Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4

Николай Кутев, Величка Милушева - Намираме експлицитно всичките би-омбилични фолирани полусиметрични повърхнини в четиримерното евклидово пространство R^4

Supersymmetry flows, semi-symmetric space sine-Gordon models and the Pohlmeyer reduction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Semi-Symmetric Algebras: General Constructions. Part II

2000 Mathematics Subject Classification: 15A69, 15A78.

Integrability vs supersymmetry: Poisson structures of the pohlmeyer reduction

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion : a continuum model of matrix metabolism and transport

The functional properties of cartilaginous tissues are determined predominantly by the content, distribution, and organization of proteoglycan and collagen in the extracellular matrix. Extracellular matrix accumulates in tissue-engineered cartilage constructs by metabolism and transport of matrix molecules, processes that are modulated by physical and chemical factors. Constructs incubated under free-swelling conditions with freely permeable or highly permeable membranes exhibit symmetric surface regions of soft tissue. The variation in tissue properties with depth from the surfaces suggests the hypothesis that the transport processes mediated by the boundary conditions govern the distribution of proteoglycan in such constructs. A continuum model (DiMicco and Sah in Transport Porus Med 50:57-73, 2003) was extended to test the effects of membrane permeability and perfusion on proteoglycan accumulation in tissue-engineered cartilage. The concentrations of soluble, bound, and degraded proteoglycan were analyzed as functions of time, space, and non-dimensional parameters for several experimental configurations. The results of the model suggest that the boundary condition at the membrane surface and the rate of perfusion, described by non-dimensional parameters, are important determinants of the pattern of proteoglycan accumulation. With perfusion, the proteoglycan profile is skewed, and decreases or increases in magnitude depending on the level of flow-based stimulation. Utilization of a semi-permeable membrane with or without unidirectional flow may lead to tissues with depth-increasing proteoglycan content, resembling native articular cartilage.

Learning the Kernel Matrix with Semi-Definite Programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space -- classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -- using the labelled part of the data one can learn an embedding also for the unlabelled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method to learn the 2-norm soft margin parameter in support vector machines, solving another important open problem. Finally, the novel approach presented in the paper is supported by positive empirical results.

Elementos finitos em fluidos dominados pelo fenômeno de advecção: um método semi-Lagrangeano.

Os escoamentos altamente convectivos representam um desafio na simulação pelo método de elementos finitos. Com a solução de elementos finitos de Galerkin para escoamentos incompressíveis, a matriz associada ao termo convectivo é não simétrica, e portanto, a propiedade de aproximação ótima é perdida. Na prática as soluções apresentam oscilações espúrias. Muitos métodos foram desenvolvidos com o fim de resolver esse problema. Neste trabalho apresentamos um método semi- Lagrangeano, o qual é implicitamente um método do tipo upwind, que portanto resolve o problema anterior, e comparamos o desempenho do método na solução das equações de convecção-difusão e Navier-Stokes incompressível com o Streamline Upwind Petrov Galerkin (SUPG), um método estabilizador de reconhecido desempenho. No SUPG, as funções de forma e de teste são tomadas em espaços diferentes, criando um efeito tal que as oscilações espúrias são drasticamente atenuadas. O método semi-Lagrangeano é um método de fator de integração, no qual o fator é um operador de convecção que se desloca para um sistema de coordenadas móveis no fluido, mas restabelece o sistema de coordenadas Lagrangeanas depois de cada passo de tempo. Isto prevê estabilidade e a possibilidade de utilizar passos de tempo maiores.Existem muitos trabalhos na literatura analisando métodos estabilizadores, mas não assim com o método semi-Lagrangeano, o que representa a contribuição principal deste trabalho: reconhecer as virtudes e as fraquezas do método semi-Lagrangeano em escoamentos dominados pelo fenômeno de convecção.

Magneto - Transport of electron symmetric and antisymmrtric states in highly doped InGaAs/InAlAs single quantum well

Beating patterns in longitudinal resistance caused by the symmetric and antisymmetric states were observed in a heavily doped InGaAs/InAlAs quantum well by using variable temperature Hall measurement. The energy gap of symmetric and antisymmetric states is estimated to be 4meV from the analysis of beating node positions. In addition, the temperature dependences of the subband electron mobility and concentration were also studied from the mobility spectrum and multicarrier fitting procedure.

A novel extremely broadband superluminescent diode based on symmetric graded tensile-strained bulk InGaAs

A novel broadband superluminescent diode (SLD), which has a symmetric graded tensile-strained bulk InGaAs active region, is developed. The symmetric-graded tensile-strained bulk InGaAs is achieved by changing the group III TMGa source flow only during its growth process by low-pressure metalorganic vapor-phase epitaxy (LP-MOVPE), in which the much different tensile strain is introduced simultaneously. At 200mA injection current, the full width at half maximum (FWHM) of the emission spectrum of the SLID can be up to 122nm, covering the range of 1508-1630nm, and the output power is 11.5mW.

Suppression of exciton recombination in symmetric GaAs0.7Sb0.3/GaAs/GaAs0.7P0.3 coupled quantum wells induced by an in-plane magnetic field

Suppression of the exciton recombination in GaAs0.7Sb0.3/GaAs/GaAs0.7P0.3 coupled quantum well (CQW) induced by an external magnetic field is investigated theoretically. Unlike the usual electro-Stark effect, the exciton energy dispersion of an exciton is modified by an external in-plane magnetic field, the ground state of the magnetoexciton shifts from a zero in-plane center of mass (CM) momentum to a finite CM momentum, and the Lorentz force induces the spatial separation of electron and hole. Consequently, this effect renders the ground state of magnetoexciton stable against radiative recombination due to momentum conservation. This effect depends sensitively on the thickness and height of GaAs0.7Sb0.3 layer, therefore it could provide us useful infometion about the band alignment of CQW. (C) 2004 American Institute of Physics.

Spin-dependent tunneling through a symmetric semiconductor barrier: The Dresselhaus effect

Spin-dependent tunneling through a symmetric semiconductor barrier is studied including the k(3) Dresselhaus effect. The spin-dependent transmission of an electron can be obtained analytically. By comparing with previous work [Phys. Rev. B 67, 201304(R) (2003) and Phys. Rev. Lett. 93, 056601 (2004)], it is shown that the spin polarization and interface current are changed significantly by including the off-diagonal elements in the current operator, and can be enhanced considerably by the Dresselhaus effect in the contact regions.

Enhancement of stimulated emission in 12-fold symmetric quasi-crystals

In this paper, we investigate the stimulated emission in a 12-fold symmetric quasiperiodic photonic crystal. The stimulated emission peaks in the quasiperiodic photonic crystal are more abundant and stronger than those in a periodic crystal. Also, more stimulated emission peaks appear as the crystal size and the gain increase, and some frequencies of the peaks are independent of the incident direction. These phenomena may be due to wave localization in the quasiperiodic photonic crystal.

In-plane optical anisotropy of symmetric and asymmetric (001) GaAs/Al(Ga)As superlattices and quantum wells

Two sensitive polarized spectroscopies, reflectance difference spectroscopy and photocurrent difference spectroscopy, are used to study the characteristic of the in-plane optical anisotropy in the symmetric and the asymmetric (001) GaAs/Al(Ga)As superlattices (SLs). The anisotropy spectra of the symmetric and the asymmetric SLs show significant difference: for symmetric ones, the anisotropies of the 1HH-->1E transition (1H1E) and 1L1E are dominant, and they are always approximately equal and opposite; while for asymmetric ones, the anisotropy of 1H1E is much less than that of 1L1E and 2H1E, and the anisotropy of 3H2E is very strong. The calculated anisotropy spectra within the envelope function model agree with the experimental results, and a perturbation approach is used to understand the role of the electric field and the interface potential in the anisotropy. (C) 2001 American Institute of Physics.

Triclinic deformation and anisotropic strain relaxation of an InAs film on a GaAs(001) substrate measured by a series of symmetric double crystal X-ray diffraction

We presented a series of symmetric double crystal X-ray diffraction (DCXD) measurements, (0 0 4), (2 2 0) and (2 - 2 0) diffraction, to investigate the strain relaxation in an InAs film grown on a GaAs(0 0 1) substrate. The strain tensor and rotation tensor were calculated according to the DCXD results. It is found that the misfit strain is relaxed nearly completely and the strain relaxation caused a triclinic deformation in the epilayer. The lattice parameter along the [1 1 0] direction is a little longer than that along the [1 - 1 0] direction. Furthermore, a significant tilt, 0.2 degrees, towards the [1 1 0] direction while a very slight one: 0.002 degrees, towards [1 - 1 0] direction were discussed. This anisotropic strain relaxation is attributed to the asymmetric distribution of misfit dislocations, which is also indicated by the variation of the full-width at half-maximum (FWHM) of (0 0 4) diffraction along four azimuth angles. (C) 1998 Elsevier Science B.V. All rights reserved.

Resonant subband Landau level coupling in symmetric quantum well

Subband structure and depolarization shifts in an ultrahigh mobility GaAs/Al0.24Ga0.76As quantum well are studied using magnetoinfrared spectroscopy via resonant subband Landau level coupling. Resonant couplings between the first and up to the fourth subbands are identified by well-separated antilevel-crossing split resonance, while the hy-lying subbands were identified by the cyclotron resonance linewidth broadening in the literature. In addition, a forbidden intersubband transition (first to third) has been observed. With the precise determination of the subband structure, we find that the depolarization shift can be well described by the semiclassical slab plasma model and the possible origins for the forbidden transition are discussed.