A Positive Doubly Power Bounded Operator with a Nonpositive Inverse Exists on any Infinite-dimensional AL-Space

In this paper we construct a positive doubly power bounded operator with a nonpositive inverse on an AL-space.     

Pro-torus actions on Poincaré duality spaces

In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if ‘torus’ is replaced by ‘pro-torus’.     

Unique solvability of the periodic Cauchy problem for wave-hierarchy problems with dissipation

Wave-hierarchy problems appear in a variety of applications such as traffic flows, roll waves down an open inclined channel and multiphase flows. Usually, these are described by the compressible Navier-Stokes equations with specific non-linearities; in a fluidized bed model they contain an additional pressure gradient term and are supplemented by an elliptic equation for this unknown pressure. These equations admit solutions periodic in space as well as in time, i.e. periodic travelling waves. Therefore, the corresponding initial value problem with periodic boundary conditions is solved locally in time in appropriate Sobolev spaces. Some remarks are made concerning global solutions, the occurrence of clusters or voids and the bifurcation of time periodic solutions, respectively.     

Spectral theory and L∞-time decay estimates for Klein–Gordon equations on two half axes with transmission: The tunnel effect

Consider two copies N₁, N₂ of the interval [0, ∞]. Consider Klein-Gordon equations with (different) constant coefficients on ? × N_j ( = time × space). Assume the coincidence of the values of the solution at the boundary points of the N_j for all times and a transmission condition relating its first (one-sided) space derivatives at these points. Under a symmetry condition, we extend the spatial part of the equation and the transmission conditions to a self-adjoint operator (by Friedrichs extension) and reformulate our problem in terms of an abstract wave equation in a suitable Hilbert space. We derive an expansion of the solution in generalized eigenfunctions of this self-adjoint extension and show, that the L^∞-norms (in space) of the solution and its first k space derivatives at the time t decay for t → ∞ at least as const. t^¼, if the initial conditions satisfy a compatibility condition of order k derived in this paper. The loss of decay rate in comparison with the full line case (const. t^?½, cf. [28]) is caused by the tunnel effect. Further we show that an abstract wave equation in a Hilbert space with a Friedrichs extension as spatial part can always be derived from a stationarity principle for an associated action-type functional. This yields a physical legitimation of our model by the principle of stationary action and moreover a criterion for the physical interpretability of all models created by the linear interaction concept [4, 6, 8, 10], in particular for the coupling of media of different dimension (alternative to [13, 16] for similar models).     

Physical foundation of quantitative Auger analysis

The possibility of using an Auger peak height in the dN (E) /dE spectrum and an integrated N (E) spectrum as a measure of the Auger current is discussed and necessary relations are presented. The methods of the background determination are reviewed and discussed.

The relation between the Auger current and the atomic cancentration of a corresponding sample component is derived and the state of art in the field of theoretical and experimental determination of factors appearing in this relation (ionization cross-section, Auger transition probability. backscattering factor, and inelastic mean free path of Auger electrons) is presented.

Approaches to the quantitative Auger analysis (QAA) of homogeneous, isotropic samples, including corrections for matrix factors, are presented and discussed. Problems arising when heterogeneous samples are analyzed are discussed and practical approaches to such an analysis are presented.

The role of crystalline effects (the dependence of the Auger signal from crystalline samples on the direction of the primary electron beam and angular distribution of Auger electron emission from such samples) in QAA is discussed and examples of such crystalline effects are presented together with their physical foundation.

Some rules are suggested allowing the quantitative Auger analysis to be performed with the smallest possible error.     

Synthesis and photophysical properties of fluorescent 2-aryl-1,3-dialkylbenzimidazolium ions and a l-alkyl-2-arylbenzimidazole with excited state intramolecular proton-transfer

To improve the solubility, photostability and fluorescence quantum yield (Φ) of 2-arylbenzimidazolium ions the N-1 hydrogen was replaced by an alkyl group before N-3 was quatemized; this substitution did not reduce Φ, proving the absence of steric inhibition to attainment of coplanarity in the excited state. A related symmetrical 2,2′-arylenebis(1,3-dimethyldibenzimidazolium ion) had Φ = 0.86. The related 2,5-bis(1-methyl-2-benzimidazolyl)phenol had Φ = 0.38 at 22° as well as a very large Stokes' shift due to proton-transfer. These findings supported a new insight into the electron distribution of the first excited singlet state of oligophenylenes. The compounds are of interest as laser dyes and scintillation fluors.     

Spectroscopic studies of biologically active organotin(IV) derivatives of 2-[N-(2,4,6-tribromophenylamido]propanoic acid

Herein we describe the synthesis and characterization of compounds having the formulae R₂SnL₂ and R₃SnL, where R = Me, n-Bu, Ph and n-Oct and L = 2-[N-(2,4,6-tribromophenylamido]propanoic acid. All the complexes have been characterized by various spectroscopic methods (IR and ¹H, ¹³C, ¹¹⁹Sn NMR), elemental analysis, mass spectrometry and physical data. These compounds were also screened for their biological activity and found some encouraging results.     

Trichloroisocyanuric acid as a novel oxidizing agent for the oxidation of 1,3,5-trisubstituted pyrazolines under both heterogeneous and solvent free conditions

Trichloroisocyanuric acid is used as an effective oxidizing agent for the oxidation of 1,3,5-trisubstituted pyrazolines to their corresponding pyrazoles under both heterogeneous and also solvent free conditions with good yields at room temperature.