IMBEDDING OF TRANSFORMATION GROUPS IN AFFINE ONES AND RENORMALIZATION OF TWO-DIMENSIONAL HOMOGENEOUS σ-MODELS

1993 ◽  
Vol 08 (31) ◽  
pp. 2937-2942
Author(s):  
A. V. BRATCHIKOV
Keyword(s):  
Homogeneous Space ◽  
Transformation Group ◽  
Affine Group ◽  
Coupling Constants ◽  
Transformation Groups ◽  
Two Dimensional

The BLZ method for the analysis of renormalizability of the O(N)/O(N − 1) model is extended to the σ-model built on an arbitrary homogeneous space G/H and in arbitrary coordinates. For deriving Ward-Takahashi (WT) identities an imbedding of the transformation group G in an affine group is used. The structure of the renormalized action is found. All the infinities can be absorbed in a coupling constants renormalization and in a renormalization of auxiliary constants which are related to the imbedding.

Structural studies of digitoxin and related cardenolides by two-dimensional NMR

1990 ◽  
Vol 68 (2) ◽  
pp. 272-277 ◽  
Author(s):  
Torbjörn Drakenberg ◽  
Peter Brodelius ◽  
Deane D. McIntyre ◽  
Hans J Vogel
Keyword(s):  
Nmr Spectroscopy ◽  
Nmr Spectra ◽  
Chair Conformation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Structural Studies ◽  
Solution Conformation ◽  
Phase Sensitive ◽  
Multiple Relay ◽  
C Nmr

The 1H and 13C NMR spectra of the cardenolides digitoxigenin, digoxigenin, digitoxin, and mono- and bis-digitoxigenin digitoxosides have been completely assigned by two-dimensional NMR spectroscopy. The techniques used include phase-sensitive COSY, multiple relay COSY, and carbon–proton correlation (HETCOR and HMQC) spectra. Various aspects of the solution conformation of the steroid moiety of digitoxin and digoxigenin could be determined from coupling constants and NOE difference experiments and they are indicative of an all-chair conformation. The carbohydrate rings in digitoxin and the mono- and bis-digitoxigenin digitoxosides are also in the chair conformation. Keywords: cardenolides, digitoxigenin, digitoxin, 2-dimensional NMR, conformational analysis.

S-matrix Theory

2020 ◽  
pp. 622-675
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Matrix Theory ◽  
Point Of View ◽  
Integrable Models ◽  
Geometrical Interpretation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Recursive Structure ◽  
Mathematical Point ◽  
S Matrix ◽  
Dynamical Principle

Chapter 17 discusses the S-matrix theory of two-dimensional integrable models. From a mathematical point of view, the two-dimensional nature of the systems and their integrability are the crucial features that lead to important simplifications of the formalism and its successful application. This chapter deals with the analytic theory of the S-matrix of the integrable models. A particular emphasis is put on the dynamical principle of bootstrap, which gives rise to a recursive structure of the amplitudes. It also covers several dynamical quantities, such as mass ratios or three-coupling constants, which have an elegant mathematic formulation that is also of easy geometrical interpretation.

A Mapping Problem and Jp-Index. I

1970 ◽  
Vol 22 (4) ◽  
pp. 705-712 ◽  
Author(s):  
Masami Wakae ◽  
Oma Hamara
Keyword(s):  
Cyclic Group ◽  
Prime Order ◽  
Transformation Group ◽  
Classical Group ◽  
Cohomology Ring ◽  
Transformation Groups ◽  
Normal Space ◽  
Mapping Problem ◽  
Countable Basis ◽  
Kakutani Theorem

Indices of normal spaces with countable basis for equivariant mappings have been investigated by Bourgin [4; 6] and by Wu [11; 12] in the case where the transformation groups are of prime order p. One of us has extended the concept to the case where the transformation group is a cyclic group of order pt and discussed its applications to the Kakutani Theorem (see [10]). In this paper we will define the Jp-index of a normal space with countable basis in the case where the transformation group is a cyclic group of order n, where n is divisible by p. We will decide, by means of the spectral sequence technique of Borel [1; 2], the Jp-index of SO(n) where n is an odd integer divisible by p. The method used in this paper can be applied to find the Jp-index of a classical group G whose cohomology ring over Jp has a system of universally transgressive generators of odd degrees.

Convenient Sign Determination of Various Coupling Constants in Alkynylplatinum(II) Phosphine Complexes

1991 ◽  
Vol 46 (1) ◽  
pp. 35-38 ◽  
Author(s):  
Bernd Wrackmeyer
Keyword(s):  
Coupling Constants ◽  
Two Dimensional ◽  
Model Compounds ◽  
Standard Equipment ◽  
Phosphine Complexes ◽  
Sign Determination

(1)The utilization of two-dimensional (2 D) 13C /1H , 31P/1H and 195Pt/1H heteronuclear shift correlations for the sign determination of various coupling constants [e.g., 2J(31PPt13C) > 0 (trans), 2J(31PPt13C) < 0 (cis), 3J( 31PPtC13C) > 0 (cis, trans), 4J(31PPtCC1H ) > 0 (trans), 4J(31PCC1H ) < 0 (cis), 3J(195PtCC1H ) > 0, 2J(31PC1H ) < 0, etc.] is demonstrated, using standard equipment. The complexes [trans-(Bu3P)2Pt(C ≡ C -H)2] and [cis-(Et2PCH2CH2PEt2)Pt(C ≡ C - H)2] (2) serve as model compounds.

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