Open subsets of projective spaces with a good quotient by an action of a reductive group

The aim of the paper is to describe all open subsets of a projective space with an action of a reductive group which admits a good quotient. As in the case of Mumford’s geometric invariant theory (which concerns projective good quotients) the problem can be reduced to the case of an action of a torus. We also show how to distinguish examples of open subsets with a good quotient coming from Mumford’s theory and give examples of open subsets with non-quasi-projective quotients.     

On the preparation of synthetic carbon adsorbents using the sulfonated ion exchange resin duolite C-20

Thermal analysis was used to study thermal behavior of the sulfonated ion exchange resin Duolite C20 in the hydrogen, sodium and calcium forms. The aim of this paper was to prepare spherical carbon adsorbents. SEM and AFM microscopic methods have been applied to describe their surface characteristics. It was stated that structural parameters of prepared active carbons depend on the kind of cation present in the resin. The use of calcium form of Duolite C20 as the initial polymer precursor allowed to obtain the active carbon with better yield and better developed pore structure compared with other forms of this ion exchanger.     

Far infrared study of polymorphism of trimethylchlorosilane

The far infrared spectra in the range of 16 – 500 cm^?1 for (CH₃)₃SiCl were measured in the temperature range of 90 – 300 K by the use of Fourier transform technique. Two solid phases were found, the high-temperature phase being easily supercooled down to liquid nitrogen temperature. On the basis of the characteristic features of the spectra suggestions concerning the structure of the low-temperature phase are given.     

Probabilistic viscosity algorithm for the scalar conservation law

We derive an algorithm for solving the initial value problem for u_t = ½σ²u_xx + f(u)u_x. The approach is based on the representation of the solution to the above equation in the form of the functional of Brownian motion. For small σ we get the approximation for u_t = f(u)u_x. A comparison with the random choice method is illustrated by the numerical example.     

Heat kernel regularization of quantum fields

We discuss some consequences of the existence of a heat kernel regularization (HKR) for quantum fields. We demonstrate that HKR applies in certain examples, using methods which should be useful more generally.Supported in part by the National Science Foundation under Grant PHY/DMS 86-45122Supported in part by a German National Scholarship Foundation fellowship     

Properties of star-branched and linear chains in confined space: a computer simulation study

We studied the properties of simple models of linear and star-branched polymer chains confined in a slit. The polymer chains were built of united atoms and were restricted to a simple cubic lattice. Two macromolecular architectures of the chain linear and star-branched with three branches (of equal length) were studied. The excluded volume was the only potential introduced into the model and thus, the system was athermal. The chains were put between two parallel and impenetrable surfaces. Monte Carlo simulations with a sampling algorithm based on chain’s local changes of conformation were carried out. The differences and similarities in the global size and the structure and of linear and star-branched chains were shown and discussed.     

Determination of Fe(II)-Fe(III) and Fe(III)-Ni(II) by the two-component potentiometric complexometric titration

Summary The two-component complexometric potentiometric titration has been applied to the simultaneous determination of Fe(III) and Fe(II), and of Fe(III) and Ni(II) in solution. In each case the two analytes were determined by reading the end-points directly from the titration curve. The end-points are determined in a sense arbitrarily, but they are repeatable and easy to be detected precisely. However, the apparent (found) analytical results are biased. They are effectively corrected with the use of a set of two calibration equations (uncomplete second degree polynomials), which approximate the relationship between found endpoints and true concentrations of analytes in solution. The regression coefficients in the equations are determined on the basis of titration data obtained for standard solutions whose compositions correspond to a 2² factorial. Permanent address: Department of Analytical Chemistry, Jagiellonian University, Krakow     

Dirac Superfield Quantization in Odd Superspace

We generalize the superfield method of Dirac quantization to the odd sector of superspace for N = 2 extended models. We discuss the mechanism of generating constraints in the odd sector of supersymmetric classical mechanics and then Dirac quantization in the odd superspace in superfield version. An example of supersymmetric system, defined by odd superfields, and the application of the method in the odd superspace is given.     

An infinite dimensional Morse theory with applications

In this paper we construct an infinite dimensional (extraordinary) cohomology theory and a Morse theory corresponding to it. These theories have some special properties which make them useful in the study of critical points of strongly indefinite functionals (by strongly indefinite we mean a functional unbounded from below and from above on any subspace of finite codimension). Several applications are given to Hamiltonian systems, the one-dimensional wave equation (of vibrating string type) and systems of elliptic partial differential equations.