Relations Between BZMV^(dM)-Algebra and Other Algebras

Some properties of BZMV dM -algebra are proved, and a new operator is introduced. It is shown that the substructure of BZMV dM -algebra can produce a quasi-lattice implication algebra. The relations between BZMV dM -algebra and other algebras are discussed in detail. A pseudo-distance function is defined in linear BZMV dM -algebra, and its properties are derived.

Asymptotic Results for Goodness-of-Fit Tests Using a Class of Generalized Spacing Methods with Estimated Parameters

A class of pseudo distances is used to derive test statistics using transformed data or spacings for testing goodness-of-fit for parametric models. These statistics can be considered as density based statistics and expressible as simple functions of spacings. It is known that when the null hypothesis is simple, the statistics follow asymptotic normal distributions without unknown parameters. In this paper we emphasize results for the null composite hypothesis: the parameters can be estimated by a generalized spacing method (GSP) first which is equivalent to minimize a pseudo distance from the class which is considered;subsequently the estimated parameters are used to replace the parameters in the pseudo distance used for estimation;goodness-of-fit statistics for the composite hypothesis can be constructed and shown to have again an asymptotic normal distribution without unknown parameters. Since these statistics are related to a discrepancy measure, these tests can be shown to be consistent in general. Furthermore, due to the simplicity of these statistics and they come a no extra cost after fitting the model, they can be considered as alternative statistics to chi-square statistics which require a choice of intervals and statistics based on empirical distribution (EDF) using the original data with a complicated null distribution which might depend on the parametric family being considered and also might depend on the vector of true parameters but EDF tests might be more powerful against some specific models which are specified by the alternative hypothesis.

Some Results on Space-Like Self-Shrinkers

We study space-like self-shrinkers of dimension n in pseudo-Euclidean space Rm^m＋n with index m. We derive drift Laplacian of the basic geometric quantities and obtain their volume estimates in pseudo-distance function. Finally, we prove rigidity results under minor growth conditions in terms of the mean curvature or the image of Gauss maps.

The Hadamard Theorem and Borel-Carathéodory Theorem on Riemann Surfaces

In this paper, we first define a kind of pseudo-distance function and annulus domain on Riemann surfaces, then prove the Hadamard Theorem and the Borel-Carathéodory Theorem on any Riemann surfaces.

A Rigidity Result of Spacelike Self-Shrinkers in Pseudo-Euclidean Spaces

In this paper, the author proves that the spacelike self-shrinker which is closed with respect to the Euclidean topology must be flat under a growth condition on the mean curvature by using the Omori-Yau maximum principle.