several appliances have been used for palatal expansion for treatment of posterior cross bite. the purpose of this study was to evaluate the stress induced in the apical and crestal alveolar bone and the pattern of tooth displacement following expansion via removable expansion plates or fixed-banded palatal expander using the finite element method (fem) analysis.two 3d fem models were designed ...

A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes into flat domains, while preserving the distances measured on the manifold. Recently, attention has been given to embedding shapes into the eigenspace of the Laplace–Beltrami operator. The L...

The problem of using the Karhunen – Lò eve transform with partial data is addressed. Given a set of empirical eigenfunctions , we show how to recover the modal coefficients for each gappy snapshot by a least-squares procedure. This method gives an unbiased estimate of the data that lie in the gaps and permits gaps to be filled in a reasonable manner. In addition , a scheme is advanced for findi...

In this paper, we review recent advances in the approximation of multivariate functions using eigenfunctions of the Laplace operator subject to homogeneous Neumann boundary conditions. Such eigenfunctions are known explicitly on a variety of domains, including the d-variate cube, equilateral triangle and numerous other higher dimensional simplices. Practical construction of truncated expansions...

This paper proposes a new approach to solve finite-horizon optimal stopping problems for a class of Markov processes that includes one-dimensional diffusions, birth-death (BD) processes, and jump-diffusions and continuous-time Markov chains obtained by time changing diffusions and BD processes with Lévy subordinators. When the expectation operator has a purely discrete spectrum in the Hilbert s...

This note starts from work done by Dai, Geary, and Kadanoff[1] on exact eigenfunctions for Toeplitz operators. It builds methods for finding convergent expansions for eigenvectors and eigenvalues of singular, largen Toeplitz matrices, using the infinite-n case[1] as a starting point. One expansion is derived from operator equations having a two-dimensional continuous spectrum of right eigenvalu...

In this paper we give necessary and sufficient conditions under which kernels of dot product type k(x, y) = k(x · y) satisfy Mercer’s condition and thus may be used in Support Vector Machines (SVM), Regularization Networks (RN) or Gaussian Processes (GP). In particular, we show that if the kernel is analytic (i.e. can be expanded in a Taylor series), all expansion coefficients have to be nonneg...

In this paper a new analysis of the characteristics and propagation of random fluctuations in Monte Carlo (MC) eigenvalue calculations is presented. In particular, random fluctuations in the fission source distribution produced from a fixed set of initial neutron source locations are considered. Unlike previous analyses, this work relies on spectral theory to analyze a general class of MC eigen...

Using tools from semiclassical analysis, we give weighted L∞ estimates for eigenfunctions of strictly convex surfaces of revolution. These estimates give rise to new sampling techniques and provide improved bounds on the number of samples necessary for recovering sparse eigenfunction expansions on surfaces of revolution. On the sphere, our estimates imply that any function having an s-sparse ex...

Abstract We study the eigenvalues and eigenfunctions of one-dimensional weighted fractal Laplacians. These Laplacians are defined by self-similar measures with overlaps. first prove existence eigenfunctions. then set up a framework for to discretize equation defining eigenfunctions, obtain numerical approximations eigenvalue eigenfunction using finite element method. Finally, we show that conve...