Ordinary and strong density continuity of complex analytic functions

In the paper we prove that the complex analytic functions are (ordinarily) density continuous. This stays in contrast with the fact that even such a simple function asG:²²,G(x,y)=(x,y ³ ), is not density continuous [1]. We will also characterize those analytic functions which are strongly density continuous at the given pointa . From this we conclude that a complex analytic functionf is strongly density continuous if and only iff(z)=a+bz, wherea, b andb is either real or imaginary.     

Simple formula for nuclear charge radius

A new formula for the nuclear charge radius is proposed, dependent on the mass numberA and neutron excessN-Z in the nucleus. It is simple and it reproduces all the experimentally available mean square radii and their isotopic shifts of even-even nuclei much better than other frequently used relations.This work is partly supported by the Polish Committee of Scientific Research under contract No. 203119101     

Spectrochemical Properties of Noncubical Transition Metal Complexes in Solutions. IX. The Mixed Tetragonal Distorted Bis(Salicylato)Cobalt(II) Complex in Various Solvents

Mixed cobalt(II) complexes with the monodentate ligands: 2-hydroxybenzoic acid deprotonated (sal^–, the salicylate ion) and water, have been investigated. The combined results of the spectrophotometric and conductance measurements, as well as known the X-ray structure for solids, were used to determine the structure of the studied complexes in solution. The electronic absorption spectra in aqueous acid (0.01M HClO₄), ethylene glycol (glycol), formamide (FM), N,N-dimethylformamide (DMF), and dimethyl sulfoxide (DMSO) solutions have been recorded. The d-d electronic spectra have been treated by the crystal-field model (CFM) and angular overlap model (AOM). Low-symmetry splittings of the broad asymmetric bands in the experimental spectra (solutions at room temperature) were found by Gaussian analysis. The effect of the and bonding of the monodentate ligands (with oxygen-donor ligators) on the central metal ion was described in the ligand–field framework. A comparison of the stereochemistry of the complex species in various solutions was made.     

On Calderón-Toeplitz operators

We discuss boundedness and Schatten ideal criteria for a class of Toeplitz style operators based on the Calderón reproducing formula. These operators are a variation on Calderón-Zygmund operators but our results also apply to classical Toeplitz operators acting on the weighted Bergman space of the upper half plane.     

Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers

A symmetry-adapted perturbation theory based on Kohn-Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchange-correlation potentials has been applied to the He2, Ne2, (H2O)2, and (CO2)2 dimers. It is shown that SAPT(KS) is able to recover the electrostatic, first-order exchange, second-order induction, and exchange-induction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, first-order exchange, and second-order induction energies has been provided.     

Modifying the thermosensitivity of copolymers of sodium styrene sulfonate and<Emphasis Type="Italic"> N</Emphasis>-isopropylacrylamide with dodecyltrimethylammonium chloride

The interactions between copolymers of sodium styrene sulfonate (SSS) and N-isopropylacrylamide (NIPAM), anionic polyelectrolytes, and dodecyltrimethylammonium chloride (DTAC), a cationic surfactant, were studied in aqueous solutions of various ionic strengths. The copolymers were found to be thermoresponsive, showing a lower critical solution temperature (LCST). The influence of the polymer composition, the surfactant concentration, and the ionic strength on the LCST was studied. The surfactant was found to interact strongly with the polymer, forming mixed polymer-surfactant micelles. The critical aggregation concentration (cac) of the polymer-surfactant system was found from fluorescence spectroscopy using pyrene as a fluorescent probe. A strong dependence of the anionic polyelectrolyte-cationic surfactant interactions on the structure of the ionic comonomer was observed.     

Generation of ortho-quinone methides upon thermal extrusion of sulfur dioxide from benzosultones

3H-1,2-Benzoxathiole 2,2-dioxides (benzosultones) undergo thermal extrusion of sulfur dioxide to form ortho-quinone methides that enter Diels-Alder reaction with maleimides to form chroman 2,3-dicarboxylic acid derivatives.     

Functionalization of Electrode Surfaces with Monolayers of Azocompounds and Gold Clusters

Properties of monolayers of azocrown compound self-assembled on gold substrates were studied using voltammetry and scanning tunneling microscopy. The surface concentrations of this compound in monolayers were determined from the area of the voltammetric reduction peaks. The area per one molecule estimated from voltammetry experiments is 0.65 nm². This value was comparable with the limiting molecular area of the compound in the Langmuir–Blodgett film at the air–water interface. We also observed the presence of gold clusters and other gold structures by STM when a gold electrode modified with azocrown compound was dipped into the tetrachloroaurate solution. Even better spectra of clusters were obtained following one voltammetric scan in the range 0.5 to ?0.6 V. After more cycles or if we condition the electrode at 0.4 V the clusters aggregate into wires.     

Boundedness of solutions of a system of integro-differential equations

Let b: [?1, 0] →$\text{R}$ be a nondecreasing, strictly convex C²-function with b(? 1) = 0, and let g: $\text{R}$ⁿ → $\text{R}$ⁿ be a locally Lipschitzian mapping, which is the gradient of a function G: $\text{R}$ⁿ → $\text{R}$. Consider the following vector-valued integro-differential equation of the Levin-Nohel type

$\text{x}\text{?}\text{(t)=?∝}{}_{\mathrm{?1}}{}^0\text{b(θ)g(x(t + θ))dθ}$

. (E) This equation is used in applications to model various viscoelastic phenomena. By LaSalle's invariance principle, every bounded solution x(t) goes to a connected set of zeros of g, as time t goes to infinity. It is the purpose of this paper to give several geometric criteria assuring the boundedness of solutions of (E) or some of its components.     

Effect of temperature and concentration on the structure of N-methylacetamide-water complexes: Near-infrared spectroscopic study

Generalized two-dimensional (2D) FT-NIR correlation spectroscopy and chemometric methods have been used to study temperature-dependent spectral changes in pure N-methylacetamide (NMA) and NMA-water mixtures. We also examined the effect of varying water content on the structure of the mixture. It has been found that the extent of self-association of NMA in CCl4 is very high; the association occurs even at concentration of 0.001 M. In the pure liquid NMA, the population of the monomers is negligible and the structure is dominated by the linear associates. An increase in temperature reduces the number of hydrogen bonds, but in contrast to alcohols their strength remains nearly the same. This reflects a difference in the mechanism of thermal breaking of the associates of NMA and alcohols. The present results reveal that the interaction between NMA and water in the NMA-rich region (X(H2O) < 0.1) does not have a significant effect on the intrinsic structure of NMA. The structure of NMA is dominant, and the molecules of water do not form separate clusters but are dispersed and incorporated into the structure of NMA. We did not observe the presence of the free OH groups in the mixture. This led to the suggestion that each molecule of water forms two hydrogen bonds to two different molecules of NMA. An analysis of the asynchronous spectra reveals that most of the peaks observed in the asynchronous spectra, constructed from the temperature-dependent data, simply result from the frequency shift. This assumption is supported by the simulation studies.