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Separation Theorem (separation + theorem)

Distribution by Scientific Domains

Business, Economics, Finance and Accounting	50%

Selected Abstracts

A note on Bar Induction in Constructive Set Theory

MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 3 2006
Michael Rathjen
Abstract Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive Zermelo-Fraenkel Set Theory, CZF. It is shown that CZF augmented by decidable Bar Induction proves the 1-consistency of CZF. This answers a question of P. Aczel who used Bar Induction to give a proof of the Lusin Separation Theorem in the constructive set theory CZF. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

How many-body perturbation theory (MBPT) has changed quantum chemistry

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2009
Werner KutzelniggArticle first published online: 26 AUG 200
Abstract The history of many-body perturbation theory (MBPT) and its impact on Quantum Chemistry is reviewed, starting with Brueckner's conjecture of a linked-cluster expansion and the time-dependent derivation by Goldstone of such an expansion. A central part of this article is the time-independent formulation of quantum chemistry in Fock space and its diagrammatic representation including the particle-hole picture and the inversion of a commutator. The results of the time-independent derivation of MBPT are compared with those of Goldstone. It is analyzed which ingredients of Goldstone's approach are decisive. The connected diagram theorem is derived both in a constructive way based on a Lie-algebraic formulation and a nonconstructive way making use of the separation theorem. It is discussed why the Goldstone derivation starting from a unitary time-evolution operator, ends up with a wave operator in intermediate normalization. The Møller,Plesset perturbation expansions of Bartlett and Pople are compared. Examples of complete summations of certain classes of diagrams are discussed, for example, that which leads to the Bethe-Goldstone expansion. MBPT for energy differences is analyzed. The paper ends with recent developments and challenges, such as the generalization of normal ordering to arbitrary reference states, contracted Schrödinger k -particle equations and Brillouin conditions, and finally the Nakatsuji theorem and the Nooijen conjecture. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source]

CONSISTENT MARKET EXTENSIONS UNDER THE BENCHMARK APPROACH

MATHEMATICAL FINANCE, Issue 1 2009
Damir Filipovi
The existence of the growth optimal portfolio (GOP), also known as the Kelly portfolio, is vital for a financial market to be meaningful. The GOP, if it exists, is uniquely determined by the market parameters of the primary security accounts. However, markets may develop and new security accounts become tradable. What happens to the GOP if the original market is extended? In this paper we provide a complete characterization of market extensions which are consistent with the existence of a GOP. We show that a three fund separation theorem applies for the extended GOP. This includes, in particular, the introduction of a locally risk free security, the savings account. We give necessary and sufficient conditions for a consistent exogenous specification of the prevailing short rates. [source]

OPTIMAL EXPORT AND HEDGING DECISIONS WHEN FORWARD MARKETS ARE INCOMPLETE

BULLETIN OF ECONOMIC RESEARCH, Issue 1 2007
Kit Pong Wong
D81; F23; F31 ABSTRACT This paper examines the behaviour of the competitive firm that exports to two foreign countries under multiple sources of exchange rate uncertainty. There is a forward market between the home currency and one foreign country's currency, but there are no hedging instruments directly related to the other foreign country's currency. We show that the separation theorem holds when the firm optimally exports to the foreign country with the currency forward market. The full-hedging theorem holds either when the firm exports exclusively to the foreign country with the currency forward market or when the relevant spot exchange rates are independent. In the case that the relevant spot exchange rates are positively (negatively) correlated in the sense of regression dependence, the firm optimally opts for a short (long) forward position for cross-hedging purposes. [source]