-algebra can be represented on a Hilbert space of dimension n except n = 1, 2. It is known that a two dimensional Q-algebra is just a two dimensional commutative operator algebra on a two dimensional Hilbert space. In this paper we study a finite n-dimensional semisimple Q-algebra on a finite n-dimensional Hilbert space. In particular we describe a three dimensional Q-algebra of the disc algebra on a three dimensional Hilbert space. Our studies are related to the Pick interpolation problem for a uniform algebra.     

样条空间S~μ_k（△）的维数

本文考虑了欧式空间Ｒ￣ｎ中任意单纯形剖分上的样条函数空间．证明了当ｋ≥（３μ＋１）２￣（ｎ－２）＋１时，计算任意单纯形剖分Δ上的ｋ次μ阶光滑样条空间的维数，可归结为计算每个σ－关联域（ｉ－单纯形σ∈Δ）Ｒ（σ）上的２￣（ｎ－ｉ－１）μ次μ阶光滑（ｉ≤ｎ－１）样条空间的维数。这里σ－关联域Ｒ（σ）是指Δ中所有包含σ的单纯形所成的单纯形剖分．     

Mathematical analysis of investment systems

Investment systems are studied using a framework that emphasize their profiles (the cumulative probability distribution on all the possible percentage gains of trades) and their log return functions (the expected average return per trade in logarithmic scale as a function of the investment size in terms of the percentage of the available capital). The efficiency index for an investment system, defined as the maximum of the log return function, is proposed as a measure to compare investment systems for their intrinsic merit. This efficiency index can be viewed as a generalization of Shannon's information rate for a communication channel. Applications are illustrated.     

The VC dimension of k‐uniform random hypergraphs

A set of vertices is shattered in a hypergraph if any of its subsets is obtained as the intersection of an edge with the set. The VC dimension is the size of the largest shattered subset. Under the binomial model of k‐uniform random hypergraphs, the threshold function for the VC dimension to be larger than a given integer is obtained. The same is done for the testing dimension, which is the largest integer d such that all sets of cardinality d are shattered. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Estimating market shares in each market segment using the information entropy concept

Sales data of a certain product for the various competitors are usually available at the aggregate level. However these data give no clue to the heterogeneities in the sales pattern across different market segments. Heterogeneities are caused by different purchasing behavior in each market segment; as a purchaser in a segment will be attracted to the attributes of the product most important to that segment. This concept can be formalized via a simple attraction model that utilizes an elasticity measure for each quality or price attribute [G.S. Carpenter, L.G. Cooper, D.M. Hanssens, D.F. Midgley, Modeling asymmetric competition, Marketing Science 7 (4) (1998) 393–412]. Assessment of these elasticities is not difficult since customer response – in each market segment – to perception of quality and price is tracked by most firms [J. Ross, D. Georgoff, A survey of productive and quality issues in manufacturing. The state of the industry, Industrial Management 3 (5) (1991) 22–25]. This paper attempts to formulate a generic framework based on the information entropy concept that utilizes such an attraction model to estimate competitors’ sales in each market segment.     

Dynamics for the stochastic nonlocal Kuramoto-Sivashinsky equation

Dynamics for the stochastic Kuramoto-Sivashinsky equation with a nonlocal term is studied. We prove that the stochastic equation has a finite-dimensional random attractor.     

On the role of heterogeneous and imperfect information in a laboratory financial market

In this paper, we analyze the behavior of a group of heterogeneously informed investors in an laboratory asset market. Our experimental setting is inspired by Huber et al. (On the benefit of information in markets with heterogeneously informed traders: an experimental study, 2004). However, instead of their system of cumulative and exogenously given information structure, we introduce an information market where the traders can buy an imperfect prediction of the future value of the dividend with a maximum anticipation of four periods. The accuracy of the prediction decreases with the chosen time horizon, whereas its price remains constant. Our results confirm a non-strictly monotonic increasing value of the information.