Borehole measurement of the newtonian gravitational constant

It has been reported that the geophysically determined Newtonian gravitational constant is consistently larger than the laboratory value by 1 to 2% on the basis of gravity measurements in Australian mines. This discrepancy may have strong implications for the physics of gravitation. To test whether similar results can be observed in a different geological environment, gravity measurements in a Michigan borehole have been examined. Although these results cannot be taken as conclusive, owing to the large uncertainties involved in mass determination on a geophysical scale, these measurements are generally consistent with those of the Australian experiment.     

牛顿与近似牛顿混合算法的收敛速率

研究交替使用牛顿迭代与近似年牛顿迭代解无约束最优化问题的混合算法。研究这一类算法的收敛特征，得到了两步超二阶收敛和两步至少２（１＋ｐ）（０＜ｐ≤１）阶收敛的充要条件；对单和函数的极小化问题，给出了具有二步四阶收敛速度的混合算法。     

混合不精确牛顿法

林正华提出的一个求解非线性方程组的混合牛顿与二阶拟牛顿迭法是有效的，但有缺点，本文中提出了一个改进的算法：在每一迭代步，只需求解线性方程组的近似解。在合理的假设下证明了本算法具有与林算法相同的收敛性质。     

Quasars and gravitational lenses

Despite the expenditure of large amounts of telescope time and other resources, most of the fundamental questions concerning quasi-stellar objects (quasars) remain unanswered. A complex phenomenology of radio, infrared, optical, and x-ray properties has accumulated but has not yielded even a satisfactory classification system. The large red shifts (distances) of quasars make them very valuable tools for studying cosmology and the properties of intervening matter in the Universe through observations of absorption lines and gravitational lenses.     

Galaxies as gravitational lenses

The probability that a galaxy gathers light from another remote galaxy, and deflects and focuses it toward an observer on Earth, is calculated according to various cosmologic models. I pose the question of whether an object called a quasar is a single, intrinsically luminous entity or the result of accidental alignment, along the line of sight, of two normal galaxies, the more distant of which has its light amplified by the gravitational-lens effect of the nearer galaxy. If galaxies are distributed at random in the universe, the former alternative is true. But, if we assume that most galaxies exist in pairs, we can find about 30 galaxies occurring exactly one behind the other in such a way as to enable amplification of the order of 50. This model explains also the variations in intensity in quasars, but fails to explain others of their observed properties.     

Galaxies as gravitational lenses

Of all the galaxies in the visible part of the universe, 500 million are seen through intervening galaxies. In some instances the foreground galaxy will act as a gravitational lens and produce distorted and (in brightness) greatly amplified images of the galaxy behind it; such images may simulate starlike superluminous objects such as quasars (quasi-stellar objects). The number of gravitational lenses is several times greater than the number of quasars yet observed. In other instances the superposition of the image upon a visible foreground galaxy may simulate morphological configurations resembling N-type, dumbbell, spiral, or barred-spiral galaxies.     

Resonant-mass detectors of gravitational radiation

A network of second-generation low-temperature gravitational radiation detectors is nearing completion. These detectors, sensitive to mechanical strains of order 10(-18), are possible because of a variety of technical innovations hat have been made in cryogenics, low-noise superconducting instrumentation, and vibration isolation techniques. Another five orders of magnitude improvement in energy sensitivity of resonant-mass detectors is possible before the linear amplifier quantum limit is encountered.     

对Choleski-PCG Newton算法的一些改进

对无约束最优化问题提出了一种不精确牛顿算法模型ACPN（α）,是对DengN．Y．和WangZ．Z文（CanNewtonmethodbesurpassed．见ChineseScienceBulletin,1998,Vol．43,No．20,p．132～134）中Choleski-PCGNewton算法的改进。新算法对于变量个数在35～186范围内的无约束问题更有效,并打破了所构造的点列必须恰Q－2阶收敛的局限,对进一步改进算法有提示作用。     

具有全局收敛性的非单调不精确牛顿法

对大规模非线性方程组F＝0（其中F：Rn→Rn连续可微）提出2种非单调不精确牛顿法。在算法选代过程中，每步求出F的局部线性化模型的一个近似解，而不要求F的某种范数单调递减，因此具有不精确牛顿法的优点，并且对非常病态的非线性方程组是有效的。在合理假设下证明此算法仍具有全局收敛性。     

Testing cosmogonic models with gravitational lensing

Gravitational lensing provides a strict test of cosmogonic models because it is directly sensitive to mass inhomogeneities. Detailed numerical propagation of light rays through a universe that has a distribution of inhomogeneities derived from the standard CDM (cold dark matter) scenario, with the aid of massive, fully nonlinear computer simulations, was used to test the model. It predicts that more widely split quasar images should have been seen than were actually found. These and other inconsistencies rule out the Cosmic Background Explorer (COBE)-normalized CDM model with density parameter Omega = 1 and the Hubble constant (H(o)) = 50 kilometers second(-1) megaparsec(-1); but variants of this model might be constructed, which could pass the stringent tests provided by strong gravitational lensing.     

关于牛顿恒等式的归纳证明

在代数学中,牛顿恒等式是联系多项式根的幂和与其系数关系的一个重要恒等式。用数学归纳法给出牛顿恒等式的一个自然证明。