Synthesis and characterization of a symmetric bis(7-hydroxyflavylium) containing a methyl viologen bridge

A symmetric bis(flavylium) constituted by two 7-hydroxyflavylium moieties linked by a methylviologen bridge was synthesized. The thermodynamic and kinetics of the network of chemical reactions involving bis(flavylium) and the model compound 7-hydroxy-4'-methylflavylium was completely characterized by means of direct and reverse pH jumps (stopped flow) and flash photolysis. Both compounds follow the usual pH-dependent network of chemical reactions of flavylium derivatives. The equilibrium species of the model compound are the flavylium cation (acidic species) and the trans-chalcone (basic species) with an apparent pK'(a)=2.85. In the case of the bis(flavylium) it was possible to characterize by (1)H NMR spectroscopy three species with different degrees of isomerization: all flavylium, flavylium-trans-chalcone, and all trans-chalcone. Representation of the time-dependent mole fraction distribution of these three forms after a pH jump from equilibrated solutions of all-flavylium cation (lower pH values) to higher pH values, shows that formation of trans-chalcone is not completely stochastic (two independent isomerizations), the isomerization of one flavylium showing a small influence on the isomerization of the other. The radical of the methyl viologen bridge is formed upon reduction of the bis(trans-chalcone) with dithionite. The system is reversible after addition of an oxidant in spite of the occurrence of some decomposition.     

A cancellation conjecture for free associative algebras

We develop a new method to deal with the Cancellation Conjecture of Zariski in different environments. We prove the conjecture for free associative algebras of rank two. We also produce a new proof of the conjecture for polynomial algebras of rank two over fields of zero characteristic.

     

A Hilbert-Nagata theorem in noncommutative invariant theory

Nagata gave a fundamental sufficient condition on group actions on finitely generated commutative algebras for finite generation of the subalgebra of invariants. In this paper we consider groups acting on noncommutative algebras over a field of characteristic zero. We characterize all the T-ideals of the free associative algebra such that the algebra of invariants in the corresponding relatively free algebra is finitely generated for any group action from the class of Nagata. In particular, in the case of unitary algebras this condition is equivalent to the nilpotency of the algebra in Lie sense. As a consequence we extend the Hilbert-Nagata theorem on finite generation of the algebra of invariants to any finitely generated associative algebra which is Lie nilpotent. We also prove that the Hilbert series of the algebra of invariants of a group acting on a relatively free algebra with a non-matrix polynomial identity is rational, if the action satisfies the condition of Nagata.

     

Binomial free resolutions for normal toric surfaces

We construct the minimal free resolution of the residue field over a normal toric surface.

     

Plasma enhanced synthesis of N doped vertically aligned carbon nanofibers on 3D graphene

Graphene and carbon nanotubes/fibers (CNT/CNF) hybrid structures are emerging as frontier materials for high-efficiency electronics, energy storage, thermoelectric, and sensing applications owing to the utilization of extraordinary electrical and physical properties of both nanocarbon materials. Recent advances show a successful improvement in the structure and surface area of layered graphene by incorporating another dimension and structural form—three-dimensional graphene (3DG). In this study, vertically aligned CNFs were grown using plasma enhanced chemical vapor deposition on a relatively new form of compressed 3DG. The latter was synthesized using a conventional thermal chemical vapor deposition. The resulting free-standing hybrid material is in-situ N doped during synthesis by ammonia plasma and is produced in the form of a hybrid paper. Characterization of this material was done using electrochemical and spectroscopic measurements. The N doped hybrid showed relatively higher surface area and improved areal current density in electrochemical measurements than compressed pristine 3DG, which makes it a potential candidate for use as an electrode material for supercapacitors, sensors, and electrochemical batteries.     

Multiplicities in the Trace Cocharacter Sequence of Two 4 × 4 Matrices

We find explicitly the generating functions of the multiplicities in the pure and mixed trace cocharacter sequences of two 4 × 4 matrices over a field of characteristic 0. We determine the asymptotic behavior of the multiplicities and show that they behave as polynomials of 14th degree.Partially supported by Grant MM-1106/2001 of the Bulgarian Foundation for Scientific Research.     

New types of unstable step-flow growth on Si(111)-(7 x 7) during molecular beam epitaxy: scaling and universality

New types of unstable homoepitaxial growth of vicinal surfaces are studied using ex situ atomic force microscopy. The growth features are two types of step bunching with straight step edges between 700 and 775 degrees C and one type of simultaneous bunching and meandering at 800 degrees C. The results of a quantitative size scaling analysis of the straight steps are discussed from the perspective of universality classes in bunching theory.     

R(1rho) relaxation for two-site chemical exchange: general approximations and some exact solutions

Analytic expressions for the nuclear magnetic spin relaxation rate constant for magnetization spin-locked in the rotating reference frame under an applied radiofrequency field, R(1rho), are obtained for two-site chemical exchange. The theoretical approach is motivated by Laguerre's method and obtains R(1rho) as the root of a (p1,q1) Padé approximant. The general formula for R(1rho) obtained by this approach is substantially simpler than existing expressions and is equally or slightly more accurate, in most cases. In addition, particular solutions for the R(1rho) rate constant are presented for two special cases: equal populations of the two exchanging sites, or placement of the radiofrequency carrier at the average resonance frequency of the two sites. The solutions are exact when the R1 and R2 relaxation rate constants are identical, and nearly exact under realistic experimental conditions.     

On the Reality of Minkowski Space

Should physicists deal with the question of the reality of Minkowski space (or any relativistic spacetime)? It is argued that they should since this is a question about the dimensionality of the world at the macroscopic level and it is physics that should answer it.