Local stability of mappings with bounded distortion on Heisenberg groups

This is the second of the author’s three papers on stability in the Liouville theorem on the Heisenberg group. The aim is to prove that each mapping with bounded distortion of a John domain on the Heisenberg group is close to a conformal mapping with order of closeness \(\sqrt {K - 1} \) in the uniform norm and order of closeness K ? 1 in the Sobolev norm L _p ¹ for all \(p < \tfrac{C}{{K - 1}}\).In this paper we prove a local variant of the desired result: each mapping on a ball with bounded distortion and distortion coefficient K near to 1 is close on a smaller ball to a conformal mapping with order of closeness \(\sqrt {K - 1} \) in the uniform norm and order of closeness K ? 1 in the Sobolev norm L _p ¹ for all \(p < \tfrac{C}{{K - 1}}\). We construct an example that demonstrates the asymptotic sharpness of the order of closeness of a mapping with bounded distortion to a conformal mapping in the Sobolev norm.     

On quasiplanes in Euclidean spaces

A variational inequality for the images of -dimensional hyperplanes under quasiconformal maps of the -dimensional Euclidean space is proved when

     

High temperature (T>300 K) light emitting diodes for 8–12 μm spectral range

Contrary to conventional light emitting diodes for visible and very near infrared utilizing interband (ω>E_g) luminescence, the longer infrared emitting diodes (LIREDs) we describe here utilize intraband (ω<E_g) electron transitions and emit beyond the fundamental absorption range of the material used. Made of indirect band gap semiconductors (like Ge, Si) and, therefore, free from the Auger recombination impact, LIREDs efficiently operate at higher temperatures (T>300 K) in the longer wavelength atmospheric window (8–12 μm). Electrically modulated power emitted is comparable to that for black body sources whereas shorter rise–fall times are due to recombination processes (200 μs) and not dependent on pixel thermal mass and thermal conduction. LIREDs can be made of different semiconductor structures provided the controllable modulation of free carrier concentration in the device base is achieved. The main parameters of Ge based LIREDs under injection mode are reported.     

Local order, entropy and predictability of financial time series

We consider time series of financial data as the Dow Jones Index with respect to the existence of local order. The basic idea is that in spite of the high stochasticity in average there might be special local situations where there local order exist and the predictability is considerably higher than in average. In order to check this assumption we discretise the time series and investigate the frequency of the continuation of definite words of length n first. We prove the existence of relatively long-range correlations under special conditions. The higher order Shannon entropies and the conditional entropies (dynamical entropies) are calculated, characteristic fluctuations are found. Instead of the dynamic entropies which yield mean values of the uncertainty/predictability we finally investigate the local values of the uncertainty/predictability and the distribution of these quantities. Received 19 January 2000     

On robust stability of a class of polynomial families

In this paper,we discuss the robust stability of a class of polynomial families more general than the interval polynomial family and diamond polynomial family.We prove that the Hurwitz stability of some special cases of this class of polynomial families can be determined by checking finite polynomials.We also give an example to illustrate that it is not always possible to determine the Hurwitz stability of all this class of polynomial families by checking finite polynomials.     

局部Lipschitz方程解的叠代逼近

设X=L_p或l_p(p≥2),T:D(T)→X是局部Lipschitz和严格增殖算子.本文给出非线性方程T_x=y的解的叠代逼近并讨论了局部Lipschitz和严格伪收缩映射不动点的叠代逼近.     

Multilevel Iterative Algorithms for Accelerating Spectral Approximations of Integral Equations

In this paper, spectral collocation and Nyström methods for integral equations are discussed. Some multilevel correction schemes are presented for infinitely accelerating the covergence even if the exact solution is not so smooth.     

SOLUTIONS OF MAGNETOHYDRODYNAMICS EQUATIONS-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC-PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS (Ⅳ)

This work is the continuation of the discussion of Refs.[1 3].(A) We turn the Magnetohydrodynamics equaitons of isentropic compresible andnon-dissipative magneto-flow into the form of the ideal hydrodynamics equations in thispaper;we can obtain the general Chaplygin equation from Ref.[3],and the generalsduction of this equation.(B)We apply the theory of functions of a complex rariable under Dirac-paulirepresentation,turn the general Magnetohydrodyamics equations of incompressiblemageto-flow into two nonlinear equaitons for flow function and"magneto-flow function",and obtain the exact stable solution of incompressible magnetohydrodynamics equationsunder the condition of stable magnetic field(i.e.under conditon of equality for kinematicalviscid coefficient or viscid diffusion coefficient with magnetic diffusion coefficient).     

1.3μm波长光纤偏振参数自动测试仪

本文介绍一种用于1.3μm波长的光纤偏振参数自动测试仪。它利用光路集成封装和计算机自动控制及信号处理等关键技术,方便、可靠、自动地进行1.3μm光纤及其器件偏振参数的测试,对于消光比为40dB以下的偏振态测量,误差优于0.3dB.     

Cooperativity in a spin transition ferrous polymer: Interacting domain model, thermodynamic, optical and EPR study

A new thermodynamic model is proposed in order to account for the high spin low spin conversion in metal-organic polymers. The model, based on the idea that the spin conversion occurs in interacting domains of like-spin metal ions, allows to explain most of the important features of various types of spin conversion. The sine qua non condition of the existence of spin transitions with hysteresis is obtained. In the case of very large cooperativity, the model predicts unusual behaviour of the spin conversion system due to a low-temperature metastable high spin state. Existence of such a state is interesting in the context of the light induced excited spin state trapping recently observed in some ferrous compounds. The model is applied to interpret the spin transition in polycrystalline ferrous polymer [Fe _1-y Cu _y (Htrz)₂ trz] (BF ₄) with y = 0.00, 0.01 and 0.10, detected by differential scanning calorimetry, optical reflectivity and electron paramagnetic resonance. The domain size and the interaction energy between the domains are estimated as, respectively, n = 11 and for the y = 0 compound. As the copper content is growing, n and tend to decrease, resulting in transformations of the shape of hysteresis loop which becomes less steep, narrows and shifts to lower temperatures. The electron paramagnetic resonance gives further evidence of the presence of like-spin domains. Received 27 November 1998 and Received in final form 19 April 1999