Perturbed sites and host—guest—host exciton cascade in the biphenyl isotopic mixed crystal phosphorescence

An interesting energy cascade is observed in the phosphorescence spectra of 1% biphenyl-h₁₀ in biphenyl-d₁₀ (2–15 K); strongly perturbed host sites, with energy levels below that of the protonated guest, quench the guest sites at higher temperatures (11–15 K). The identification of the perturbed sites is based on vibrational characteristics (both intensity and frequency), obtained with the help of phosphorescence spectra of biphenyl-h₁₀ and biphenyl-d₁₀ in an argon matrix, indicating an isotope dependent vibronic structure. A partial vibrational analysis is presented, resulting in confirmation of the first triplet state of biphenyl as orbitally ungerade. The dynamics of the triplet excitation are discussed, including several possible mechanisms explaining the non-Boltzmann nature of the low-temperature steady state.     

Ab initio SCF Calculation of the Fluoronium Ion: Geometry,electronic structure and vibrational constants

An ab initio SCF calculation of 42 points of the energy hypersurface of the fluoronium ion is presented using a contracted F(5s/3p), H(2s) gaussian basis set. In its equilibrium structure a bond length of 1.812 a.u. and a HFH bond angle of 127.2° are predicted. The calculated vibrational frequencies for H₂F⁺, HDF⁺, and D₂F⁺ are in good agreement with the experimental data.     

Tachibana-type theorems and special Holonomy

Annals of Global Analysis and Geometry - In the present paper, we consider star-shaped mean convex hypersurfaces of the real, complex and quaternionic hyperbolic space evolving by a class of...     

Signed graphs with at most three eigenvalues

Czechoslovak Mathematical Journal - We investigate signed graphs with just 2 or 3 distinct eigenvalues, mostly in the context of vertex-deleted subgraphs, the join of two signed graphs or...     

Asymmetric Information in a Capital Accumulation Differential Game with Spillover and Learning Effects

Journal of Optimization Theory and Applications - This paper considers a capital accumulation game where the installation costs of investments are lowered by the firm’s own capital stock...     

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Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions

Methodology and Computing in Applied Probability - We present closed-form solutions to some double optimal stopping problems with payoffs representing linear functions of the running maxima and...     

A New Technique for Preserving Conservation Laws

Foundations of Computational Mathematics - This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We...     

Upper bounds of Schubert polynomials

Science China Mathematics - Let w be a permutation of {1, 2, …, n}, and let D(w) be the Rothe diagram of w. The Schubert polynomial ${\mathfrak{S}_w}\left(x \right)$ can be realized as the...     

4-Manifold topology I: Subexponential groups

The technical lemma underlying the 5-dimensional topologicals-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating ₁-null immersions of disks. These conjectures are theorems precisely for those fundamental groups (good groups) where the ₁-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations: (1) extension and (2) direct limit. The finitely generated groups in this class are amenable and no amenable group is known to lie outside this class.Oblatum 20-II-1995 & 26-V-1995The first author is supported by the IHES, the Guggenheim foundation and the NSF.The second author is supported by the IHES and the Humboldt foundation.