Dirichlet problem for the general Beltrami equation in Jordan domains

We study the Dirichlet problem for the general degenerate Beltrami equations $ \bar{\partial}f=\mu \partial f+\nu \overline{{\partial f}} $ in a Jordan domain. Some criteria for the existence of regular solutions are given.     

Schrödinger Operators with δ and δ′-Potentials Supported on Hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity.     

Stress Integration of the Hoek-Brown Material Model Using Incremental Plasticity Theory

This paper presents the formulation of the stress integration procedure for the Hoek-Brown (HB) material model with non-associative yielding condition by using the incremental plasticity method. Main idea of this method is to reach the solution by calculating the plastic matrix according to the method of incremental plasticity (used for elastic constitutive matrix corrections), and with the use of the total strain increment. Computational procedure is implemented within the PAK program package. Results of this procedure were compared with the solutions obtained by other program that contains this material model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of pitching on performance of VAWTs

Self- starting is the major obstacle to be overcome for successful design of a vertical axis wind turbine (VAWT). In the past has been suggested that pitching the turbine blades such that pitch angle is not 90 degrees allows for self-starting. To understand the physics surrounding pitching, an analysis is carried out for a common airfoil profile, NACA 0012. The vortex model is used to predict aerodynamic performance of VAWT with pitched blades at various angles. As a result of the analysis carried out for the airfoil at various pitch angles, it was shown that the “dead band” phenomenon could be overcome, but only slightly. At the same time, to overcome the “dead band” with a level on confidence, torques in the tip speed ratio (TSR ) range of 0.75 to 2.75 must be increased to values further above zero. The paper aimed at giving an insight into the small wind turbine starting behavior and its influence parameters. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Complexity and in-approximability of a selection problem in robust optimization

We establish strong NP-hardness and in-approximability of the so-called representatives selection problem, a tool selection problem in the area of robust optimization. Our results answer a recent question of Dolgui and Kovalev (4OR Q J Oper Res 10:181–192, 2012).     

Criterion for Cannon’s Conjecture

The Cannon Conjecture from the geometric group theory asserts that a word hyperbolic group that acts effectively on its boundary, and whose boundary is homeomorphic to the 2-sphere, is isomorphic to a Kleinian group. We prove the following Criterion for Cannon’s Conjecture: a hyperbolic group G (that acts effectively on its boundary) whose boundary is homeomorphic to the 2-sphere is isomorphic to a Kleinian group if and only if every two points in the boundary of G are separated by a quasi-convex surface subgroup. Thus, the Cannon’s conjecture is reduced to showing that such a group contains “enough” quasi-convex surface subgroups.     

Fast decoding of Gabidulin codes

Gabidulin codes are the analogues of Reed–Solomon codes in rank metric and play an important role in various applications. In this contribution, a method for efficient decoding of Gabidulin codes up to their error correcting capability is shown. The new decoding algorithm for Gabidulin codes (defined over ${\mathbb{F}_{q^m}}$ ) directly provides the evaluation polynomial of the transmitted codeword. This approach can be seen as a Gao-like algorithm and uses an equivalent of the Euclidean Algorithm. In order to achieve low complexity, a fast symbolic product and a fast symbolic division are presented. The complexity of the whole decoding algorithm for Gabidulin codes is ${\mathcal{O} (m^3 \, \log \, m)}$ operations over the ground field ${\mathbb{F}_q}$ .     

Electrophilically Activated Nitroalkanes in Synthesis of 3,4-Dihydroquinozalines

Nitroalkanes activated with polyphosphoric acid serve as efficient electrophiles in reactions with various nucleophilic amines. Strategically placed second functionality allows for the design of annulation reactions enabling preparation of various heterocycles. This strategy was employed to develop an innovative synthetic approach towards 3,4-dihydroquinazolines from readily available 2-(aminomethyl)anilines.     

1H,4H-1,4-diborabuckminsterfullerene with pyridine molecules and ytterbium endo-atom

The competition between the ytterbium endo-atom and the pyridine exo-molecules as nucleophiles interacting with the electron-deficient 1H,4H-1,4-diborabuckminsterfullerene was studied using the quantum chemical DFT PBE0 method. The equilibrium structural parameters, dipole moments, IR spectra, and exothermic effects of the formation of the C₅₈B₂•Py₂ adduct and the endohedral Yb@C₅₈B₂•Py₂ complex were determined. The concept of the state of oxidation/reduction of an atom in a chemical compound has been clarified. The localization of the ytterbium(II) under a pair of equivalent carbon atoms bonded to boron(III) atoms is predicted. The introduction of ytterbium(II) into the adduct cavity weakens exo-bonds with pyridine molecules without changing the oxidation state of boron(III). Each nitrogen atom retains a lone electron pair, coordinated by a boron(III). The ytterbium(II) endo-atom retains 14 electrons in f states.