Boundedness of Riesz transforms for elliptic operators on abstract Wiener spaces

Let (E,H,μ) be an abstract Wiener space and let D_V:=VD, where D denotes the Malliavin derivative and V is a closed and densely defined operator from H into another Hilbert space . Given a bounded operator B on , coercive on the range , we consider the operators A:=V^*BV in H and in , as well as the realisations of the operators and in L^p(E,μ) and respectively, where 1<p<∞. Our main result asserts that the following four assertions are equivalent:

(1) with for ;

(2) admits a bounded H^∞-functional calculus on ;

(3) with for ;

(4) admits a bounded H^∞-functional calculus on .

Moreover, if these conditions are satisfied, then . The equivalence (1)–(4) is a non-symmetric generalisation of the classical Meyer inequalities of Malliavin calculus (where , V=I, ). A one-sided version of (1)–(4), giving L^p-boundedness of the Riesz transform in terms of a square function estimate, is also obtained. As an application let −A generate an analytic C₀-contraction semigroup on a Hilbert space H and let −L be the L^p-realisation of the generator of its second quantisation. Our results imply that two-sided bounds for the Riesz transform of L are equivalent with the Kato square root property for A. The boundedness of the Riesz transform is used to obtain an L^p-domain characterisation for the operator L.

Wick calculus for nonlinear Gaussian functionals

This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random variables. Some conditions are described for random variables whose Wick product or whose renormalization are integrable random variables. Relevant results on multiple Wiener integrals, second quantization operator, Malliavin calculus and their relations with the Wick product and Wick renormalization are also briefly presented. A useful tool for Wick product is the S-transform which is also described without the introduction of generalized random variables.     

半局部E-凸性下分式多目标规划的最优性条件与对偶

In this paper, some necessary and sufficient optimality conditions are obtained for a fractional multiple objective programming involving semilocal E-convex and related functions. Also, some dual results are established under this kind of generalized convex functions. Our results generalize the ones obtained by Preda[J Math Anal Appl, 288(2003) 365-382].     

Integration of the sine-Gordon equation with a self-consistent source of the integral type in the case of multiple eigenvalues

The paper is dedicated to the evolution of the scattering data for a Dirac-type nonself-adjoint operator with multiple eigenvalues whose potential is a solution of the sine-Gordon equation with a self-consistent source of the integral type.     

Computing bounded-degree phylogenetic roots of disconnected graphs

The Phylogenetic kth Root Problem (PRk) is the problem of finding a (phylogenetic) tree T from a given graph G=(V,E) such that (1) T has no degree-2 internal nodes, (2) the external nodes (i.e., leaves) of T are exactly the elements of V, and (3) (u,v)E if and only if the distance between u and v in tree T is at most k, where k is some fixed threshold k. Such a tree T, if exists, is called a phylogenetic kth root of graph G. The computational complexity of PRk is open, except for k4. Recently, Chen et al. investigated PRk under a natural restriction that the maximum degree of the phylogenetic root is bounded from above by a constant. They presented a linear-time algorithm that determines if a given connected G has such a phylogenetic kth root, and if so, demonstrates one. In this paper, we supplement their work by presenting a linear-time algorithm for disconnected graphs.     

Vibrations and stability of axially traveling laminated beams

In this paper, vibrations and stability of an axially traveling laminated composite beam are investigated analytically via the method of multiple scales. Based on classical laminated beam theory, the governing equations of motion for a time-variant axial speed are obtained using Newton’s second law of motion and constitutive relations. The method of multiple scales, an approximate analytical method, is applied directly to the gyroscopic governing equations of motion and complex eigenfunctions and natural frequencies of the system are obtained. The stability boundaries of the system near resonance are determined via the Routh-Hurwitz criterion. Finally, a parametric study is conducted which considers the effects of laminate type and configuration as well as the mean speed and amplitude of speed fluctuations on the vibration response, natural frequencies and stability boundaries of the system.     

On the Tail Mean-Variance optimal portfolio selection

In the present paper we propose the Tail Mean-Variance (TMV) approach, based on Tail Condition Expectation (TCE) (or Expected Short Fall) and the recently introduced Tail Variance (TV) as a measure for the optimal portfolio selection. We show that, when the underlying distribution is multivariate normal, the TMV model reduces to a more complicated functional than the quadratic and represents a combination of linear, square root of quadratic and quadratic functionals. We show, however, that under general linear constraints, the solution of the optimization problem still exists and in the case where short selling is possible we provide an analytical closed form solution, which looks more “robust” than the classical MV solution. The results are extended to more general multivariate elliptical distributions of risks.     

Multiple lump solutions of the (2+1)-dimensional Konopelchenko–Dubrovsky equation

In this paper, multiple lump solutions of the (2+1)-dimensional Konopelchenko–Dubrovsky equation are obtained by means of the Hirota bilinear method. With the aid of positive quartic-quadratic-functions, we can get the 1-lump solutions, 3-lump solutions, and 6-lump solutions. Via the density plots and three-dimensional plots, the dynamic properties of multiple lump solutions are discussed by choosing the appropriate parameters. It is expected that our results are valuable for revealing the high-dimensional dynamic phenomenon of the nonlinear evolution equations.     

一类具有多重时滞的分数阶中立型微分系统的相对可控性

本文对一类具有多重时滞的Caputo分数阶中立型微分控制系统的相对可控性和相对U可控性进行了研究.首先利用Laplace变换得到系统解的一个新的表达式,接着由Grammian矩阵得出系统相对可控的充分必要条件.最后给出了一类非线性分数阶中立型微分控制系统相对U可控的充分必要条件.     

基于投影模型的区间直觉模糊多属性决策方法研究

本文首先定义了一种新区间直觉模糊投影方法,其能更好地度量投影向量之间的相关性。其次,根据区间直觉模糊正负理想方案与备选方案的投影关系, 构建了基于投影方法的未知属性权重求解模型,并在此基础上设计了一种基于投影值的贴近度方法,能实现对备选方案有效排序;最后,用实例验证了该方法的有效性和可行性。