Quantum Groups and Double Quiver Algebras

For a finite dimensional semisimple Lie algebra and a root q of unity in a field k, we associate to these data a double quiver . It is shown that a restricted version of the quantized enveloping algebras is a quotient of the double quiver algebra .*The author is partially supported by the National Science Foundation of China (Grant. 10271014) and Natural Science Foundation of Beijing City (grant. 1042001)     

Bridging the Length Scales: Micromechanics of Granular Media

Aristotle's statement that the whole is more than the sum of its parts aptly describes the essence of a granular material's rich and complex behaviour, which ultimately arises from internal mechanisms developed on many length scales. Recently, non-invasive experimental studies have given remarkable insight into the evolution of these mechanisms, thereby providing benchmarks and a unique opportunity for the theoretical modelling of these systems. This paper focuses on the challenges of capturing these multiscale mechanisms within the framework of continuum theory. In particular, a new approach toward developing a non-local micropolar constitutive model of granular media using micromechanics and internal variable theory is discussed. To demonstrate the predictive potential of these models, we present their application in the analysis of two fundamental problems to the mechanics of granular media: (i) formation and evolution of shear bands (the precursors of material failure), (ii) the classical Flamant problem. Finally, we briefly discuss the computational challenges in bridging the gap between micromechanical studies of granular media and the applications of continuum theory on the macro-scale via a finite element analysis of the flat punch problem. In practice, this problem is used to assess the load bearing capacity of a material and is fundamental to civil and structural engineering.     

Field Theory on Kappa-spacetime

A general formalism is developed, that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for the -deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable -product. Fields are elements of this function algebra. As an example, the Klein-Gordon equation is defined and derived from an action.     

On <Emphasis Type="Italic">osp</Emphasis>(<Emphasis Type="Italic">M</Emphasis>∣2<Emphasis Type="Italic">n</Emphasis>) Integrable Open Spin Chains

We consider open spin chains based on osp(M2n) Yangians and solve the reflection equations for some classes of reflection matrices, including the diagonal ones. Having then integrable open spin chains, we write the analytical Bethe Ansatz equations. More details and references can be found in D. Arnaudon et al.: Nucl. Phys B 668 (2003) 469 and 687 (2004) 257.     

De Broglie Tired Light Model and the Reality of the Quantum Waves

In the early 1960s of the 20th century de Broglie was able to explain the cosmological observable red shift, without ad hoc assumptions. Starting from basic quantum considerations he developed his tired light model for the photon. This model explains in a single and beautiful causal way the cosmological redshift without need of assuming the Big Bang and consequently a beginning for the universe. Evidence coming from Earth sciences seems also to confirm these ideas and furthermore concrete proposal of laboratorial scale experiments that can test the model are reviewed.     

Theoretical Study of Formamide Tautomers—A Discussion of Enol-Keto Isomerizations and Their Corresponding Energies

In order to gain insight into the formamide molecule, seven tautomers and twelve transition states are found after being modeled by the density function theory of Becke's three-parameter hybride (B3LYP) type and ab initio Möller–Plesset second-order perturbation (MP2)-type methods. The isomerization phenomena between enol-keto tautomers and transition states via internal rotation or the proton transfer process are surveyed. A localized analysis is also introduced to ascertain the bond character caused by the delocalization of electrons, which will force the formamide tautomers to become planar. The trans effect in the molecule increases molecular stability.     

Lipase-mediated deracemization of secondary 1-phenyl-substituted propargylic alcohols of different topology

Acetylation of (±)-1-phenylnon-2-yn-1-ol, (±)-1-phenylhept-1-yn-3-ol, and (±)-1-phenylundec-4-yn-3-ol ((±)-5) in the presence of lipase from Candida cylindracea (CCL) proceeds slowly to give products with ee 20%. The acetates of these alcohols are hydrolyzed in the presence of porcine pancreatic lipase (PPL) equally unsatisfactorily. The (⁶-arene)tricarbonylchromium complex of alcohol (±)-5 is acetylated in the presence of CCL up to 22% conversion to give (R)-acetate whose oxidative decomplexation followed by saponification results in alcohol (R)-(–)-5 with ee 95%. The configuration of alcohols (–)-5 and (+)-5 was determined by NMR spectroscopy of their esters with (R)- and (S)-Mosher"s acids.