具非孤立奇点的映射芽的右等价

本文先给出了两映射芽是Ｃ＿ｊ－等价的充要条件，然后用Ｃ＿Ｊ－等价和Ｒ＿Ｉ－等价理论给出了具有非孤立奇点的映射芽的Ｍ－确定性的几个充分条件。     

Ordered Compactifications of Products of Two Totally Ordered Spaces

We describe the semilattice of ordered compactifications of X × Y smaller than _o X × _o Y where X and Y are certain totally ordered topological spaces, and where _o Z denotes the Stone–ech ordered- or Nachbin-compactification of Z. These basic cases are used to illustrate techniques for describing the semilattice of ordered compactifications of X × Y smaller than _o X × _o Y for arbitrary totally ordered topological spaces X and Y. Such products X × Y provide many counterexamples in the theory of ordered compactifications.     

Experimental investigation of GH singularity field of the growing crack-tip for different ductile metals

The displacementsu _x ,u _y inx, y directions at growing crack tip of the specimens with double edge cracks for four different alumium alloys and two coppers are measured by using moire method and optical spatial filtering technique. From experimental displacement fields, the displacement singularity fields are obtained and compared with GH theoretical field. Unknown constantsA and _yo in theoretical solution are determined from experimental data. The theoretical singularity field thus compared is given for plane-stress, mode-I, strain-hardening materials. The error in both the experimental and theoretical evaluations is within ± 10%. The experiments show that there exists dominant singularity region around a growing crack-tip. In the experiments, the strain hardening indexn amounts from 3.158 to 14. The shape of this dominant region ranges from butterfly wing to oblate or circular shape. The size and shape of GH dominant region depend on the material property, the specimen geometry and loading type. Inside GH-field, there is a 3-D deformed damage zone, where no GH singularity exists. Very near to the crack-tip, there is a fracture process zone.The project is supported by the National Science Foundation of China.     

Localization properties of highly singular generalized functions

We study the localization properties of generalized functions defined on a broad class of spaces of entire analytic test functions. This class, which includes all Gelfand-Shilov spaces S _α ^β (R ^k ) with β < 1, provides a convenient language for describing quantum fields with a highly singular infrared behavior. We show that the carrier cone notion, which replaces the support notion, can be correctly defined for the considered analytic functionals. In particular, we prove that each functional has a uniquely determined minimal carrier cone. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 179–194, May, 2007.     

Strong curvature naked singularities in generalized Vaidya space-times

In this paper, following recent results on generalized Vaidya solutions by Wang, we prove that under certain conditions on generalized mass function, strong curvature naked singularities exist in radiation collapse in monopole-Vaidya space-times and also in charged-Vaidya space-times. We thus unify and generalize results of Dwivedi-Joshi and Lake-Zannias. The general case also covers de Sitter-Vaidya space-time recently treated by Wagh-Maharaj with a view to study existence of naked singularities.     

Spherical Orthotomic and Spherical Antiothotomic

In this paper the spherical orthotomic and the spherical antiorthotomic are defined and their local diffeomorphic types are determined.     

Valuations and multiplier ideals

We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are a formula for the complex integrability exponent of a plurisubharmonic function in terms of Kiselman numbers, and a proof of the openness conjecture by Demailly and Kollár. Our technique also yields new proofs of two recent results: one on the structure of the set of complex singularity exponents for holomorphic functions; the other by Lipman and Watanabe on the realization of ideals as multiplier ideals.

     

左端固定右端被滑动夹子夹住的非线性弹性梁方程的一个存在定理

通过运用积分方程并考察非线性项的“高度”对一类含有各阶导数的四阶两点边值问题建立了一个解的存在定理.在力学上,这类问题描述了一个左端固定右端被滑动夹子夹住的非线性弹性的形态.