A Brief Account on Lagrange’s Algebraic Identity

In Indiscrete Thoughts [18], G.-C. Rota remarked, ??The mystery, as well as the glory of mathematics, lies not so much in the fact that abstract theories do turn out to be useful in solving problems, but, wonder of wonders, in the fact that a theory meant for one type of problem is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended. These coincidences occur so frequently, that they must belong to the essence of mathematics.?? Indeed, it happens often that abstract mathematics leads to concrete applications, and real-life problems constitute a source of inspiration for sophisticated theories. The strong synergy between pure mathematics and its applications advocates for teaching methods that intertwine physical intuition with mathematical abstraction, and recognize the universality of mathematical laws throughout the sciences.     

Tapered plasmonic waveguides with efficient and broadband field transmission

In this paper we suggest, numerically simulate and discuss a tapered plasmonic nanostructure which allows efficient transmission of the wave beam energy into a weakly subwavelength (λ/4 … λ/2) spatial region within a broad frequency range. The frequency stable location of this region becomes possible due to unusual plasmonic modes we have theoretically revealed and used. Our structure is promising for prospective transducers between conventional optical waveguides and subwavelength nanoguides or nanocircuits.     

Family constraining of iterative algorithms

In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image processing situations when a single constraining operator was used. In the field of image reconstruction from projections a priori information about the original image, such as smoothness or that it belongs to a certain closed convex set, may be used to improve the reconstruction quality. We study here constraining of iterative processes by a family of operators rather than by a single operator.     

Slow dynamics of a colloidal lamellar phase

We used x-ray photon correlation spectroscopy to study the dynamics in the lamellar phase of a platelet suspension as a function of the particle concentration. We measured the collective diffusion coefficient along the director of the phase, over length scales down to the interparticle distance, and quantified the hydrodynamic interaction between the particles. This interaction sets in with increasing concentration and can be described qualitatively by a simplified model. No change in the microscopic structure or dynamics is observed at the transition between the fluid and the gel-like lamellar phases.     

From a cycloheptatrienylzirconium allyl complex to a cycloheptatrienylzirconium imidazolin-2-iminato "pogo stick" complex with imido-type reactivity

The reaction of the cycloheptatrienylzirconium half-sandwich complex [(η(7)-C(7)H(7))ZrCl(tmeda)] (1) (tmeda = N,N,N',N'-tetramethylethylenediamine) with Li(Im(Dipp)N), generated from bis(2,6-diisopropylphenyl)imidazolin-2-imine (Im(Dipp)NH) with methyllithium, yields the imidazolin-2-iminato complex [(η(7)-C(7)H(7))Zr(Im(Dipp)N)(tmeda)] (2). The corresponding tmeda-free complex [(η(7)-C(7)H(7))Zr(Im(Dipp)N)] (5) can be synthesized via the 1,3-bis(trimethylsilyl)allyl complex [(η(7)-C(7)H(7))Zr{η(3)-C(3)H(3)(TMS)(2)}(THF)] (3; TMS = SiMe(3)), which undergoes an acid-base reaction with Im(Dipp)NH to form 5 and 1,3-bis(trimethylsilyl)propene. 5 exhibits an unusual one-legged piano stool ("pogo stick") geometry with a particularly short Zr-N bond of 1.997(2) ?. Addition of 2,6-dimethylphenyl or tert-butyl isocyanide affords the complexes [(η(7)-C(7)H(7))Zr(Im(Dipp)N)(CNR)] (R = o-Xy, 6; R = t-Bu, 7), while the reaction with 2,6-dimethylphenyl isocyanate results in a [2 + 2] cycloaddition to form the ureato(1-) complex [(η(7)-C(7)H(7))Zr{Im(Dipp)N(C═O)N-o-Xy}] (8). 5 can also act as an initiator for the ring-opening polymerization of ε-caprolactone. These reactivity patterns together with density functional theory calculations reveal a marked similarity of the bonding in imidazolin-2-iminato and conventional imido transition-metal complexes.     

Influence of Cyclodextrins on the Kinetics of Oxidation of Amino Acids and BSA by Hydrazyl Radicals

The kinetics of oxidation of amino acids (Arg, His, Lys, Phe, Thr and Tyr), a dipeptide (Gly-His), and BSA (bovine serum albumin) by two persistent water soluble free radicals of the hydrazyl type has been studied.The rate decreases in the order Arg>Lys>Tyr>Thr>HisBSAPheGly-His with bothfree radicals. Addition to the reaction mixture of - and -cyclodextrin decreases the oxidation rate, probably due to amino acidencapsulation in the cyclodextrin cavity. -Cyclodextrin protects more efficiently against oxidation than -cyclodextrin.     

The Cu- and Zn-complex-catalyzed methanolysis of the chemical warfare nerve agents soman,sarin, and VX

The catalytic methanolysis of the chemical warfare nerve agents soman, sarin, and VX was investigated by using Cu or Zn complexes. Although VX withstood decontamination, the decomposition yield being around 96%, the soman and sarin deposited on different surfaces were almost fully destroyed under ambient conditions. The catalytic tests performed on a wide range of contaminated surfaces confirm the activity of the investigated catalytic systems, these complexes being suitable, from an economical point of view, for use in the formulation of a possible decomposition kit with military or civilian applicability.     

Syndiospecific polymerization of styrene with BzCpTiCl3 and methylaluminoxane as cocatalysts

Benzyl cyclopentadienyl titanium trichloride (BzCpTiCl₃) was synthesized from benzyl bromide, cyclopentadienyl lithium, and titanium tetrachloride and used in combination with methylaluminoxane (MAO) for the syndiospecific polymerization of styrene. Kinetic measurements of the polymerization were carried out at different temperatures. The polymerization with BzCpTiCl₃/MAO differs from the polymerization with cyclopentadienyl titanium trichloride in its behavior toward the Al/Ti ratio. In addition, high activities are observed at high Al/Ti ratios. By analyzing the polymerization runs and the physical properties of the polymers with differential scanning calorimetry, ¹³C NMR spectroscopy, wide‐angle X‐ray scattering measurements, and gel permeation chromatography, we found that the phenyl ring coordinates to the titanium atom during polymerization. Other known substitutions of the cyclopentadienyl ring (V. Scholz, Dissertation, University of Hamburg, 1998) in principle influence the polymerization activity. The physical properties of the polymers produced by the catalysts already known are nearly identical. BzCpTiCl₃ is the first catalyst that leads to polystyrene obviously different from the polystyrene produced by other highly active catalysts. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2805–2812, 2001     

Surface and electrochemical analysis for the understanding of TiO2 nanopores/nanotubes changes in post‐elaboration treatment

The electrochemical stability of TiO₂ nanoarchitecture fabricated in fluoride electrolyte presented in this paper is related to 2D and 3D geometries that present a shift from nanopores toward nanotubes. The fabrication conditions involve a 60 V applied voltage for 2 hours of anodizing in order to create the ordered structures, in a mixture of low‐water glycerol electrolyte and fluoride. With the use of different ultrasonication times, a variety of nanotubes/nanopores were observed. The surface interfacial aspects were investigated mainly by surface microscopy and hydrophilic/hydrophobic balance for the grown structures ultrasonicated at various periods of time. The electrochemical behavior of the nanotube‐structured surface was performed by potentiodynamic evaluation and electrochemical impedance spectroscopy in a simulated body fluid solution. As a most important result, all surface analysis and electrochemical data interpretation permitted the proposition of a model for elaboration of different nanostructures from nanopores to nanotubes. These different surface nanoarchitectures were obtained as a result of ultrasonication at various periods of time. Copyright © 2010 John Wiley & Sons, Ltd.