Mathematical Review

2021 ◽  
pp. 1337-1395
Author(s):  
Fabio Petri
Keyword(s):  
Mathematical Review

scholarly journals Mathematical Review on the Local Linearizing Method of Drift Coefficient

2008 ◽  
Vol 21 (5) ◽  
pp. 801-811
Author(s):  
Min Yoon ◽  
Young-Soo Choi ◽  
Yoon-Dong Lee
Keyword(s):  
Mathematical Review ◽  
Drift Coefficient

The general theory of two-stage learning: A mathematical review with illustrations from memory development.

1982 ◽  
Vol 91 (3) ◽  
pp. 634-665 ◽  
Author(s):  
Charles J. Brainerd ◽  
Mark L. Howe ◽  
Alain Desrochers
Keyword(s):  
General Theory ◽  
Memory Development ◽  
Two Stage ◽  
Mathematical Review

HADAMARD STATES, ADIABATIC VACUA AND THE CONSTRUCTION OF PHYSICAL STATES FOR SCALAR QUANTUM FIELDS ON CURVED SPACETIME

1996 ◽  
Vol 08 (08) ◽  
pp. 1091-1159 ◽  
Author(s):  
WOLFGANG JUNKER
Keyword(s):  
Pseudodifferential Operators ◽  
Cauchy Surface ◽  
Positive Energy ◽  
Hyperbolic Spacetime ◽  
Vacuum States ◽  
Mathematical Review ◽  
Scalar Quantum ◽  
Klein Gordon ◽  
Hadamard States ◽  
Adiabatic Vacuum

Quasifree states of a linear Klein-Gordon quantum field on globally hyperbolic spacetime manifolds are considered. After a short mathematical review techniques from the theory of pseudodifferential operators and wavefront sets on manifolds are used to develop a criterion for a state to be an Hadamard state. It is proven that ground- and KMS-states on certain static spacetimes and adiabatic vacuum states on Robertson-Walker spaces are Hadamard states. A counterexample is given which shows that the idea of instantaneous positive energy states w.r.t. a Cauchy surface does in general not yield physical states. Finally, the problem of constructing Hadamard states on arbitrary curved spacetimes is solved in principle.

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