Homological Algebra for Persistence Modules

Foundations of Computational Mathematics - We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either...     

Spatiotemporal traveling and solitary wave solutions to the generalized nonlinear Schrödinger equation with single- and dual-power law nonlinearity

Nonlinear Dynamics - We generalize previously obtained solutions to the generalized nonlinear Schrödinger equation (NLSE) with cubic-quintic nonlinearity and distributed coefficients to obtain...     

Spectra of second-order Raman scattering in porous silicon

Spectra of second-order Raman scattering in porous silicon are investigated. A band shift towards lower energies in second-order spectra is observed, as well as the correlation between the values of band shift in first-and second-order spectra. It is demonstrated that the observed effect cannot be interpreted using the conventional concepts of the mechanisms of scattering in microcrystalline samples. An interpretation of the revealed effect is suggested.     

Five-step phase-shifting algorithms with unknown values of phase shift

The presented work offers new algorithms for phase evaluation in interferometric measurements. Several phase-shifting algorithms with an arbitrary but constant phase-shift between captured intensity frames are proposed. These phase calculation algorithms need to measure five frames of the intensity of the interference field. The algorithms are similarly derived as so called Carré algorithm. The phase evaluation process then does not depend on the linear phase shift errors. Furthermore, the detailed analysis of the algorithms with respect to most important factors, which affect interferometric measurements, is carried out. It is also studied the dependency of the evaluation algorithms on the phase shift values, and the proposed phase calculation algorithms are compared with respect to the resulting phase errors. The influence of most important factors in the measurement and evaluation process was simulated as systematic and random errors using a proposed mathematical model.     

The average a posteriori error of numerical methods

Summary The definition of the average error of numerical methods (by example of a quadrature formula to approximateS(f)= f d on a function classF) is difficult, because on many important setsF there is no natural probability measure in the sense of an equidistribution. We define the average a posteriori error of an approximation by an averaging process over the set of possible information, which is used by (in the example of a quadrature formula,N(F)={(f(a ₁), ...,f/fF} is the set of posible information). This approach has the practical advantage that the averaging process is related only to finite dimensional sets and uses only the usual Lebesgue measure. As an application of the theory I consider the numerical integration of functions of the classF={f:[0,1]/f(x)–f(y)||x–y|}. For arbitrary (fixed) knotsa _i we determine the optimal coefficientsc _i for the approximation and compute the resulting average error. The latter is minimal for the knots . (It is well known that the maximal error is minimal for the knotsa _i .) Then the adaptive methods for the same problem and methods for seeking the maximum of a Lipschitz function are considered. While adaptive methods are not better when considering the maximal error (this is valid for our examples as well as for many others) this is in general not the case with the average error.     

Spectres infrarouges et raman du complexe solide MgBr22Et2O: Changement de phase et isomérie de rotation des molécules d'éther coordonnées

Infrared and Raman spectra of solid magnesium bromide dietherate MgBr₂2Et₂O have been studied at different temperatures between 300 and 90 °K in the 4000 to 30 cm^? range. Infrared spectra of this compound at various pressures up to 10 kbar have also been investigated. The MgBr₂2Et₂O crystal has two phases and there is a reversible transition between them. This phase transition concerns primarily the conformational change of (C₂Hg₅)₂O molecules and much less the arrangement of the ligands around the central magnesium atom. At room temperature or low pressure the GG conformation appears to be predominant while at low temperature or high pressure there is only TG (or TT) conformation of ether molecules. The enthalpy difference and transition temperature between the phases have been determined calorimetrically. An assignment of the spectra of both phases is given. The analysis of intramolecular vibrations gives information about the relative contribution of conformational change and coordination effect to the frequency shifts of (C₂H₅)₂O vibrations. The assignment of magnesium-ligand vibrations on the other hand allows us to estimate the Mg-Br and Mg-O force constants.     

Determination of chloride by stripping chronopotentiometry with silver-film electrode

The experimental parameters of cathodic stripping chronopotentiometry of chloride at a silver-film electrode are investigated and optimized. The chloride preconcentration is achieved in the form of silver chloride by a controlled potential oxidation of the working electrode under vigorous stirring. Cathodic stripping of the deposit is obtained by the constant current, under the condition of diffusive mass transfer. Deaeration of the solution is not necessary. A detection limit of 35 μ dm⁻³ (10⁻⁶ mol dm⁻³) is obtained at a deposition time of 180 s, with a reproducibility of 6.7 % (expressed as relative standard deviation, RSD).     

Stability of nanodispersions: a model for kinetics of aggregation of nanoparticles

In the course of aggregation of very small colloid particles (nanoparticles) the overlap of the diffuse layers is practically complete, so that one cannot apply the common DLVO theory. Since nanopoarticles are small compared to the extent of the diffuse layer, the process is considered in the same way as for two interacting ions. Therefore, the Br?nsted concept based on the Transition State Theory was applied. The charge of interacting nanoparticles was calculated by means of the Surface Complexation Model and decrease of effective charge of particles was also taken into account. Numerical simulations were performed using the parameters for hematite and rutile colloid systems. The effect of pH and electrolyte concentration on the stability coefficient of nanosystems was found to be more pronounced but similar to that for regular colloidal systems. The effect markedly depends on the nature of the solid which is characterized by equilibrium constants of surface reactions responsible for surface charge, i.e., by the point of zero charge, while the specificity of counterions is described by their association affinity, i.e., by surface association equilibrium constants. The most pronounced is the particle size effect. It was shown that extremely small particles cannot be stabilized by an electrostatic repulsion barrier. Additionally, at the same mass concentration, nanoparticles aggregate more rapidly than ordinary colloidal particles due to thier higher number concentration.     

Detailed characterization of (3 x 3) iodine adlayer on Pt(111) by unequal-sphere packing model

A simple unequal-sphere packing model is applied to study the iodine (3x3) adlayer on the Pt(111) surface. By using a newly introduced parameter, defined as the average adsorbate height, three characteristic adlattices, (3x3)-sym, (3x3)-asym, and (3x3)-lin, have been selected and characterized in great detail, including the exact adatom registry. The (3x3)-sym iodine adlattice, observed in many experimental studies, appears to be, on average, the closest one to the substrate surface. A special contour plot of average adsorbate height vs X and Y positions of the (3x3) iodine unit cell indicates the existence of two local minima, which are related to preferential formation of (3x3)-sym and (3x3)-asym iodine adlattices. Our model gives good agreement with experimental findings, and explains the mechanism of preferential appearance of (3x3)-sym and (3x3)-asym structures.