On geodesic mappings of equidistant generalized Riemannian spaces

In this paper geodesic mappings of equidistant generalized Riemannian spaces are discussed. It is proved that each equidistant generalized Riemannian space of basic type admits non-trivial geodesic mapping with preserved equidistant congruence. Especially, there exists non-trivial geodesic mapping of equidistant generalized Riemannian space onto equidistant Riemannian space. An example of geodesic mapping of an equidistant generalized Riemannian spaces is presented.     

On Possible Singular Solutions to the Navier — Stokes Equations

In this paper, we exclude the possibility of existence of a singular solution of the selfsimilar type proposed by Jean Leray More precisely, using a slightly stronger hypothesis we give a simpler proof to the analogous result established by J. Ne?as, M. Rú?i?ka and V. ?verák. We also discuss the possible existence of a singular solution of pseudo-selfsimilar type.     

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...     

Eigenmobilities in background electrolytes for capillary zone electrophoresis: III. Linear theory of electromigration

A mathematical model of capillary zone electrophoresis (CZE) based on the conception of eigenmobilities, which are the eigenvalues of a matrix M tied to the linearized governing equations is presented. The model considers CZE systems, where constituents, either analytes or components of the background electrolyte (BGE), are weak electrolytes--acids, bases, or ampholytes. There is no restriction on the number of components nor on the valence of the constituents nor on pH of the BGE. An electrophoretic system with N constituents has N eigenmobilities. In most BGEs one or two eigenmobilities are very close to zero so their corresponding eigenzones move very slowly. However, there are BGEs where no eigenmobility is close to zero. The mathematical model further provides: the transfer ratio, the molar conductivity detection response, and the relative velocity slope. This allows the assessment of the indirect detection, conductivity detection and peak broadening (distortion) due to electromigration dispersion. Also, we present a spectral decomposition of the matrix M to matrices allowing the assessment of the amplitudes of system eigenpeaks (system peaks). Our model predicted the existence of BGEs having no stationary injection zone (or water zone, gap, peak, dip). A common practice of using the injection zone as a marker of the electroosmotic flow must fail in such electrolytes.     

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.