Weighted Sobolev embedding with unbounded and decaying radial potentials

We prove embedding results of weighted W1,p(RN) spaces of radially symmetric functions. The results then are used to obtain ground and bound state solutions of quasilinear equations with unbounded or decaying radial potentials.     

The proportional hazards regression model with staggered entries: A strong martingale approach

The proportional hazards regression model, when subjects enter the study in a staggered fashion, is studied. A strong martingale approach is used to model the two-time parameter counting processes. It is shown that well-known univariate results such as weak convergence and martingale inequalities can be extended to this two-dimensional model. Strong martingale theory is also used to prove weight convergence of a general weighted goodness-of-fit process and its weighted bootstrap counterpart.     

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.     

Coupling and Poisson approximation

We give an overview of the Stein-Chen method for establishing Poisson approximations of various random variables. Couplings of certain variables are used to gives explicit bounds for the total variation distance between the distribution of a random variable and a Poisson variable. Some applications are given. In some cases, explicit couplings may be used to obtain good estimates; in other applications it suffices to show the existence of couplings with certain monotonicity properties.Supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.     

Synthesis of the D-Galactopyranoside Derivative of C_(60)

ThefascinatingsbocturesandpropertiesoffullereneshaveoPeneduPanewfieldofchendstry.Inparticular,F.Wudletal.l'2haveshownthatwatersofubleC6ocomPoundsinhibittheHITVen-zymesprotease(HIVP)andreversetranscriPtase(HIVRT).IthasbeenafocusofstUdytoinvestigatethebiologicalactivitiesofthesenovelsubstances.Fortheirpossiblemedicaluses,tolinkC6omoleculetonaturalProductssuchassugars,pephdes,amioacides,andsoonisanimPortantmethodinthisfield.Vasella3reportedthefirstglucosidederivativeofC6o'InthispaPer,w…     

超微粒子－有机聚合物薄膜的研究

我们用离子团束－飞行时间质谱（ＩＣＢ－ＴｏＦＭＳ）系统制备了金（Ａｕ）超微粒子－聚乙烯（ＰＥ）薄膜和Ｃ＿（６０）－聚乙烯薄膜。用透射电子显微镜（ＴＥＭ）分析了所制备的样品。它们的结构是Ａｕ超徽粒子镶嵌在多晶的ＰＥ薄膜中，其中Ａｕ原子团呈球形，直径分布在２．０－５．０ｎｍ窄范围内，当沉积基底温度为９０℃时，Ａｕ原子团相互靠近，几乎连接起来，但仍保持原来大小。基底温度为１４０℃蒸积的Ｃ＿（６０）－ｐＥ薄膜具有晶态结构，其晶格常数为１．４５４ｎｍ。     

The Remainder in Ruijsenaars’ Asymptotic Expansion of Barnes Double Gamma Function

We show that the remainder in Ruijsenaars’ asymptotic expansion of the logarithm of Barnes double gamma function gives rise to a completely monotone function. Fourier expansions of the multiple Bernoulli polynomials are also obtained. Research supported by the Carlsberg Foundation.     

A Universal Logic Approach to Adaptive Logics

In this paper, adaptive logics are studied from the viewpoint of universal logic (in the sense of the study of common structures of logics). The common structure of a large set of adaptive logics is described. It is shown that this structure determines the proof theory as well as the semantics of the adaptive logics, and moreover that most properties of the logics can be proved by relying solely on the structure, viz. without invoking any specific properties of the logics themselves.     

Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

Spectral Properties of Image Measures Under the Infinite Conflict Interaction

We introduce the conflict interaction with two positions between a couple of image probability measures and consider the associated dynamical system. We prove the existence of invariant limiting measures and find the criteria for these measures to be a pure point, absolutely continuous, or singular cotinuous as well as to have any topological type and arbitary Hausdorff dimension.