Atomic dipole approximation and energies of interactions between purine and pyrimidine bases. I. Electrostatic interactions of adenine with uracil,thymine, thiouracils,dihydrouracil, and 5-fluorouracil

The atomic dipole approximation has been employed to calculate the energies of electrostatic interaction between adenine and various pyrimidine derivatives. Minima of the interaction energy for various planar configurations were determined. Inclusion of the “monopole–dipole” and “dipole–dipole” terms in the multipole expansion improves considerably the agreement with experimental data. The effect of sulfur substitution has been investigated in detail. Formation of N? H…?S hydrogen bonds is less favorable than of N? H…?O bonds, due largely to the lower atomic dipole of the sulfur atom resulting from the shift of the π-electron charge toward the neighboring carbon. The results are relevant to the interactions of thiouracils in nucleic acids.     

On spatial contagion and multivariate GARCH models

We propose a method for defining and measuring spatial contagion between two financial markets via conditional copulas. Some theoretical results on monotonicity and asymptotic properties of Gaussian copulas with respect to conditioning are presented. Next, we combine the spatial contagion approach with time series models. We investigate which model from a large family of multivariate GARCH is the best tool for modelling spatial contagion. In an empirical study, we show that among models designed for general fit, a two‐step model fitting procedure reduces the ability to describe the contagion effect. This is a feature of copula‐GARCH models. Copyright © 2013 John Wiley & Sons, Ltd.     

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM—The International Journal on Mathematics Education—by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers’ and didacticians’ engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice.     

On the Milnor K-theory of the function fields of quasihomogeneous cones

Let V be a quasihomogeneous normal variety. The aim of this paper is to describe the Milnor K-theory of the function field of V in terms of the second residue homomorphisms associated with subvarieties and resolution data of V.Supported by KBN, 2 P301 010 06.     

Exponentially Tapered Josephson Junction: Some Analytic Results

We investigate the dynamical properties of an exponentially tapered Josephson junction using a simple one-dimensional model described by a perturbed (nearly integrable) sine-Gordon equation. An approximate analytic solution is based on the linearization about a rapidly oscillating background. We compare the analytic results with direct numerical simulations for the magnetic field patterns in the junction. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 348–353, August, 2005     

Nonequilibrium solvent polarization in kinetics of SN2 reactions

The solvent effect on the experimental activation barriers for the reactions of methyl iodide with chloride and thiocyanate ions was analyzed according to the Marcus and Shaik theories, considering S_N2 mechanism in terms of a single electron shift. The linear increase in the solvent reorganization energy of the Marcus theory (after removing contributions from the specific solvation) with the solvent Pekar factor, describing the effect of the nonequilibrium solvent polarization, was observed for six aprotic solvents. The direct support of the title effect based on the Shaik theory was less evident; however, in general, the calculated activation barriers in 10 solvents change parallel with the experimental ones. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 35: 61–66, 2003     

Retention behavior of peptides in hydrophilic-interaction chromatography

Selected hydrophilic interaction chromatography (HILIC) columns packed with bare silica, bridge-ethyl hybrid silica, or an amide sorbent chemistry were utilized for an investigation of chromatographic behavior and separation selectivity of tryptic peptides. Retention model was proposed allowing for retention prediction of peptides with correlation coefficient R(2)~0.92-0.97 for various columns. The values of optimized amino acid retention coefficients were compared to those obtained for reversed-phase liquid chromatography (Gilar et al., Anal. Chem. 2010, 82, 265-275) and used to elucidate the impact of different amino acid on peptide HILIC retention. In contrast to reversed-phase chromatography, where presence of Phe, Trp, Ile, and Leu amino acid residues in sequence strongly promoted, and presence of hydrophilic His, Lys and Arg residues strongly reduced peptide retention, the effects of these amino acid residues in HILIC were opposite (His, Lys and Arg promote, Phe, Trp, Ile and Leu demote peptide retention in HILIC). Retention coefficient optimized for pH experiments illustrated the impact of silanols on HILIC retention.     

On the connectivity of graphs generated by a sum of random mappings

We consider four models of random directed multigraphs with n labeled vertices of out-degree d. First we establish formal relationships between our models with respect to exact and asymptotic (as n → ∞) probabilities of possessing a graph monotone property. We also study the asymptotic behavior of the strength of connectivity of the underlying simple graphs when d = o(n). © 1993 John Wiley & Sons, Inc.