Finite-Band Potentials with Trigonal Curves

We construct Dubrovin equations and trace formulas for finite-band operators with trigonal curves and present some examples.     

The Action Functional for Moyal Planes

Modulo some natural generalizations to noncompact spaces, we show in this Letter that Moyal planes are nonunital spectral triples in the sense of Connes. The action functional of these triples is computed, and we obtain the expected result, i.e. the noncommutative Yang–Mills action associated with the Moyal product. In particular, we show that Moyal gauge theory naturally fits into the rigorous framework of noncommutative geometry.     

Generalized Complex Spectral Decomposition for a Quantum Decay Process

By extending the notion of mixed states to functionals acting on the space of observables with diagonal singularity we obtain a well-defined complex spectral decomposition of the time evolution for a quantum decaying system. In this formalism, generalized Gamow states are obtained with well-defined physical properties.     

Spectral decomposition of an elementary 3-fermion 2-body operator

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P²_g∧I¹A³∑_{1≤i≤j≤3}P²_g(i, j)A³ acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here P_g² denotes the projection operator onto a 2-particle antisymmetric function g², while A³ denotes the 3-particle antisymmetrizing operator.     

Equivariant Spectral Triples on the Quantum SU(2) Group

We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L ₂-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SU_q(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L ₂-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India.     

Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two‐dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time‐dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd.     

On the spectra of finite-dimensional quadratic Bose operators

A complete study of the spectrum of a finite-dimensional Bose operator is carried out in the paper. The cases in which the spectrum is discrete or continuous are studied. Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 835–854, June, 1997. Translated by A. M. Chebotarev     

Spectral Theory for Slowly Oscillating Potentials II. Schrödinger Operators

This paper continues the investigation about the singularity theory in dual rich quasi–Banach spaces given in T. Runst [Ru 2]. The abstract results are applied to the study of the solution structure of semilinear elliptic boundary value problems in spaces of Besov – Triebel – Lizorkin type.     

A virtual instrumentation based protocol for the automated implementation of the inner field compensation method

One influential parameter which mediates interactions between many types of molecules and biological membranes stems from the lumped contributions of the transmembrane potential, dipole potential and the difference in the surface potentials on both sides of a membrane. With relevance to cell physiology, such electrical features of a biomembrane are prone to undergoing changes as a result of interactions with the aqueous surrounding. Among the most useful tools devoted to exploring changes of electrical parameters of a lipid membrane induced by certain extracellular ions, lipid composition, and embedded membrane peptides and proteins, are spectroscopic imaging and the inner field compensation (IFC) method. In this work we layout the principles of a fully computerized version of the IFC method, which makes it more readily available to users. As a direct application, we deployed this improved version of the IFC method to time-resolve changes induced by alamethicin monomers upon membrane dipole potential, following their aggregation within an artificial lipid membrane. Intriguingly, even prior crossing the membrane core, the membrane-bound alamethicin monomers are shown to significantly increase the dipole potential of the monolayer they reside in. Such data further emphasize the yet less-explored interplay between membrane-based protein and peptides, and the membrane dipole potential.     

Mode beating in spot-size converter lasers

An anomalous modulation in the wavelength spectrum has been observed in lasers with spot-size converters. This intensity modulation is shown to be caused by beating between the fundamental lasing mode and radiation modes in the taper. This results in a periodic modulation in the net gain spectrum, which causes wavelength jumps between adjacent net gain maxima, and a drive current dependent spectral width that is expected to affect system performance. The amplitude of this spectral modulation is reduced significantly by either using an angled rear-facet which reflects the beating radiation modes away from the laser axis, or by using a nonlinear, adiabatic taper.