Crystallized structure for level 0 part of modified quantum affine algebra Uq (sl2)

Crystal base of the level 0 part of the modified quantum affine algebra Uq(sl2)_0 is given by path. Weyl group actions, extremal vectors and crystal structure of all irreducible components are described explicitly.     

On the second law of thermodynamics

The second law of thermodynamics has two distinct aspects to its foundations. The first concerns the question of why entropy goes up in the future, and the second, of why it goes down in the past. Statistical physicists tend to be more concerned with the first question and with careful considerations of definition and mathematical detail. The second question is of quite a different nature; it leads into areas of cosmology and quantum gravity, where the mathematical and physical issues are ill understood.     

Algebraic classification of higher dimensional spacetimes

We algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes.We discuss some consequences of this work.     

Nontangential Limit of the Weyl m-Functions for the Ergodic Schrödinger Equation

This paper deals with the spectral and qualitative problems associated with the one-dimensional ergodic Schrödinger equation. Let A ₂ be the set of those energies for which the real projective flow admits an invariant linear measure with square integrable density function. On this set we calculate the directional derivative of the Floquet coefficient and prove the existence of a nontangential limit of the Weyl m-functions in the L ¹-topology. In particular, we verify that the known Dieft–Simon inequality for the derivative of the rotation number obtained from Kotani's theory is in fact an equality. In the bounded orbit case we deduce the uniform boundedness of the Weyl m-functions and obtain necessary and sufficient conditions to assure their uniform convergence.     

Modified classification of non-self-adjoint second-order difference equations

This paper is concerned with the classification of non-self-adjoint second-order difference equations. The relationship between the number of summable solutions of non-self-adjoint difference equations and that of the discrete linear Hamiltonian system is discussed. A classification for non-self-adjoint second-order difference equations is established, which is independent of the choice of the rotated half plane and the fixed point.     

Tilted algebras and configurations of self-injective algebras of Dynkin type

We give an easier way to calculate a bijection from the set of isoclasses of tilted algebras of Dynkin type Δ to the set of configurations on the translation quiver ?Δ.     

应变花埋丝技术在齿科修复学上的应用研究

本文通过采用三维应变花埋丝技术，对固定义齿修复的牙周应力分布进行了定量分析研究，绘制了修复前后牙周的应力分布随基牙倾斜角度的变化曲线，测得下颌第二磨牙用作固定桥基牙时近中倾斜的最大角度为７０度，从生物力学的角度证明，固定义齿修复有利于倾斜基牙牙周组织健康、为齿科临床上广泛开展倾斜基牙固定修复提供了依据。     

A note on generalized quasi‐Einstein manifolds

In this note, we get a necessary and sufficient condition such that the scalar curvature of generalized m‐quasi‐Einstein manifold with $m=1$ is constant. In particular, we discuss a class of generalized quasi‐Einstein manifolds which are more general than $(m,\rho )$‐quasi‐Einstein manifolds and prove that these manifolds with dimension four are either Einstein or locally conformally flat under some suitable conditions.     

Continuity of magnetic Weyl calculus

We investigate continuity properties of the operators obtained by the magnetic Weyl calculus on nilpotent Lie groups, using modulation spaces associated with unitary representations of certain infinite-dimensional Lie groups.     

The Helmholtz–Weyl decomposition in weighted Sobolev spaces

Let f∈L_{2, ? µ}(?³), where where x = (x₁, x₂, x₃) is the Cartesian system in ?³, x′ = (x₁, x₂), , µ∈?₊\?. We prove the decomposition f = ? ?u + g, with g divergence free and u is a solution to the problem in ?³ Given f∈L_{2, ? µ}(?³) we show the existence of u∈H(?³) such that where Since f, u, g are defined in ?³ we need a sufficiently fast decay of these functions as |x|→∞. Copyright © 2010 John Wiley & Sons, Ltd.