We present a single generalized method for computing skeletons for arbitrary objects in both 2D and 3D space. We also present a method for computing the multiscale boundary-collapse importance metric for arbitrary 2D shapes in an incremental fashion, the results of which are comparable to the AFMM Star for 2D shapes. Finally, we reveal an approach which potentially allows the same importance me...

We construct a matrix model equivalent (exactly, not asymptotically), to the random plane partition model, with almost arbitrary boundary conditions. Equivalently, it is also a random matrix model for a TASEP-like process with arbitrary boundary conditions. Using the known solution of matrix models, this method allows to find the large size asymptotic expansion of plane partitions, to ALL order...

We have used the multiquadric (MQ) approximation scheme for the solution of elliptic partial differential equations with Dirichlet and/or Neumann boundary conditions. The scheme has the advantage of using the data points in arbitrary locations with an arbitrary ordering. Two-dimensional Laplace, Poisson, and biharmonic equations describing the various physical processes have been taken as the t...

We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for whic...

Let φn be an arbitrary compact topological manifold. We shall define a new topological object, Ω(t)φn , known as a lure, that alters the Minkowski Content of φn by acting on the boundary of φn, ∂φn by stretching or shrinking the boundary. After the notion of a lure has been established for compact manifolds, we shall relax the requirement that the manifold be locally Euclidean, by defining Λn t...

Free vibration characteristics of continuous grading fiber orientation (CGFO) beams resting on variable Winkler and two-parameter elastic foundations have been studied. The beam is under different boundary conditions and assumed to have arbitrary variations of fiber orientation in the thickness direction. The governing differential equations for beam vibration are being solved using Generalized...

In this study, nonlinear analysis for thick cylindrical pressure vessels with arbitrary variable thickness made of hyperelastic functionally graded material properties in nearly incompressible state and clamped boundary conditions under non-uniform pressure loading is presented. Thickness and pressure of the shell are considered in axial direction by arbitrary nonlinear profiles. The FG materia...

This paper presents a method for interactive design by means of extending the PDE based approach for surface generation. The governing partial differential equation is generalized to arbitrary order allowing complex shapes to be designed as single patch PDE surfaces. Using this technique a designer has the flexibility of creating and manipulating the geometry of shape that satisfying an arbitra...

We present exact calculations of the Potts model partition function Z(G, q, v) for arbitrary q and temperature-like variable v on n-vertex square-lattice strip graphs G for a variety of transverse widths Lt and for arbitrarily great length Ll, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These have the form Z(G, q, v) = ∑NZ,G,λ j=1 cZ,G,j(λZ,G...