Macdonald polynomials from Sklyanin algebras: A conceptual basis for thep-adics-quantum group connection

We establish a previously conjectured connection betweenp-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which interpolate between the zonal spherical functions of related real andp-adic symmetric spaces. The elliptic quantum algebras underlie theZ _n -Baxter models. We show that in then limit, the Jost function for the scattering offirst level excitations in the 1+1 dimensional field theory model associated to theZ _n -Baxter model coincides with the Harish-Chandra-likec-function constructed from the Macdonald polynomials associated to the root systemA ₁. The partition function of theZ ₂-Baxter model itself is also expressed in terms of this Macdonald-Harish-Chandrac-function, albeit in a less simple way. We relate the two parametersq andt of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular thep-adic regimes in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of q-deforming Euler products.Work supported in part by the NSF: PHY-9000386     

Rigorous bounds on the storage capacity of the dilute Hopfield model

We study a neural network model consisting ofN neurons where a dendritic connection between each pair of neurons exists with probabilityp and is absent with probability 1-p. For the Hopfield Hamiltonian on such a network, we prove that ifp c[(lnN)/N]^1/2, the model can store at leastm= _cpN patterns, where _c 0.027 ifc 3 and decreases proportional to 1/(–lnc) forc small. This generalizes the results of Newman for the standard Hopfield model.     

Substituent dependence of the d-d transition band in the electronic absorption spectra of arylferrocenes and the corresponding arylferricenium salts

The electronic absorption spectra of 22 arylferrocenes and their arylferricenium salts with pentacyanopropenide (PCNP) were recorded. The attemptedHammett correlation of _max of the d-d transition bands of arylferrocenes revealed that this band is substituent dependent only for strong electron-withdrawing substituents. Excellent correlation of _max of the d-d transition bands with ⁺ constants was found in the case of arylferricenium cations. Good correlations of _max was also found with theE _1/2 oxidation potentials measured by cyclic voltametry.

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Substituentenabhängigkeit des d-d-Überganges in den Elektronenabsorptions-Spektren von Arylferrocenen und entsprechenden Arylferricenium-Salzen

Zusammenfassung Elektronenabsorptions-Spektren von 22 Arylferrocenen und ihren Arylferricenium-Pentacyanopropenid-Salzen wurden gemessen. VersuchteHammett-Korrelationen des längstwelligen d-d-Überganges (_max) zeigten, daß diese Bande nur von stark elektronenanziehende Substituenten abhängig ist. Im Fall der Arylferricenium-Kationen wurde eine ausgezeichnete Korrelation zwischen _max der d-d-Bande und den ⁺-Konstanten festgestellt. Eine gute Korrelation der _max-Werte wurde auch mit denE _1/2 Oxidationspotentialen gefunden, die durch cyclische Voltametrie meßbar sind.

     

Zur reaktionvon cyclotri- und cyclotri- und cyclotetrasilazanen mit silylfluoriden

Fluorosilyl substituted cyclosilazanes are formed by treating lithium salts of hexamethylcyclotri- and octa-methylcyclotetrasilazanes with silicon tetrafluoride and organo-substituted silicon fluorides. Disubstituted compounds are obtained by the reaction of dilithium hexamethylcyclotrisilazane with silicon fluorides or by the reaction of lithium hexamethylcyclotrisilazane with silicon fluorides at higher temperature. Cyclosilazanes with bulky ligands react with butyllithium with elimination of butane as a first step and then react further with a silicon fluoride compound, with LiF-elimination, to give a mixed substituted cyclosilazane. Ring coupling through a silicon bridge is achieved by the reaction of a fluorosilyl-substituted cyclotrisilazane with lithium hexamethylcyclotrisilazane. The mass,¹H and¹⁹F NMR spectra of the compounds are reported.     

Alkoxylierung von bis(trimethylsilyl)-aminofluorsilanen,sowie siloxanbildung unter äthereliminierung

The reaction of bis(trimethylsilyl)aminofluorsilanes, (Me₃Si)₂NSiF₂R (R = CH₃ or F), with sodium alcoholates or sodium phenylate yields under elimination of NaF alkoxy- and aryloxy-aminofluorosilanes of the composition (Me₃Si)₂NSiF(R)OR′(R′ = CH₃, C₂H₅, C₃H₇, C₆H₅). A disiloxane is formed by thermal elimination of diethyl ether from bis(trimethylsilyl)aminomethylfluoroethoxysilane. The IR, mass, ¹H and ¹⁹F NMR spectra of the above-mentioned compounds are reported. ab]Die Reaktion von Bis(trimethylsilyl)-aminofluorsilanen des Typs (Me₃Si)₂NSiF₂R (R = F, CH₃) mit Natriumalkoholaten und Natriumphenolat führt unter NaF-Abspaltung zu Alkyl- und Aryloxyaminofluorsilanen der Zusammensetzung: (Me₃Si)₂NSiF(R)OR′ (R′ = CH₃, C₂H₇, C₆H₅, C₆H₅). Ein Disiloxan könnte durch die thermische Eliminierung von Diäthyläther aus Bis(trimethylsilyl)aminomethyl-fluor-äthoxy-silylarnin erhalten werden.Die IR-, Massen-, ¹H- und ¹⁹F-NMR-Spektren der dargestellten Verbindungen werden mitgeteilt.     

Temperature-dependent behavior of a symmetric long-chain bolaamphiphile with phosphocholine headgroups in water: from hydrogel to nanoparticles

The temperature-dependent self-assembly of the single-chain bolaamphiphile dotriacontan-1,1'-diyl-bis[2-(trimethylammonio)ethyl phosphate] (PC-C32-PC) was investigated by transmission electron microscopy (TEM), differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FT-IR), X-ray scattering, rheological measurements, and dynamic light scattering (DLS). At room temperature this compound, in which two phosphocholine headgroups are connected by a C(32) alkyl chain, proved to be capable of gelling water very efficiently by forming a dense network of nanofibers (Kohler et al. Angew. Chem., Int. Ed. 2004, 43, 245). A specific feature of this self-assembly process is that it is not driven by hydrogen bonds but solely by hydrophobic interactions of the long alkyl chains. The nanofibers have a thickness of roughly the molecular length and show a helical superstructure. A model for the molecular structure of the fibrils which considers the extreme constitution of the bolaamphiphile is proposed. Upon heating the suspensions three different phase transitions can be detected. Above 49 degrees C, the temperature of the main transition where the alkyl chains become "fluid", a clear low-viscosity solution is obtained due to a breakdown of the fibrils into smaller aggregates. Through mechanical stress the gel structure can be destroyed as well, indicating a low stability of these fibers. The gel formation is reversible, but as a drastic rearrangement of the molecules takes place, metastable states occur.     

TRANSFER OF EXCITATION ENERGY BETWEEN PORPHYRIN CENTERS OF A COVALENTLY-LINKED DIMER*

Abstract— Three covalently-linked porphyrin hybrid dimers were synthesized, each containing a metallotetraarylporphyrin [Zn(II), Cu(II), or Ni(II)], and a free base tetraarylporphyrin. Transfer of singlet excitation energy from the metalloporphyrin center to the free base porphyrin center was determined by measuring fluorescence properties. The Zn hybrid dimer displayed excellent intramolecular transfer of energy ( 85%) from the excited singlet state of the Zn(II) chromophore to the free base chromophore. No evidence for such transfer of the excited singlet state energy was found in the Ni(II) or Cu(II) analogues. From our experimental data, the fluorescence quantum yield of the Zn hybrid dimer was the same as for the free base monomer porphyrin (0.11; Seybold and Gouterman, 1969). Thus, the covalent attachment of another fluorescent porphyrin center effectively doubled the antenna size without decreasing the quantum yield even though the fluorescence quantum yield of the Zn(II) containing monomer was substantially less (0.03, according to Seybold and Gouterman, 1969) than that of the free base porphyrin. The donor-acceptor distance and the rate constant for energy transfer were calculated using the Forster equation. Assuming random orientation, a donor-acceptor distance of 15 Å was calculated with an associated rate constant (k_ci) for energy transfer of 1.9 ± 10₉ s_–1.     

Modular bis(oxazoline) ligands for palladium catalyzed allylic alkylation: unprecedented conformational behaviour of a bis(oxazoline) palladium eta3-1,3-diphenylallyl complex

New families of enantiopure bis(oxazolines) with 4,5-trans (5 a-g) or 4,5-cis (6 c) stereochemistry at the individual rings have been prepared in high yield. Their eta(3)-allyl palladium complexes (8 a-g, 9 c and 10) have been used as catalytic precursors in allylic alkylation reactions with excellent enantioselectivities (up to 96 %) for the trans oxazoline derivatives, while Pd/6 c system was inactive. NMR studies on palladium eta(3)-1,3-diphenylallyl intermediates (11 a, c and e) showed the presence of syn/syn- and syn/anti-allyl isomers in solution; this resembles the first example of eta(3)-eta(1)-eta(3) isomerism in Pd allylic complexes containing bis(oxazolines) derived from malonic acid.     

Calculation and optimization of parameters of radiating distributed feedback structures

A simple method is suggested for calculation of reflection, radiation and transmission coefficients for the distributed feedback structure in the second diffraction order. The method is based on a slight difference between coefficients of reflectionR and radiationI of the surface wave for = (where is the light wavelength corresponding to a precise resonance for the grating length I) and those for =_l (where _l is the light wavelength corresponding to the resonance for the finite grating length). The simplicity of the method makes it possible to use it for optimization of the distributed feedback structure by a number of parameters. The technique can be used in the case of thin-film and diffused waveguides for both TE and TM modes.     

A Comparative Loading and Release Study of Vancomycin from a Green Mesoporous Silica

Since its first use as a drug delivery system, mesoporous silica has proven to be a surprisingly efficient vehicle due to its porous structure. Unfortunately, most synthesis methods are based on using large amounts of surfactants, which are then removed by solvent extraction or heat treatment, leading to an undesired environmental impact because of the generated by-products. Hence, in the present study, we followed the synthesis of a silica material with a wormhole-like pore arrangement, using two FDA-approved substances as templates, namely Tween-20 and starch. As far as we know, it is the first study using the Tween-20/starch combo as a template for mesoporous silica synthesis. Furthermore, we investigated whether the obtained material using this novel synthesis had any potential in using it as a DDS. The material was further analyzed by XRD, TEM, FT-IR, N₂ adsorption/desorption, and DLS to investigate its physicochemical features. Vancomycin was selected as the active molecule based on the extensive research engaged towards improving its bioavailability for oral delivery. The drug was loaded onto the material by using three different approaches, assuming its full retention in the final system. Thermal analysis confirmed the successful loading of vancomycin by all means, and pore volume significantly decreased upon loading, especially in the case of the vacuum-assisted method. All methods showed a slower release rate compared to the same amount of the pure drug. Loadings by physical mixing and solvent evaporation released the whole amount of the drug in 140 min, and the material loaded by the vacuum-assisted method released only 68.2% over the same period of time, leading us to conclude that vancomycin was adsorbed deeper inside the pores. The kinetic release of the three systems followed the Higuchi model for the samples loaded by physical mixing and vacuum-assisted procedures, while the solvent evaporation loading method was in compliance with the first-order model.