Group theory of constrained reaction mechanisms

1985 ◽  
Vol 63 (7) ◽  
pp. 1972-1975
Author(s):  
Paul G. Mezey
Keyword(s):  
Group Theory ◽  
Potential Energy ◽  
Algebraic Structure ◽  
Reaction Mechanisms ◽  
One Dimensional ◽  
The Family ◽  
The One ◽  
Energy Hypersurface ◽  
Potential Energy Hypersurface

It is shown that the family of all possible reaction mechanisms on a given potential energy hypersurface, which reaction mechanisms are constrained by a localstabilitycriterion, has an algebraic structure. The fundamental relations among all such "λ-constrained" reaction mechanisms are described in terms of a group, the one dimensional homotopygroup π1(Y). In contrast with the energy-dependentgroup π1(F) of fundamentalreactionmechanisms, proposed earlier for the lowenergydomainsF of potential energy hypersurfaces, the new group π1(Y) is fully determined by the distributionofcatchmentregions, representingchemicalspecies on the potential energy hypersurface.

scholarly journals LOCAL FRACTIONAL SUPERSYMMETRY FOR ALTERNATIVE STATISTICS

1996 ◽  
Vol 11 (11) ◽  
pp. 899-913 ◽  
Author(s):  
N. FLEURY ◽  
M. RAUSCH DE TRAUBENBERG
Keyword(s):  
Group Theory ◽  
Braid Group ◽  
Equation Of Motion ◽  
Coset Space ◽  
One Dimensional ◽  
The One

A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to obtain a local fractional supersymmetry, i.e. a fractional supergravity which is then quantized à la Dirac to obtain an equation of motion for a particle which is in a representation of the braid group and should describe alternative statistics. A formulation invariant under general reparametrization is given by means of a curved fractional superline.

scholarly journals Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 417 ◽  
Author(s):  
Hu Zhao ◽  
Hong-Ying Zhang
Keyword(s):  
Algebraic Structure ◽  
Rough Sets ◽  
Lattice Structure ◽  
Single Domain ◽  
One Dimensional ◽  
Basic Properties ◽  
Approximation Operators ◽  
Rough Approximation ◽  
The One ◽  
Comprehensive Study

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied. However, they did not do a comprehensive study on the algebraic structure of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators. In the present paper, we will provide the lattice structure of the pessimistic multigranulation neutrosophic rough approximation operators. In particular, in the one-dimensional case, for special neutrosophic relations, the completely lattice isomorphic relationship between upper neutrosophic rough approximation operators and lower neutrosophic rough approximation operators is proved.

scholarly journals Gas-phase reaction between calcium monocation and fluoromethane: Analysis of the potential energy hypersurface and kinetics calculations

2009 ◽  
Vol 131 (14) ◽  
pp. 144309 ◽  
Author(s):  
Adrián Varela-Álvarez ◽  
V. M. Rayón ◽  
P. Redondo ◽  
C. Barrientos ◽  
José A. Sordo
Keyword(s):  
Potential Energy ◽  
Gas Phase ◽  
Phase Reaction ◽  
Gas Phase Reaction ◽  
Energy Hypersurface ◽  
Potential Energy Hypersurface

Integration of one-dimensional equations of motions

2020 ◽  
pp. 79-90
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Potential Energy ◽  
Field Change ◽  
One Dimensional ◽  
System A ◽  
Small Correction ◽  
The Law ◽  
The One ◽  
The Given ◽  
Equations Of Motions

If the potential energy is independent of time, the energy of the system remains constant during the motion of a closed system. A system with one degree of freedom allows for the determination of the law of motion in quadrature. In this chapter, the authors consider motion of the particles in the one-dimensional fields. They discuss also how the law and the period of a particle moving in the potential field change due to adding to the given field a small correction.

A theoretical approach to the acid-catalyzed hydration of the carbonyl group: the case of formaldehyde

1991 ◽  
Vol 69 (9) ◽  
pp. 1376-1387 ◽  
Author(s):  
Daniel Peeters ◽  
Georges Leroy
Keyword(s):  
Reaction Mechanism ◽  
Potential Energy ◽  
Water Molecules ◽  
Hydration Reaction ◽  
Second Derivatives ◽  
Hydrated Proton ◽  
Energy Reaction ◽  
Derivatives Of ◽  
Energy Hypersurface ◽  
Potential Energy Hypersurface

The analysis of the hydration of formaldehyde in the presence of a hydrated proton was performed. Molecular quantum chemistry methods were used to explore the potential energy hypersurface. Calculations were performed at RHF-4-31G level. The structures were obtained through the use of first and second derivatives of the potential energy hypersurface thereby guaranteeing the nature of the extremum. The incidence of one or two water molecules on the reaction is discussed. It has been found that a low energy reaction path exists when the hydration process is catalyzed by a proton and two water molecules. The reaction mechanism rests on successive addition/elimination processes and reveals the respective roles of the oxygen lone pairs and of the C=O double bond upon the mechanism. Key words: ab initio calculations, carbonyl reactivity, acid catalysis, hydration, reaction mechanism.

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