Bismuth nanoparticles electrooxidation: theory and experiment

The article presents the findings of microscopic and electrochemical studies of electrooxidation of bismuth particle of varying sizes. Bismuth particles were immobilized on the surface of indifferent carbon containing screen-printed electrodes. The calculations and experimental studies demonstrated that the transition from macroparticles to nanoparticles caused a shift of the maximum current potential of bismuth oxidation into the area with more negative potentials. A positive correlation between experimental and calculated data confirms once again a relevant application of the earlier proposed mathematical model and the possible use of the shift of the maximum current potential of electrooxidation to describe electrochemical activity and energy properties of metal nanoparticles.     

ON THE INTERPRETATION OF ABSORPTION SPECTRA OF LEAVES–II. THE NON-ABSORBED RAY OF THE SIEVE EFFECT and THE MEAN OPTICAL PATHLENGTH IN THE REMAINDER OF THE LEAF

Abstract— The sieve effect and scattering within leaves are analysed by the use of a simple model. By plotting the leaf transmittance (corrected for light not entering the leaf) vs the transmittance of an equivalent amount of homogeneous plastid pigments, an intercept is found where the latter is zero. This minimum transmittance represents the fraction of the leaf area devoted to the ray of the sieve effect which strikes no chloroplasts. It varied between 7% and 0.2% in non-senescent leaves. When this was subtracted from the leaf spectrum, the peak absorbance was greater than that of the homogeneous leaf pigments in all cases. The ratio of the leaf absorbance to that of the homogeneous pigments, at the same wavelength, is the apparent optical pathlength, which increases with decreasing absorbance. By plotting this ratio vs the absorbance of the equivalent homogeneous pigment, an intercept is found where the latter is zero. This intercept is interpreted as an estimate of the true mean scattering pathlength. Leaves with high chlorophyll contents had low pathlengths (mean and SD = 2.30 ± 0.25); with moderate and low contents, the values were higher (2.75 ± 0.28, 3.95 ± 0.77). Another application of the model gave values between 3 and 4 for the true scattering pathlength.     

Spectrum of the One-dimensional Schrödinger Operator With a Periodic Potential Subjected to a Local Dilative Perturbation

We study the spectrum of the one-dimensional Schr?dinger operator with a potential, whose periodicity is violated via a local dilation. We obtain conditions under which this violation preserves the essential spectrum of the Schr?dinger operator and an infinite number of isolated eigenvalues appear in a gap of the essential spectrum. We show that the considered perturbation of the periodic potential is not relative compact in general.     

On groups with many almost normal subgroups

Summary An anti-FC-group is a group in which every subgroup either is finitely generated or has only a finite number of coniugates. In this article a classification is given of (generalized) soluble anti-FC-groups which neither are central-by-finite nor satisfy the maximal condition on subgroups. Moreover, groups in which every non-cyclic subgroup has only a finite number of coniugates are characterized.     

Symplectic packings and algebraic geometry

Oblatum 9-XI-1992 & 17-VI-1993     

The Newton Polygon and Elliptic Problems with Parameter

In the study of the resolvent of a scalar elliptic operator, say, on a manifold without boundary there is a well-known Agmon-Agranovich-Vishik condition of ellipticity with parameter which guarantees the existence of a ray of minimal growth of the resolvent. The paper is devoted to the investigation of the same problem in the case of systems which are elliptic in the sense of Douglis-Nirenberg. We look for algebraic conditions on the symbol providing the existence of the resolvent set containing a ray on the complex plane. We approach the problem using the Newton polyhedron method. The idea of the method is to study simultaneously all the quasihomogeneous parts of the system obtained by assigning to the spectral parameter various weights, defined by the corresponding Newton polygon. On this way several equivalent necessary and sufficient conditions on the symbol of the system guaranteeing the existence and sharp estimates for the resolvent are found. One of the equivalent conditions can be formulated in the following form: all the upper left minors of the symbol satisfy ellipticity conditions. This subclass of systems elliptic in the sense of Douglis-Nirenberg was introduced by A. KOZHEVNIKOV [K2].