Hawking Absorption and Planck Absolute Entropy of Kerr-Newman Black Hole

We find the existence of a quantum thermal effect, “Hawking absorption.” near the inner horizon of the Kerr–Newman black hole. Redefining the entropy, temperature, angular velocity, and electric potential of the black hole, we give a new formulation of the Bekenstein–Smarr formula. The redefined entropy vanishes for absolute zero temperature of the black hole and hence it is interpreted as the Planck absolute entropy of the KN black hole.     

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’.     

Uncharged encapsulated iron(II) complexes: transfer chemical potentials and solvation in water-methanol and water-t-butanol mixtures

Summary Transfer chemical potentials have been determined from measured solubilities for four uncharged encapsulated iron(II) complexes containing three diimine ligating moieties and O₃BOBu-n and O₃BF capping groups, in H₂O–MeOH andt-BuOH–H₂O solvent mixtures, The trends in transfer chemical potentials are discussed in terms of the natures of the encapsulating ligands, and are compared with those for a selection of other iron(II)-diimine complexes.     

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).     

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.