Note on the Dynamics of Gravitational Sources
This paper is concerned with multipole structure for the sources of the gravitational field in the full (axially symmetric) nonlinear gravitational theory. Definitions proposed recently by Janis and N...
This paper is concerned with multipole structure for the sources of the gravitational field in the full (axially symmetric) nonlinear gravitational theory. Definitions proposed recently by Janis and N...
Oblique Incidence on Plane Boundary between Two General Gyrotropic Plasma Media
The problem of a characteristic electromagnetic wave incident obliquely on a plane boundary between two different gyrotropic plasma media is solved. Two characteristic transmitted waves and two charac...
The problem of a characteristic electromagnetic wave incident obliquely on a plane boundary between two different gyrotropic plasma media is solved. Two characteristic transmitted waves and two charac...
Inequality with Applications in Statistical Mechanics
J. Math. Phys. 6, 1812 (1965); doi:10.1063/1.1704727
Issue Date: November 1965
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We prove for Hermitian matrices (or more generally for completely continuous self-adjoint linear operators in Hilbert space) A and B that Tr (eA+B) 
Tr (eAeB). The inequality is shown to be sharper than the convexity property (0 
1) Tr (e
A+(1−)B) [Tr (eA)][Tr (eB)]1−, and its possible use for obtaining upper bounds for the partition function is discussed briefly.
©1965 The American Institute of Physics
Tr (eAeB). The inequality is shown to be sharper than the convexity property (0 1) Tr (eA+(1−)B) [Tr (eA)][Tr (eB)]1−, and its possible use for obtaining upper bounds for the partition function is discussed briefly.
©1965 The American Institute of Physics
| History: | Received 18 March 1965 |
| Permalink: |
http://link.aip.org/link/?JMAPAQ/6/1812/1 |
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REFERENCES (5)
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- Theorem I, and Lemma 2 in Sec. 2 (for positive-definite matrices only), have recently been proved independently by S. Golden, Phys. Rev. 137, B1127 (1965).
- D. Ruelle,
Helv. Phys. Acta 36, 789 (1963) . - R. B. Griffiths,
Phys. Rev. 136, A751 (1964) . - H. Weyl,
Proc. Natl. Acad. Sci. U.S. 35, 408 (1949) ;
see also G. Polya, - K. Fan,
Proc. Natl. Acad. Sci. U.S. 35, 652 (1949) .
