scholarly journals Generalized Birkhoff system and a kind of combined gradient system

2015 ◽  
Vol 64 (18) ◽  
pp. 184501
Author(s):  
Mei Feng-Xiang ◽  
Wu Hui-Bin
Keyword(s):  
Gradient System ◽  
Birkhoff System

scholarly journals Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials

2021 ◽  
Author(s):  
Alexander Mielke
Keyword(s):  
Gradient Flow ◽  
Careful Analysis ◽  
Flow Equation ◽  
Uniqueness Result ◽  
Gradient System ◽  
Independent System ◽  
Exact Relation ◽  
Flow Equations ◽  
Total Variation Flow ◽  
Energetic Solutions

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.

scholarly journals Genetic recombination as a generalised gradient flow

2021 ◽  
Author(s):  
Frederic Alberti
Keyword(s):  
Arbitrary Number ◽  
Genetic Recombination ◽  
Reaction Network ◽  
Gradient Flow ◽  
Mass Action ◽  
Gradient System ◽  
Gradient Structure ◽  
Law Of Mass Action ◽  
Reversible Chemical Reaction ◽  
Time Partitioning

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.

scholarly journals The temperature dependence of gradient system response characteristics

2019 ◽  
Vol 83 (4) ◽  
pp. 1519-1527 ◽  
Author(s):  
Manuel Stich ◽  
Christiane Pfaff ◽  
Tobias Wech ◽  
Anne Slawig ◽  
Gudrun Ruyters ◽  
...  
Keyword(s):  
Temperature Dependence ◽  
System Response ◽  
Gradient System ◽  
Response Characteristics

PRODUCTION OF OXYGEN 15 USING A RELATIVELY LOW ENERGY PARTICLE ACCELERATOR WITH A VACUUM GRADIENT SYSTEM AS A WINDOW

1971 ◽  
Vol 112 (4) ◽  
pp. 707-714 ◽  
Author(s):  
J. MANTEL ◽  
C. J. DAMICO ◽  
R. S. KURTZMAN
Keyword(s):  
Low Energy ◽  
Particle Accelerator ◽  
Gradient System ◽  
Energy Particle

scholarly journals Asymptotics for a gradient system with memory term

2009 ◽  
Vol 137 (09) ◽  
pp. 3013-3013 ◽  
Author(s):  
Alexandre Cabot
Keyword(s):  
Memory Term ◽  
Gradient System ◽  
With Memory

Form Invariance and Lie Symmetries of the Rotational Relativistic Birkhoff System

2002 ◽  
Vol 19 (4) ◽  
pp. 449-451 ◽  
Author(s):  
Luo Shao-Kai
Keyword(s):  
Lie Symmetries ◽  
Birkhoff System ◽  
Form Invariance

A SIMPLE RAPID METHOD FOR DETERMINATION OF SPECIFIC GRAVITY OF SMALL SAMPLES OF URINE

PEDIATRICS ◽  
1959 ◽  
Vol 24 (5) ◽  
pp. 814-818
Author(s):  
Allen S. Goldman
Keyword(s):  
Specific Gravity ◽  
Present Report ◽  
Total Sample ◽  
Mineral Oil ◽  
Small Samples ◽  
Gradient System ◽  
Small Opening ◽  
Flotation Method ◽  
Made In

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.)

Ammonia flux measurements above a corn canopy using relaxed eddy accumulation and a flux gradient system

2019 ◽  
Vol 264 ◽  
pp. 104-113 ◽  
Author(s):  
Andrew J. Nelson ◽  
Nebila Lichiheb ◽  
Sotiria Koloutsou-Vakakis ◽  
Mark J. Rood ◽  
Mark Heuer ◽  
...  
Keyword(s):  
Gradient System ◽  
Flux Gradient ◽  
Relaxed Eddy Accumulation ◽  
Flux Measurements ◽  
Ammonia Flux ◽  
Corn Canopy

scholarly journals A Gradient System for Low Rank Matrix Completion

Axioms ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 51 ◽  
Author(s):  
Carmela Scalone ◽  
Nicola Guglielmi
Keyword(s):  
Sparse Matrix ◽  
Matrix Completion ◽  
Low Rank ◽  
Frobenius Norm ◽  
Gradient System ◽  
Large Matrix ◽  
Rank Matrix ◽  
Matrix Differential Equations ◽  
Low Rank Matrix Completion ◽  
Matrix Differential

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.

Sign in / Sign up

Export Citation Format

Share Document