534,769 research outputs found
An Extension of the Fluctuation Theorem
Heat fluctuations are studied in a dissipative system with both mechanical
and stochastic components for a simple model: a Brownian particle dragged
through water by a moving potential. An extended stationary state fluctuation
theorem is derived. For infinite time, this reduces to the conventional
fluctuation theorem only for small fluctuations; for large fluctuations, it
gives a much larger ratio of the probabilities of the particle to absorb rather
than supply heat. This persists for finite times and should be observable in
experiments similar to a recent one of Wang et al.Comment: 12 pages, 1 eps figure in color (though intelligible in black and
white
A general conservative extension theorem in process algebras with inequalities
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc
Maharam Extension for Nonsingular Group Actions
We establish a generalization of the Maharam Extension Theorem to nonsingular
group actions. We also present an extension of Krengel Representation Theorem
of dissipative transformations to nonsingular actions
Arveson's extension theorem in *-algebras
Arveson's extension theorem asserts that B(H) is an injective object in the
category of operator systems. Calling every self adjoint unital subspace of a
unital *-algebra, a quasi operator system, we show that Arveson's theorem
remains valid in the much larger category of quasi operator systems. This shows
that Arveson's theorem as a non commutative extension of Hahn-Banach theorem,
is of purely algebraic nature.Comment: 21 page
Some applications of Ball's extension theorem
We present two applications of Ball's extension theorem. First we observe that Ball's extension theorem, together with the recent solution of Ball's Markov type 2 problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice {0,1,...,m}^n, equipped with the ā_p^n metric, in any 2-uniformly convex Banach space is of order min {n^(1/2 1/p),m^(1-2/p)}
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