Exact upper bounds for the number of the polynomials with given discriminants

We generalize the result of Davenport on the sum of absolute values of discriminants of integer polynomials of degree three. For the first time, we find the exact upper bound for the number of polynomials with given discriminant in the class of cubic polynomials of bounded height for the whole interval of values of discriminants.     

A review on preparative and semi-preparative offgel electrophoresis for multidimensional protein/peptide assessment

Mass spectrometry (MS) techniques are commonly used for protein identification and further analysis of selected protein spots after high resolution 2-D electrophoresis. Complementary gel-free approaches have been developed during the last few years and have shown to be useful tools in modern proteomics. The development and application of various gel-free electrophoresis devices for performing protein fractionation according to the pI differences is therefore a topic of interest. This review describes the current state of isoelectric focusing (IEF) gel-free electrophoresis based on the Agilent offgel 3100 fractionator. The review includes, therefore, (i) an overview on IEF as well as other previous IEF gel-free electrophoresis developments; (ii) offgel fundamentals and future trends; (iii) advantages and disadvantages of current offgel procedures; (iv) requirements of isolated protein pellets for further offgel fractionation; (v) offgel fraction requirements to perform the second dimensional analysis by advance electrophoresis and chromatographic techniques; and (vi) effect of the offgel operating conditions on the stability of metal–protein complexes.     

Efficient Method for the Synthesis of Functionalized Basic Maleimides

A three‐step procedure involving Diels–Alder condensation of maleic anhydride with furane, formation of N‐substituted imide upon reaction with appropriate diamine, and a final retro Diels–Alder regeneration of the maleic carbon–carbon double bond is proposed for an unequivocal synthesis of N‐substituted basic maleimides. The novel method is characterized by mild reaction conditions, easy work‐up, high yields, and no need for additional catalysis.     

Incorporation dynamics of molecular guests into two-dimensional supramolecular host networks at the liquid-solid interface

The objective of this work is to study both the dynamics and mechanisms of guest incorporation into the pores of 2D supramolecular host networks at the liquid-solid interface. This was accomplished by adding molecular guests to prefabricated self-assembled porous monolayers and the simultaneous acquisition of scanning tunneling microscopy (STM) topographs. The incorporation of the same guest molecule (coronene) into two different host networks was compared, where the pores of the networks either featured a perfect geometric match with the guest (for trimesic acid host networks) or were substantially larger than the guest species (for benzenetribenzoic acid host networks). Even the moderate temporal resolution of standard STM experiments in combination with a novel injection system was sufficient to reveal clear differences in the incorporation dynamics in the two different host networks. Further experiments were aimed at identifying a possible solvent influence. The interpretation of the results is aided by molecular mechanics (MM) and molecular dynamics (MD) simulations.     

Conformational energetics of interpolyelectrolyte complexation between ι-carrageenan and poly(methylaminophosphazene) measured by high-sensitivity differential scanning calorimetry

The interaction of poly(methylaminophosphazene) hydrochloride (PMAP·HCl) of varying degrees of ionization (f) with the potassium salt of ι-carrageenan was studied by high-sensitivity differential scanning calorimetry at a KCl concentration of 0.15 M, which is included for the purpose of stabilizing the helix conformation of the polysaccharide up to 55 °C. The conditions of strong (pH 3.8, I = 0.15), moderate (pH 7.4, I = 0.15), and weak (pH 7.4, I = 0.25) electrostatic interactions of the polyelectrolytes were considered. The thermodynamic parameters of the helix-coil transition of ι-carrageenan were determined as a function of the polycation/polyanion ratio. We show that the interpolyelectrolyte reaction between PMAP·HCl and ι-carrageenan results in a complete unfolding of the polysaccharide helix under conditions of strong electrostatic interaction and increases its stability under conditions of medium and weak electrostatic interactions. The formation of stoichiometric PMAP-carrageenan interpolyelectrolyte complexes proceeded via a cooperative mechanism at pH 3.8 (f = 0.5) and pH 7.4 (f = 0.2) at an ionic strength of 0.15. In contrast, the complexation at pH 7.4 and an ionic strength of 0.25 could be considered to be a consecutive competitive binding of charged units of poly(methylaminophosphazene) to the oppositely charged polysaccharide matrix in the helix or coil conformation. Binding constants of the polycation to the helix and coil forms of ι-carrageenan were estimated. They revealed a preferential binding of the polycation to the helix form of the polysaccharide.     

Accurate ab initio quartic force fields of cyclic and bent HC2N isomers

Highly correlated ab initio quartic force fields (QFFs) are used to calculate the equilibrium structures and predict the spectroscopic parameters of three HC(2)N isomers. Specifically, the ground state quasilinear triplet and the lowest cyclic and bent singlet isomers are included in the present study. Extensive treatment of correlation effects were included using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted as CCSD(T). Dunning's correlation-consistent basis sets cc-pVXZ, X = 3,4,5, were used, and a three-point formula for extrapolation to the one-particle basis set limit was used. Core-correlation and scalar relativistic corrections were also included to yield highly accurate QFFs. The QFFs were used together with second-order perturbation theory (PT) (with proper treatment of Fermi resonances) and variational methods to solve the nuclear Schro?dinger equation. The quasilinear nature of the triplet isomer is problematic, and it is concluded that a QFF is not adequate to describe properly all of the fundamental vibrational frequencies and spectroscopic constants (though some constants not dependent on the bending motion are well reproduced by PT). On the other hand, this procedure (a QFF together with either PT or variational methods) leads to highly accurate fundamental vibrational frequencies and spectroscopic constants for the cyclic and bent singlet isomers of HC(2)N. All three isomers possess significant dipole moments, 3.05 D, 3.06 D, and 1.71 D, for the quasilinear triplet, the cyclic singlet, and the bent singlet isomers, respectively. It is concluded that the spectroscopic constants determined for the cyclic and bent singlet isomers are the most accurate available, and it is hoped that these will be useful in the interpretation of high-resolution astronomical observations or laboratory experiments.     

Calcium‐Selective Electrodes for Measurements in the Presence of Anionic Surfactants

Calcium selective electrodes with various membrane formulations were studied in solutions containing CaCl₂ and sodium dodecylsulfate (NaDS). It is shown that electrodes based on neutral ionophores ETH 1001 and ETH 129 cannot be used as Ca²⁺ ion sensors in these solutions because of strong anion interference from DS^? anion. Among other formulations, that based on calcium bis(tetramethylbutylphenyl)phosphate in tri(2‐ethylhexyl)phosphate appear the most promising. The interpretation of the ISE response in solutions under study relied on a novel approach which considers three forms of calcium: Ca²⁺ free ions, Ca in Ca(DS)₂ precipitate, and Ca²⁺ bound by the DS^? micelles. Data needed for the respective calculations were obtained by DS^? selective electrode based on tetradecylammonium, and Na⁺ selective glass electrode.     

Vibrational characterization of L-leucine phosphonate analogues: FT-IR, FT-Raman, and SERS spectroscopy studies and DFT calculations

This study reports the Raman (FT-Raman) and absorption infrared (FT-IR) spectra, based on calculated wavenumbers and normal modes of vibrations, of the following compounds: L-Leu-D-NH-CH(Me)-PO(3)H(2) (LI), L-Leu-NH-C(Me)(2)-PO(3)H(2) (LII), L-Leu-D-NH-CH(Et)-PO(3)H(2) (LIII), L-Leu-L-NH-CH(Et)-PO(3)H(2) (LIV), L-Leu-L-NH-CH(EtOH)-PO(3)H(2) (LV), L-Leu-NH-C(Me)(Et)-PO(3)H(2) (LVI), L-Leu-L-NH-CH(PrA)-PO(3)H(2) (LVII), L-Leu-L-NH-CH(c-Pr)-PO(3)H(2) (LVIII), L-Leu-L-NH-CH(t-Bu)-PO(3)H(2) (LIX), L-Leu-L-NH-CH(BuA)-PO(3)H(2) (LX), L-Leu-L-NH-CH(c-Bu)-PO(3)H(2) (LXI), and L-Leu-L-NH-C(Adm)-PO(3)H(2) (LXII). The equilibrium geometries and vibrational wavenumbers were calculated using density functional theory (DFT) at the B3LYP, 6-311++G** level using Gaussian 03, Raint, GaussSum 0.8, and Gar2ped software. We briefly compare and analyze the experimental and calculated vibrational wavenumbers in the range 4000-400 cm(-1). In addition, the Raman wavenumbers are compared to those from the surface-enhanced Raman scattering (SERS) spectra for the phosphono analogues of l-leucine (l-Leu) adsorbed on a colloidal silver surface in an aqueous solution. The geometries of these molecules etched on the silver surface were deduced from observed changes in both the intensity and broadness of Raman bands in the spectra of the bound versus free species. For example, LVI appears to adsorb onto the colloidal silver particles mainly through the amine group and amide bond, which assists in the adsorption process, whereas LII shows strongly enhanced SERS bands due to the rocking, twisting, and stretching vibrations of the N(amid)C(sg)(Me)(2)P fragment, suggesting that this peptide's interaction with the silver surface occurs mainly via this fragment. On the other hand, the most dominant SERS bands of LIII and LIV due to the P═O bond stretches reflect P═O···Ag complex formation.     

Turn-on fluorescence in tetraphenylethylene-based metal-organic frameworks: an alternative to aggregation-induced emission

Coordinative immobilization of functionalized tetraphenylethylene within rigid porous metal-organic frameworks (MOFs) turns on fluorescence in the typically non-emissive tetraphenylethylene core. The matrix coordination-induced emission effect (MCIE) is complementary to aggregation-induced emission. Despite the large interchromophore distances imposed by coordination to metal ions, a carboxylate analogue of tetraphenylethylene anchored by Zn(2+) and Cd(2+) ions inside MOFs shows fluorescence lifetimes in line with those of close-packed molecular aggregates. Turn-on fluorescence by coordinative ligation in a porous matrix is a powerful approach that may lead to new materials made from chromophores with molecular rotors. The potential utility of MCIE toward building new sensing materials is demonstrated by tuning the fluorescence response of the porous MOFs as a function of adsorbed small analytes.