Computation of the Mordell-Tornheim zeta values

In this paper the authors present several algorithmic formulas which are potentially useful in computing the following Mordell-Tornheim zeta values:

for the special cases

   and

Some interesting (known or new) consequences and illustrative examples are also considered.

     

Peptide Bond Formation in the Protonated Serine Dimer Following Vacuum UV Photon-Induced Excitation

Possible routes for intra-cluster bond formation (ICBF) in protonated serine dimers have been studied. We found no evidence of ICBF following low energy collision-induced dissociation (in correspondence with previous works), however, we do observe clear evidence for ICBF following photon absorption in the 4.6–14 eV range. Moreover, the comparison of photon-induced dissociation measurements of the protonated serine dimer to those of a protonated serine dipeptide provides evidence that ICBF, in this case, involves peptide bond formation (PBF). The experimental results are supported by ab initio molecular dynamics and exploration of several excited state potential energy surfaces, unraveling a pathway for PBF following photon absorption. The combination of experiments and theory provides insight into the PBF mechanisms in clusters of amino acids, and reveals the importance of electronic excited states reached upon UV/VUV light excitation.     

Monte Carlo-based QSAR modeling of dimeric pyridinium compounds and drug design of new potent acetylcholine esterase inhibitors for potential therapy of <Emphasis Type="Italic">myasthenia gravis</Emphasis>

The Monte Carlo method was used for QSAR modeling of dimeric pyridinium compounds as acetylcholine esterase inhibitors. QSAR model was developed for a series of 39 dimeric pyridinium compounds. QSAR models were calculated with the representation of the molecular structure by the simplified molecular-input line-entry system. One split into the training and test set have been examined. The statistical quality of the developed model is very good. The calculated model for dimeric pyridinium derivatives had following statistical parameters: r ² = 0.9477 for the training set and r ² = 0.9332 the test set. Structural indicators considered as molecular fragments responsible for the increase and decrease in the inhibition activity have been defined. The computer-aided design of new dimeric pyridinium compounds potential acetylcholine esterase inhibitors with the application of defined structural alerts has been presented.     

Configurational entropy of binary hard-disk glasses: nonexistence of an ideal glass transition

We study the thermodynamics of a binary hard-disk mixture in which the ratio of disk diameters is kappa=1.4. We use a recently developed molecular dynamics algorithm to calculate the free-volume entropy of glassy configurations and obtain the configurational entropy (degeneracy) of the supercompressed liquid as a function of density. We find that the configurational entropy of the glasses near the kinetic glass transition is very close to the mixing entropy, suggesting that the degeneracy is zero only for the phase-separated crystal. We explicitly construct an exponential number of jammed packings with densities spanning the spectrum from the accepted "amorphous" glassy state to the phase-separated crystal, thus showing that there is no ideal glass transition in binary hard-disk mixtures. This construction also demonstrates that the ideal glass, defined as having zero configurational entropy, is not amorphous, but instead is nothing more than a phase-separated crystal. This critique of the presumed existence of an ideal glass parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al., Phys. Rev. Lett. 84, 2064 (2000)]. We also perform free-energy calculations to determine the equilibrium phase behavior of the system. The calculations predict a first-order freezing transition at a density below the kinetic glass transition. However, this transition appears to be strongly kinetically suppressed and is not observed directly. New simulation techniques are needed in order to gain a more complete understanding of the thermodynamic and kinetic behavior of the binary disk mixture and, in particular, of the demixing process during crystallization.     

The weak and strong asymptotic equivalence relations and the generalized inverse<Superscript>*</Superscript>

We discuss the relationship between the weak and strong asymptotic equivalence relations and the generalized inverse in the class A \mathcal {A} of all nondecreasing unbounded positive functions on a half-axis [a,+∞) (a > 0). As a main result, we prove a proper characterization of the functional class R _∞ ∩ A \mathcal {A} , where R _∞ is the class of all rapidly varying functions. Also, we prove a characterization of the functional class PI ^* ∩ A \mathcal {A} .     

Synthesis of N-(3- and 4-substituted phenyl)-O-isobutyl thionocarbamates from O-isobutyl xanthate and amines using a nano-platinum multi-walled carbon nanotube catalyst

Abstract  

Twelve N-(3- and 4-substituted phenyl)-O-isobutyl thionocarbamates, eight of which are novel, were synthesized from O-isobutyl xanthate and 3- and 4-substituted anilines in the presence of a nano-platinum aminophenyl modified multi-walled carbon nanotube catalyst. The nano-Pt catalyst was prepared on a carbon nanotube support modified by diazotization, nitro group reduction, and subsequent microwave-assisted nano-Pt precipitation. The catalyst was characterized by Fourier transform infrared (FT-IR) spectroscopy, elemental analysis, thermogravimetric analysis, and transmission electron microscopy. The nano-platinum/modified carbon nanotube catalyst was compared with a commercial Pt/active carbon catalyst in terms of product purity and yield. The results obtained by the use of the catalysts were additionally compared with those obtained by reaction of sodium isobutyl xanthogenacetate and 3- and 4-substituted anilines. Full structure characterization of the synthesized N-(substituted phenyl)-O-isobutyl thionocarbamates was achieved using FT-IR, ¹H and ¹³C NMR, and mass spectrometric methods, and their purity was proved by elemental analysis and gas chromatography. The new catalytic method offers advantages over the commercial method, such as higher yields and no product purification is required, thus conforming to the principles of ecologically friendly syntheses.     

Photocatalytic degradation of metoprolol in water suspension of TiO<Subscript>2</Subscript> nanopowders prepared using sol–gel route

Nanocrystalline titanium dioxide (TiO₂) powders have been synthesized by sol–gel method using titanium tetrachloride (TiCl₄) or tetrabutyl titanate (Ti(OC₄H₉)₄ as precursors, different alcohols and calcination temperatures in the range from 400 to 650 °C. The photocatalytic activity of as-prepared powders has been tested for the degradation of metoprolol tartrate salt, a selective β-blocker used to treat a variety of cardiovascular diseases, and compared to photocatalytic activity obtained from Degussa P25. Nanosized TiO₂ powders prepared from TiCl₄ and amyl-alcohol, calcined at 550 °C, displayed an activity comparable to Degussa P25, whereas the sample from the same series, calcined at 650 °C, showed higher photocatalytic activity in the whole range of the catalyst loading. Structural, morphological and surface properties of synthesized TiO₂ nanopowders have been investigated by XRD, SEM, EDS and BET measurements, as well as FTIR and Raman spectroscopy, in order to find out the material properties which enable rapid an efficient decomposition of metoprolol under UV radiation.     

Effect of lithium salt on the stability of dispersions of fumed silica in the ionic liquid BMImBF4

We have investigated the stability and interactions in dispersions of colloidal fumed silica, Aerosil 200, and the ionic liquid 1-butyl-3-methylimidazolium tetraflouroborate (BMImBF(4)) as a function of the Li salt concentration (LiBF(4)). Photon correlation spectroscopy was used to study the aggregation behavior at low silica concentrations, and Raman spectroscopy was used to investigate the interactions in the ionic liquid and with the silica surface. We find that the addition of LiBF(4) increases the stability of the dispersions, with smaller agglomerates of silica particles and higher gelation concentrations in the presence of Li salt. The increased stability with the addition of Li salt is explained by the formation of a more stable solvation layer, where Li ions accumulate on the surface. This leads to an increased interaction between lithium ions and the BF(4)(-) anions in the solvation layer, as seen by Raman spectroscopy. Upon gelation, the Li ions are expelled from the surface because hydrogen bonding between the silica particles are formed. For both neat BMImBF(4) and Li-salt-doped BMImBF(4)/silica dispersions, a weak gel phase was found preceding the formation of a strong gel at slightly higher silica concentrations.     

Solvent and Structural Effects on the UV–Vis Absorption Spectra of Some 4,6-Disubstituted-3-Cyano-2-Pyridones

A series of 4,6-disubstituted-3-cyano-2-pyridones was synthesized and their UV?CVis absorption spectra were recorded in the region 200?C600?nm in the set of selected solvents. The effects of solvent dipolarity/polarizability and solvent?Csolute hydrogen-bonding interactions on the spectral shifts were analyzed by means of the linear solvation energy relationship concept of Kamlet and Taft. The influence of solvents as well as substituents on the 2-pyridone/2-hydroxypyridine tautomeric equilibration was evaluated. The absorption band maximum of the 2-hydroxypyridine form is found to appear at a shorter wavelength than that of the 2-pyridone form in all investigated solvents. The replacement of the methyl and phenyl groups at position 6 of the pyridone ring, by a hydroxy group, significantly changes the solvatochromic behavior of the investigated pyridones.     

Influence of surface modified TiO2 nanoparticles by gallates on the properties of PMMA/TiO2 nanocomposites

Nanocomposites based on poly(methyl methacrylate) (PMMA) and TiO₂ nanoparticles were synthesized by in situ radical polymerization of MMA in solution. The surface of TiO₂ nanoparticles was modified with four gallic acid esters (octyl, decyl, lauryl and cetyl gallate). The content of gallates present on the surface of TiO₂ was calculated from the TGA results. The influence of length of hydrophobic tail of amphiphilic alkyl gallates on dispersability of surface modified TiO₂ nanoparticles in PMMA matrix, the molecular weight and glass transition temperature of PMMA, as well as the thermal stability of the prepared PMMA/TiO₂ nanocomposites in nitrogen and air was investigated. The influence of content of TiO₂ nanoparticles on the properties of these nanocomposites was also examined. The formation of a charge transfer complex between the surface Ti atoms and the gallates was confirmed by FTIR and UV spectroscopy. TEM micrographs of the PMMA/TiO₂ nanocomposites revealed that degree of TiO₂ aggregation can be significantly lowered by increasing the length of aliphatic part of the used gallates. The molecular weight of PMMA slightly decreases with the increase of TiO₂ content, indicating that used TiO₂ nanoparticles act as radical scavengers during the polymerization of MMA. The presence of surface modified TiO₂ nanoparticles do not have an influence on the mobility of PMMA chain segments leading to the same values of glass transition temperature for all investigated samples. Thermal and thermo-oxidative stability of the PMMA matrix are improved by introducing TiO₂ nanoparticles modified with gallates.