An Addendum to Birkhoff's Theorem

In spherically symmetric systems, in spite of Birkhoff's Theorem, the rates of clocks in vacuum regions on either side of moving mass shells must be continually readjusted to stay in synchrony. This shows up as time-dependence of the metric in terms of the globally meaningful time coordinate.     

The Classical Solutions of Two-dimensional Gravity

The solutions of two-dimensional gravityfollowing from a non-linear Lagrangian =f(R)g are classified, and their symmetry andsingularity properties are described. Then a conformaltransformation is applied to rewrite these solutions as analogoussolutions of two-dimensional Einstein-dilaton gravityand vice versa.     

ON NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF CARATHÉODORY SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS

Given two one-sided Markov chains, the authors illustrate a procedure for ascertaining whether they are essentially the same. Precisely, they show how one can determine whether they are block-isomorphic. An application to hydrology is investigated with an example.     

LITTLEWOOD-PALEY THEOREM FOR SCHR(O)DINGER OPERATORS

Let H be a Schr(o)dinger operator on Rn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.     

SOME GENERALIZATIONS OF KY FAN''''S BEST APPROXIMATION THEOREM

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map on metrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derived for the map studied. Our work generalizes severl results in approximation theory.     

论动量矩定理的矩心选择与速度瞬心问题

本文阐明应用动量矩定理如以平面运动物体的速度瞬心为矩心，则矩心速度应取速度瞬心沿 固定瞬心轨迹的速度（不等于零）．本文直接导出了有关各项公式，从而澄清了基本概念．     

拱坝考虑扭转作用的拱冠梁法的积分方程数值解法

本文利用Ｂｅｔｔｉ定理提出一种分析拱坝应力的新方法──积分方程法。该法适用于中、小型拱 坝的设计。与现有的方法相比，该法具有计算简便，适用范围广的特点。     

Recovering the Cosmological Constant in Scalar-Tensor Cosmologies

We extend the cosmic no-hair theorem to a general class of scalar-tensor nonminimally coupled theories of gravity where ordinary matter is also present in the form of a perfect fluid. We give a set of conditions for obtaining an asymptotic de Sitter expansion, independently of any initial data, by a sort of time-dependent (effective) cosmological constant. Finally we apply the results to some specific models.     

ON THE SEPARATION PROPERTY OF SYMMETRIC ORDINARY SECOND-ORDER DIFFERENTIAL EXPRESSIONS

A 1-variable calculus type argument is used to show that, for a function f : R ² → R, if for all (a, b) ? R ² we have that f o c is smooth for every smooth curve c : R → R ² nonsingular except at 0 and with c(0) = (a, b), then f is smooth. This strengthens Boman's theorem. In fact, we use an even more special collection of smooth curves to prove Boman's theorem. It is shown using a related special collection of smooth curves how the upper half cone can be viewed largely as a model for polar coordinates. Our proof here shows how the use of Frölicher spaces can reduce questions in several dimensions to those of one real variable.     

The quasi-metric of complexity convergence

For any weightable quasi-metric space (X, d) having a maximum with respect to the associated order ≤ _d , the notion of the quasi-metric of complexity convergence on the the function space (equivalently, the space of sequences) X^ω , is introduced and studied. We observe that its induced quasi-uniformity is finer than the quasi-uniformity of pointwise convergence and weaker than the quasi-uniformity of uniform convergence. We show that it coincides with the quasi-uniformity of pointwise convergence if and only if the quasi-metric space (X, d) is bounded and it coincides with the quasi-uniformity of uniform convergence if and only if X is a singleton. We also investigate completeness of the quasi-metric of complexity convergence. Finally, we obtain versions of the celebrated Grothendieck theorem in this context.