Let u^ be a Ritz-Galerkin approximation, corresponding to the solution u of an elliptic boundary value problem, which is based on a uniform subdivision in the interior of the domain. In this paper we show that by "averaging" the values of Uu in the neighborhood of a point x we may (for a wide class of problems) construct an approximation to u(x) which is often a better approximation than UyAx) ...

Assessment of exposure to airborne endotoxins has been studied for several years, especially in occupational environments, but a large number of procedures are used for sampling and analysis. This lack of standardization makes it very difficult to compare results and set internationally accepted threshold limit values (TLVs) or occupational exposure limits (OELs) for endotoxin exposure. This pa...

Abstract In this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and provide a priori error estimates for them. The abstract analysis is exemplified by considering spline spaces equip corresponding explicit constants. This complements our results recently obtained based on classical Ritz (Numer Math 144(4)...

We introduce a variational method for approximating distribution functions of dynamics with a “Liouville operator” L̂, in terms of a nonequilibrium action functional for two independent (left and right) trial states. The method is valid for deterministic or stochastic Markov dynamics, and for stationary or time-dependent distributions. A practical Rayleigh-Ritz procedure is advanced, whose input...

a r t i c l e i n f o a b s t r a c t The article describes a program that solves the least-squares optimization problem for finding the energy levels of a quantum-mechanical system based on a set of measured energy separations or wavelengths of transitions between those energy levels, as well as determining the Ritz wavelengths of transitions and their uncertainties. The energy levels are dete...

Ice-sheet modelers tend to be more familiar with the Newtonian, vectorial formulation of continuum mechanics, in which the motion of an ice sheet or glacier is determined by the balance of stresses acting on the ice at any instant in time. However, there is also an equivalent and alternative formulation of mechanics where the equations of motion are instead found by invoking a variational princ...

We make use of the Pad e approximants and Krylov's sequence x; Ax; ; : : :; A m?1 x in the projection methods to compute a few Ritz values of a hermitian matrix A of order n. This process consists of approaching the poles of R x () = ((I ?A) ?1 x; x), the mean value of the resolvant of A, by those of m ? 1=m] Rx (), where m ? 1=m] Rx () is the Pad e approximant of order m of the function R x ()...

We report our measurements of the absolute transition frequencies 5 P 3/2 , F = 3 to nS and nD Rydberg states 87 Rb with high principal quantum numbers in a wide range values ( n 45-124). The were performed using Electromagnetically Induced Transparency (EIT) ladder-type three-level systems. measure an accuracy ≤ 2 MHz. determine Rydberg-Ritz parameter for from experimental frequencies. Our hig...

Ω fvdxdy. There have been a lot of work related to the finite element approximation to problem (1) in the framework of both semidiscrete and fully discrete schemes. For example, some superconvergence properties of conforming linear finite element (FE) were obtained by V. Thomeé with necessary help of Ritz projection and Lin Qun with a new analysis form, i.e., an analysis for the “short side” in...