Theorie der Chiralit�tsfunktionen

Ruch, Ernst; Schönhofer, Alfred

doi:10.1007/bf00532232

Cited by 169 publications

(53 citation statements)

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“…This result is motivated by finiteness questions in chemistry [10,16,17] and algebraic statistics [4] involving chains of invariant ideals I k (k = 1, 2, . .…”

Section: Theorem 11 Every Ideal Of R = A[x] Invariant Under S X Is mentioning

confidence: 99%

Finite generation of symmetric ideals

Aschenbrenner

Hillar

2007

Trans. Amer. Math. Soc.

136

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Abstract. Let A be a commutative Noetherian ring, and let R = A[X] be the polynomial ring in an infinite collection X of indeterminates over A. Let S X be the group of permutations of X. The group S X acts on R in a natural way, and this in turn gives R the structure of a left module over the group ring R[S X ]. We prove that all ideals of R invariant under the action of S X are finitely generated as R[S X ]-modules. The proof involves introducing a certain well-quasi-ordering on monomials and developing a theory of Gröbner bases and reduction in this setting. We also consider the concept of an invariant chain of ideals for finite-dimensional polynomial rings and relate it to the finite generation result mentioned above. Finally, a motivating question from chemistry is presented, with the above framework providing a suitable context in which to study it.

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“…This result is motivated by finiteness questions in chemistry [10,16,17] and algebraic statistics [4] involving chains of invariant ideals I k (k = 1, 2, . .…”

Section: Theorem 11 Every Ideal Of R = A[x] Invariant Under S X Is mentioning

confidence: 99%

Finite generation of symmetric ideals

Aschenbrenner

Hillar

2007

Trans. Amer. Math. Soc.

136

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“…A possibility to correlate the signs of the CD measurements for special transitions (the Cotton effect) to the absolute molecular configuration, using special classes of molecules, is based on the so called sector rules, helicity rules, or chirality functions [1,7,8] which have been developed over the last thirty years. Sector rules correspond to particular classes of molecules which are determined by decomposing the chiral molecule into an achiral perturbing group (a ligand), or several such groups, and an achiral skeleton [7,8] and then taking into consideration the symmetry of the latter. It is discussed below that in some cases very similar sector rules can also be derived for helical twisting power.…”

Section: Introductionmentioning

confidence: 99%

Helical twisting power and circular dichroism in nematic liquid crystals doped with chiral molecules

Osipov

Kuball

2001

The European Physical Journal E

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Explicit expressions for the helical twisting power of a chiral dopant in the nematic phase have been obtained in the mean field approximation taking into account chiral dispersion intermolecular interactions. The results of the theory enable one to explain a correlation between the signs of helical twisting power and circular dichroism of selected electronic transitions which have recently been established experimentally for some mono- and bis-aminoantroquinones. Helical twisting power is proportional to the pseudoscalar parameter that specifies the chirality of the dopant molecule in terms of its dipole and quadrupole matrix elements. This expression is simplified for a special class of molecules in which chirality is induced by a perturbing achiral group into an achiral skeleton. In this case both helical twisting power and circular dichroism are approximately proportional to some simple pseudoscalar functions that specify the location of the achiral perturbing group with respect to the symmetry planes of the unperturbed achiral skeleton. Simple sector rules have been proposed to determine the sign change of the helical twisting power associated with the change of location of the perturbing group

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“…The reciprocal 1 IT of the mixing temperature f always lies between l/r (1) and MT (1 \ This reflects nothing more than the concavity of S(U): Since entropy should increase by any equalization l/Thas to be "between" 1 IT (]) and 1/T (2) (in the sense of Figure 1! ).…”

Section: The Problemmentioning

confidence: 97%

“…The starting point of this paper is the concept of an order structure (partial order) for (thermodynamic) states of classical or quantum systems in very general state spaces as introduced independently by Ruch and Schönhofer [1] and Uhlmann [2]; see also [3]. There are various indications that this concept should allow a more detailed understanding of irreversibility.…”

Section: Introductionmentioning

confidence: 99%