Evidence of formation of H2CN by a concerted reaction

We have investigated the possibility of formation of H₂CN by the concerted reaction H₂ + CN → H₂CN at energy regimes of over 60 kcal/mol relative to the global minimum. We have concluded that this concerted reaction is possible in principle provided that H₂ is vibrationally excited.     

Noncommutative Geometry and Integrable Models

A construction of conservation laws for -models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing theordinary calculus of differential forms with other differentialcalculi and introducing an analogue of the Hodge operator on thelatter. The general method is illustrated with several examples.     

From nonassociativity to solutions of the KP hierarchy

A recently observed relation between ‘weakly nonassociative’ algebras $\mathbb{A}$ (for which the associator ( $\mathbb{A},\mathbb{A}^2 ,\mathbb{A}$ ) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus $\mathbb{A}$ ′ of { $\mathbb{A}$ ) is recalled. For any such algebra there is a nonassociative hierarchy of ODEs, the solutions of which determine solutions of the KP hierarchy. In a special case, and with matrix algebra $\mathbb{A}$ ′, this becomes a matrix Riccati hierarchy which is easily solved. The matrix solution then leads to solutions of the scalar KP hierarchy. We discuss some classes of solutions obtained in this way.     

Algebraic identities associated with KP and AKNS hierarchies

Explicit KP and AKNS hierarchy equations can be constructed from a certain set of algebraic identities involving a quasi-shuffle product. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Moral coherence,moral worth and explanations of moral motivation

Moral internalism and moral externalism compete over the best explanation of the link between judgment and relevant motivation but, it is argued, they differ at best only verbally. The internalist rational-conceptual nature of the link’ as accounted by M. Smith in The Moral Problem is contrasted to the externalist, also rational, link that requires in addition support from the agent’s psychological-dispositional profile; the internalist link, however, is found to depend crucially on a, similarly to the externalist, psychologically ‘loaded’ profile. It is also argued that the differentiation of the two competing explanations is insufficient partly because they both fail to consider crucial quantitative parameters of the judgment-motivation link. Such parameters become very important particularly in the light of Smith’s claim that this link is grounded on the observable “striking fact” where changes in the set of one’s moral beliefs systematically bring about changes in one’s moral behavior. Examples of algorithms measuring moral coherence and moral worth are provided to serve as evidence for what it comes down to, vis-à-vis the alleged fact, only a verbal dispute between the two camps. Finally, the ‘misfiring’ of these explanations is understood in connection to the irreducibility of concepts such as ‘moral worth’, and/or, ‘moral sensitivity’.     

Moral Sensitivity and Desire Attachment: In What Sense are they Constituents of One’s Rational Profile?

A quantitative interpretation is given of the (in)coherence that moral agents experience as a tension between their ordered moral judgments over n physically incompatible actions, and the competitive ordering of motivating intensities (or, desires). Then a model describing one’s tendency to reduce the experienced in-coherence is constructed. In this model, moral sensitivity (S) and desire attachment (e) function as primitives that motivate from opposing perspectives the reduction of incoherence. Two distinct sub-processes of this reduction are therefore initiated by (S) and (e) co-ordinated (more or less efficiently) by the agent’s degree of rationality (R) characteristic of her capacity to handle such internal tensions. This process ends when a new equilibrium between what motivates and what resists (further) reduction has been reached. A macro-equilibrium is described involving (R) constrained by weakness-of-will (W _w ). A reinterpretation of the Aristotelian characters (enkratês, akratês, etc.) and an exegesis of Hume’s ‘Calm Passions’ follow as applications.

Predissociation lifetime of the 1σ g 2 2σ g diabatic state of He 2 + : a one-channel approach

Summary This work is concerned with the application of a one-channel model to obtaining predissociation lifetimes and transition rates in a system of crossing diabatic states. The calculation focuses on the first shape resonance of the 1 _g ² 2 _g diabatic state of He ₂ ⁺ , which is relatively stable with respect to tunneling. This resonance predissociates as a result of the 1 _g ² 2 _g state being crossed by the 1 _g 1 _u ² dissociative diabatic state near the resonance level. We have estimated its predissociation lifetime to be of the order of 10^–11 s.     

Can methylene amidogene and its isomers be formed by a concerted reaction?

We have explored the possibility of occurrence of the concerted formation of the methylene amidogene radical and its cis isomer from H₂ and CN at energy regimes of over 60 kcal/mol relative to the ground state of the radical. We have concluded that for the cases of parallel and perpendicular orientations of H₂ and CN, a concerted reaction is possible in principle provided that H₂ is vibrationally excited. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Connes' Distance Function on One-Dimensional Lattices

We show that there is an operator with a simplegeometric significance which yields the ordinarygeometry of an open and closed linear equidistantlattice via Connes' distance function. Some relatedaspects of distances on graphs are brieflydiscussed.     

Noncommutative NLS equation

In the framework of noncommutative field theory we discuss a deformation (ncNLS) of the nonlinear Schrödinger (NLS) equation. In particular, a first order equation in the deformation parameter is obtained which generates a (Seiberg-Witten-type) map from NLS to ncNLS solutions.