We introduce a shape detection framework called Contour Context Selection for detecting objects in cluttered images using only one exemplar. Shape based detection is invariant to changes of object appearance, and can reason with geometrical abstraction of the object. Our approach uses salient contours as integral tokens for shape matching. We seek a maximal, holistic matching of shapes, which c...

Following the success of using the null-field integral approach to determine the torsional rigidity of a circular bar with circular inhomogeneities (Chen and Lee in Comput Mech 44(2):221–232, 2009), an extension work to an elliptic bar containing elliptic inhomogeneities is done in this paper. For fully utilizing the elliptic geometry, the fundamental solutions are expanded into the degenerate ...

We present a computer algebra approach to proving identities on Bernoulli and Euler polynomials by using the extended Zeilberger’s algorithm given by Chen, Hou and Mu. The key idea is to use the contour integral definitions of the Bernoulli and Euler numbers to establish recurrence relations on the integrands. Such recurrence relations have certain parameter free properties which lead to the re...

In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...

Herein I present multiple solutions to an improper integral using elementary calculus and real analysis. The integral, sometimes known as the Dirichlet integral, is often evaluated using complex-analytic methods, e.g. via contour integration. While the proofs presented here may not be as direct as certain complex-analytic approaches, they do illustrate the unique real variable techniques for de...

Using a circular contour integral representation for the generalized Marcum-Q function, ( ), we derive a new closed-form formula for the moment generating function (MGF) of the output signal power of a dual-diversity selection combiner (SC) in bivariate (correlated) Nakagamifading with positive integer fading severity index. This result involves only elementary functions and holds for any value...

A (coordinate) gauge of general type is introduced where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour C. For a special class of contours the gauge condition reduces to k µ (x)A µ (x) = 0 where k µ (x) is a tangent vector to the contour C. A simple proof of the nonabelian Stokes theorem is given demonstrating the advantage...

Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for different representations of the inverse Fourier integral. In this article, we present the optimal contour of the Fourier integral, takin...

This is an extended version of the paper hep-th/9802134. Dual QCD Lagrangian is derived by making use of the coordinate gauge of general type where the 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an (arbitrary) contour C. As another application a simple proof of the nonabelian Stokes theorem is given.

Professional scientists and engineers frequently analyze problems with heuristic techniques to get crude solutions quickly without worrying about the details of mathematical justification and firm error estimates. The method of steepest descent is one such technique that is widely used to evaluate functions represented by complex integrals. Routine application of the method however requires the...