Stability and convergence of the spectral Lagrange-Galerkin method for mixed periodic/non-periodic convection-dominated diffusion problems

We present a convergence analysis of the spectral Lagrange-Galerkinmethod for mixed periodic/non-periodic convection-diffusionproblems. The scheme is unconditionally stable, independentof the diffusion coefficient, even in the case when numericalquadrature is used. The theoretical predictions are illustratedby a series of numerical experiments. For the periodic case,our results present a significant improvement on those givenby Süli & Ware (1991) SIAM J. Numer.Anal.28, 423-445).     

Conjugated Biradical Intermediates: Spectroscopic,Kinetic, and Trapping Studies of 2,2-Dimethyl-1,3-perinaphthadiyl

The biradical 2,2-dimethyl-1,3-perinaphthadiyl ( a ) was generated from two different precursors, the naphthocyclopropane 1 and the azo compound 2 , and from each by three different pathways (pyrolysis, direct photolysis, and triplet sensitization, Scheme 1). The combined evidence from flash photolysis, low-temperature spectroscopy, and product analyses provides a detailed mechanistic picture of the formation and decay of this reactive intermediate which is persistent at 77 K in the triplet ground state (³ a ) and rather long-lived (400 μs) at room temperature. When formed in its lowest singlet state (¹ a ), the biradical is too short-lived to undergo intersystem crossing to ³ a or bimolecular reactions. Thus, ³ a is formed exclusively from the excited triplet state of the precursor compounds, ³ 1 * or ³ 3 *. The monomolecular decay of ³ a is retarded by the spin barrier; ³ a initiates the polymerization of acrylonitrile and is trapped by ³O₂.     

Transfer matrices, hyperbolic geometry and absolutely continuous spectrum for some discrete Schrödinger operators on graphs

We prove the existence of absolutely continuous spectrum for a class of discrete Schrödinger operators on tree like graphs. We consider potentials whose radial behaviour is subject only to an ?^∞ bound. In the transverse direction the potential must satisfy a condition such as periodicity. The graphs we consider include binary trees and graphs obtained from a binary tree by adding edges, possibly with weights. Our methods are motivated by the one-dimensional transfer matrix method, interpreted as a discrete dynamical system on the hyperbolic plane. This is extended to more general graphs, leading to a formula for the Green's function. Bounds on the Green's function then follow from the contraction properties of the transformations that arise in this generalization. The bounds imply the existence of absolutely continuous spectrum.     

Absolutely Continuous Spectrum for the Anderson Model on a Tree: A Geometric Proof of Klein’s Theorem

We give a new proof of a version of Klein’s theorem on the existence of absolutely continuous spectrum for the Anderson model on the Bethe Lattice at weak disorder.     

Bestimmung von Plasma-Kallikrein mit einem chromogenen Peptid-Substrat: Methodik und klinische Anwendung

Ohne Zusammenfassung

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Determination of plasma kallikrein with a chromogenic peptide substrate: Method and clinical evaluation

     

No Zero Energy States for the Supersymmetric x 2 y 2 Potential

We show that the positive supersymmetric matrix-valued differential operator H = p _x ² + p _y ² + x ² y ² + x₃ + y₁ has no zero modes, i.e., H = 0 implies = 0. The result depends on a virial type argument for the corresponding supercharge. The model may be regarded as a simple relative of dimensional reductions of supersymmetric Yang–Mills theories.     

Multistable randomly switching oscillators: The odds of meeting a ghost

We consider oscillators whose parameters randomly switch between two values at equal time intervals. If random switching is fast compared to the oscillator’s intrinsic time scale, one expects the switching system to follow the averaged system, obtained by replacing the random variables with their mean. The averaged system is multistable and one of its attractors is not shared by the switching system and acts as a ghost attractor for the switching system. Starting from the attraction basin of the averaged system’s ghost attractor, the trajectory of the switching system can converge near the ghost attractor with high probability or may escape to another attractor with low probability. Applying our recent general results on convergent properties of randomly switching dynamical systems [1, 2], we derive explicit bounds that connect these probabilities, the switching frequency, and the chosen initial conditions.     

Analyticity of the Ground State Energy for Massless Nelson Models

We show that the ground state energy of the translationally invariant Nelson model, describing a particle coupled to a relativistic field of massless bosons, is an analytic function of the coupling constant and the total momentum. We derive an explicit expression for the ground state energy which is used to determine the effective mass.