Thin Walled Beams with Residual Stress

A one-dimensional variational problem for an anisotropic, partially inhomogeneous, residually stressed, rectangular thin-walled beam is derived, by Γ-convergence, from the three-dimensional theory of linear elasticity with residual stress.      

The initial boundary value problem for the nonlinear parabolic equation in unbounded domain

In this paper we consider the mixed problem for the equation u _tt  + A ₁ u + A ₂(u _t ) + g(u _t ) = f(x, t) in unbounded domain, where A ₁ is a linear elliptic operator of the fourth order and A ₂ is a nonlinear elliptic operator of the second order. Under natural assumptions on the equation coefficients and f we proof existence of a solution. This result contains, as a special case, some of known before theorems of existence. Essentially, in difference up to previous results we prove theorems of existence without the additional assumption on behavior of solution at infinity.      

Theoretical calculations of homoconjugation equilibrium constants in systems modeling acid-base interactions in side chains of biomolecules using the potential of mean force

The potentials of mean force (PMFs) were determined for systems forming cationic and anionic homocomplexes composed of acetic acid, phenol, isopropylamine, n-butylamine, imidazole, and 4(5)-methylimidazole, and their conjugated bases or acids, respectively, in three solvents with different polarity and hydrogen-bonding propensity: acetonitrile (AN), dimethyl sulfoxide (DMSO), and water (H(2)O). For each pair and each solvent a series of umbrella-sampling molecular dynamics simulations with the AMBER force field, explicit solvent, and counterions added to maintain a zero net charge of a system were carried out and the PMF was calculated by using the Weighted Histogram Analysis Method (WHAM). Subsequently, homoconjugation-equilibrium constants were calculated by numerical integration of the respective PMF profiles. In all cases but imidazole stable homocomplexes were found to form in solution, which was manifested as the presence of contact minima corresponding to hydrogen-bonded species in the PMF curves. The calculated homoconjugation constants were found to be greater for complexes with the OHO bridge (acetic acid and phenol) than with the NHN bridge and they were found to decrease with increasing polarity and hydrogen-bonding propensity of the solvent (i.e., in the series AN > DMSO > H(2)O), both facts being in agreement with the available experimental data. It was also found that interactions with counterions are manifested as the broadening of the contact minimum or appearance of additional minima in the PMF profiles of the acetic acid-acetate, phenol/phenolate system in acetonitrile, and the 4(5)-methylimidazole/4(5)-methylimidzole cation conjugated base system in dimethyl sulfoxide.     

Some new classes of Banach-Mackey spaces

Some weakenings of property (K) of Antosik for locally convex spaces are introduced: local property (K) and, for spaces with Schauder-type decompositions, two variants of property (K) defined in terms of block- and tail-sequences. It is shown that if a space enjoys any of these new properties, then it is Banach-Mackey. An application to the barrelledness of the spaces of Pettis integrable functions is given, and examples are provided to distinguish between the various K-type properties.     

Mass spectrometry of pyrimidine derivatives: Electron impact-induced decomposition of molecular ions of 4-amino-substituted and 4-amino-disubstituted 1,2-dihydro-1-methylpyrimidin-2-ones

Electron impact (EI) mass spectra of fourteen 4-amino-substiruted 1,2-dihydro-1-methylpyrimidin-2-ones are reported. The EI-induced decomposition of their molecular ions is significantly dependent on the chemical nature of the substituents. The routes of mass decomposition established suggest the presence of the tautomeric forms in the gas phase of some investigated compounds.     

The Hilbert-Space Structure of Non-Hermitian Theories with Real Spectra

We investigate the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. After describing a general framework to reformulate such models in terms of Hermitian Hamiltonians defined on the Hilbert space L ₂(-, ), we discuss the significance of the algebra of physical observables.     

Unifying ultrafast magnetization dynamics

We present a microscopic model that successfully explains the ultrafast equilibration of magnetic order in ferromagnetic metals at a time scale tau(M) of only a few hundred femtoseconds after pulsed laser excitation. It is found that tau(M) can be directly related to the so-called Gilbert damping factor sigma that describes damping of GHz precessional motion of the magnetization vector. Independent of the spin-scattering mechanism, an appealingly simple equation relating the two key parameters via the Curie temperature T(C) is derived, tau(M) approximately c(0)h/k(B)T(C)sigma, with h and k(B) the Planck and Boltzmann constants, respectively, and the prefactor c(0) approximately 1/4). We argue that phonon-mediated spin-flip scattering may contribute significantly to the sub-ps response.     

Chain version of the constant coupling theory with application to classical Heisenberg model

The version of the constant coupling theory, based on exact solutions of some onedimensional systems is proposed. The theory is applied to classical Heisenberg model. The expressions for the order parameters, internal energy, free energy, entropy and critical temperature are given. A good agreement of the presented results with predictions of high temperature series expansion is obtained.     

Regioselective reactions of enaminones with enones—II: Intramolecular rearrangement involving carbon to oxygen acyl migrations

Intramolecular dynamic behaviour helps in predicting the regioselectivity of reactions in ambident molecules. Thus the enaminones (1) react on the C-2 carbon atom with benzoquinone. Reaction proceeds with an intramolecular acyl shift following formation of the initial reaction complex upon reaction at position C-2 of the enaminone and the quinone. Under certain conditions the reaction is regiospecific and proceeds stereospecifically.     

Solvent-induced isotope effects in NMR spectroscopy. A study of hydrogen bonding between the carbonyl group in chalcone and trifluoracetic acid (TFA-d or TFA) in chloroform solution

Splittings, δ_i, were observed for each carbon atom, C_i, of chalcone in spectra obtained from coaxial 5 and 10 mm NMR sample tubes containing solutions equimolar in the concentration of the ketone and of TFA or TFA-d as hydrogen-bond donors, respectively. It was found that a linear expression, δ_i = (K–1)x_HΔ_i+x_Dδ_i(D, H) relates these splittings, δ_i, induced by the isotopic substitution in a hydrogen bond, to the parameter Δ_i, denoting the change in chemical shift for each carbon site in complexed and free ketone, and δ_i(D, H), the solvent-induced isotope effect in a complex. The origin of the phenomenon is briefly discussed. It is also shown that the secondary deuterium isotope effect can give the same information about the form of the potential energy well in the hydrogen-bond as the primary H/D isotopte shifts.