The Gap Phenomena of Yang-Mills Fields over the Complete Manifold.
A generalization of the Schwarz-Ahlfors lemma fo the theory of harmonic maps.
A Minimal Complete Class Theorem for Decision Problems Where the Parameter Space Contains Only Finitely Many Points.
Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.
In the Fourier theory of functions of one variable, it is common to extend a function and its Fourier transform holomorphically to domains in the complex plane C, and to use the power of complex function theory. This depends on first extending the exponential function eixξ of the real variables x and ξ to a function eizζ which depends holomorphically on both the complex variables z and ζ . Our thesis is this. The natural analog in higher dimensions...
Nontrivial solutions for a class of superquadratic elliptic equations
Using a version of the Local Linking Theorem and the Fountain Theorem, we obtain some existence and multiplicity results for a class of superquadratic elliptic equations.
Global higher integrability of jacobians on bounded domains
Polaroid type operators and compact perturbations
A bounded linear operator T acting on a Hilbert space is said to be polaroid if each isolated point in the spectrum is a pole of the resolvent of T. There are several generalizations of the polaroid property. We investigate compact perturbations of polaroid type operators. We prove that, given an operator T and ε > 0, there exists a compact operator K with ||K|| < ε such that T + K is polaroid. Moreover, we characterize those operators for which a certain polaroid type property is stable under...
Regularization for high-dimensional covariance matrix
In many applications, high-dimensional problem may occur often for various reasons, for example, when the number of variables under consideration is much bigger than the sample size, i.e., p >> n. For highdimensional data, the underlying structures of certain covariance matrix estimates are usually blurred due to substantial random noises, which is an obstacle to draw statistical inferences. In this paper, we propose a method to identify the underlying covariance structure by regularizing...
Note on Qi's inequality and Bougoffa's inequality.
Further development of an open problem concerning an integral inequality.
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