Phonon dispersion curves and densities of lithium-intercalated iron phosphorus trisulfide

Summary The lattice dynamics of Li-intercalated FePS₃ has been studied by means of a force constant model generated by a set of short-range two-body potentials. The intercalated phases have been investigated for the three stoichiometric compositions: Li_0.5FePS₃, LiFePS₃, Li_1.5FePS₃, with the aim of analysing the evolution of the host lattice normal modes as a function of the concentration, and of finding the dispersion of the new phonon branches induced by lithium. The above special values of lithium concentration have been chosen because the size of the unit cell keeps the same as in the host material. The force constants are fitted to the infrared data and the phonon dispersion curves and the phonon energy densities have been calculated. A spectroscopic method for monitoring lithium migration in the host material is proposed.     

Combinatorial volume preserving flows and taut foliations

A -injective closed surface in an orientable 3-manifold with a tangentially smooth, transversely C ⁰ taut foliation can be homotoped to an immersed surface which is either transverse to the foliation except at isolated saddle tangencies or mapped into a leaf. Received: November 11, 1997     

An optimal rigidity theorem for complete submanifolds in a sphere

It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.     

Crosstalks of two-waveguide and three-waveguide directional couplers

Crosstalks of two-waveguide and three-waveguide directional couplers are analyzed mathematically based on the relationship between the coupled mode and the normal mode. Numerical techniques such as the finite-difference method and the beam propagation method are employed to confirm the validity of the derived expressions. The calculation results show that two-waveguide directional coupler is superior to any type of three-waveguide couplers from the practical viewpoint of the crosstalk and the coupling length.     

New construction of special Lagrangian submanifolds in <Emphasis Type="Italic">T</Emphasis>*R<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript> equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T＊R^n and a kind of austere submanifold from conormal bundle of minimal surface of R^3 are constructed.     

New construction of special Lagrangian submanifolds in T^＊R^n equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T~*R~n and a kind of austere submanifold from conormal bundle of minimal surface of R~3 are constructed.     

Generalizing Mutational Equations for Uniqueness of Some Nonlocal 1st-Order Geometric Evolutions

The mutational equations of Aubin extend ordinary differential equations to metric spaces (with compact balls). In first-order geometric evolutions, however, the topological boundary need not be continuous in the sense of Painlevé–Kuratowski. So this paper suggests a generalization of Aubin’s mutational equations that extends classical notions of dynamical systems and functional analysis beyond the traditional border of vector spaces: Distribution-like solutions are introduced in a set just supplied with a countable family of (possibly non-symmetric) distance functions. Moreover their existence is proved by means of Euler approximations and a form of “weak” sequential compactness (although no continuous linear forms are available beyond topological vector spaces). This general framework is applied to a first-order geometric example, i.e. compact subsets of ℝ ^N evolving according to the nonlocal properties of both the current set and its proximal normal cones. Here neither regularity assumptions about the boundaries nor the inclusion principle are required. In particular, we specify sufficient conditions for the uniqueness of these solutions.      

On the index of finite determinacy of vector fields with resonances

In this paper we study normal forms for a class of germs of 1-resonant vector fields on R^n with mutually different eigenvalues which may admit extraneous resonance relations. We give an estimation on the index of finite determinacy from above as well as the essentially simplified polynomial normal forms for such vector fields. In the case that a vector field has a zero eigenvalue, the result leads to an interesting corollary, a linear dependence of the derivatives of the hyperbolic variables on the central variable.     

关于Locale Wallman紧化的一点注记

本文证明了在正规locale范畴中,Banaschewski-Mulvey形式的紧正则反射与Johnstone形式的Wallman紧化一致,从而推广了Johnstone在文献[4]中的主要结果.     

Extended Gauss–Markov Theorem for Nonparametric Mixed-Effects Models

The Gauss–Markov theorem provides a golden standard for constructing the best linear unbiased estimation for linear models. The main purpose of this article is to extend the Gauss–Markov theorem to include nonparametric mixed-effects models. The extended Gauss–Markov estimation (or prediction) is shown to be equivalent to a regularization method and its minimaxity is addressed. The resulting Gauss–Markov estimation serves as an oracle to guide the exploration for effective nonlinear estimators adaptively. Various examples are discussed. Particularly, the wavelet nonparametric regression example and its connection with a Sobolev regularization is presented.