Abstract:
The paper describes some properties of new quaternized polysulfones obtained by quaternization of chloromethylated polysulfone with different tertiary amines - N,N-dimethylethylamine and N,N-dimethyloctylamine. Hydrophilic/hydrophobic properties, morphological aspects and compatibility with red blood cells and platelets are affected by the alkyl radicals and by history of the formed films. The results obtained are useful in biomedical applications, including evaluation of bacterial adhesion to the surfaces, or utilization of modified polysulfones as semipermeable membranes.

Abstract:
Equivariant elliptic cohomology with complex coefficients was defined axiomatically by Ginzburg, Kapranov and Vasserot and constructed by Grojnowski. We give an invariant definition of S^1-equivariant elliptic cohomology, and use it to give an entirely cohomological proof of the rigidity theorem of Witten for the elliptic genus. We also state and prove a rigidity theorem for families of elliptic genera.

Abstract:
This study presents nonlinear differential equations capable to generate continuous functions similar to pulse sequences. First are studied some basic properties of second-order differential equations with time-dependent coefficients generating bounded oscillating functions similar to test-functions (the function and its derivative being equal to zero at the same time moments). The necessary intercorrelations between the phase of generated oscillations and the time-dependent coefficients is presented, being shown also that the external command function should be set to a constant value at these time moments so as to determine the amplitude and the sign of generated oscillations. Then some possibilities of using previous differential equation for generating positive-definite functions with null values for the function and its derivative at the same time moments and with constant slope for its amplitude are presented, being shown that the corresponding external command function should present also alternating components. Finally all previous results are used for determining a set of second-order differential equations with time dependent coefficients and a set of external command and corrective functions for generating a pulse sequence useful for modelling time series.

Abstract:
For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and Goresky-Kottwitz-MacPherson from equivariant cohomology to equivariant K-theory.

Abstract:
A real Banach algebra of Newton interpolating series, used to approximate the solutions of multipoint boundary value problems for ODE's, is studied.

Abstract:
This study presents mathematical aspects of wave equation considered on closed space intervals. It is shown that a solution of this equation can be represented by a certain superposition of traveling waves with null values for the amplitude and for the time derivatives of the resulting wave in the endpoints of this interval. Supplementary aspects connected with the possible existence of initial conditions for a secondorder differential system describing the amplitude of these localized oscillations are also studied, and requirements necessary for establishing a certain propagation direction for the wave (rejecting the possibility of reverse radiation) are also presented. Then it is shown that these aspects can be extended to a set of adjacent closed space intervals, by considering that a certain traveling wave propagating from an endpoint to the other can be defined on each space interval and a specific mathematical law (which can be approximated by a differential equation) describes the amplitude of these localized traveling waves as related to the space coordinates corresponding to the middle point of the interval. Using specific differential equations, it is shown that the existence of such propagating law for the amplitude of localized oscillations can generate periodical patterns and can explain fracture phenomena inside materials as well.

Abstract:
Dielectric analysis (DEA) shows changes in the properties of a materials as a response to the application on it of a time dependent electric field. Dielectric measurements are extremely sensitive to small changes in materials properties, that molecular relaxation, dipole changes, local motions that involve the reorientation of dipoles, and so can be observed by DEA. Electrical double layer (EDL), consists in a shielding layer that is naturally created within the liquid near a charged surface. The thickness of the EDL is given by the characteristic Debye length what grows less with the ionic strength defined by half summ products of concentration with square of charge for all solvent ions (co-ions, counterions, charged molecules). The typical length scale for the Debye length is on the order of 1 nm, depending on the ionic contents in the solvent; thus, the EDL becomes significant for nano-capillaries that nanochannels. The electrokinetic e ects in the nanochannels depend essentialy on the distribution of charged species in EDL, described by the Poisson-Boltzmann equation those solutions require the solvent dielectric permittivity. In this work we propose a model for solvent low-frequency permittivity and a DEA profile taking into account both the porous silicon electrode and aqueous solvent properties in the Debye length range.

Abstract:
Modern transport systems have the challenge to integrate more and more functions. This increases the weight of the structures. On the other hand demands and the legal regulations for emissions can only be fulfilled if the weight is reduced. This results in an ongoing increase of the usage of lightweight materials. Due to its low density and high strength Aluminium Alloys are the most used lightweight metals. However, some other physical properties hamper the processing of these alloys. The publication shows ways to overcome these challenges applying appropriate material preparation and handling in combination with specialized welding equipment for Aluminium welding. Application examples demonstrate the state of the art in Aluminium welding.

Abstract:
We present experimental and theoretical work showing that a flat metallic slab can collimate and focus light impinging on the slab from a punctual source. The effect is optimised when the radiation is around the bulk, not at the surface, plasma frequency. And the smaller the imaginary part of the permittivity is, the better the collimation. Experiments for Ag in the visible as well as calculations are presented. We also discuss the interesting case of the Aluminium whose imaginary part of the permittivity is very small at the plasma frequency in UV radiation. Generalization to other materials and radiations are also discussed.

Abstract:
The purpose of this paper is to present a theory of Reich's fixed point theorem for multivalued operators in terms of fixed points, strict fixed points, multivalued weakly Picard operators, multivalued Picard operators, data dependence of the fixed point set, sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, and the generated fractal operator.