A generalization and short proof of a theorem of Hano on affine vector fields

We prove that a bounded affine vector field on a complete Finsler manifold is a Killing vector field. This generalizes the analogous result of Hano for Riemannian manifolds. Even though our result is more general, the proof is significantly simpler.Comment: 3 page

New families of q and (q;p)-Hermite polynomials

In this paper, we construct a new family of q-Hermite polynomials denoted by Hn(x,s|q). Main properties and relations are established and proved. In addition, is deduced a sequence of novel polynomials, Ln(. ,.|q), which appear to be connected with well known (q,n)-exponential functions E{q,n}(.), introduced by Ernst in his work entitled: (A New Method for q-calculus, Uppsala Dissertations in Mathematics, Vol. 25, 2002). Relevant results spread in the literature are retrieved as particular cases. Fourier integral transforms are explicitly computed and discussed. A (q;p)-extension of the Hn(x,s|q) is also provided

Homotheties of Finsler manifolds

We give a new and complete proof of the following theorem, discovered by Detlef Laugwitz: (forward) complete and connected finite dimensional Finsler manifolds admitting a proper homothety are Minkowski vector spaces. More precisely, we show that under these hypotheses the Finsler manifold is isometric to the tangent Minkowski vector space of the fixed point of the homothety via the exponential map of the canonical spray of the Finsler manifold.Comment: 13 page

A Solvation/Desolvation Indicator Based on van der Waals Interactions between Solvents and Porphyrins.

Solvation is a ubiquitous phenomenon associated with molecules in solutions. It often determines the equilibria of molecular systems and the rates of chemical reactions. Van der Waals interactions (a general term) includes weak interactions among noncharged compounds and it contributes significantly to solvation. The distinct observation of van der Waals interaction between solvent and porphyrin derivatives is reported herein. Bis(imidazolylporphyrinatozinc) structures connected through a 1,3-butadiyne moiety give two types of coordination polymers, E (extended) and S (stacked) polymers, exclusively. E polymers have larger solvent-accessible surface areas than the corresponding S polymers. Therefore, E polymers are better solvated than S polymers, providing an indicator of solvation and desolvation for the solvents used. A simple method (like a litmus test) was developed to evaluate the solvation ability of various solvents. Sixty-seven solvents and liquid compounds were tested, under the same conditions, using a conventional UV/Vis spectrometer. The results revealed a new liquid group with high solvation ability towards the porphyrins, and clarified van der Waals interaction assisted by secondary interaction on the substituents. The indicator system should contribute to the solution chemistry of molecules and materials, and to supramolecular chemistry interactions among hetero components.Solvation is a ubiquitous phenomenon associated with molecules in solutions. It often determines the equilibria of molecular systems and the rates of chemical reactions. Van der Waals interactions (a general term) includes weak interactions among noncharged compounds and it contributes significantly to solvation. The distinct observation of van der Waals interaction between solvent and porphyrin derivatives is reported herein. Bis(imidazolylporphyrinatozinc) structures connected through a 1,3-butadiyne moiety give two types of coordination polymers, E (extended) and S (stacked) polymers, exclusively. E polymers have larger solvent-accessible surface areas than the corresponding S polymers. Therefore, E polymers are better solvated than S polymers, providing an indicator of solvation and desolvation for the solvents used. A simple method (like a litmus test) was developed to evaluate the solvation ability of various solvents. Sixty-seven solvents and liquid compounds were tested, under the same conditions, using a conventional UV/Vis spectrometer. The results revealed a new liquid group with high solvation ability towards the porphyrins, and clarified van der Waals interaction assisted by secondary interaction on the substituents. The indicator system should contribute to the solution chemistry of molecules and materials, and to supramolecular chemistry interactions among hetero components

D3h -Symmetric Porphyrin-Based Rigid Macrocyclic Ligands for Multicofacial Multinuclear Complexes in a One-Nanometer-Sized Cavity.

The one-step synthesis of D3h -symmetric cyclic porphyrin trimers 1 composed of three 2,2\u27-[4,4\u27-bis(methoxycarbonyl)]bipyridyl moieties and three porphyrinatozinc moieties was achieved from a nickel-mediated reductive coupling of meso-5,15-bis(6-chloro-4-methoxycarbonylpyrid-2-yl)porphyrinatozinc. Although cyclic trimers 1 were obtained as a mixture that included other cyclic and acyclic porphyrin oligomers, an extremely specific separation was observed only for cyclic trimers 1 when using columns of silica gel modified with pyrenylethyl, cyanopropyl, and other groups. Structural analysis of cyclic trimers 1 was carried out by means of NMR spectroscopy and X-ray crystallography. Treatment of an η(3) -allylpalladium complex with a cyclic trimer gave a tris(palladium) complex containing three η(3) -allylpalladium groups inside the space, which indicated that the bipyridyl moieties inside the ring could work as bidentate metalloligands.The one-step synthesis of D3h -symmetric cyclic porphyrin trimers 1 composed of three 2,2\u27-[4,4\u27-bis(methoxycarbonyl)]bipyridyl moieties and three porphyrinatozinc moieties was achieved from a nickel-mediated reductive coupling of meso-5,15-bis(6-chloro-4-methoxycarbonylpyrid-2-yl)porphyrinatozinc. Although cyclic trimers 1 were obtained as a mixture that included other cyclic and acyclic porphyrin oligomers, an extremely specific separation was observed only for cyclic trimers 1 when using columns of silica gel modified with pyrenylethyl, cyanopropyl, and other groups. Structural analysis of cyclic trimers 1 was carried out by means of NMR spectroscopy and X-ray crystallography. Treatment of an η(3) -allylpalladium complex with a cyclic trimer gave a tris(palladium) complex containing three η(3) -allylpalladium groups inside the space, which indicated that the bipyridyl moieties inside the ring could work as bidentate metalloligands

Studies of a random sampling and stochastic processes on the ring of Studies of a random sampling and stochastic processes on the ring of ρ-adic integers-adic integers

東京理科大学201

Solvoluminescence of Cerium(III) Thiocyanate Complex.

A cerium(III) thiocyanate complex shows bright-blue emission at approximately 450 nm in acetonitrile, the quantum yield of which reaches more than 40 % at 298 K. Non-coordinating solvents such as acetonitrile give blue emission whereas oxygen-coordinating and nitrogen-coordinating solvents afford near UV and green emissions, respectively.A cerium(III) thiocyanate complex shows bright-blue emission at approximately 450 nm in acetonitrile, the quantum yield of which reaches more than 40 % at 298 K. Non-coordinating solvents such as acetonitrile give blue emission whereas oxygen-coordinating and nitrogen-coordinating solvents afford near UV and green emissions, respectively