Uncertainty principles for the continuous wavelet transform in the Hankel setting

Shapiro’s dispersion and Umbrella theorems are proved for the continuous Hankel wavelet transform. As a side results, we extend local uncertainty principles for set of finite measure to the latter transform.     

Minimality conditions for wave speed in anisotropic smectic C∗ liquid crystals

We discuss minimality conditions for the speed of monotone travelling waves in a sample of smectic C^∗ liquid crystal subject to a constant electric field, dealing with both isotropic and anisotropic cases. Such conditions are important in understanding the properties of domain wall switching across a smectic layer, and our focus here is on examining how the presence of anisotropy can affect the speed of this switching. We obtain an estimate of the influence of anisotropy on the minimal speed, sufficient conditions for linear and non‐linear minimal speed selection mechanisms to hold in different parameter regimes, and a characterisation of the boundary separating the linear and non‐linear regimes in parameter space.     

The optimal reinsurance strategy — the individual claim case

This paper is concerned with the optimal form of reinsurance when the cedent seeks to maximize the adjustment coefficient of the retained risk (related to the probability of ultimate ruin)-which we prove to be equivalent to maximizing the expected utility of wealth, with respect to an exponential utility with a certain coefficient of risk aversion-and restricts the reinsurance strategies to functions of the individual claims, which is the case for most nonproportional treaties placed in the market.Assuming that the premium calculation principle is a convex functional we prove the existence and uniqueness of solutions and provide a necessary optimality condition (via needle-like perturbations, widely known in optimal control). These results are used to find the optimal reinsurance policy when the reinsurance loading is increasing with the variance. The optimal contract is described by a nonlinear function, of a similar form than in the aggregate case.     

On extending some maximum principles to convex domains with nonsmooth boundaries

The goal of this paper is to extend some maximum principles to the case of bounded convex domains with nonsmooth boundaries. Copyright © 2010 John Wiley & Sons, Ltd.     

Semilinear differential inclusions via weak topologies

The paper deals with the multivalued initial value problem x^′∈A(t,x)x+F(t,x) for a.a. t∈[a,b], x(a)=x₀ in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous in x and the investigation includes the case when both A and F have a superlinear growth in x. We prove the existence of local and global classical solutions in the Sobolev space W1,p([a,b],E) with 1<p<∞. Introducing a suitably defined Lyapunov-like function, we are able to investigate the topological structure of the solution set. Our main tool is a continuation principle in Frechét spaces and we prove the required pushing condition in two different ways. Some examples complete the discussion.     

Non-negative mixed finite element formulations for a tensorial diffusion equation

We consider the tensorial diffusion equation, and address the discrete maximum–minimum principle of mixed finite element formulations. In particular, we address non-negative solutions (which is a special case of the maximum–minimum principle) of mixed finite element formulations. It is well-known that the classical finite element formulations (like the single-field Galerkin formulation, and Raviart–Thomas, variational multiscale, and Galerkin/least-squares mixed formulations) do not produce non-negative solutions (that is, they do not satisfy the discrete maximum–minimum principle) on arbitrary meshes and for strongly anisotropic diffusivity coefficients.     

Si在TiAl3中取代行为的第一性原理研究

采用基于密度泛函理论的第一性原理方法,研究了Si原子在TiAl3中的格点取代行为.通过对不同原子被置换后的c/a值、形成能以及电子态密度的计算和比较,发现Si原子倾向于取代TiAl3中的Al原子,其取代行为主要由系统的电子结构决定,计算结果与实验相符.为了进一步研究Si原子的取代行为,对Si原子占据的格点以松散或紧凑分布下体系的总能、形成能以及电子态密度进行了计算,结果表明Si原子倾向于取代TiAl3中松散分布的Al(2)原子.对c/a值的计算表明,随Al(2)格点Si原子浓度的增加,c/a值逐渐增大;而当Si取代Al(1)格点时,c/a值随Si原子浓度的增加而减小.研究表明,Si在TiAl3中的极限固溶度介于12.5at%-18.75at%之间.     

Lattice strain and p-d repulsion affecting electronic structure of wurtzite Zn1-xCdxO alloys

In the paper, density of states, band structure and electron density difference of Zn1-xCdxO are calculated by first principles, here x varies from 0 to 0.75 at intervals of 0.125, and the band gap obtained from band structure changes from 0.968 eV to 0.043 eV. The lattice strain and p-d repulsion theory are used to investigate variation of the band gap, the results obtained show that the variation is mainly due to the lattice tensile strain. The p-d repulsion in Zn1-xCdxO cannot be neglected. In addition, electron density difference can be used to verify the results.