双光子吸收效应对孤子和孤子对传输的影响

用分步傅立叶变换法求解含双光子吸收效应的光孤子NLS方程,研究了双光子吸收效应对一阶孤子和孤子对传输的影响,发现双光子吸收效应除对孤子产生等效损耗外,还影响了孤子对在传输中的相互作用。在特定的双光子吸收系数条件下双光子吸收效应可以使孤子对平行地向前传输。     

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.     

Representation of Hilbert algebras and implicative semilattices

In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.     

Comparison of volumes by means of the areas of central sections

The Busemann–Petty problem asks whether origin-symmetric convex bodies in Rⁿ with smaller areas of all central hyperplane sections necessarily have smaller n-dimensional volume. The solution was completed in the end of the 1990s, and the answer is affirmative if n4 and negative if n5. Since the answer is negative in most dimensions, it is natural to ask what information about the volumes of central sections of two bodies does allow to compare the n-dimensional volumes of these bodies in all dimensions. In this article we give an answer to this question in terms of certain powers of the Laplace operator applied to the section function of the body.     

Reciprocally convex functions

We say that f is reciprocally convex if x?f(x) is concave and x?f(1/x) is convex on (0,+∞). Reciprocally convex functions generate a sequence of quasi-arithmetic means, with the first one between harmonic and arithmetic mean and others above the arithmetic mean. We present several examples related to the gamma function and we show that if f is a Stieltjes transform, then −f is reciprocally convex. An application in probability is also presented.     

Indentation responses of piezoelectric films

Frictionless indentation responses of transversely isotropic piezoelectric film/rigid substrate systems under circular cylindrical indenter (i.e., punch), conical indenter (i.e., cone), and spherical indenter (i.e., sphere) are investigated. Both insulating and conducting indenters are considered. The technique of Hankel transformation is employed to derive the corresponding dual integral equations for the mixed boundary value indentation problems. For the two limiting cases of infinitely thick and infinitely thin piezoelectric films, closed-form solutions are obtained. For piezoelectric films of finite thickness, a numerical method is constructed to solve the dual integral equations and semi-empirical models having only two unknown parameters are proposed for the responses of indentation force, electric charge and electric potential, and contact radius. With the two parameters inferred from the numerical results, the semi-empirical formulae are found to provide good estimates of the indentation responses for the two limiting cases of infinitely thick and thin piezoelectric films, as well as those in between. The inferred parameters in the proposed semi-empirical formulae for normalized indentation force and electric charge are checked against four different piezoelectric materials and are found to be insensitive to the selection of piezoelectric materials. It is believed that the proposed semi-empirical indentation formulae are useful in developing experimental indentation techniques to extract the material properties of piezoelectric films.     

有限维希尔伯特空间q广义相干态振幅平方压缩

构造了有限维希尔伯特空间q变形非简谐振子广义相干态,研究了它的振幅平方压缩效应,结果表明,该量子态存在振幅平方压缩效应,并且给出了压缩条件与参数s,r,q之间的关系。     

Kac-系统与Morita等价

本文讨论与Hilbert C~*-模相关的Kac-系统在C~*-代数上的作用的性质,给出了两个Morita等价的C~*-代数(在Kac-系统的作用下得到的C~*-代数的余交叉积是Morita等价的)。从而,Baaj和Skandalis等人的结论是本文定理的特殊情况。     

Introduction to Hardy Spaces

Basic material from the theory of Hardy spaces is presented. The principle of positive energy representations is used as motivation to introduce these spaces.     

Structural characterization of nanopatterned surfaces

In this work, chemically and topographically nanopatterned surfaces were produced by a top-down processing approach for biosensing devices. The nanopatterning was the result of the combination of plasma polymerisation (pp) of biofunctional materials and colloidal lithography techniques. The morphological and chemical properties induced by the plasma deposition-etching treatment were characterised by optical method combining ellipsometry and Fourier Transform Infrared spectroscopy studies. This method supported by atomic force microscopy measurements, allowed the full optical characterization of each step of the top-down process. The optical characterization of the end-up nanopatterned samples demonstrated that the chosen process is able to produce well-defined nanostructured surfaces with controlled chemical and morphological properties.