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Asymptotic scales-asymptotic algebras

Integral Transforms and Special Functions, 1998
J.F. Colombeau and other authors have introduced algebras of generalized functions in order to solve differential problems which have no solution in spaces of distributions. These algebras are based on properties of polynomial growth with respect to a parameter.
Delcroix, Antoine, Scarpalezos, Dimitri
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Asymptotic Normality of Scaling Functions

SIAM Journal on Mathematical Analysis, 2004
The properties of probability measures are investigated. It is shown that if \(m\) is a probability measure on \(R\) with finite first moment, then the solution of the scaling equation \[ \phi (x) = \int_{R} \alpha \phi (\alpha x - y)\,dm(y),\quad x \in {\mathbb R} , \] is also a probability measure with the scale \(\alpha > 1\).
Goodman, Timothy   +2 more
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Asymptotics for Scaled Kramers--Smoluchowski Equations

SIAM Journal on Mathematical Analysis, 2016
The Kramers-Smoluchowski equation for density \(\rho\) of diffusing material is a linear parabolic equation, which takes the form of \[ \rho_t = (\rho_{\xi} + \epsilon^{-2}\Phi'\rho)_{\xi} \] in the one-dimensional space, and is similarly generalized to the multidimensional settings.
Evans, Lawrence C., Tabrizian, Peyam R.
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Asymptotic-Freedom Scales

Physical Review Letters, 1980
Using Monte Carlo methods with Wilson's lattice cutoff, the asymptotic-freedom scales of SU(2) and SU(3) gauge theories without quarks are calculated.
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Asymptotic scaling in turbulent pipe flow

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007
The streamwise velocity component in turbulent pipe flow is assessed to determine whether it exhibits asymptotic behaviour that is indicative of high Reynolds numbers. The asymptotic behaviour of both the mean velocity (in the form of the log law) and that of the second moment of the streamwise component of velocity in the outer and ...
McKeon, B. J., Morrison, J. F.
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Scaling, asymptotic scaling and improved perturbation theory

Il Nuovo Cimento A, 1994
Contrary to recent claims, we show that lattice perturbation theory reproduces quite accurately Monte Carlo results of short-distance quantities. We argue that the present numerical situation strongly suggests the occurrence of a (zero temperature) deconfining transition in QCD at non-zero lattice coupling.
A. Patrascioiu, E. Seiler
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Onset of asymptotically free scaling

Physical Review D, 1982
We argue that the onset of asymptotically free scaling for the string tension in SU(2) lattice gauge theories need not be associated with the bulk transitions seen in the Monte Carlo specific-heat data. This is specifically realized in a class of constrained models where these two crossover phenomena are completely separated.
Richard C. Brower   +2 more
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Exclusive photonuclear reactions and asymptotic scaling

Physical Review C, 1990
Recent measurements of electron-deuteron elastic scattering at high momentum transfer have placed an empirical lower limit on the momentum transfer for the onset of asymptotic scaling. The implications that this limit has for the {sup 2}H({gamma},{ital p}){ital n}, {sup 2}H({gamma},{ital d}){pi}{sup 0}, and {sup 3}He({gamma},{ital d})H reactions will ...
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Asymptotic Scaling for Euclidean Lattices

2013
We calculate numerically-exact values for the absorption time (or mean walk length) for a particle performing a nearest-neighbor random walk on a finite, nth generation triangular lattice of non-uniform connectivity with a deep trap at one vertex. We show that although the Euclidean lattice is not self-similar, there exists a scaling relation which ...
R. A. Garza-López, J. J. Kozak
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