scholarly journals Existence of standing pulse solutions to a skew-gradient system

2021 ◽  
Vol 302 ◽  
pp. 185-221
Author(s):  
Yung-Sze Choi ◽  
Jieun Lee
Keyword(s):  
Author(s):  
Alexander Mielke

AbstractWe consider a non-negative and one-homogeneous energy functional $${{\mathcal {J}}}$$ J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional $${{\mathcal {E}}}(t,u)= t {{\mathcal {J}}}(u)$$ E ( t , u ) = t J ( u ) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system.


Author(s):  
Frederic Alberti

AbstractIt is well known that the classical recombination equation for two parent individuals is equivalent to the law of mass action of a strongly reversible chemical reaction network, and can thus be reformulated as a generalised gradient system. Here, this is generalised to the case of an arbitrary number of parents. Furthermore, the gradient structure of the backward-time partitioning process is investigated.


2019 ◽  
Vol 83 (4) ◽  
pp. 1519-1527 ◽  
Author(s):  
Manuel Stich ◽  
Christiane Pfaff ◽  
Tobias Wech ◽  
Anne Slawig ◽  
Gudrun Ruyters ◽  
...  

PEDIATRICS ◽  
1959 ◽  
Vol 24 (5) ◽  
pp. 814-818
Author(s):  
Allen S. Goldman

THE THERAPY of infants with disturbances in fluid balance is greatly assisted by knowledge of the specific gravity of the urine. Frequently only a few milliliters can be collected at any one time, while a minimum sample of 25 ml is necessary for use of the smallest urinometers currently available. The existing methods of determining specific gravity of one drop of urine are somewhat laborious, and require expensive equipment and the services of a relatively skilled technician. The present report describes a method which is rapid and simple and requires only a few drops of urine in its use. It is similar in principle to the determination of specific gravity of blood by the copper-sulfate method. For use with urine, mixtures are employed of two relatively nonvolatile liquids, immiscible with water, and with specific gravities nearly equally above and below the range in urine. The specific gravity of urine is determined by allowing one drop to fall into each of a series of tubes containing a mixture of the two liqquids made up to various specific gravities ranging from 1.005 to 1.030 (Fig. 1). That mixture in which the drop of urine comes most nearly to remaining still (neither rising nor falling after coming to rest) approximates the specific gravity of the urine. The total sample needed is only a few drops, which can be quite small if a dropper with a small opening (2 mm) is used. The determination takes a few minutes. A year's supply of the mixtures can be made in one afternoon and costs less than $6.00. MATERIALS The two solutions used were selected from the flotation method of Kirk, using a density gradient system. These are Liquid 1, dibutyl-n-phthalate (Eastman), specific gravity 1.04820°; and Liquid 2, kerosene, specific gravity 0.8220°. (Similar results were obtained by substituting California mineral oil, specific gravity 0.842-0.88420°, for kerosene.)


2019 ◽  
Vol 264 ◽  
pp. 104-113 ◽  
Author(s):  
Andrew J. Nelson ◽  
Nebila Lichiheb ◽  
Sotiria Koloutsou-Vakakis ◽  
Mark J. Rood ◽  
Mark Heuer ◽  
...  

Axioms ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 51 ◽  
Author(s):  
Carmela Scalone ◽  
Nicola Guglielmi

In this article we present and discuss a two step methodology to find the closest low rank completion of a sparse large matrix. Given a large sparse matrix M, the method consists of fixing the rank to r and then looking for the closest rank-r matrix X to M, where the distance is measured in the Frobenius norm. A key element in the solution of this matrix nearness problem consists of the use of a constrained gradient system of matrix differential equations. The obtained results, compared to those obtained by different approaches show that the method has a correct behaviour and is competitive with the ones available in the literature.


1968 ◽  
Vol 25 ◽  
pp. 271-282 ◽  
Author(s):  
Robert C. Leif

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