SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems

Dissertação para obtenção do Grau de Doutor em Matemática

Recovering the Elliott invariant from the Cuntz semigroup

Let A be a simple, separable C*-algebra of stable rank one. We prove that the Cuntz semigroup of C (T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yields a description of the Cuntz semigroup of C (T, A) in terms of the Elliott invariant of A. Second, suitably interpreted, it shows that the Elliott functor and the functor defined by the Cuntz semigroup of the tensor product with the algebra of continuous functions on the circle are naturally equivalent.

Twisted Poincare invariant quantum field theories

It is by now well known that the Poincare group acts on the Moyal plane with a twisted coproduct. Poincare invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincare action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the Poincare group, ensuring also the invariance of the S-matrix under the twisted action of the group. A significant new contribution here is the construction of the Poincare generators using quantum fields.

Ciratefi: An RST-invariant template matching with extension to color images

Template matching is a technique widely used for finding patterns in digital images. A good template matching should be able to detect template instances that have undergone geometric transformations. In this paper, we proposed a grayscale template matching algorithm named Ciratefi, invariant to rotation, scale, translation, brightness and contrast and its extension to color images. We introduce CSSIM (color structural similarity) for comparing the similarity of two color image patches and use it in our algorithm. We also describe a scheme to determine automatically the appropriate parameters of our algorithm and use pyramidal structure to improve the scale invariance. We conducted several experiments to compare grayscale and color Ciratefis with SIFT, C-color-SIFT and EasyMatch algorithms in many different situations. The results attest that grayscale and color Ciratefis are more accurate than the compared algorithms and that color-Ciratefi outperforms grayscale Ciratefi most of the time. However, Ciratefi is slower than the other algorithms.

Least energy solutions of a critical Neumann problem with a weight

We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.

Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices

The minimal irreducible representations of U-q[gl(m|n)], i.e. those irreducible representations that are also irreducible under U-q[osp(m|n)] are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra U-q[gl(m|n)((2))]. The U-q[osp(m|n)] invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from U-q[gl(m|n)((2))], which exhibit novel features not previously seen in the untwisted or non-super cases.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

MHC class II expression is regulated in dendritic cells independently of invariant chain degradation

We have investigated the mechanisms that control MHC class II (MHC II) expression in immature and activated dendritic cells (DC) grown from spleen and bone marrow precursors. Degradation of the MHC II chaperone invariant chain (li), acquisition of peptide cargo by MHC II, and delivery of MHC II-peptide complexes to the cell surface proceeded similarly in both immature and activated DC. However, immature DC reendocytosed and then degraded the MHC II-peptide complexes much faster than the activated DC. MHC II expression in DC is therefore not controlled by the activity of the protease(s) that degrade Ii, but by the rate of endocytosis of peptide-loaded MHC II. Late after activation, DC downregulated MHC II synthesis both in vitro and in vivo.

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.