The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations

The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated solution sets, based on a Leray-Schauder type fixed point theorem, are obtained.     

The time arrow in a Planck gas

In this paper the quantum heat transport equation (QHT) is applied to the study of thermal properties of Planck gas, i.e., a gas of massive particles with mass equal to the Planck massM _P = (łc/G)^1/2 and whose relaxation time equals the Planck timeτ _p = (łG/c ⁵)^1/2. The quantum of thermal energy for a Planck gas,E ^Planck = 10¹⁹GeV, and the quantum thermal diffusion coefficientD ^Planck = (ħG/c)^1/2 are calculated. Within the framework of QHT the thermal phenomena in a Planck gas can be divided into two classes: for a time period shorter thanτ _p , the time reversal symmetry holds and for a time period longer thanτ _p , time symmetry is broken, i.e., a time arrow is created.     

Conversion of nitrogen oxides in N2:O2:CO2 and N2:O2:CO2:NO2 mixtures subjected to a dc corona discharge

This paper concerns the influence of a direct current (dc) corona discharge on production and reduction of NO, NO₂ and N₂O in N₂:O₂:CO₂ and N₂:O₂:CO₂:NO₂ mixtures. The corona discharge was generated in a needle-to-plate reactor. The positively polarized electrode consisted of 7 needles. The grounded electrode was a stainless steel plate. The gas flow rate through the reactor was varied from 28 to 110 cm³/s. The time-averaged discharge current ranged from 0 to 6 mA. It was found that in the N₂:O₂:CO₂ mixture the corona discharge produced NO, NO₂ and N₂O. In the N₂:O₂:CO₂:NO₂ mixture the reduction of NO₂ was between 6–56%, depending on the concentration of O₂, gas flow rate and corona discharge current. The NO₂ reduction was accompanied by production of NO and N₂O. The results show that efficient reduction of nitrogen oxides by a corona discharge cannot be expected in the mixtures containing N₂ and O₂ if reducing additives are not employed.     

Copper(II) and oxovanadium(IV) complexes of α-hydroxymethylserine

Summary Potentiometric and spectroscopic measurements were used to characterize the binding ability of -hydroxy-methylserine (Hms) with copper(II) and oxovanadium(IV) ions. The ligand was found to be generally a more efficient chelating agent than serine. Both of the deprotonated hydroxyl groups of Hms can be involved in coordination to vanadyl ions, whereas copper(II) binds in the same way as with serine.     

PM3 study of the proton affinities of 2-, 3-, and 4-monosubstituted pyridines in the gas phase

Heats of formation (ΔH_f) and proton affinities (PA) of 2-, 3-, and 4-monosubstituted pyridines in the gas phase are calculated using the AM1 and PM3 semiempirical methods. The following substitutents are considered: NO₂, CN, CF₃, CHO, F, Cl, COCH₃, H, CH₃, OCH₃, SCH₃, NH₂, and N(CH₃)₂. The results are compared with the experimental data. Both methods reproduce the ΔH_f with comparble accuracy; the rms deviations are 4.1 (AM1) and 4.5 kcal/mol (PM3) for the free bases and 9.5 (AM1) and 9.7 kcal/mol (PM3) for their conjugated acids. The PA are systematically underestimated by both methods, but AM1 appears to be clearly better than PM3 for reproducing the experimental values. The rms deviations for AM1 and PM3 are 5.1 and 9.6 kcal/mol, respectively. This is due to a cancellation of systematic errors in the calculated ΔH_f in the AM1 case and to a summation of the errors in the PM3 case. Both methods correctly reproduce conformations of the molecules under consideration.     

Anion radical formation in the reaction of chloranilic acid with n-methylpiperidine in acetonitrile

Reaction of chloranilic acid with N-methylpiperidine in acetonitrile has been studied. The product of the reaction is an unusually stable anion radical of quinone. The presence of radicals has been confirmed by EPR measurements. Stability constant, extinction coefficients and thermodynamic reaction parameters are reported. Mechanism of the reaction is proposed. This revised version was published online in June 2006 with corrections to the Cover Date.     

Self-exciting vibrations and Hopf's bifurcation in non-linear stability analysis of rail vehicles in a curved track

The main objective of this article is to present the authors' view of and results on non-linear lateral stability of rail vehicles in a curved track. Three elements are exploited in order to secure this objective. Firstly, physical genesis of the problem is discussed, and its similarity to straight track analysis is emphasised. Results of the theories of self-exciting vibrations and bifurcation are the key elements here. Secondly, the method suitable for analysis in a curved track is presented. New necessary elements, extending the better established methods for straight track are clearly mentioned and described. The methodology of building original stability maps, being the basis for the analysis and valid for whole range of curve radii and straight track is represented. Thirdly, a sample of the analysis is shown in order to give the idea how the method can be utilised. The case study refers to the influence of wheel/rail profiles on the stability in circularly curved track and straight track as well. Two different pairs of wheel/rail profiles are used and the corresponding results compared. The main contributions of the article are: a discussion of the physical nature of phenomena related to the stability in a curved tracks, and the method (procedure) established for the reasons of the analysis. Another and more general contribution is our say in the hot polemics on the advisability of stability analysis in curves and the advantages of the non-linear critical speed over the linear one.     

A New Crystal Phase Molybdate Yb2Mo4O15: The Synthesis and Upconversion Properties

A new upconversion nanocrystal phase Yb₂Mo₄O₁₅:Er is developed by using a facile aqueous‐precipitation procedure combined with thermal annealing. Nanocrystals of Yb₂Mo₄O₁₅ are exclusively synthesized, with particle sizes ranging from 1 to 20 nm. The optical properties are characterized and a high upconversion quantum yield is determined to be ≈1.3% at room temperature, under excitation of ≈500 mW cm^?2 IR (975 nm). To the best of our knowledge, this is the first work concerning the synthesis of nanocrystalline Yb₂Mo₄O₁₅ and the characterization of its upconversion properties, which possesses the potential to be utilized in bio‐probing and thin‐film optoelectronic device applications.     

Electric-field-induced steering in soliton direction of propagation in chiral nematic liquid crystals

In this work we demonstrate the properties of spatial solitary waves in chiral nematic liquid crystals with an external electric field. Such self-trapped beams, called nematicons, were created due to the optical reorientation nonlinearity for a light power of a few tens of milliwatts. We show that the direction of propagation of such nematicons can be changed by applying an external electric field. Additionally, this effect can be modified by changing the input polarization of the light beam. The experimental results were obtained in four independent guiding layers created by a chiral nematic structure.