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...     

Approximation by a binomial type law

Kaunas Academy of Agriculture, 4324 Noreikiškés, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 221–228, April–June, 1992.     

A connection between Fano configurations and Minkowski planes of odd order

It is shown in this paper that a pair of points contained in a Fano configuration in a projective plane of odd order cannot induce a Minkowski plane. From this result we derive that no pair of points in the Hughes plane of order 9 can induce a Minkowski plane.     

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.     

Spectral properties of random Schrödinger operators with unbounded potentials

We investigate spectral properties of random Schrödinger operators H = - + _n()(1 + |n|) acting onl ²(Z ^d), where _n are independent random variables uniformly distributed on [0, 1].Research partially supported by a Sloan Doctoral Dissertation Fellowship and NSERC under grant OGP-0007901Research partially supported by NSF grant DMS-9101716     

Flow-injection analysis with a small cylindrical wire type electrode

An amperometric detector with a small thin mercury film electrode is described. The device demonstrates advantageous operational characteristics such as small dispersion (D<2) and “memory effect” (me<0.6%), extensive maximum sample frequency (msf −200 samples/h), and high sensitivity. It has been proven useful in flow-injection analysis at a constant potential under hydrodynamic conditions.