Antiplane Problem of Periodically Stacked Parallel Cracks in an Infinite Orthotropic Plate

The antiplane problem of the periodic parallel cracks in an infinite linear elastic orthotropic composite plate is studied in this paper. The antiplane problem is turned into the boundary value problem of partial differential equation. By constructing proper Westergaard stress function and using the periodicity of the hyperbolic function, the antiplane problem of the periodic parallel cracks degenerates into an algebra problem. Using the complex variable function method and the undetermined coefficients method, as well as with the help of boundary conditions, the boundary value problem of partial differential equation can be solved, and the analytic expressions for stress intensity factor, stress, and displacement near the periodical parallel cracks tip are obtained. When the cracks spacing tends to infinity, the antiplane problem of the periodic parallel cracks degenerates into the case of the antiplane problem of a single central crack

C1'γ regularity for fully nonlinear elliptic equations on a convex polyhedron

In this note, we prove the boundary and global C 1,γ regularity for viscosity solutions of fully nonlinear uniformly elliptic equations on a convex polyhedron by perturbation and iteration techniques

On the spectrum of operators concerned with the reduced singular Cauchy integral

We investigate spectrums of the reduced singular Cauchy operator and its real and imaginary components

HDIdx: High-Dimensional Indexing for Efficient Approximate Nearest Neighbor Search

Fast Nearest Neighbor (NN) search is a fundamental challenge in large-scale data processing and analytics, particularly for analyzing multimedia contents which are often of high dimensionality. Instead of using exact NN search, extensive research efforts have been focusing on approximate NN search algorithms. In this work, we present "HDIdx", an efficient high-dimensional indexing library for fast approximate NN search, which is open-source and written in Python. It offers a family of state-of-the-art algorithms that convert input high-dimensional vectors into compact binary codes, making them very efficient and scalable for NN search with very low space complexity

Relative Well-Posedness of Constrained Systems with Applications to Variational Inequalities

The paper concerns foundations of sensitivity and stability analysis, being primarily addressed constrained systems. We consider general models, which are described by multifunctions between Banach spaces and concentrate on characterizing their well-posedness properties that revolve around Lipschitz stability and metric regularity relative to sets. The enhanced relative well-posedness concepts allow us, in contrast to their standard counterparts, encompassing various classes of constrained systems. Invoking tools of variational analysis and generalized differentiation, we introduce new robust notions of relative coderivatives. The novel machinery of variational analysis leads us to establishing complete characterizations of the relative well-posedness properties with further applications to stability of affine variational inequalities. Most of the obtained results valid in general infinite-dimensional settings are also new in finite dimensions.Comment: 25 page

Dirac Fermion in Strongly-Bound Graphene Systems

It is highly desirable to integrate graphene into existing semiconductor technology, where the combined system is thermodynamically stable yet maintain a Dirac cone at the Fermi level. Firstprinciples calculations reveal that a certain transition metal (TM) intercalated graphene/SiC(0001), such as the strongly-bound graphene/intercalated-Mn/SiC, could be such a system. Different from free-standing graphene, the hybridization between graphene and Mn/SiC leads to the formation of a dispersive Dirac cone of primarily TM d characters. The corresponding Dirac spectrum is still isotropic, and the transport behavior is nearly identical to that of free-standing graphene for a bias as large as 0.6 V, except that the Fermi velocity is half that of graphene. A simple model Hamiltonian is developed to qualitatively account for the physics of the transfer of the Dirac cone from a dispersive system (e.g., graphene) to an originally non-dispersive system (e.g., TM).Comment: Apr 25th, 2012 submitte