On the converse problem for the Gross-Pitaevskii equations with a large parameter

In this paper, analytical equations for the central film thickness in slender elliptic contacts are investigated. A comparison of state-of-the-art formulas with simulation results of a multilevel elastohydrodynamic lubrication solver is conducted and shows considerable deviation. Therefore, a new film thickness formula for slender elliptic contacts with variable ellipticity is derived. It incorporates asymptotic solutions, which results in validity over a large parameter domain. It captures the behaviour of increasing film thickness with increasing load for specific very slender contacts. The new formula proves to be significantly more accurate than current equations. Experimental studies and discussions on minimum film thickness will be presented in a subsequent publication.

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Asymptotic Analysis of the Wright Function with a Large Parameter

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125731 ◽

2021 ◽

pp. 125731

Author(s):

Alireza Ansari ◽

Hassan Askari

Keyword(s):

Asymptotic Analysis ◽

Wright Function ◽

Large Parameter

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Gamma Factors, Root Numbers, and Distinction

Canadian Journal of Mathematics ◽

10.4153/cjm-2017-011-6 ◽

2018 ◽

Vol 70 (3) ◽

pp. 683-701 ◽

Cited By ~ 1

Author(s):

Nadir Matringe ◽

Omer Offen

Keyword(s):

Linear Group ◽

General Linear Group ◽

Quadratic Extension ◽

Root Number ◽

Converse Problem ◽

Root Numbers ◽

Special Values ◽

Distinguished Representations ◽

Local Invariants ◽

Gamma Factor

AbstractWe study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of p-adic fields. We show that the local Rankin–Selberg root number of any pair of distinguished representation is trivial, and as a corollary we obtain an analogue for the global root number of any pair of distinguished cuspidal representations. We further study the extent to which the gamma factor at 1/2 is trivial for distinguished representations as well as the converse problem.

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Spectral properties of the equation (∇ + ieA) × u = ±mu

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s030821050000127x ◽

2001 ◽

Vol 131 (5) ◽

pp. 1065-1089

Author(s):

Daniel M. Elton

Keyword(s):

Spectral Properties ◽

Time Variable ◽

Two Dimensional ◽

Vector Product ◽

Relativistic Invariance ◽

Speed Of Light ◽

Large Parameter ◽

Real Vector ◽

Pauli Equation ◽

Minkowski Metric

We develop a spectral theory for the equation (∇ + ieA) × u = ±mu on Minkowski 3-space (one time variable and two space variables); here, A is a real vector potential and the vector product is defined with respect to the Minkowski metric. This equation was formulated by Elton and Vassiliev, who conjectured that it should have properties similar to those of the two-dimensional Dirac equation. Our equation contains a large parameter c (speed of light), and this motivates the study of the asymptotic behaviour of its spectrum as c → +∞. We show that the essential spectrum of our equation is the same as that of Dirac (theorem 3.1), whereas the discrete spectrum agrees with Dirac to a relative accuracy δλ/mc2 ~ O(c−4) (theorem 3.3). In other words, we show that our equation has the same accuracy as the two-dimensional Pauli equation, its advantage over Pauli being relativistic invariance.

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