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The Relaxed Work Functional in Linear Viscoelasticity

Mathematics and Mechanics of Solids, 2004
The relaxed work from a history H' to a history H is defined as the minimum work required to approach H via a sequence of continuations of H'. I prove three basic properties of the relaxed work: subadditivity, lower semicontinuity with respect to H for fixed H', and two dissipation inequalities.
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Approximate Relaxation Function for Concrete

Journal of the Structural Division, 1979
Presented is an approximate algebraic formula for calculating the relaxation function for aging concrete. The formula is general; it applies to any form of the creep function. Compared to the previously used effective modulus method, the formula reduces the error from up to 37% to within 2% relative to the exact solution according to the superpositon ...
Sang Sik Kim, Zdenek P. Bazant
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Spin-Relaxation Functions

1997
The spin-relaxation functions are the time dependences of the observables one measures in relaxation experiments. A list of relaxation functions for typical measuring procedures is given in Table 10.1 on page 93.
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New relaxations for composite functions

2019
Mixed-integer nonlinear programs are typically solved using branch-and-bound algorithms. A key determinant of the success of such methods is their ability to construct tight and tractable relaxations. The predominant relaxation strategy used by most state-of-the-art solvers is the factorable programming technique.
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On compatibility functions in probabilistic relaxation

Photogrammetria, 1985
Abstract The first stage in the analysis of remotely sensed data is image segmentation and classification. The early approaches to this problem were based on the Bayesian decision rule for classifying pixels x on individual basis. Recent studies showed that the segmentation performance can be considerably enhanced by incorporating contextual ...
J. Foglein, J. Kittler
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Multiscale relaxation of convex functionals

2003
Summary: The \(\Gamma\)-limit of a family of functionals \[ u\mapsto \int_\Omega f\Biggl({x\over\varepsilon}, {x\over \varepsilon^2}, D^su\Biggr)\,dx \] is obtained for \(s= 1,2\) and when the integrand \(f= f(x,y,v)\) is a continuous function, periodic in \(x\) and \(y\), and convex with respect to \(v\). The 3-scale limits of second-order derivatives
FONSECA I., ZAPPALE, ELVIRA
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Relaxation functions in dipolar materials

Journal of Statistical Physics, 1995
We compare two simple “cartoons” of relaxation processes in dipolar materials: the “first passage” relaxation function introduced by K. Weron (1991) and the “average” relaxation function expressing the proportion of dipoles which did not change their imposed aligned orientation up to a certain time, the latter providing a description closer to what is ...
Karina Weron   +2 more
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Relaxation function for the non-Debye relaxation spectra description

Chemical Physics, 2014
Abstract This study presents the new relaxation function describing the non-Debye relaxation phenomena. The relaxation function is based on a new theoretical model of the relaxation polarization. The non-Debye relaxation is explained with the model of nonlinear damped oscillator.
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Stress relaxation function of glass

Solid State Communications, 1971
It has been found by Douglas and others that the stress relaxation function of glass has the form S = S0 exp[ -(t/τ)α]. Simple phenomenological considerations, utilizing the theory of Brownian motion, can explain this law and yield proper values of α and τ.
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Relaxation function of linear polymers

Journal of engineering physics, 1982
The relaxation function of linear polymers possessing a discrete realxation time spectrum is analyzed.
Z. P. Shul'man   +5 more
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