Mixed Aggregates of the Dilithiated Koga Tetraamine: NMR Spectroscopic and Computational Studies

A combination of ¹H, ⁶Li, ¹³C, and ¹⁵N NMR spectroscopies and density functional theory computations explores the formation of mixed aggregates by a dilithium salt of a C₂‐symmetric chiral tetraamine (Koga's base). Lithium halides, acetylides, alkoxides, and monoalkylamides form isostructural trilithiated mixed aggregates with few exceptions. ⁶Li–¹³C and ⁶Li–¹⁵N couplings reveal heretofore undetected transannular contacts (laddering) with lithium acetylides and lithium monoalkylamides. Marked temperature‐dependent ¹⁵N chemical shifts seem to be associated with this laddering. Computational studies shed light on the general structures of the aggregates, their penchant for laddering, and the stereochemical consequences of aggregation.     

Memory effects in the two-level model for glasses

We study an ensemble of two-level systems interacting with a thermal bath. This is a well-known model for glasses. The origin of memory effects in this model is a quasistationary but nonequilibrium state of a single two-level system, which is realized due to a finite-rate cooling and slow thermally activated relaxation. We show that single-particle memory effects, such as negativity of the specific heat under reheating, vanish for a sufficiently disordered ensemble. In contrast, a disordered ensemble displays a collective memory effect [similar to the Kovacs effect], where nonequilibrium features of the ensemble are monitored via a macroscopic observable. An experimental realization of the effect can be used to further assess the consistency of the model.     

Efficient power scaling of laser radiation by spectral beam combining

The possibility of achieving multikilowatt laser radiation by spectrally combining beams using volume Bragg gratings (VBGs) is shown. The VBGs recorded in a photothermorefractive glass exhibit long-term stability of all its parameters in high-power laser beams with power density >1 MW/cm2 in the cw beam of total power on a kilowatt level. We consider an architecture-specific beam-combining scheme and address the cross-talk minimization problem based on optimal channel positioning. Five-channel high efficiency spectral beam combining resulted in a >750 W near-diffraction-limited cw beam has been demonstrated experimentally.     

Multi-phonon capture of charge carriers by dislocation kinks in semiconductors

In view of the problem of recombination-enhanced motion of dislocations in semiconductors, we studied the thermal capture of an electron by a smooth dislocation kink. Multi-phonon capture becomes possible due to localization of the carrier on the kink. The localized state on the smooth kink is studied in the deformation potential approximation. In this case the potential created by the kink is described by Poschl-Teller function, which enables to find the analytical expressions for the eigenstates and the corresponding wave functions. With the use of the ground state wave function we find the multi-phonon capture cross-section for two limiting temperature cases, corresponding to the thermally activated and quantum transitions between vibronic terms.     

On the product property of the pluricomplex Green function

We prove that the pluricomplex Green function has the product property for any domains and .

     

Pluripolar hulis and holomorphic coverings

The aim of the paper is to study the behavior of (complete) pluripolar sets under special holomorphic mappings (proper mappings and coverings). Research was supported in part by the KBN Grant 2 P03A 017 14. The author is a fellow of the Foundation for Polish Science.     

Solution of Vizing's Problem on Interchanges for the case of Graphs with Maximum Degree 4 and Related Results

Let G be a Class 1 graph with maximum degree 4 and let be an integer. We show that any proper t‐edge coloring of G can be transformed to any proper 4‐edge coloring of G using only transformations on 2‐colored subgraphs (so‐called interchanges). This settles the smallest previously unsolved case of a well‐known problem of Vizing on interchanges, posed in 1965. Using our result we give an affirmative answer to a question of Mohar for two classes of graphs: we show that all proper 5‐edge colorings of a Class 1 graph with maximum degree 4 are Kempe equivalent, that is, can be transformed to each other by interchanges, and that all proper 7‐edge colorings of a Class 2 graph with maximum degree 5 are Kempe equivalent.     

Exponential Dichotomy and Time-Bounded Solutions for First-Order Hyperbolic Systems

The paper is devoted to studying a class of strongly hyperbolic systems of the first order. We show that if the characteristic roots of the full symbol are outside an open strip containing the real axis, then the homogeneous system possesses an exponential dichotomy and the inhomogeneous system is solvable in the space of time-bounded and almost periodic functions. We also discuss some results on the behavior of solutions for nonlinear equations in the neighborhood of a stationary point.     

Twistor quantization of the space of half-differentiable vector functions on the circle revisited

We discuss the twistor quantization problem for the classical system (V _d ,A _d ), represented by the phase space V _d , identified with the Sobolev space H ₀^1/2 (S ¹,ℝ ^d ) of half-differentiable vector functions on the circle, and the algebra of observables A _d , identified with the semi-direct product of the Heisenberg algebra of V _d and the algebra Vect(S ₁) of tangent vector fields on the circle.