Search results for "classical"
showing 10 items of 2294 documents
Ein Kriterium f�r die Approximierbarkeit von Funktionen aus sobolewschen R�umen durch glatte Funktionen
1981
The present paper provides a necessary and sufficient criterion for an element of a Sobolev space W k p (Ω) to be approximated in the Sobolev norm by Ck(En)-smooth functions. Here Ω is a bounded open set of n-dimensional Euclidean space En with convex closure $$\bar \Omega$$ and boundary ∂Ω having n-dimensional Lebesgue measure zero. No further boundary regularity (such as e.g. the segment property) is required.Our main tools are the Hardy-Littlewood maximal functions and a slightly strengthened version of a well-known extension theorem of Whitney.This work was inspired by and is very close in spirit to the pertinent parts of Calderon-Zygmund [6].
Bounded compositions on scaling invariant Besov spaces
2012
For $0 < s < 1 < q < \infty$, we characterize the homeomorphisms $��: \real^n \to \real^n$ for which the composition operator $f \mapsto f \circ ��$ is bounded on the homogeneous, scaling invariant Besov space $\dot{B}^s_{n/s,q}(\real^n)$, where the emphasis is on the case $q\not=n/s$, left open in the previous literature. We also establish an analogous result for Besov-type function spaces on a wide class of metric measure spaces as well, and make some new remarks considering the scaling invariant Triebel-Lizorkin spaces $\dot{F}^s_{n/s,q}(\real^n)$ with $0 < s < 1$ and $0 < q \leq \infty$.
Tunnel effect and symmetries for Kramers–Fokker–Planck type operators
2011
AbstractWe study operators of Kramers–Fokker–Planck type in the semiclassical limit, assuming that the exponent of the associated Maxwellian is a Morse function with a finite number n0 of local minima. Under suitable additional assumptions, we show that the first n0 eigenvalues are real and exponentially small, and establish the complete semiclassical asymptotics for these eigenvalues.
The McShane, PU and Henstock integrals of Banach valued functions
2002
Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals of vector valued functions are characterized.
Psychometric Properties of an Emotional Adjustment Measure
2007
Item response theory (IRT) provides valuable methods for the analysis of the psychometric properties of a psychological measure. However, IRT has been mainly used for assessing achievements and ability rather than personality factors. This paper presents an application of the IRT to a personality measure. Thus, the psychometric properties of a new emotional adjustment measure that consists of a 28-six graded response items is shown. Classical test theory (CTT) analyses as well as IRT analyses are carried out. Samejima's (1969) graded-response model has been used for estimating item parameters. Results show that the bank of items fulfills model assumptions and fits the data reasonably well,…
Determination of Particle Size Distributions in Multiphase Systems Containing Nonspherical Fluid Particles
2015
The presented results are obtained by means of an automated image analysis software capable of measuring particle diameters in photographs taken in situ by a 2D photo-optical measurement device. Initially, the applicability of this measurement method must be proven for fluid particle systems on the basis of spherical-shaped particles. As a first approach in targeting the issue of irregularly shaped fluid particles, a pure gas-liquid system is analyzed to investigate the influence of the variation of operating parameters. In the second step, the spherical shape is changed by reducing the surface-active auxiliaries. The usage of shape factors helps to interpret the appearance of the 2D projec…
A thermodynamics-based formulation of gradient-dependent plasticity
1998
Abstract A nonlocal thermodynamic theoretical framework is provided as a basis for a consistent formulation of gradient-dependent plasticity in which a scalar internal variable measuring the material isotropic hardening/softening state is the only nonlocal variable. The main concepts of this formulation are: i) the ‘regularization operator’, of differential nature, which governs the relation between the above nonlocal variable and a related local variable (scalar measure of plastic strain) and confers a unified character to the proposed formulation (this transforms into a formulation for nonlocal plasticity if the regularization operator has an integral nature); ii) the ‘nonlocality residua…
A unified residual-based thermodynamic framework for strain gradient theories of plasticity
2011
Abstract A unified thermodynamic framework for gradient plasticity theories in small deformations is provided, which is able to accommodate (almost) all existing strain gradient plasticity theories. The concept of energy residual (the long range power density transferred to the generic particle from the surrounding material and locally spent to sustain some extra plastic power) plays a crucial role. An energy balance principle for the extra plastic power leads to a representation formula of the energy residual in terms of a long range stress, typically of the third order, a macroscopic counterpart of the micro-forces acting on the GNDs (Geometrically Necessary Dislocations). The insulation …
Non-linear systems under delta correlated processes handled by perturbation theory
1998
Statistical responses in terms of moment and correlation functions of non-linear systems driven by non-normal delta correlated external pulses are derived. The procedure takes full advantage of the perturbation theory approach. Then, by means of a proper coordinate transformation, the system is replaced by a quasi-linear system for which the statistical quantities can be exactly found.
A stabilized finite element method for particulate two-phase flow equations laminar isothermal flow
1997
A finite element method for the solution of particulate two-phase flows is presented. The governing system has the form of compressible Navier-Stokes equations with unknown pressure. Therefore, the proposed method must capture the main features of stabilized methods used for incompressible as well as for compressible Navier-Stokes equations. Solution of the resulting nonlinear algebraic system of equations is based on the linearization using Newton method in conjunction with Generalized Minimal Residual iterative solver and Incomplete LU preconditioning. The method has been tested for three test cases including venturi tube flow, flow over backward step and mixing of flows in t-junction.