Theoretical analysis of solvent effects on nitrogen NMR chemical shifts in oxazoles and oxadiazoles

Using quantum chemistry methods we have evaluated the solvent effects on the ¹⁴N NMR chemical shifts in five oxa- and oxadiazoles dissolved in twelve solvents. These solvents differ in their polarity with the dielectric constants varying from 2 to 80. Moreover, three of them have a hydrogen-bond donor character. All possible hydrogen-bonding in the water solution with the oxygen and nitrogen (hydrogen-acceptor) centers in oxazoles (2) and oxadiazoles (3) have been considered in our studies. It has been shown that both the pure solvent and hydrogen-bonding effects are significant and result in ¹⁴N magnetic shielding increase. In water solutions the pure solvent effect is larger than the hydrogen-bonding effect. In addition, the solvent effect has been analyzed in terms of its direct and indirect contributions. It should be emphasized that our theoretical results for ¹⁴N chemical shifts in oxa- and oxadiazoles remain in a very good agreement with the accurate experimental data.     

Identification of inherent noise components of semiconductor devices on an example of optocouplers

In the paper, a method of estimation of parameters of Gaussian and non-Gaussian components in the noise signal of semiconductor devices in a frequency domain is proposed. The method is based on composing estimators of two spectra, corresponding to 1/f^α noise (Gaussian component) and two-level RTS noise (non-Gaussian component). The proposed method can be applied for precise evaluation of the corner RTS frequency fRTS in the noise spectrum.     

Error bounds for non-selfadjoint PDE eigenvalue problems

We introduce a posteriori bounds for the eigenfunctions (eigenvalues) of non-selfadjoint diagonalizable PDE-eigenvalue problems which incorporates an inexact solution of the corresponding generalized matrix eigenvalue problem. The estimates combine the standard perturbation results with the saturation assumption for the eigenfunctions. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gagliardo–Nirenberg inequalities in regular Orlicz spaces involving nonlinear expressions

We consider a triple of N-functions (M,H,J) that satisfy the Δ^′-condition, and suppose that an additive variant of interpolation inequality holds

where , is an arbitrary set invariant with respect to external and internal dilations. We show that the above inequality implies its certain nonlinear variant involving the expressions and . Various generalizations of this inequality to the more general class of N-functions, measures and to higher order derivatives are also discussed and the examples are presented.     

Leitmann’s direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales

The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. This includes the discrete-time, the quantum, and the continuous/classical calculus of variations as particular cases. In this note we follow Leitmann’s direct method to give explicit solutions for some concrete optimal control problems on an arbitrary time scale.     

Monotonicity methods in generalized Orlicz spaces for a class of non‐Newtonian fluids

The paper concerns existence of weak solutions to the equations describing a motion of some non‐Newtonian fluids with non‐standard growth conditions of the Cauchy stress tensor. Motivated by the fluids of strongly inhomogeneous behavior and having the property of rapid shear thickening, we observe that the L^p framework is not suitable to capture the described situation. We describe the growth conditions with the help of general x‐dependent convex function. This formulation yields the existence of solutions in generalized Orlicz spaces. As examples of motivation for considering non‐Newtonian fluids in such spaces, we recall the electrorheological fluids, magnetorheological fluids, and shear thickening fluids. The existence of solutions is established by the generalization of the classical Minty method to non‐reflexive spaces. The result holds under the assumption that the lowest growth of the Cauchy stress is greater than the critical exponent q=(3d+ 2)/(d+ 2), where d is for space dimension. The restriction on the exponent q is forced by the convective term. Copyright © 2009 John Wiley & Sons, Ltd.     

Maximum principles and nonexistence results for radial solutions to equations involving p‐Laplacian

We obtain the variant of maximum principle for radial solutions of, possibly singular, p‐harmonic equations of the form as well as for solutions of the related ODE. We show that for the considered class of equations local maxima of |w| form a monotone sequence in |x| and constant sign solutions are monotone. The results are applied to nonexistence and nonlinear eigenvalue problems. We generalize our previous work for the case h≡0. Copyright © 2010 John Wiley & Sons, Ltd.     

Hydrogen adsorption on Pd(133) surface

An approach based on measurements of the total energy distribution (TED) of field emitted electrons is used in order to examine properties of the Pd(133) from the aspect of hydrogen adsorption. The most favourable sites offered to a hydrogen atom to be adsorbed are indicated and an attempt to ascribe the peaks of the enhancement factor R in the TED spectrum to the specific adsorption sites is made.      

Adaptive solution of elliptic PDE-eigenvalue problems.

In this paper we introduce a new adaptive algorithm (AFEMLA) for elliptic PDE-eigenvalue problems. In contrast to other approaches the algebraic eigenvalue problem does not have to be solved to full accuracy. We incorporate the iterative solution of the resulting finite dimensional algebraic eigenvalue problems in the adaptation process in order to balance the cost with the costs for the iterative eigenvalue method. We present error estimates that incorporate the discretization errors, approximation errors in the eigenvalue solver and roundoff errors. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)