wM空间的刻画

利用g-函数给出对wM空间的若干等价刻画,主要结论为：X为wM空间当且仅当X满足下述条件之一：（1）存在空间X上的g-函数g,使得若对每一nN,yn∈g（n,p）且g（n,xn）∩g（n,yn）≠,则xn有聚点;（2）存在空间X上的g-函数g,使得若对每一nN,g（n,p）∩g（n,p）≠且xn∈g（n,yn）,则xn有聚点。     

用g-函数刻画度量化的几个问题

利用g-函数刻画度量空间和广义度量空间是一个有趣的研究热点.作者回答了Nagata提出的一个问题,并讨论下降g-函数的若干性质.     

Fast calculation of the g-functions of geothermal borehole fields using similarities in the evaluation of the finite line source solution

Numerical methods are proposed for the efficient evaluation of the g-functions of geothermal bore fields using the finite line source solution. The presented methods reduce the calculation time for the calculation of g-functions by reducing the number of numerical evaluations of the analytical finite line source solution. A similarity identification method is presented to identify pairs of boreholes for which the finite line source solution takes the same value. A load history reconstruction method is presented to evaluate the g-function at non-uniform time-steps. Using the proposed numerical methods, the calculation time for the g-function of a rectangular field of 12?×?12 boreholes is reduced by a factor 308. The numerical methods allow the evaluation of g-functions of bore fields with large amounts of boreholes in irregular configurations. The g-function of a field of 512 randomly positioned boreholes is calculated in 27 minutes.