Strong solutions of stochastic equations with rank-based coefficients

We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We show that strong existence and uniqueness hold until the first time three particles collide. Motivated by this result, we improve significantly the existing conditions for the absence of such triple collisions in the case of finite-dimensional systems, and provide the first condition of this type for systems with a countable infinity of particles.     

A proof of the rooted tree alternative conjecture

Bonato and Tardif [A. Bonato, C. Tardif, Mutually embeddable graphs and the tree alternative conjecture, J. Combinatorial Theory, Series B 96 (2006), 874-880] conjectured that the number of isomorphism classes of trees mutually embeddable with a given tree T is either 1 or infinite. We prove the analogue of their conjecture for rooted trees. We also make some progress towards the original conjecture for locally finite trees and state some new conjectures.     

Properties of biopolymer compositions based on products of collagen hydrolysis and polysaccharides

Physicochemical properties of biopolymer compositions based on products of collagen hydrolysis and polysaccharides were studied. The effect of the component ratio on their compatibility was examined.     

Spin fluctuations in hydrogen-stabilized Laves phase UTi2H5

Uranium Laves phase UTi₂ does not exist in a pure form, but can be stabilised by the presence of hydrogen, which can be absorbed in concentration exceeding 5?H atoms/f.u. Low temperature specific heat, magnetic susceptibility, and resistivity indicate that UTi₂H₅ is a spin fluctuator close to the verge of magnetic ordering. Its susceptibility follows at high temperatures the Curie–Weiss law with U effective moment µ_eff[ ?= 3.1?µ_B/U and paramagnetic Curie temperature Θ_p = ?200 K. The temperature dependence of specific heat exhibits a pronounced and weakly field dependent upturn in C_p/T versus T below 10 K reflecting the effect of spin fluctuations. It can be described by an additional T^½ term. The Sommerfeld coefficient γ = 256?mJ/mol K² classifies the compound as a mid-weight heavy fermion. Spin fluctuations are affecting also electrical and thermal transport and thermoelectric power, which all resemble UAl₂. A lattice anomaly at ≈ 240?K, attributed to the melting of hydrogen sublattice, reflects in most of bulk properties.     

Spectroscopic Studies of the Magnetic Excitation and Spin-Phonon Couplings in a Single-Molecule Magnet

Large separations between ground and excited magnetic states in single-molecule magnets (SMMs) are desirable to reduce the likelihood of spin reversal in the molecules. Spin-phonon coupling is a process leading to magnetic relaxation. Both the reversal and coupling, making SMMs lose magnetic moments, are undesirable. However, direct determination of large magnetic states separations (>45 cm⁻¹) is challenging, and few detailed investigations of the spin-phonon coupling have been conducted. The magnetic separation in [Co(12-crown-4)₂](I₃)₂(12-crown-4) ( 1 ) is determined and its spin-phonon coupling is probed by inelastic neutron scattering (INS) and far-IR spectroscopy. INS, using oriented single crystals, shows a magnetic transition at 49.4(1.0) cm⁻¹. Far-IR reveals that the magnetic transition and nearby phonons are coupled, a rarely observed phenomenon, with spin-phonon coupling constants of 1.7–2.5 cm⁻¹. The current work spectroscopically determines the ground–excited magnetic states separation in an SMM and quantifies its spin-phonon coupling, shedding light on the process causing magnetic relaxation.     

Time-dependent density functional calculations of optical rotatory dispersion including resonance wavelengths as a potentially useful tool for determining absolute configurations of chiral molecules

The optical rotations for six organic molecules (verbenone, fenchone, camphor, nopinone, Tr?ger's base, dimethyl-cyclopropane) and the transition metal complex [Co(en)(3)](3+) were calculated as a function of wavelength using time-dependent density functional theory (TDDFT). In the calculations, a realistic behavior of the optical rotation in the vicinity of an electronic transition was obtained by using a phenomenological damping parameter of the order of 0.2 eV (0.007 au). In comparison with experiment, for the molecules studied here the sign and order of magnitude of the optical rotation as well as the excitation energies were reasonably well reproduced in most computations. These findings apply to the investigated wavelength ranges typically between about 200 and 650 nm even when using comparatively small basis sets. Such calculations might therefore routinely be applied to help assigning the absolute configurations of chiral molecules. Supplementary calculations of the circular dichroism (CD) and comparison with experimental CD were used for further assessment of the optical rotation calculations. In particular, a combined study of optical rotation and CD turned out to be useful in cases where the optical rotatory dispersion in a specific energy range exhibits a considerable blue or red shift or where it is difficult to reproduce because of an interplay of several competing Cotton effects. The influence of basis set, density functional, and the damping parameter was also investigated.     

Calculation of circular dichroism spectra from optical rotatory dispersion, and vice versa, as complementary tools for theoretical studies of optical activity using time-dependent density functional theory

A comparison of two theoretical methods based on time-dependent density functional theory for the calculation of the linear dispersive and absorptive properties of chiral molecules has been made. For this purpose, a recently proposed computational method for the calculation of circular dichroism (CD) spectra from the imaginary part of the optical rotation parameter has been applied to six rigid organic molecules. The results have been compared to the CD spectra obtained from the rotatory strengths and from the Kramers-Kronig transformation of optical rotatory dispersion (ORD) curves. We have also investigated a criterion based on the Kramers-Kronig integration formula to determine a number of excitations in truncated CD spectra which may yield a reasonable low frequency resonant ORD. It has been tested by calculating the ORD from the sum-over-states formula both in the nonresonant and resonant regions. Finally, we have applied these methods to model the resonant optical activity of proline at low pH.     

6,6'-Disubstituted benzothiazole trimethine cyanines--new fluorescent dyes for DNA detection

The influence of methyl-, 2-hydroxyethyl-, dimethyl-, diethyl- and benzoyl-amino substituents in the 6,6'-positions of benzothiazole heterocycle of trimethine cyanines on their spectral-luminescent properties and behavior in presence of DNA, RNA and BSA was studied. It was shown that incorporation of 6,6'-substituents generally leads to the increase in dyes tendency to aggregation, resulting in the considerable decrease in the emission intensity of the disubstituted dyes as compared to the unsubstituted ones. Emission of the studied 6,6'-disubstited dyes in DNA presence is considerably more intensive than in presence of RNA, that points on the existing of DNA binding preference for the mentioned dyes. Insertion of benzoyl-amino groups into the 6,6'-positions permitted us to design the DNA-sensitive dyes on the basis of symmetric trimethine cyanines with unsubstituted polymethine chain, while typically such dyes slightly respond on the presence of biopolymers. 6,6'-Benzoyl-amino-disubstituted trimethine cyanines are proposed as efficient dyes for DNA detection.     

Synthesis and use of carboxymethylated lignosulfonates

The conditions for preparing carboxymethylated lignosulfonate derivatives were examined. The complexation of carboxymethyl groups of lignosulfonates with tanning chromium compounds was demonstrated. The possibility of using modified lignosulfonates in leather retanning and filling was shown.