A note on scheduling to meet two min-sum objectives

We consider a single machine scheduling problem with two min-sum objective functions: the sum of completion times and the sum of weighted completion times. We propose a simple polynomial time (1+(1/γ),1+γ)-approximation algorithm, and show that for γ>1, there is no (x,y)-approximation with 1<x<1+(1/γ) and 1<y<1+(γ-1)/(2+γ).     

Properties of Josephson junctions in the inhomogeneous magnetic field of a system of ferromagnetic particles

The effect of an array of ferromagnetic nanoparticles on the field-dependent critical current of the short overlap Josephson junction is experimentally studied. Large reversible variations of the maximum critical current are observed depending on the magnetic state of the particles. The pronounced commensurability effects are detected which are proved by the additional peaks of magnetic field induced diffraction pattern.     

Inferring mixed-culture growth from total biomass data in a wavelet approach

It is shown that the presence of mixed-culture growth in batch fermentation processes can be very accurately inferred from total biomass data by means of the wavelet analysis for singularity detection. This is accomplished by considering simple phenomenological models for the mixed growth and the more complicated case of mixed growth on a mixture of substrates. The main quantity provided by the wavelet analysis is the Hölder exponent of the singularity that we determine for our illustrative examples. The numerical results point to the possibility that Hölder exponents can be used to characterize the nature of the mixed-culture growth in batch fermentation processes with potential industrial applications. Moreover, the analysis of the same data affected by the common additive Gaussian noise still lead to the wavelet detection of the singularities although the Hölder exponent is no longer a useful parameter.     

Deformations of functionals and bifurcations of extremals

We study homology characteristics of critical values and extremals of Lipschitz functionals defined on bounded closed convex subsets of a reflexive space that are invariant under deformations. Sufficient conditions for the existence of a bifurcation point of a multivalued potential operator (the switch principle for the typical number of an extremal) are established.     

Asymptotics in the Baum—Katz formula for random fields

In 1996, D. Deng established an analog of the Baum—Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained.     

Production of Ωscb baryons in photon-photon collisions

Methods for calculating the total and differential cross sections for the production of Ω_scb baryons in photon-photon collisions and the results of respective calculations are described.     

Effect of accumulation on the formation of multiply charged ions in solids under grazing incidence of multiple laser radiation

The effect of accumulation on the formation of multiply charged ions in optically opaque solids as a function of the number and the angle of incidence of laser pulses is investigated by mass spectrometry. It is revealed that the accumulation effect manifests itself at prethreshold power densities q = 10⁸–10⁹ W/cm² irrespective of the angle of incidence of laser radiation α = 18°–85° and at subthreshold power densities q > 10¹⁰ W/cm² in the case of grazing incidence of laser radiation at an angle α = 85°. The accumulation effect brings about an increase in the maximum charge multiplicity Z _max of tungsten ions and a decrease in the number of impurity ions and in their intensity. No accumulation effect is observed at subthreshold power densities when laser radiation is incident at an angle α = 18°.     

Influence of the prehistory of NaNbO3-Gd1/3NbO3 ceramics and single crystals on their dielectric properties

The dielectric properties of a ceramic and a single crystal of the same composition 0.9NaNbO₃-0.1Gd_1/3NbO₃ (NNG10) with different prehistories of the material are investigated in the low-and infralow-frequency ranges. It is revealed that the dielectric aging of the material based on the NaNbO₃ antiferroelectric with a smeared phase transition differs in character from similar phenomena observed in relaxor ferroelectrics.     

Influence of the defect structure on the electrical conductivity of Pb5Ge3O11 single crystals at high temperatures

The impedance spectra of Pb₅Ge₃O₁₁ single crystals are measured in the frequency range from 5 Hz to 13 MHz at temperatures of 600 to 800 K in dry air and in a dry or wet nitrogen gas. It is found that the temperature and the gas composition significantly affect the electrical properties of the compound. The data obtained are used to discuss the origin of crystal lattice defects and their influence on charge transfer. It is concluded that the conduction is mixed in character (p-type electronic and ionic due to oxygen ions). The proton conduction is shown experimentally to be feasible. The possible mechanisms of proton transport in Pb₅Ge₃O₁₁ are discussed.