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Journal of Engineering Mathematics, 1990
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hill, D. L., Hill, J. M.
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SIAM Review, 1998
The author considers the problem \[ u_t= ku_{yy},\quad t>0,\quad x\in\mathbb{R},\quad y>\max\{0,- mx\}\equiv T(-mx), \] \[ u(x,y,t)= u_0,\quad x0,\quad y+ mx=0, \] \[ u(x,y,0)= 0,\quad x\in\mathbb{R},\quad y> T(-mx), \] \[ u_t(x,0,t)+ cu_x(x,0,t)= -Q,\quad t, x>0, \] where \(Q= -hu_y(x,0,t)\). He finds the solution \[ u(x,y,t)= u_0[1- ef(mx+ y/2\sqrt{k(
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ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1993
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El-Wakil, S. A. +3 more
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SIAM Journal on Applied Mathematics, 1980
It is shown how group-theoretic methods, or similarity methods, can be applied to determine the class of self-similar solutions for a one-dimensional, time-dependent problem in shock hydrodynamics,with a chemical reaction taking place behind the shock.
Logan, J. David, de Jesus Perez, Jose
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Closed form solution of similarity algorithms

Proceedings of the 33rd international ACM SIGIR conference on Research and development in information retrieval, 2010
Algorithms defining similarities between objects of an information network are important of many IR tasks. SimRank algorithm and its variations are popularly used in many applications. Many fast algorithms are also developed. In this note, we first reformulate them as random walks on the network and express them using forward and backward transition ...
Yuanzhe Cai +3 more
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Mathematical Models and Methods in Applied Sciences, 1999
A study on similarity solutions for a mathematical model for thawing in a saturated porous medium is considered when change of phase induces a density jump and the influence of pressure on the melting temperature is considered. The mathematical analysis is made for different cases, depending on the sign of the three physical parameters.
FASANO, ANTONIO, PRIMICERIO, MARIO, TARZIA D. A: +2 more
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2011
In this note, I provide some detailed computation of constructing translating solutions from self-similar solutions for Lagrangian mean curvature flow discussed in [6] and explore the related geometric meanings. This method works for all mean curvature flows and has great potential to find other new translating solutions.
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Journal of Law, Medicine & Ethics, 2018
Advancements in the field of biotechnology have accelerated the development of drugs that are manufactured from cultures of living cells, commonly referred to as “biologics.” Due to the complexity of the production process, generic biologics are unlikely to be chemically identical to the reference product, and accordingly are referred to as ...
Lisa, Diependaele, Julian, Cockbain, Sigrid, Sterckx +2 more
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IMA Journal of Applied Mathematics, 1990
By making use of the similarity method, the authors study the generalized Burgers equation of the form \[ u_ t+uu_ x=()\Delta (t)u_{xx}. \] They show that if \(\Delta\) (t) has one of the following forms \[ \exp ((\alpha t+\beta)/(\gamma t+\delta)),\quad ((\alpha t+\beta)/(\gamma t+\delta))^ r,\quad \exp (2\gamma \tan^{-1}(\alpha t+\beta)), \] then the
Doyle, J., Englefield, M. J.
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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1975
AbstractThe general similarity solution of the heat equation is used to find approximate numerical solutions of a direct Stefan problem. The constructed algorithm is shown to converge and is illustrated by numerical examples.
Milinazzo, F., Bluman, G. W.
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heat transfer
mixed convection
medicine