Coadjoint orbits of Lie groups play important roles in several areas of mathematics and physics. In particular, in representation theory, Kirillov showed in the 1960's that for nilpotent Lie groups there is a one-one correspondence between coadjoint orbits and irreducible unitary representations. Subsequently this result was extensively generalized by Kostant, Auslander-Kostant, Duflo, Vogan an...

Q : dimensionless heat loss from the fin, q/(klw f φ ) Abstract Rt: dimensionless thermal resistance A reversed trapezoidal fin with fluid in the inside wall is analyzed using a two-dimensional analytical method. Thermal resistance for the reversed trapezoidal fin is presented as a function of the fin length and fin base height. The relationship between the inside fluid convection characteristi...

The quantized vortex state is investigated in a Bose-Einstein condensate, confined in a multiply connected geometry formed by a Laguerre-Gaussian optical trap. Solving the Gross-Pitaevskii equation variationally, we show that the criterium for vortex stability is that the interatomic interaction strength must exceed a critical interaction strength. The time evolution of a freely expanding Lague...

We demonstrate a simple, scalable fabrication method for producing large-area arrays of vertically stacked metallic micro-rings, embedded in a deformable polymer sheet. Unusual polarisation-dependent hotspots are found to dominate the reflection images. To understand their origin, the arrays are characterized using point-scanning optical spectroscopy and directly compared to numerical simulatio...

Let $G$ be a tamely ramified reductive $p$-adic‎ ‎group‎. ‎We study distinction of a class of irreducible admissible representations‎ ‎of $G$ by the group of fixed points $H$ of an involution‎ ‎of $G$‎. ‎The representations correspond to $G$-conjugacy classes of‎ ‎pairs $(T,phi)$‎, ‎where $T$ is a‎ ‎tamely ramified maximal torus of $G$ and $phi$ is a quasicharacter‎ ‎of $T$ whose restriction t...

We prove the existence of a continuous BV minimizer with C boundary value for the p-area (pseudohermitian or horizontal area) in a parabolically convex bounded domain. We extend the domain of the area functional from BV functions to vector-valued measures. Our main purpose is to study the first and second variations of such a generalized area functional including the contribution of the singula...

The problem of one pair of identical nucleons sitting in N single particle levels of a potential well and interacting through the pairing force is treated introducing, in the Hamiltonian formalism , even Grassmann variables. The eigenvectors are analytically expressed solely in terms of these with coefficients fixed by the eigenvalues and the single particle energies. For these a specific model...

A program, INV2P5DSB, has been developed to simultaneously estimate the depth of a 2.5-D sedimentary basin and regional background from observed gravity anomalies. The density contrast is assumed to be varying parabolically with depth above the basement interface. The main program is supported with two subroutines GRAV2P5D and SIMEQ and a function GPRM. The analysis of gravity anomalies due to ...

*Correspondence: [email protected] School of Applied Mathematics, Xiamen University of Technology, Xiamen, China Abstract The anisotropic parabolic equations with variable exponents are considered. If some of diffusion coefficients {bi(x)} are degenerate on the boundary, the others are always positive, then how to impose a suitable boundary value condition is researched. The existence of weak...

Free asymmetric transverse vibration of a polar orthotropic thin annular plate with parabolically varying thickness in radial direction have been computed on the basis of classical plate theory considering both the peripheries of the plate elastically restrained against translation and rotation. The fourth order linear differential equation with variable coefficients governing the motion in the...