Modified General Relativity and Cosmology

Aspects of the modified general relativity theory of Rastall, Al-Rawaf and Taha are discussed in both the radiation- and matter-dominated flat cosmological models. A nucleosynthesis constraint on the theory's free parameter is obtained and the implication for the age of the Universe is discussed. The consistency of the modified matter-dominated model with the neoclassical cosmological tests is demonstrated.     

A New Look at Relativity Transformations

A free system, considered to be a comparisonsystem, allows for the notion of objective existence andinertial frame. Transformations connecting inertialframes are shown to be either Lorentz or generalizedGalilei.     

Slicing the Oppenheimer-Snyder Collapse: Harmonic versus Maximal Slicing

In continuing our studies of temporal slicings of spacetimes, we consider the collapse from rest of an initially homogeneous dust sphere, known as Oppenheimer-Snyder collapse. It is shown that in the case of harmonic slicing the whole spacetime becomes covered by slices extending to spatial infinity in contrast to maximal slicing. The behavior of the lapse function is discussed, especially for various data on the initial slice, and it is demonstrated that not every choice of the initial lapse leads to meaningful slicings.     

Circular Orbits in Stationary Axisymmetric Spacetimes

Several types of characteristics of spatially circular timelike trajectories in stationary axisymmetric spacetimes are related in a simple and covariant manner. The relations allow us to establish straightforward links between different phenomena often studied on circular orbits: mechanics of a single test particle, precession of gyroscopes with respect to important vectors defined along the orbit, geometrical parameters (curvatures) of the trajectory provided by the Frenet-Serret formalism, and geometrical properties (vorticity and shear) of the whole circular congruence.     

Effective Nonlocal Euclidean Gravity

A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newtonian constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value < 1 for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.     

Metric for an Oblate Earth

In linearized general relativity the metric ofa body is described by a scalar potential and athree-vector potential. We here present a simpletransformation derivation of the linearized metric interms of these potentials, and calculate the exactscalar and vector potentials for a field with oblatespheroidal symmetry. The results for the externalpotentials do not depend on details of the densitydistribution inside the earth; both the scalar and vectorpotentials are fully determined by the total mass, thetotal angular momentum, and a radial parameter, all ofwhich are accurately known from observation. The scalar potential is accurate to roughly10^-6 and the vector potential, which hasnever been accurately measured, should be accurate toabout 10^-5. Applications include an accuratetreatmen t of the details of the motion of satellites, and theprecession of a gyroscope in earth orbit.     

Nonlinear approximation with general wave packets

We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.     

Lp APPROXIMATION BY GENERAL BERNSTEIN-DURRMEYER OPERATOR DEFINED ON SIMPLEX

As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.     

稀土夹心化合物的SCF-X~α-SW研究 I: Cp~2Sm, Cp~2Yb 和Cp~3Sm

对Cp~2Sm、C~p~2Y~b和Cp~3Sm 进行了非相对论和相对论SCF-X~α-SW计算, 用轨道相互作用、分子轨道图形、布居数分析等方法讨论了化学键图象。在Cp~2Ln(Ln=稀土元素)中以Cp为主要成分的轨道能级两种方案结果变化不大。而相对论间接效应的存在, 使Ln4f能级明显升高, 与Cp~2Ln易被氧化的实验结果一致。二价的Cp~2Ln成键轨道中Ln成分是d>f>p>s, 与三价的Cp~3Sm、LnF~3比较, Ln的s、p、d成分变化不大, 而Lnf成分明显减少, 使Cp~2Ln共价性明显地低于Cp~3Sm和LF~3。     

Electromagnetic Modes in Schwarzschild Geometry in an Annular Region

The fundamental electromagnetic modes in a spherical annular cavity with perfectly conducting walls at r = a and r = b are calculated, in the presence of a weak Schwarzschild gravitational field. Explicit expressions are given for the case of a thin shell, (b - a)/a 1. The modified angular frequency for mode ,m can be written as = = ₀ \{ 1 - (GM/a)[2 - ( + 1)/(₀ a)²] where ₀ is the nongravitational frequency. This formula (being independent of m) holds for the magnetic as well as for the electric modes.