A hybrid evolutionary algorithm for the two-dimensional packing problem

This paper presents a hybrid evolutionary algorithm for the two-dimensional non-guillotine packing problem. The problem consists of packing many rectangular pieces into a single rectangular sheet in order to maximize the total area of the pieces packed. Moreover, there is a constraint on the maximum number of times that a piece may be used in a packing pattern. The set of packing patterns is processed by an evolutionary algorithm. Three mutation operators and two types of quality functions are used in the algorithm. The best solution obtained by the evolutionary algorithm is used as the initial solution in a tree search improvement procedure. This approach is tested on a set of benchmark problems taken from the literature and compared with the results published by other authors.     

Nevanlinna–Pick Problem and Uniqueness of Left Inverses in Convex Domains,Symmetrized Bidisc and Tetrablock

In the paper we discuss the problem of uniqueness of left inverses (solutions of two-point Nevanlinna–Pick problem) in bounded convex domains, strongly linearly convex domains, the symmetrized bidisc and the tetrablock.     

On a Unique Ergodicity of Some Markov Processes

It is proved that the sufficient condition for the uniqueness of an invariant measure for Markov processes with the strong asymptotic Feller property formulated by Hairer and Mattingly (Ann Math 164(3):993–1032, 2006) entails the existence of at most one invariant measure for e-processes as well. Some application to time-homogeneous Markov processes associated with a nonlinear heat equation driven by an impulsive noise is also given.     

Integers without divisors in a given progression

An asymptotic formula is given for the number of integers n ≤ x which do not have divisors in a fixed arithmetical progression. This extends a previous result of Banks et al. (Forum Math 20:1005–1037, 2008) who considered the case of progressions with prime difference.     

Generalized covariance inequalities

We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.     

The Ising version of the t–J model

The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.     

Measurements in Situ and Spectral Analysis of Wind Flow Effects on Overhead Transmission Lines

In the paper an important issue of vibrations of the transmission line in real conditions was analyzed. Such research was carried out by the authors of this paper taking into account the cross-section of the cable being in use on thetransmission line. Analysis was performed for the modern ACSR high voltage transmission line with span of 213.0 m. The purpose of the investigation was to analyze the vibrations of the power transmission line in the natural environmentand compare with the results obtained in the numerical simulations. Analysis was performed for natural and wind excited vibrations. The numerical model was made using the Spectral Element Method. In the spectral model, for variousparameters of stiffness, damping and tension force, the system response was checked and compared with the results of the accelerations obtained in the situ measurements. A frequency response functions (FRF) were calculated. Thecredibility of the model was assessed through a validation process carried out by comparing graphical plots of FRF functions and numerical values expressing differences in acceleration amplitude (MSG), phase angle differences (PSG) and differences in acceleration and phase angle total (CSG) values. Particular attention was paid to the hysteretic damping analysis. Sensitivity of the wave number was performed for changing of the tension force and section area of thecable. The next aspect constituting the purpose of this paper was to present the wide possibilities of modelling and simulation of slender conductors using the Spectral Element Method. The obtained results show very good accuracy in the range of both experimental measurements as well as simulation analysis. The paper emphasizes the ease with which the sensitivity of the conductor and its response to changes in density of spectral mesh division, cable cross-section,tensile strength or material damping can be studied.     

Synthesis of new 2-oxosparteine derivatives

For the first time, substituents to the 3-position of 2-oxosparteine have been introduced. The synthesis of 3-phenylthiolupanine, 3,3-di(phenylthio)lupanine, 3-dehydrolupanine, 3-bromodehydro-lupanine and 2-thiono-3-dehydrosparteine has been described. The stereochemistry of these compounds has been determined and by NMR spectroscopy and X-ray crystallography.     

Desymmetrization of malonamides via an enantioselective intramolecular Buchwald-Hartwig reaction

A new form of enantioselective nitrogen arylation reaction is described. Beginning with symmetrical α-(2-bromobenzyl)malonamides, intramolecular palladium-catalyzed cross-coupling using a catalyst system including 3.3 mol % Pd(OAc)₂ and 6.6 mol % of the chiral biaryl monophosphine (R)-MOP, desymmetrized quinolinone products are obtained in nearly quantitative yields in enantiomeric ratios up to 88:12. This Letter represents a rare example of enantioselective Buchwald-Hartwig reaction.