A standard isosurface extraction algorithm for a 3D image is the Marching Cubes algorithm [4]. The image is assumed to be defined on a regular lattice of size N0×N1×N2 with integer points (x, y, z) where 0 ≤ x < N0, 0 ≤ y < N1, and 0 ≤ z < N2. The image values themselves are F (x, y, z). An isosurface is of the form F (x, y, z) = c for some specified level value c where x, y, and z are treated ...

and Applied Analysis 3 Remark 1.5. In Theorem 1.2 setting α z constant zero and P z,w a polynomial in variable w that vanishes exactly on a finite set of holomorphic functions S, we obtain Corollary 1.6 which generalizes the famous Montel’s criterion that a holomorphic family omitting 2 or more values is normal. Corollary 1.6. Let F be a family of holomorphic functions on a domain D. Let S be a...

Abstract: Firstly, we construct kernels for integral relations among solutions of the confluent Heun equation (CHE). Additional kernels are systematically generated by applying substitutions of variables. Secondly, we establish integral relations between known solutions of the CHE that are power series and solutions that are series of special functions. Thirdly, by using one of the integral rel...

Any nonlinear equation of the form y′′ = ∑N n=0 an(z)y n has a (generally branched) solution with leading order behaviour proportional to (z − z0) about a point z0, where the coefficients an are analytic at z0 and aN (z0) 6= 0. We consider the subclass of equations for which each possible leading order term of this form corresponds to a one-parameter family of solutions represented near z0 by a...

An experimental set-up of the method of caustics was proposed for the accurate evaluation of stress intensity factor. The stress intensity factor evaluation was based on a new formula which was based on the caustic shape area. The new formula was based on the shape area of the caustics. The stress optical constants were evaluated according to the new formula of the stress intensity factor. The ...

Let (f, g) be a pair of complex analytic functions on a singular analytic space X. We give “the correct” definition of the relative polar curve of (f, g), and we give a very formal generalization of Lê’s attaching result, which relates the relative polar curve to the relative cohomology of the Milnor fiber modulo a hyperplane slice. We also give the technical arguments which allow one to work w...

Let X be a Banach space and Z a nonempty closed subset of X. Let J :Z → R be a lower semicontinuous function bounded from below. This paper is concerned with the perturbed optimization problem infz∈Z{J (z)+ ‖x − z‖}, denoted by (x, J )-inf for x ∈X. In the case when X is compactly fully 2-convex, it is proved in the present paper that the set of all points x in X for which there does not exist ...

Martı́n González-Alonso and Michael J. Ramsey-Musolf Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125, USA (Received 25 December 2012; published 14 March 2013) We study the impact of a leptophobic Z0 gauge boson on the C1q and C2q parameters that describe the low-energy, pari...

Given a probability measure μ with infinite support on the unit circle ∂D = {z : |z| = 1}, we consider a sequence of paraorthogonal polynomials hn(z, λ) vanishing at z = λ where λ ∈ ∂D is fixed. We prove that for any fixed z0 6∈ supp(dμ) distinct from λ, we can find an explicit ρ > 0 independent of n such that either hn or hn+1 (or both) has no zero inside the disk B(z0, ρ), with the possible e...