Optimal Pricing of a Product Diffusing in Rich and Poor Populations

We consider a market consisting of two populations, termed rich and poor for convenience. If a product is priced such that it is very expensive for the poor, but affordable to the rich, then it becomes a status symbol for the poor and this makes it more desirable for the poor. At a lower price, the product is affordable by both populations. However, as more of the poor buy the product, it ceases to be a status symbol and becomes less appealing to the rich. We present a two-state nonlinear optimal control problem that aims to obtain profit-maximizing prices over time in this environment. We find that there are three categories of optimal price paths. One is status-symbol pricing with high initial price, declining over time. The other two are mass-market pricing, with price declining in one, and price increasing and then decreasing in the other.     

Composition operators acting on holomorphic Sobolev spaces

We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.

     

Spectral-fractional step Runge-Kutta discretizations for initial boundary value problems with time dependent boundary conditions

In this paper we develop a technique for avoiding the order reduction caused by nonconstant boundary conditions in the methods called splitting, alternating direction or, more generally, fractional step methods. Such methods can be viewed as the combination of a semidiscrete in time procedure with a special type of additive Runge-Kutta method, which is called the fractional step Runge-Kutta method, and a standard space discretization which can be of type finite differences, finite elements or spectral methods among others. Spectral methods have been chosen here to complete the analysis of convergence of a totally discrete scheme of this type of improved fractionary steps. The numerical experiences performed also show the increase of accuracy that this technique provides.

     

‘Classical’ convergence theorems for generalized continued fractions

In this paper the classical convergence theorems by Śleszyński-Pringsheim, Worpitzky and Van Vleck for ordinary continued fractions will be generalized to continued fractions generalizations (along the lines of the Jacobi–Perron algorithm) with four-term recurrence relations.      

Saddle points and Lagrangian-type duality for discrete minmax fractional subset programming problems with generalized convex functions

In this paper we present four sets of saddle-point-type optimality conditions, construct two Lagrangian-type dual problems, and prove weak and strong duality theorems for a discrete minmax fractional subset programming problem. We establish these optimality and duality results under appropriate (b,?,ρ,θ)-convexity hypotheses.     

基于分形理论的开放式基金信息性风险防范研究

开放式基金防范由于证券市场信息的非对称性导致的系统性风险,是开放式基金投资决策中的一个重要问题。本文基于分形市场理论及对中国股市的实证研究,提出了开放式基金防范信息性风险的有效策略。     

中国股市价格-交易量动态因果关系研究

研究了中国股票市场交易量是否含有预测未来收益变动的有价值信息 .实证结果表明 :交易量和收益序列存在即期的正相关关系 ;过去交易量包含未来绝对收益变动的有价值信息 ;中国股票市场交易量和收益序列存在双向的线性因果关系 ,交易量不仅传递价格绝对变动量的信息 ,而且在很大程度上还传递价格变动方向的信息 .     

Letter: Parametrization of the Kerr-NUT Solution

The dragging of the Kerr-NUT solution does not tend to zero at infinity. To modify this solution in order to produce a good asymptotic behaviour we transform it by introducing two further parameters with the aid of a SU(1,1) transformation followed by a unitary transformation. By imposing a certain relation between these parameters we obtain a new solution with a good asymptotic behaviour for any value of l, the NUT parameter. The new solution corresponds to a parametrized Kerr solution and we show that l is linked to the form of its ergosphere.     

Role of Prehistories in the Initial Value Problems of Fractional Viscoelastic Equations

The fractional viscoelastic equation (FVE), which is a second-order differential equation with fractional derivatives describing the dynamical behavior of a single-degree-of-freedom viscoelastic oscillator, is considered. Some viscoelastic damped mechanical systems may be described by FVEs. However, FVEs with conventional nonzero initial values cannot generally be solved. In this paper, the prehistories of the unknown functions before the initial times, referred to as the initial functions, are taken into account to solve FVEs. Mathematically, appropriate initial functions are essential for unique solutions of FVEs. Physically, the initial functions reflect the processes of giving the initial values. FVEs are solved for some initial functions both by analytical and numerical methods. The initial functions affect the solutions of FVEs. It is discussed how the solutions depend on the initial functions. Implication of the solutions to viscoelastic materials will be discussed.     

Fractional Derivatives of Holomorphic Functions on Bounded Symmetric Domains of C~n

.9J.AnirnductionLetQbeaboundedsymmetricdomaininthecon1plexvectorspaceC",Oen,withBergman-Silovboundaryb,rthegroupofholomorphicautomorphismsofaandnitsisotropygroup.ItisknownthatDiscircularandstar-shapedwitl1respecttoOandbiscircular.ThegroupflistransitiveonbandbhasauniquenormalizedO-invariantmeasuredwithd(b)=1-Hua[2]constructedbygrouprepresentationtl1eoryasystem{%,}ofhomogeneouspolyno-l,J k-l\mails,k=O,l,..',v=l,..',))l*'nI*=('J k-l),coml>leteandorthogonalonnandortl1onor-malonb.ByH(Q)weden…