37. General Proof of the Pole and Polar Property of the Circle

E. Budden

doi:10.2307/3604955

General proof of Osterwalder-Schrader positivity for the Wilson action

Communications in Mathematical Physics ◽

10.1007/bf01221251 ◽

1987 ◽

Vol 113 (3) ◽

pp. 369-373 ◽

Cited By ~ 20

Author(s):

P. Menotti ◽

A. Pelissetto

Keyword(s):

General Proof

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General proof of Carruthers theorem

Physics Letters B ◽

10.1016/0370-2693(67)90308-5 ◽

1967 ◽

Vol 24 (8) ◽

pp. 411-412 ◽

Cited By ~ 17

Author(s):

Y.S. Jin

Keyword(s):

General Proof

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ON THE INSTABILITY OF PERIODIC WAVES FOR DISPERSIVE EQUATIONS—REVISITED

Nagoya Mathematical Journal ◽

10.1017/nmj.2021.9 ◽

2021 ◽

pp. 1-23

Author(s):

FÁBIO NATALI ◽

SABRINA AMARAL

Keyword(s):

Traveling Wave ◽

Orbital Stability ◽

Traveling Wave Solutions ◽

Spectral Stability ◽

Dispersive Equations ◽

Periodic Waves ◽

General Proof ◽

Wave Solutions ◽

Periodic Traveling Wave

Abstract The purpose of this paper is to present an extension of the results in [8]. We establish a more general proof for the moving kernel formula to prove the spectral stability of periodic traveling wave solutions for the regularized Benjamin–Bona–Mahony type equations. As applications of our analysis, we show the spectral instability for the quintic Benjamin–Bona–Mahony equation and the spectral (orbital) stability for the regularized Benjamin–Ono equation.

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AN APPLICATION OF THE TOPOLOGICAL DEGREE TO GRAVITATIONAL LENSES

Modern Physics Letters A ◽

10.1142/s0217732398000115 ◽

1998 ◽

Vol 13 (02) ◽

pp. 83-86 ◽

Cited By ~ 4

Author(s):

MARCO LOMBARDI

Keyword(s):

Point Source ◽

Mass Distribution ◽

Topological Degree ◽

General Theorem ◽

Gravitational Lens ◽

Gravitational Lenses ◽

General Proof ◽

Special Case

In this letter we provide a new proof of a general theorem on gravitational lenses, first proven by Burke (1981) for the special case of thin lenses. The theorem states that a transparent gravitational lens with non-singular mass distribution produces an odd number of images of a point source. Our general proof shows that the topological degree finds natural and interesting applications in the theory of gravitational lenses.

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The general proof of certain fundamental equations in the theory of metallic conduction

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1934.0036 ◽

1934 ◽

Vol 144 (851) ◽

pp. 101-117 ◽

Cited By ~ 71

Keyword(s):

Wave Equation ◽

Periodic Potential ◽

Thermal Motion ◽

Electronic Conduction ◽

Modern Theory ◽

General Proof ◽

Metallic Conduction ◽

Fundamental Equations

In the modern theory of electronic conduction the electrons are considered, when the thermal motion of the lattice is neglected, as moving in a periodic potential with the property V ( x + la , y + ma , z + na ) = V ( x, y, z ). The wave equation for an electron in this field is { h 2/8π2 m ∇ 2 + E K - V} ψ K = 0. Block has shown that this equation has solutions of the form ψ K = e i K.R U K (R), where U K has the periodicity of the lattice.

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