Circularly Polarized Luminescence from Cyclic (Alkyl)(Amino) Carbene Derived Propellers

Organic circularly polarized luminescence (CPL)-active molecular emitters featuring dynamic propeller-like luminophores were prepared in one step from cyclic(alkyl)(amino) carbenes (CAACs). These molecules exhibit through-space arene-arene π-delocalization and rapid intramolecular inter-system crossing (ISC) in line with their helical character.     

Various approaches to multiobjective linear programming problems with interval costs and interval weights

Central European Journal of Operations Research - Optimization problems are often subject to various kinds of inexactness or inaccuracy of input data. Here, we consider multiobjective linear...     

Hydrogen-bonded coordination network in crystal structures of [Cu(3-PM)4Cl2] and [Cu(4-PM)4Cl]Cl, (PM = pyridylmethanol)

The crystal and molecular structures of [Cu(3-PM)₄Cl₂] (1) and [Cu(4-PM)₄Cl]Cl (2) have been determinated by X-ray crystallography. Complex 1 crystallizes in the triclinic system, space group P–1, with lattice parameters a = 7.972(2) Å, b = 8.293(2) Å, c = 10.707(2) Å, = 105.73(3)°, = 90.04(3)°, = 110.38(3)°, and Z = 1 at 100 K. The coordination geometry of each Cu atom is approximately octahedral formed by four nitrogen atoms of pyridine rings of 3-pyridylmethanol molecules in the equatorial plane and two chlorine atoms occupying the axial positions. The O—HsO, C—HsCl, and O—HsCl intermolecular hydrogen bonds and s stacking link the molecules in 3-D hydrogen-bonded coordination network. Complex 2 crystallizes in the tetragonal system, space group P4/n, with lattice parameters a = 10.464(1) Å, c = 11.339(2) Å, and Z = 2 at 217 K and a = 10.352(1) Å, c = 11.201(2) Å, and Z = 2 at 293 K. The coordination geometry of Cu atom in the [Cu(4-PM)₄Cl]⁺ ion is approximately square pyramidal formed by four nitrogen atoms of pyridine rings of 4-pyridylmethanol molecules in equatorial plane and one chlorine atom in axial position. The O—HsCl and C—HsCl intermolecular hydrogen bonds link the molecules in 2-D hydrogen-bonded coordination network.     

A tight Hermite–Hadamard inequality and a generic method for comparison between residuals of inequalities with convex functions

Periodica Mathematica Hungarica - We present a tight parametrical Hermite–Hadamard type inequality with probability measure, which yields a considerably closer upper bound for the mean value...     

One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian–Eulerian methods

In this paper, a new flux-based one-step hybrid remapping method for multi-material arbitrary Lagrangian–Eulerian (ALE) approach is introduced. In the vicinity of material interfaces, the swept region is intersected with pure material polygons in the Lagrangian mesh to construct the material fluxes. Far from interfaces, the fluxes are constructed in a standard swept-region manner without intersections. This method is conservative, second-order accurate and linearity-preserving (in case of straight material interfaces), and faster than method based on intersections, as shown on selected numerical examples.     

Optical properties of semiconducting iron disilicide thin films

The iron silicides samples were prepared by annealing of iron films evaporated onto silicon wafers and capped with amorphous silicon thin overlayers. Semiconducting FeSi₂ phase is formed by annealing at the temperatures from 550°C to 850°C. The optical properties of the FeSi₂ layers have been deduced from reflectance and transmittance measurements carried out in the temperature range of (77–380) K. The spectral dependence of the absorption coefficient favours direct allowed transitions with forbidden energy gap of 0.87eV at the room temperature. The application of a simple three-parameter semiempirical formula to the temperature dependence of the direct energy gaps leads to the following best fit parameters: the band gap at zero temperature E _g (0) = (0.895 ± 0.004)eV, the dimensionless coupling parameter S = 2.0 ± 0.3, and the average phonon energy <hw> = (46 ± 8)meV. By examining all the reported triplets of parameters for -FeSi₂ fabricated by different techniques and thermal processes, an obvious discrepancy can be found for the lattice coupling parameter and average phonon energy, although the bandgaps at 0 K are very similar. Unlike the theoretical prediction and the earlier reported result, our results do not show any evidence of a particularly strong electron-phonon interaction, which would give the lower carrier mobilities. -FeSi₂ seems to be an intriguing material where states with energies near the band edges permit ambiguous interpretation of the character of transitions. From optical model for the thin film-substrate system we found the index of refraction to be (5–5.9) in the photon energy interval from 0.65 to 1.15eV. There is also indication of an additional higher-energy absorption edge at l.05eV.     

Stochastic processes with sample paths in reproducing kernel Hilbert spaces

A theorem of M. F. Driscoll says that, under certain restrictions, the probability that a given Gaussian process has its sample paths almost surely in a given reproducing kernel Hilbert space (RKHS) is either or . Driscoll also found a necessary and sufficient condition for that probability to be .

Doing away with Driscoll's restrictions, R. Fortet generalized his condition and named it nuclear dominance. He stated a theorem claiming nuclear dominance to be necessary and sufficient for the existence of a process (not necessarily Gaussian) having its sample paths in a given RKHS. This theorem - specifically the necessity of the condition - turns out to be incorrect, as we will show via counterexamples. On the other hand, a weaker sufficient condition is available.

Using Fortet's tools along with some new ones, we correct Fortet's theorem and then find the generalization of Driscoll's result. The key idea is that of a random element in a RKHS whose values are sample paths of a stochastic process. As in Fortet's work, we make almost no assumptions about the reproducing kernels we use, and we demonstrate the extent to which one may dispense with the Gaussian assumption.

     

One-parameter imbedding techniques for the solution of nonlinear boundary-value problems

A powerful numerical tool for the solution of nonlinear boundary-value problems —the one-parameter imbedding technique—is suggested. The basic principle is more than twenty years old; however, its numerical utilization has had only a few restricted applications up until recent times. The methods are divided into two categories: one- and multi-loop techniques. It is shown that the multi-loop techniques are of correct and incorrect type. Based on correct procedures new iteration techniques may be developed. Numerical solutions of differential equations arising for the one-parameter imbedding methods are presented along with the corresponding iteration techniques. Some typical imbedding procedures are discussed, and practical application of the method is demonstrated on calculated examples.     

Nuclear polarization by electron paramagnetic resonance in paramagnetic crystals

The possibility of the polarization of nuclei in paramagnetic salts by saturation of electron paramagnetic resonance is theoretically analyzed. The proposed method assumes saturation of the forbidden transition of the typeM=±1, m=±1, ±2, for mutually perpendicular external magnetic and high-frequency fields. The analysis is carried out for the case of a large quadrupole moment of the nucleus. The degree of orientation attained is comparable in order of magnitude with Overhauser's method. This method is particularly suitable for the polarization of nuclei of transuranium elements.

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. M=± 1, m==±1, ±2 . . . .

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In conclusion the author would like to thank J. Burget, J. ajko, M. Kolá and M. ott for helping in the laborious solution of system (16).