A generalization of Borel's theorem and microlocal Gevrey regularity in involutive structures

In this paper, we use Borel's procedure to construct Gevrey approximate solutions of an initial value problem for involutive systems of Gevrey complex vector fields. As an application, we describe the Gevrey wave-front set of the boundary values of approximate solutions in wedges W of Gevrey involutive structures (M,V). We prove that the Gevrey wave-front set of the boundary value is contained in the polar of a certain cone ΓT(W) contained in RV∩TX where X is a maximally real edge of W. We also prove a partial converse.     

On <Emphasis Type="Italic">l</Emphasis><Subscript>2,<Emphasis Type="Italic">p</Emphasis></Subscript>-circle numbers

Circle numbers are defined to reflect the Euclidean area-content and, for p ≠ 2, suitably defined non-Euclidean circumference properties of the l _2,p -circles, p ∈ [1, ∞]. The resulting function is continuous, increasing, and takes all values from [2, 4]. The actually chosen dual l _2,p -geometry for measuring the arc-length is closely connected with a generalization of the method of indivisibles of Cavalieri and Torricelli in the sense that integrating such arc-lengths means measuring area content. Moreover, this approach enables one to look in a new way into the co-area formula of measure theory which says that integrating Euclidean arc-lengths does not yield area content except for p = 2. The new circle numbers play a natural role, e.g., as norming constants in geometric measure representation formulae for p-generalized uniform probability distributions on l _2,p -circles.     

The periodic risk model with investment

We consider a periodic risk model with the possibility of investing into a risky asset, given by a geometrical Brownian motion. The aim is to maximize the adjustment coefficient of the risk process. It is shown that the optimal investment strategy only depends on the averaged data of the model and is constant over time. Thus maximizing the adjustment coefficient is a very weak optimization criterion.     

On the deformation of linear r-fields

We study the question: For which (r,n) can a linear r-field on the (n-1)-sphere in an n-dimensional real linear space be deformed through a continuous path of linear r-fields into an orthonormal r-field. We provide complete answers for the cases: (r,n)=(2,4),(3,4), and provide several partial results for the cases (r,n)=(2,2m), where m is an even integer satisfying m4. Characterizations of linear r-fields are pivotal in the investigation.     

Calculating risk neutral probabilities and optimal portfolio policies in a dynamic investment model with downside risk control

This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio’s worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifying the optimal terminal wealth distribution and a stochastic linear programming model replicating the identified optimal portfolio wealth. The replicating portfolio coincides with the optimal solution to the investor’s problem if the market is frictionless. The multiperiod stochastic linear programming model tests for the absence of arbitrage opportunities and its dual feasible solutions generate all risk neutral probability measures. When there are constraints such as liquidity or position requirements, the method yields approximate portfolio policies by minimizing the initial cost of the replication portfolio. A numerical example illustrates the difference between the replicating result and the optimal unconstrained portfolio.     

Banach空间中增生算子方程的Ishikawa迭代解

在没有∑∞n=0αnβn<∞的更弱条件下,使用与完全不同的方法,证明了Ishikawa迭代序列强收敛Lipschitz连续的增生算子T的方程x+Tx=f的唯一解,并提供了更为全面和一般的收敛率的估计.本文结果是引文[3-4]中相应结果的统一和发展.     

Proton-nucleus optical model potential at low energies—a review

Ever since it was proposed more than three decades ago, the nuclear optical model has been very successful in interpreting a large body of nucleon-induced nuclear reaction data in terms of a complex nucleon-nucleus potential. Rapid progress both in the experimental measurements and the theoretical developments in the last two decades has led to a better understanding of this nucleon-nucleus optical potential. From the parameter-fitting phenomenological stage, the optical model has come a long way and it is now possible to calculate the nucleon-nucleus optical potential in a reasonable way starting from the fundamental nucleon-nucleon interaction. Excellent reviews on various aspects of the optical model exist in the literature for proton energies above 10 MeV. The present article is an attempt to review comprehensively the status of the proton-nucleus optical potential at low proton energies, below the Coulomb-barrier, for target nuclei with mass numbers lying between 40 and 130. The sets of phenomenological optical potential derived mostly from (p, n) reaction data are reviewed and their applicabilities discussed. The neutron-nucleus optical model is referred to wherever it is relevant. Microscopic calculations for one case is carried out and compared with the corresponding phenomenological values.     

Estimation of investment project profitability in the modified Cantor-Lipman model

The profitability of investment projects in the modified Cantor-Lipman model is analyzed. The possibility of making lower estimates of the investment project profitability by searching for periodic trajectories is studied. The necessary and sufficient conditions for the existence of a trajectory with the period 2 are derived. The sufficient conditions ensuring the existence of a certain trajectory with the period 2 are derived in the form of explicit requirements on the investment project structure.     

Representations of distributive semilattices in ideal lattices of various algebraic structures

We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these different topics. Received March 2, 1998; accepted in final form November 9, 2000.     

Contrarian investment strategy with data envelopment analysis concept

One of the typical issues in financial literature is that the market tends to be overly pessimistic about value stocks, many of which are past losers. Therefore, over-reactions might capture by measuring earnings surprise vary with past return levels. In this paper, we propose a new index for an effective investment strategy to capture the return-reversal effect using both Data Envelopment Analysis (DEA) and Inverted DEA in order to consider the above characteristics of the market. Our investment strategy using the new index exhibits better performance than the naive return-reversal strategy that only uses past returns or earnings surprise. In addition, the correlations between our new index and commonly used value indices are insignificant, and the value indices cannot represent the over-valued (under-valued) situations perfectly. Hence, considering both proposed and value indices like book-to-price one, we could select value stocks more effectively than by using only one of these indices.