On the Structure of the C *-Algebra Generated by Toeplitz Operators with Piece-wise Continuous Symbols

We study the C ^*-algebra generated by Toeplitz operators with piece-wise continuous symbols acting on the Bergman space on the unit disk in . We describe explicitly each operator from this algebra and characterize Toeplitz operators which belong to the algebra. To the memory of G. S. Litvinchuk     

Synthesis of Hafnium(IV) Polyaminoacetates

The interaction of hafnium(IV) salts (oxide-dichloride, chloride, and bromide) with nitrilotriacetic acid (NTA), diethylenetriamminepentaacetic acid (DTPA), 1,2-diaminocyclohexanetetraacetic acid (CDTA), 1,3-dipropylmino-2-hydroxy N,N,N′,N′-tetraacetic acid (dpta), and N-(2-hydroxyethyl)ethylenediamine triacetic acid (HEDTA) has been studied. The corresponding complexes Na₂[Hf(NTA)₂]·3H₂O (1), Na[HfDTPA]·3H₂O (2), [HfCDTA(H₂O)₂] (3), and Na[Hf₂(dpta)₂]·7.5H₂O·0.5C₂H₅OH (4) have been isolated and characterized and their structures have been determined by single crystal X-ray diffraction. Biological studies of [HfCDTA(H₂O)₂] have shown that in 5% glucose solution this complex has low toxicity and good contrasting ability.     

Role of glueballs in non-perturbative quark–gluon plasma

Discussed is how non-perturbative properties of quark gluon plasma, recently discovered in RHIC experiment, can be related to the change of properties of scalar and pseudoscalar glueballs. We set up a model with the Cornwall–Soni's glueball–gluon interaction, which shows that the pseudoscalar glueball becomes massless above the critical temperature of deconfinement phase transition. This change of properties gives rise to the change of sign of the gluon condensate at T>Tc$T>T_c$. We discuss the other physical consequences resulting from the drastic change of the pseudoscalar glueball mass above the critical temperature.     

On the Root Functions of General Elliptic Boundary Value Problems

We consider a boundary value problem for an elliptic differential operator of order 2m in a domain . The boundary of is smooth outside a smooth manifold Y of dimension 0 ≤ q < n − 1, and bears edge type singularities along Y . The Lopatinskii condition is assumed to be fulfilled on the smooth part of . The corresponding spaces are weighted Sobolev spaces , and this allows one to define ellipticity of weight γ for the problem. The resolvent of the problem is assumed to possess rays of minimal growth. The main result says that if there are rays of minimal growth with angles between neighbouring rays not exceeding π(γ + 2m)/n, then the root functions of the problem are complete in . In the case of second order elliptic equations the results remain true for all domains with Lipschitz boundary. Communicated by Michael Shapiro. Submitted: May 24, 2006; Accepted: June 15, 2006     

Fabrication of Silicon Carbide Nanocrystals by Electrical Discharge and Laser-Induced Processes in Solution

Plasma Chemistry and Plasma Processing - The capabilities of the liquid assisted electrical discharge technique with additional laser irradiation of colloids for the synthesis of SiC nanocrystals...     

Gold nanoparticle enhanced charge transfer in thin film assemblies of porphyrin-fullerene dyads

Photoinduced vectorial electron transfer in a molecularly organized porphyrin-fullerene (PF) dyad film is enhanced by the interlayer charge transfer from the porphyrin moiety of the dyad to an octanethiol protected (dcore approximately 2 nm) gold nanoparticle (AuNP) film. By using the time-resolved Maxwell displacement charge (TRMDC) method, the charge separation distance was found to increase by 5 times in a multilayer film structure where the gold nanoparticles face the porphyrin moiety of the dyad, that is, AuNP|PF, compared to the case of the PF layer alone. Films were assembled by the Langmuir-Blodgett (LB) method using octadecylamine (ODA) as the matrix compound. Atomic force microscopy (AFM) images of the monolayers revealed that AuNPs are arranged into continuous, islandlike structures and PF dyads form clusters. The porphyrin reference layer was assembled with the AuNP layer to gain insight on the interaction mechanism between porphyrin and gold nanoparticles. Interlayer electron transfer was also observed between the AuNPs and porphyrin reference, but the efficiency is lower than that in the AuNP|PF film. Fluorescence emission of the reference porphyrin is slightly quenched, and fluorescence decay becomes faster in the presence of AuNPs. The proposed mechanism for the electron transfer in the AuNP|PF film is thus the primary electron transfer from the porphyrin to the fullerene followed by a secondary hole transfer from the porphyrin to the AuNPs, resulting in an increased charge separation distance and enhanced photovoltage.     

Ytterbocenes as one- and two-electron reductants in their reactions with diazadienes: YbIII mixed-ligand bent-sandwich complexes containing a dianion of diazabutadiene

Ytterbocene [Yb(C(5)MeH(4))(2)(thf)(2)] reacts with diazabutadiene 2,6-iPr(2)C(6)H(3)-N=CH-CH=N-C(6)H(3)iPr(2)-2,6 (DAD) as a one-electron reductant to afford a bis(cyclopentadienyl) Yb(III) derivative containing a DAD radical anion [Yb(C(5)MeH(4))(2)(dad(-.))]. However, ytterbocenes [YbCp*(2)(thf)(2)] (Cp*=C(5)Me(5), C(5)Me(4)H) coordinated by sterically demanding cyclopentadienyl ligands act as two-electron reductants in their reactions with DAD. These reactions occur by abstraction of one Cp* ring and result in the formation of novel Yb(III) mixed-ligand bent-sandwich complexes, [YbCp*(dad)(thf)], in which the dianion of DAD has an uncommon terminal eta(4)-coordination to the ytterbium atom. The variable-temperature magnetic measurements of complex [Yb(C(5)Me(5))(dad)(thf)] suggest the existence of redox tautomerism for this compound.     

Emulsification in turbulent flow 2. Breakage rate constants

Systematic experimental study of the effects of several factors on the breakage rate constant, k(BR), during emulsification in turbulent flow is performed. These factors are the drop size, interfacial tension, viscosity of the oil phase, and rate of energy dissipation in the flow. As starting oil-water premixes we use emulsions containing monodisperse oil drops, which have been generated by the method of membrane emulsification. By passing these premixes through a narrow-gap homogenizer, working in turbulent regime of emulsification, we study the evolution of the number concentration of the drops with given diameter, as a function of the emulsification time. The experimental data are analyzed by a kinetic scheme, which takes into account the generation of drops of a given size (as a result of breakage of larger drops) and their disappearance (as a result of their own breakage process). The experimental results for k(BR) are compared with theoretical expressions from the literature and their modifications. The results for all systems could be described reasonably well by an explicit expression, which is a product of: (a) the frequency of collisions between drops and turbulent eddies of similar size, and (b) the efficiency of drop breakage, which depends on the energy required for drop deformation. The drop deformation energy contains two contributions, originating from the drop surface extension and from the viscous dissipation inside the breaking drop. In the related subsequent paper, the size distribution of the daughter drops formed in the process of drop breakage is analyzed for the same experimental systems.     

Commutative Algebras of Toeplitz Operators on the Reinhardt Domains

Let D be a bounded logarithmically convex complete Reinhardt domain in centered at the origin. Generalizing a result for the one-dimensional case of the unit disk, we prove that the C ^*-algebra generated by Toeplitz operators with bounded measurable separately radial symbols (i.e., symbols depending only on is commutative. We show that the natural action of the n-dimensional torus defines (on a certain open full measure subset of D) a foliation which carries a transverse Riemannian structure having distinguished geometric features. Its leaves are equidistant with respect to the Bergman metric, and the orthogonal complement to the tangent bundle of such leaves is integrable to a totally geodesic foliation. Furthermore, these two foliations are proved to be Lagrangian. We specify then the obtained results for the unit ball.     

Methyl rotation barriers in proteins from 2H relaxation data. Implications for protein structure

Side-chain 2H and backbone 15N relaxation data have been collected at multiple temperatures in the samples of the SH3 domain from alpha-spectrin. Combined analyses of the data allowed for determination of the temperature-dependent correlation times tauf characterizing fast methyl motion. Molecular dynamics simulations confirmed that tauf are dominated by methyl rotation; the corresponding activation energies approximate methyl rotation barriers. For 33 methyl groups in the alpha-spectrin SH3 domain the average barrier height was thus determined to be 2.8 +/- 0.9 kcal/mol. This value is deemed representative of the "fluid" hydrophobic protein core where some barriers are increased and others are lowered because of the contacts with surrounding atoms, but there is no local order that could produce systematically higher (lower) barriers. For comparison, the MD simulation predicts the average barrier of 3.1 kcal/mol (calculated via the potential of mean force) or 3.4-3.5 kcal/mol (rigid barriers after appropriate averaging over multiple MD snapshots). The latter result prompted us to investigate rigid methyl rotation barriers in a series of NMR structures from the Protein Databank. In most cases the barriers proved to be higher than expected, 4-6 kcal/mol. To a certain degree, this is caused by tight packing of the side chains in the NMR structures and stems from the structure calculation procedure where the coordinates are first annealed toward the temperature of 0 K and then subjected to energy minimization. In several cases the barriers >10 kcal/mol are indicative of van der Waals violations. The notable exceptions are (i) the structures solved using the GROMOS force field where tight methyl packing is avoided (3.0-3.6 kcal/mol) and (ii) the structure solved by means of the dynamic ensemble refinement method (Lindorff-Larsen, K.; Best, R. B.; DePristo, M. A.; Dobson, C. M.; Vendruscolo, M. Nature 2005, 433, 128) (3.5 kcal/mol). These results demonstrate that methyl rotation barriers, derived from the experiments that are traditionally associated with studies of protein dynamics, can be also used in the context of structural work. This is particularly interesting in view of the recent efforts to incorporate dynamics data in the process of protein structure elucidation.