Search results for " approximation"

Interpolation and approximation in L2(γ)

AbstractAssume a standard Brownian motion W=(Wt)t∈[0,1], a Borel function f:R→R such that f(W1)∈L2, and the standard Gaussian measure γ on the real line. We characterize that f belongs to the Besov space B2,qθ(γ)≔(L2(γ),D1,2(γ))θ,q, obtained via the real interpolation method, by the behavior of aX(f(X1);τ)≔∥f(W1)-PXτf(W1)∥L2, where τ=(ti)i=0n is a deterministic time net and PXτ:L2→L2 the orthogonal projection onto a subspace of ‘discrete’ stochastic integrals x0+∑i=1nvi-1(Xti-Xti-1) with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the problem is reduced to a deterministic one. The approximation numbers aX(f(X1);τ) can be used to descr…

3D digitization of transparent objects by polalization techniques in IR & by triangulation in UV

2011

Two non-conventional methods for the 3D digitization of transparent objects via non-contact measurement are reported in this thesis. 3D digitization is a well acknowledged technique for opaque objects and various commercial solutions based on different measurement approaches are available in the market offering different types of resolution at different prices. Since these techniques require a diffused or lambertian surface, their application to transparent surfaces fails. Indeed, rays reflected by the transparent surface are perturbed by diverse inter-reflections induced by the refractive properties of the object. Therefore, in industrial applications like quality control, the transparent …

A brief overview on the numerical behavior of an implicit meshless method and an outlook to future challenges

2015

In this paper recent results on a leapfrog ADI meshless formulation are reported and some future challenges are addressed. The method benefits from the elimination of the meshing task from the pre-processing stage in space and it is unconditionally stable in time. Further improvements come from the ease of implementation, which makes computer codes very flexible in contrast to mesh based solver ones. The method requires only nodes at scattered locations and a function and its derivatives are approximated by means of a kernel representation. A perceived obstacle in the implicit formulation is in the second order differentiations which sometimes are eccesively sensitive to the node configurat…

A novel numerical meshless approach for electric potential estimation in transcranial stimulation

2015

In this paper, a first application of the method of fundamental solutions in estimating the electric potential and the spatial current density distribution in the brain due to transcranial stimulation, is presented. The coupled boundary value p roblems for the electric potential are solved in a meshless way, so avoiding the use of grid based numerical methods. A multi-spherical geometry is considered and numerical results are discussed.

An analytical study of the ageostrophic motion of an air parcel

1978

The complete ageostrophic motion of an individual air parcel is discussed. It is shown that the general velocity solution of the equation describing this motion may be expressed in terms of the well-known series approximation of Philipps and a rest term; this term describes the inertial motion of the air parcel about a given initial state.

Spatio-Temporal Modeling of Zika and Dengue Infections within Colombia

2018

The aim of this study is to estimate the parallel relative risk of Zika virus disease (ZVD) and dengue using spatio-temporal interaction effects models for one department and one city of Colombia during the 2015&ndash

Time Dependent Case

1999

This chapter is devoted to finite element approximations of scalar time dependent hemivariational inequalities. We start with the parabolic case following closely Miettinen and Haslinger, 1998. At the end of this chapter we discuss, how the results can be extended to constrained problems. Our presentation will follow the structure used for the static case in Chapter 3. First, we introduce an abstract formulation of a class of parabolic hemivariational inequalities (see Miettinen, 1996, Miettinen and Panagiotopoulos, 1999).

Potentials with SuppressedS-Wave Phase Shift at Low Energies

1972

These results are valid for arbitrary range and depths of the potentials here studied. In spite of the fact that for the general solution we have worked only with a particular radial dependence, for .which an explicit solution for the phase shifts can be written down, it seems plausible that the results have a more general validity. With this generalization in mind, we show that for general shapes of the radial dependence, the phase shifts in Born approximation present the momentum dependence described above. The origin of our results become transparent in this Born approximation treatment. We consider a velocity dependent potential of the form 1 )

A Simple Method for the Consecutive Determination of Protonation Constants through Evaluation of Formation Curves

2013

A simple method is presented for the consecutive determination of protonation constants of polyprotic acids based on their formation curves. The procedure is based on generally known equations that describe dissociation equilibria. It has been demonstrated through simulation that the values obtained through the proposed method are sufficiently consistent with the actual values. In contrast with the universally known and applied Bjerrum’s method, no differences in the accuracy of determination of subsequent protonation constant values are observed. The proposed method requires the value of one of the protonation constants (e.g., of the first one, K1) of the polyprotic acid. An iterative meth…

Quasi-Modes and Spectral Instability in One Dimension

2019

In this section we describe the general WKB construction of approximate “asymptotic” solutions to the ordinary differential equation $$\displaystyle P(x,hD_x)u=\sum _{k=0}^m b_k(x)(hD_x)^ku=0, $$ on an interval α < x < β, where we assume that the coefficients bk ∈ C∞(]α, β[). Here h ∈ ]0, h0] is a small parameter and we wish to solve (above equation) up to any power of h. We look for u in the form $$\displaystyle u(x;h)=a(x;h)e^{i\phi (x)/h}, $$ where ϕ ∈ C∞(]α, β[) is independent of h. The exponential factor describes the oscillations of u, and when ϕ is complex valued it also describes the exponential growth or decay; a(x;h) is the amplitude and should be of the form $$\displaystyle a(x;h…