EG-eliminations

We propose an algorithm to put linear recurrent systems in a form which is convenient for using the systems to search for polynomial, power series, Laurent series, and other types of solutions of various linear functional systems (differential,difference and q-difference). Some algorithms to search for solutions of functional systems are described. None of the proposed algorithms requires preliminary uncoupling of linear systems     

The universe formation by space reduction cascades with random initial parameters

In this paper we discuss the creation of our universe using the idea of extra dimensions. The initial, multidimensional Lagrangian contains only metric tensor. We have found many sets of the numerical values of the Lagrangian parameters corresponding to the observed low-energy physics of our Universe. Different initial parameters can lead to the same values of fundamental constants by the appropriate choice of a dimensional reduction cascade. This result diminishes the significance of the search for the ‘unique’ initial Lagrangian. We also have obtained a large number of low-energy vacua, which is known as ‘landscape’ in the string theory.     

Two-photon excitation of substituted enediynes

Electronic spectroscopy of nine benzannelated enediynes and a related fulvene was studied under one-photon and two-photon excitation conditions. We utilize measured absorbance and emission spectra and time-resolved fluorescence decays of these molecules to calculate their radiative lifetimes and fluorescence quantum yields. The fluorescence quantum yields for the other compounds were referenced to the fluorescence quantum yield of compound 3 and used to determine relative two-photon absorption cross-sections. Further insight into experimental studies has been achieved using time-dependent density functional (TD-DFT) computations. The probability of two-photon absorption (TPA) increases noticeably for excitation to the higher excited states. The photophysical properties of benzannelated enediynes are sensitive to substitutions at both the core and the periphery of the enediyne chromophore. Considerably enhanced two-photon absorption is observed in an enediyne with donor substitution in the middle and acceptor substitution at the termini. Excited states with B symmetry are not active in TPA spectra. From a practical point of view, this study extends the range of wavelengths applicable for activation of the enediyne moiety from 350 to 600 nm and provides a rational basis for future studies in this field. Our theoretical computations confirmed that lowest energy TPA in benzannelated enediynes involves different orbitals than lowest energy one-photon absorbance and provided further support to the notion that introduction of donor and acceptor substituents at different ends of a molecule increases TPA.     

Effective interaction potentials for alkali and alkaline earth metal ions in SPC/E water and polarization model of hydrated ions

In the first paper (J. Phys. Chem. B, 2006, 110, 10878), effective ion-ion potentials in SPC/E water were obtained for Me-Me, Me-Cl-, and Cl(-)-Cl- pairs, where Me is Li+, Na+, K+, Mg2+, Ca2+, Sr2+, and Ba2+ cations. In this second part of the study of effective interionic potentials, ion-ion distribution functions obtained from implicit-water Monte Carlo simulations of electrolyte solution with these potentials have been explored. This analysis verifies the range of applicability of the primitive model of electrolyte. It is shown that this approximation can be applied to monovalent electrolyte solutions in a wide range of concentrations, whereas the nature of ion-ion interactions is notably different for 2:1 electrolytes. An improved model of ions is discussed. The model includes approximations of the ion hydration shell polarization and specific short-range ion-ion interaction. It allows approximation of the potential of mean force acting on ions in strong electric fields of highly charged macromolecules and bilayers.     

Effective interaction potentials for alkali and alkaline earth metal ions in SPC/E water and prediction of mean ion activity coefficients

The potential of mean force (PMF) acting between two simple ions surrounded by SPC/E water have been determined by molecular dynamics (MD) simulations using a spherical cavity approach. Such effective ion-ion potentials were obtained for Me-Me, Me-Cl-, and Cl(-)-Cl- pairs, where Me is a Li+, Na+, K+, Mg2+, Ca2+, Sr2+, and Ba2+ cation. The ionic sizes estimated from the effective potentials are not pairwise additive, a feature in the frequently used primitive model for electrolytes. The effective potentials were used in Monte Carlo (MC) simulations with implicit water to calculate mean ion activity coefficients of LiCl, NaCl, KCl, MgCl2, CaCl2, SrCl2, and BaCl2. Predicted activities were compared with experimental ones in the electrolyte concentration range 0.1-1 M. A qualitative agreement for LiCl and a satisfactory agreement for NaCl were found, whereas the predictions for KCl by two K+ models were less coherent. In the case of alkaline earth metal ions, all experimental activities were successfully reproduced at c = 0.1 M. However, at higher concentrations, similar deviations occurred for all divalent cations, suggesting that the dependence of the permittivity on the salt concentration and the polarization deficiency arising from the ordering of water molecules in the ion hydration shells are important in such systems.     

Reaction of N-trimethylsilyl derivatives of amides and lactams with chloro(chloromethyl)dimethylstannane: Crystal and molecular structure of 1-(chlorodimethylstannylmethyl)-2-piperidone

A general scheme of reactions between chloro(chloromethyl)dimethylstannane and N-trimethylsilylamides and -lactams was established by NMR and IR techniques. The reactions proceed via transmetallation followed by transformation of the N-stannylated intermediate (1) into (N-Sn)-coordinated O-stannylmethyl (2) and (O-Sn)-coordinated N-stannylmethyl (3) derivatives. In the cases of 2-piperidone and 2-hexahydroazepinone these products were isolated as individual compounds (2b,c and 3b,c). X-ray diffraction study of 1-(chlorodimethylstannylmethyl)-2-piperidone (3b) confirmed (3 + 2)-coordination state of the tin atom and axial positions of oxygen and halogen atoms. The experimental and quantum-chemically calculated structural parameters are discussed in comparison with those of related trigonal bipyramidal (TBP) silicon, germanium and tin derivatives. Calculation at the MP2/LanL2DZ/D95 level reveals that the stability of the (O-M)chelates increases in the following order: (O-Si) < (O-Ge) < (O-Sn).     

Thermal relaxation mechanism and role of chemical functionalization in fullerene solutions

Using molecular-dynamics simulations we investigate thermal relaxation of C60 and C84 molecules suspended in octane liquid. Pristine fullerenes exhibit relatively slow relaxation due to weak thermal coupling with the liquid. A comparison of the interfacial transport characteristics obtained from relaxation simulations with those obtained from equilibrium simulations and fluctuation-dissipation theorem analysis demonstrates that the relaxation process involves two main steps: (i) energy flow from high- to low-frequency modes within the fullerene, and (ii) energy flow from low-frequency fullerene modes to the liquid. Functionalization of fullerenes with alkene chains leads to significant reduction of the thermal relaxation time. The relaxation time of functionalized fullerenes becomes independent from the functionalizing chain length beyond approximately 10 carbon segments; this can be understood in terms of thermal conductivity along the chain and heat transfer between the chain and the solvent.     

2D and 3D Cu(hfac)2 complexes with nitronyl nitroxide biradicals

Reactions between Cu(hfac)2 and nitronyl nitroxide biradicals 1,4-bis[4-(4,4,5,5-tetramethyl-3-oxide-1-oxyl-4,5-dihydro-1H-imidazol-2-yl)pyrazol-1-yl]butane (L4) and 1,8-bis[4-(4,4,5,5-tetramethyl-3-oxide-1-oxyl-4,5-dihydro-1H-imidazol-2-yl)pyrazol-1-yl]octane (L8) gave respectively a framework compound [Cu(hfac)2]2L4 and a layered polymer compound [Cu(hfac)2]2L8. The framework of [Cu(hfac)2]2L4 consists of 66-membered condensed metallocycles. Inside the framework, the structure has macrohelixes (pitch approximately 25 A) extending along the [001] crystallographic direction. All the helixes have the same direction of winding; the crystals, therefore, are optically active, the structure corresponding either to P-isomer (P4(1)2(1)2) or to M-isomer (P4(3)2(1)2). The long distances between the Cu atoms and the O atoms of the coordinated >N-O groups (Cu-O 2.351-2.467 A) are responsible for ferromagnetic exchange interactions in Cu2+-O-N< and >N-O-Cu2+-O-N< exchange clusters.     

Debundling of single-walled nanotubes by dilution: observation of large populations of individual nanotubes in amide solvent dispersions

Large-scale debundling of single-walled nanotubes has been demonstrated by dilution of nanotube dispersions in the solvent N-methyl-2-pyrrolidone (NMP). At high concentrations some very large (approximately 100 s of micrometers) nanotube aggregates exist that can be removed by mild centrifugation. By measurement of the absorbance before and after centrifugation as a function of concentration the relative aggregate and dispersed nanotube concentrations can be monitored. No aggregates are observed below CNT approximately 0.02 mg/mL, suggesting that this can be considered the nanotube dispersion limit in NMP. After centrifugation, the dispersions are stable against sedimentation and further aggregation for a period of weeks at least. Atomic force microscopy (AFM) studies on deposited films reveal that the bundle diameter distribution decreases dramatically as concentration is decreased. Detailed data analysis suggests the presence of an equilibrium bundle number density and that the dispersions self-arrange themselves to always remain close to the dilute/semidilute boundary. A population of individual nanotubes is always observed that increases with decreasing concentration until almost 70% of all dispersed objects are individual nanotubes at a concentration of 0.004 mg/mL. The number density of individual nanotubes peaks at a concentration of approximately 10(-2) mg/mL. Both the mass fraction and the partial concentration of individual nanotubes can also be measured and behave in similar fashion. Comparison of the number density and partial concentration also of individual nanotubes reveals that the individual nanotubes have average molar masses of approximately 700,000 g/mol. The presence of individual nanotubes in NMP dispersion was confirmed by photoluminescence spectroscopy. Concentration dependence of the photoluminescence intensity confirms that the AFM measurements reflect the diameter distributions in situ. In addition, Raman spectroscopy confirms the presence of large quantities of individual nanotubes in the deposited films. Finally, the nature of the solvent properties required for dispersion are discussed.     

Direct competitive ELISA based on a monoclonal antibody for detection of aflatoxin B1. Stabilization of ELISA kit components and application to grain samples

A direct competitive enzyme-linked immunosorbent assay (ELISA) based on a monoclonal antibody has been developed and optimized for detection of aflatoxin B₁ (AFB₁), and an ELISA kit has been designed. This immunoassay was highly specific, sensitive, rapid, simple, and suitable for aflatoxin monitoring. AFB₁ concentrations determinable by ELISA ranged from 0.1 to 10 μg L⁻¹. The IC₅₀ value was 0.62 μg L⁻¹. Recovery from spiked rice samples averaged between 94 and 113%. The effect of different reagents on the stability of HRP–AFB₁ conjugate solution was studied. The performance of a stabilized enzyme tracer in ELISA was determined and compared with that of a freshly prepared control solution of HRP–AFB₁ conjugate. The results showed that stabilizing media containing 0.02% BSA, 0.1% Kathon CG, and 0.05 mol L⁻¹ calcium chloride in 0.05 mol L⁻¹ Tris-HCl buffer (pH 7.2) maintained the activity of HRP–AFB₁ at a dilution of 1:1000 for a period of at least 12 months at room temperature whereas the reference conjugate solution without the additives lost its activity within a few days. Several additives were tested for their stabilizing effect on a monoclonal antibody (MAb) immobilized on the surface of polystyrene microtitre plates. It was shown that immobilized MAb, treated with post-coating solutions containing PVA, BSA, and combinations of these substances with trehalose, retained its activity for at least 4 months at 4°C, whereas the untreated MAb-coated plate lost its activity within 2 days.