Densely continuous forms, pointwise topology and cardinal functions

We consider the space D(X, Y) of densely continuous forms introduced by Hammer and McCoy [5] and investigated also by Holá [6]. We show some additional properties of D(X, Y) and investigate the subspace D*(X) of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence τ- _p . The largest part of the paper is devoted to the study of various cardinal functions for (D*(X), τ _p ), in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, π-weight, π-character, netweight etc. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-006904. The authors would like to thank Ľubica Holá for suggestions and comments.     

Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity

We present a new approach to estimate the risk-neutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting optimization problem, used to invert the data and determine the corresponding density function, is a convex quadratic or semidefinite programming problem, depending on the formulation. Both of these problems can be efficiently solved by numerical optimization software.     

Bismuth Modified Gold Microelectrode for Pb(II) Determination in Wine Using Alkaline Medium

Electrodeposition of bismuth on gold microelectrodes for determination of Pb(II) by square wave anodic stripping voltammetry (SWASV) was accomplished by an in situ procedure in alkaline solution. A linear calibration plot for Pb(II) in the concentration range 40 to 6700 nmol L^?1 (r=0.998) was obtained, the detection limit was found to be 12.5 nmol L^?1 (S/N=3) and the relative standard deviation in solutions containing 1 μmol L^?1 Pb(II) was 4% (n=12). The analytical performance of the proposed sensor was tested by measuring the Pb(II) concentration in a wine sample. The result was in good agreement with the one obtained by GFAAS.     

Data driven rank statistics in change point analysis

The paper deals a class of rank based procedures for detection of changes with adaptively chosen scores. This is a certain continuation of the paper Antoch et al (2008). The limit behavior of the test procedures is studied both under the null as well as under a general class of alternatives. Accompanying simulation study focuses on various alternatives which are often met in practice.     

Global convergence of slanting filter methods for nonlinear programming

In this paper, we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates. Independently of how these iterates are computed, we prove that all accumulation points of the sequence generated by the algorithm are feasible. Computing the new iterates by the inexact restoration method, we prove stationarity of all accumulation points of the sequence.     

Rapid solidification processing in molten salts chemistry: X-ray analysis of deeply undercooled cryolite-alumina melts

Rapid solidification processing (cooling rate from the interval 10⁵–10⁶ K s⁻¹) was used to prepare deeply undercooled cryolite-alumina melts. Such prepared samples were analyzed by the XRD method. Besides cryolite, XRD patterns belonging to ι-Al₂O₃ were recorded. The influence of annealing on the XRD patterns of deeply undercooled melts was also investigated.     

Transient time in homogeneous nucleation

The problem of the transient time in nucleation is studied. The size-dependent transient time at a constant temperature is defined and the approximate analytical solution is found and compared with the exact numerical solution for the model Li₂O.2 SiO₂ melt. It is shown that the analytical solution for the size-dependent transient time is in agreement with the numerical result.     

Non-stationary crystallization in simple glass-forming materials

A crystal distribution function is established during the crystallization process of simple glass-forming melts on the basis of the numerical computation of the kinetic equation in a non-stationary regime for constant and non-constant temperature. Nucleation rate and time-temperature-transformation curves are determined from the calculations of the crystal distribution function at various constant temperatures for various parameters of the system (the dependence on the difference of the chemical potentials, the dependence on the surface energy etc.).