Preserving Z-sets by Dranishnikov's resolution

We prove that Dranishnikov's k-dimensional resolution is a UV^n − 1-divider of Chigogidze's k-dimensional resolution ck. This fact implies that preserves Z-sets. A further development of the concept of UV^n − 1-dividers permits us to find sufficient conditions for to be homeomorphic to the Nöbeling space νk or the universal pseudoboundary σk. We also obtain some other applications.     

On the 3D Cahn–Hilliard equation with inertial term

We study the modified Cahn–Hilliard equation proposed by Galenko et al. in order to account for rapid spinodal decomposition in certain glasses. This equation contains, as additional term, the second-order time derivative of the (relative) concentration multiplied by a (small) positive coefficient . Thus, in absence of viscosity effects, we are in presence of a Petrovsky type equation and the solutions do not regularize in finite time. Many results are known in one spatial dimension. However, even in two spatial dimensions, the problem of finding a unique solution satisfying given initial and boundary conditions is far from being trivial. A fairly complete analysis of the 2D case has been recently carried out by Grasselli, Schimperna and Zelik. The 3D case is still rather poorly understood but for the existence of energy bounded solutions. Taking advantage of this fact, Segatti has investigated the asymptotic behavior of a generalized dynamical system which can be associated with the equation. Here we take a step further by establishing the existence and uniqueness of a global weak solution, provided that is small enough. More precisely, we show that there exists such that well-posedness holds if (suitable) norms of the initial data are bounded by a positive function of which goes to + ∞ as tends to 0. This result allows us to construct a semigroup on an appropriate (bounded) phase space and, besides, to prove the existence of a global attractor. Finally, we show a regularity result for the attractor by using a decomposition method and we discuss the existence of an exponential attractor.      

Consistent approach to adsorption thermodynamics on heterogeneous surfaces using different empirical energy distribution models

Adsorption on heterogeneous surfaces with three basic energy distribution models (uniform model, exponential model, and normal-like model) is studied. Exact analytical solutions of the adsorption isotherms and the heats of adsorption are derived for the uniform and exponential models, and, with these solutions including a numerical solution for the normal-like model, the behavior of the differential heat of adsorption and the "apparent" standard adsorption entropy concerning the overall surface is described as a function of coverage and temperature. The approximations underlying the isotherms and heats of adsorption in the Temkin, Freundlich, and Langmuir-Freundlich types of adsorption are rationalized. By comparing these empirical formulas to the exact solutions, the level of these approximations is found to be identical, which is similar to the "condensation approximation". Their preconditions are that either the temperature is low enough, or the surface is strongly heterogeneous. Generally, they are suitable for the middle coverage range. The exact solutions provide a method to obtain more information on the heats, entropy, and heterogeneity of the catalyst surface from the calorimetric measurement of the heat of adsorption.     

Attachment of motile bacterial cells to prealigned holed microarrays

Construction of biomotors is an exciting area of scientific research that holds great promise for the development of new technologies with broad potential applications in areas such as the energy industry and medicine. Herein, we demonstrate the fabrication of prealigned microarrays of motile Escherichia coli bacterial cells on SiOx substrates. To prepare these arrays, holed surfaces with a gold layer on the bottom of the holes were utilized. The attachment of bacteria to the holes was achieved via nonspecific interactions using poly-l-lysine hydrobromide (PLL). Our data suggest that a single motile bacterial cell can be selectively attached to an individual hole on a surface and bacterial cell binding can be controlled by altering the pH, with the greatest occupancy occurring at pH 7.8. Cells attached to hole arrays remained motile for at least 4 h. These data indicate that holed surface structures provide a promising footprint for the attachment of motile bacterial cells to form high-density site-specific functional bacterial microarrays.     

Beyond vinyl: electronic structure of unsaturated propen-1-yl, propen-2-yl, 1-buten-2-yl, and trans-2-buten-2-yl hydrocarbon radicals

Vertical excitation energies and oscillator strengths for several valence and Rydberg electronic states of vinyl, propen-1-yl, propen-2-yl, 1-buten-2-yl, and trans-2-buten-2-yl radicals are calculated using the equation-of-motion coupled cluster methods with single and double substitutions (EOM-CCSD). The ground and the lowest excited state (n <-- pi) equilibrium geometries are calculated using the CCSD(T) and EOM-SF-CCSD methods, respectively, and adiabatic excitation energies for the n <-- pi state are reported. Systematic changes in the geometries, excitation energies, and Rydberg state quantum defects within this group of radicals are discussed.     

Estimation of the barrier to rotation of benzene in the (eta 6-C6H6)2Cr crystal via topological analysis of the electron density distribution function

The high-resolution X-ray diffraction analysis of the electron density distribution and plane-wave density functional theory has been applied to estimate the lattice energy and barrier to rotation of a benzene ring in the crystal of (eta(6)-C(6)H(6))(2)Cr. Experimental data made it possible to perform analysis of the metal-(pi-ligand) bond and estimate the nature and energy of weak H...H and H...C intermolecular interactions in the crystal. Summation of the intermolecular H...H and H...C interaction energies makes it possible to reproduce the experimental sublimation enthalpy value with high accuracy.     

Implementation of a rapid and automated high performance liquid chromatography method development strategy for pharmaceutical drug candidates

A comprehensive, fully automated strategy is demonstrated for HPLC-UV chromatographic method development using ChromSword optimization software. The strategy involves: (1) the automated screening of various column and mobile phase combinations, (2) rational selection of the best starting conditions; and (3) subsequent automated method development to generate optimized separation methods. Pharmaceutical compounds were applied to solve problematic drug impurity separations. ChromSword software automates the screening, optimization, and documentation steps thus reducing the method development time. The strategy was compared to a manual method development approach showing the automated method strategy affords better selectivity in a shorter time.     

Furan ring opening ‐ indole ring closure: Synthesis of furo[2′,3′:3,4]‐cyclohepta[1,2‐b]indolium chlorides

A new synthetic approach to furo[2′,3′:3,4]cyclohepta[1,2‐b]indolium chlorides is elaborated starting from 2‐acetylaminoaryldifurylmethanes or 2‐aminoaryldifurylmethanes under treatment with methanolic HCl solution. The reaction proceeds in three steps: recyclization, intramolecular cyclization, and disproportionation. In this case the furan ring takes part in building up both pyrrole and seven‐membered rings. The same salts can be obtained directly from 2‐acetylaminobenzaldehydes and 2‐methylfuran under similar conditions without isolation of corresponding 2‐acetylaminoaryldifurylmethanes.     

Structures and stereochemical non-rigidity of Si-substituted N-(dimethylsilylmethyl)- and N-(methylphenylsilylmethyl)amides and -lactams

Eleven new silicon-substituted N-(dimethylsilylmethyl)- and N-(methylphenylsilylmethyl)amides and -lactams bearing a chiral carbon in the amide or lactam fragment, and containing the OSiC₃X (X = Hal, OTf) coordination fragment have been synthesized and their structures determined in solution by spectroscopic means. These structures are consistent with the hypervalency model. Quantum chemical calculations adequately reflect correlations between the type of monodentate ligand X and the geometric parameters of the N-C-O-Si-X fragments.The activation parameters for enantiomerization and diastereomerization in these new compounds and the other related compounds were determined by the dynamic NMR (DNMR) method using full line-shape analysis. The free activation energy values in the absence of external nucleophiles vary from 9 to 27 kcal mol⁻¹. The entropies of activation (ΔS^#) are negative (−20 to −50 cal mol⁻¹ K⁻¹) in all cases except for the chloride derivatives of 4-phenyl-2-pyrrolidone and 4-oxazolidinone that have weaker intramolecular O → Si coordination. Irregular mechanisms of permutational isomerization were proposed on the basis of the DNMR data and the results of quantum-chemical calculations carried out by ab initio (HF) and DFT (PBE, B3PW91, 6-311++G(d,p)). Depending on the coordination environment at silicon, the mechanisms proposed involve either the dissociation of the Si-X bond followed by the Berry pseudorotation or similar in the intermediate or the cleavage of intramolecular O-Si bond with subsequent inversion at the silicon atom. The apparently simple pseudorotation mechanism involving only the pentacoordinate structures 1-21 does not appear to be favoured in any of the examples studied.     

Photodissociation dynamics of the NO dimer. I. Theoretical overview of the ultraviolet singlet excited states

Molecular orbital theory and calculations are used to describe the ultraviolet singlet excited states of NO dimer. Qualitatively, we derive and catalog the dimer states by correlating them with monomer states, and provide illustrative complete active space self-consistent field calculations. Quantitatively, we provide computational estimates of vertical transition energies and absorption intensities with multireference configuration interaction and equations-of-motion coupled-cluster methods, and examine an important avoided crossing between a Rydberg and a valence state along the intermonomer and intramonomer stretching coordinates. The calculations are challenging, due to the high density of electronic states of various types (valence and Rydberg, excimer and charge transfer) in the 6-8 eV region, and the multiconfigurational nature of the ground state. We have identified a bright charge-transfer (charge-resonance) state as responsible for the broadband seen in UV absorption experiments. We also use our results to facilitate the interpretation of UV photodissociation experiments, including the time-resolved 6 eV photodissociation experiments to be presented in the next two papers of this series.