Search results for "Cauchy distribution"
showing 10 items of 33 documents
THE CAUCHY DUAL AND 2-ISOMETRIC LIFTINGS OF CONCAVE OPERATORS
2018
We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal. In particular, the quasinormality of compressions of such operators is studied.
Convergence in discrete Cauchy problems and applications to circle patterns
2005
A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size ε \varepsilon tends to zero. The convergence is in C ∞ C^\infty and the approximation error for arbitrary derivatives is quadratic in ε \varepsilon . In application, C ∞ C^\infty -approximation of conformal maps by Schramm’s orthogonal circle patterns and lattices of cross-ratio minus one is shown.
Existence and Regularity of Solutions of Cauchy Problems for Inhomogeneous Wave Equations with Interaction
1991
The main aim of this paper is a nonrecursive formula for the compatibility conditions ensuring the regularity of solutions of abstract inhomogeneous linear wave equations, which we derive using the theory of T. Kato [11]. We apply it to interaction problems for wave equations (cf. [3]), generalizing regularity results of Lions-Magenes [12].
Existence results and asymptotic behavior for nonlocal abstract Cauchy problems
2008
AbstractThe purpose of this paper is to study the existence and asymptotic behavior of solutions for Cauchy problems with nonlocal initial datum generated by accretive operators in Banach spaces.
Parabolic-Lorentzian modified Gaussian model for describing and deconvolving chromatographic peaks.
2002
Abstract A new mathematical model for characterising skewed chromatographic peaks, which improves the previously reported polynomially modified Gaussian (PMG) model, is proposed. The model is a Gaussian based equation whose variance is a combined parabolic-Lorentzian function. The parabola accounts for the non-Gaussian shaped peak, whereas the Lorentzian function cancels the variance growth out of the elution region, which gives rise to a problematic baseline increase in the PMG model. The proposed parabolic-Lorentzian modified Gaussian (PLMG) model makes a correct description of peaks showing a wide range of asymmetry with positive and/or negative skewness. The new model is shown to give b…
New approaches based on modified Gaussian models for the prediction of chromatographic peaks
2012
Abstract The description of skewed chromatographic peaks has been discussed extensively and many functions have been proposed. Among these, the Polynomially Modified Gaussian (PMG) models interpret the deviations from ideality as a change in the standard deviation with time. This approach has shown a high accuracy in the fitting to tailing and fronting peaks. However, it has the drawback of the uncontrolled growth of the predicted signal outside the elution region, which departs from the experimental baseline. To solve this problem, the Parabolic-Lorentzian Modified Gaussian (PLMG) model was developed. This combines a parabola that describes the variance change in the peak region, and a Lor…
Levy targeting and the principle of detailed balance
2011
We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) …
3d mesh denoising using normal based myriad filter
2011
We propose a new filtering scheme for denoising of 3D objects which are represented by a triangular mesh. This scheme consists on applying myriad filter to face normals and then updating the vertices positions in order to preserve the original shape of the object. The choice of the Myriad is justified by the assumption of Cauchy distributed angles between surface normals. This filter improves the performance of a normal-based method which is adapted to the underlying mesh structure. To evaluate these methods of filtering, we use three error metrics. The first is based on the vertices, the second is based on the normals and the third is based on Hausdorff distance. Experimental results demon…
The Regularized Hadamard Expansion
2017
A local expansion is proposed for two-point distributions involving an ultraviolet regularization in a four-dimensional globally hyperbolic space-time. The regularization is described by an infinite number of functions which can be computed iteratively by solving transport equations along null geodesics. We show that the Cauchy evolution preserves the regularized Hadamard structure. The resulting regularized Hadamard expansion gives detailed and explicit information on the global dynamics of the regularization effects.
Comparison among three boundary element methods for torsion problems: CPM, CVBEM, LEM
2011
This paper provides solutions for De Saint-Venant torsion problem on a beam with arbitrary and uniform cross-section. In particular three methods framed into complex analysis have been considered: Complex Polynomial Method (CPM), Complex Variable Boundary Element Method (CVBEM) and Line Element-less Method (LEM), recently proposed. CPM involves the expansion of a complex potential in Taylor series, computing the unknown coefficients by means of collocation points on the boundary. CVBEM takes advantage of Cauchy’s integral formula that returns the solution of Laplace equation when mixed boundary conditions on both real and imaginary parts of the complex potential are known. LEM introduces th…