Completely Monotonic Fredholm Determinants

2020 ◽  
pp. 299-321
Author(s):  
Mourad E. H. Ismail ◽  
Ruiming Zhang
Keyword(s):  
Fredholm Determinants ◽  
Completely Monotonic

Complete monotonicity of entropy production in chemical reaction

1981 ◽  
Vol 46 (2) ◽  
pp. 452-456
Author(s):  
Milan Šolc
Keyword(s):  
Entropy Production ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Relative Entropy ◽  
Order Reaction ◽  
Complete Monotonicity ◽  
First Order Reaction ◽  
First Order ◽  
Completely Monotonic ◽  
Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

scholarly journals Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes

2020 ◽  
pp. 1-14
Author(s):  
SHOTA OSADA
Keyword(s):  
Point Processes ◽  
Duke Math ◽  
Random Point ◽  
Determinantal Point Processes ◽  
Fredholm Determinants ◽  
Poisson Point Processes ◽  
Translation Invariant ◽  
Ergodic Properties ◽  
Tree Representations ◽  
Invariant Kernels

Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J.120 (2003), 515–575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab.31 (2003), 1533–1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.

Application of Electrochemical Techniques to Characterization of the Corrosion Behaviors of GW63 Alloys

2007 ◽  
Vol 546-549 ◽  
pp. 571-574
Author(s):  
Xing Wu Guo ◽  
Jian Wei Chang ◽  
Shang Ming He ◽  
Peng Huai Fu ◽  
Wen Jiang Ding
Keyword(s):  
Electrochemical Impedance ◽  
Electrochemical Techniques ◽  
Open Circuit ◽  
Cyclic Polarization ◽  
Time Curve ◽  
Completely Monotonic ◽  
Treatment Conditions ◽  
Impedance Variation ◽  
Corrosion Behaviors

The corrosion behavior of GW63 (Mg-6wt.%Gd-3wt.%Y-0.4wt.%Zr) alloys in 5% NaCl aqueous solution has been investigated by PARSTAT 2273 instrument. The Open Circuit Potential (ECORR) vs. time curve, cyclic polarization (Pitting Scans) curve and Electrochemical Impedance Spectroscopy (EIS) was measured for the GW63 alloys in as-cast and T6 heat treatment conditions. The EIS results indicated that the tendency of impedance variation for as-cast condition was monotonic decreasing, however, the tendency of variation for T6 condition was not completely monotonic but the total tendency was decreasing. The values of impedance of GW63 alloy at 0.1 Hz are about 103 ohm-cm2 for as-cast and T6 condition.

scholarly journals The Johnson Equation, Fredholm and Wronskian Representations of Solutions, and the Case of Order Three

2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Pierre Gaillard
Keyword(s):  
Rational Solutions ◽  
Fredholm Determinants ◽  
Infinite Hierarchy

We construct solutions to the Johnson equation (J) first by means of Fredholm determinants and then by means of Wronskians of order 2N giving solutions of order N depending on 2N-1 parameters. We obtain N order rational solutions that can be written as a quotient of two polynomials of degree 2N(N+1) in x, t and 4N(N+1) in y depending on 2N-2 parameters. This method gives an infinite hierarchy of solutions to the Johnson equation. In particular, rational solutions are obtained. The solutions of order 3 with 4 parameters are constructed and studied in detail by means of their modulus in the (x,y) plane in function of time t and parameters a1, a2, b1, and b2.

Sign in / Sign up

Export Citation Format

Share Document