Dilatation transformation and sum rules for general potentials including self-consistent field potentials

The eigenfunctions and energies of general dilated Hamiltonians are expanded in powers of the dilatation parameter. These expansions, augmented by stationarity and stability conditions, are used to derive exact sum rules for bound and resonance states. Particular attention is paid to Hamiltonians with potentials which depend on external parameters, such as the nuclear coordinates in molecules, and to self-consistent potentials. The sum rules can be employed in practical computations to improve the quality of the results and may also serve in analyzing the results from approximate calculations.     

Influence of sorbed carbon dioxide on transition temperatures of poly(p-phenylene sulphide)

Static pressure usually increases the transition temperatures of polymers by decreasing their free volume. If the pressurizing medium is soluble in the polymer matrix, the opposing effect of increasing the free volume is possible. Those shifts of transition temperatures were monitored with a medium-pressure Differential Scanning Calorimetry (DSC) device. The influences of sorbed and surrounding gas molecules are demonstrated by changes occurring in the transition temperature regions. The results show the severe plasticizing effect of CO₂ on poly(p-phenylene sulphide) (PPS). The glass transition temperature T_G and the temperature of crystallization T_C are influenced by sorbed gas molecules. They decrease due to sorbed CO₂ molecules. Glass transition is lowered, but is difficult to interpret, as relaxation phenomena which diminish with increasing pressure occur during DSC runs. In crystallites no gas solution is usually possible, so that the melting point of PPS is mainly affected by influences other than plasticization.     

A model of nonlinear electrodynamics

A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.     

Minimal surfaces over stars

A JS surface is a minimal graph over a polygonal domain that becomes infinite in magnitude at the domain boundary. Jenkins and Serrin characterized the existence of these minimal graphs in terms of the signs of the boundary values and the side-lengths of the polygon. For a convex polygon, there can be essentially only one JS surface, but a non-convex domain may admit several distinct JS surfaces. We consider two families of JS surfaces corresponding to different boundary values, namely JS₀ and JS₁, over domains in the form of regular stars. We give parameterizations for these surfaces as lifts of harmonic maps, and observe that all previously constructed JS surfaces have been of type JS₀. We give an example of a JS₁ surface that is a new complete embedded minimal surface generalizing Scherk's doubly periodic surface, and show also that the JS₀ surface over a regular convex 2n-gon is the limit of JS₁ surfaces over non-convex stars. Finally we consider the construction of other JS surfaces over stars that belong neither to JS₀ nor to JS₁.     

香港全风化花岗岩饱和直剪试验中的剪胀问题

通过对全风化花岗岩的慢剪试验,指出了在直剪试验中出现的两种垂直位移变化形式,其对土体的剪胀剪缩性质的 反映与三轴试验是一致的。剪胀的发生与土体的密实程度密切相关;随垂直压力的增大,剪胀发生所需剪应力也增大;剪应 力达到峰值所需要剪位移总是比剪胀发生时所需的剪位移大。     

Beurling-Ahlfors扩张的伸张函数与ID-同胚

本文研究实轴上同胚在上半平面的扩张.利用拟对称函数ρ对伸张函数D作了较精细的估计.同时借助于诱导的边界函数对D、ρ在边界附近的性质作了进一步刻划.作为应用,我们分别给出上半平面存在ID-同胚扩张和IID-同胚扩张的充分条件.     

单位球B~n上小伸缩商拟共形群

本文研究了单位球Bn上小伸缩商拟共形群的离散性质,给出了几个离散判别准则和收敛定理.     

A temperature correction procedure for temperature inhomogeneity in dilatometer specimens

Dilatometry is a thermo-analytical technique used to measure the expansion or shrinkage of materials during heating or cooling, whether or not in association with a phase transformation. A temperature correction procedure has been developed to correct for the temperature inhomogeneity that exists in an inductively heated specimen during the heating/cooling process and to represent the dilation as a function of a homogeneous temperature. As an example, taking an Fe-5.91 at.% Ni specimen and subjecting it to two different cooling rates, the temperature correction has been performed for the temperature range where the austenite to ferrite phase transformation takes place as well as for the pure austenite and ferrite phases close to the temperature range of the transformation.     

具有可积伸张同胚的偏差和模不等式

本文研究了具有可积伸张的同胚，得到了这类同胚的几个偏差估计和一个模不等式．