Genetic Algorithms (Binary and Real Codes) for the Optimisation of a Fermentation Process for Butanol Production

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

The Geometric Birnbaum-Saunders regression model with cure rate

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Tensor3D: A computer graphics program to simulate 3D real-time deformation and visualization of geometric bodies

Tensor3D is a geometric modeling program with the capacity to simulate and visualize in real-time the deformation, specified through a tensor matrix and applied to triangulated models representing geological bodies. 3D visualization allows the study of deformational processes that are traditionally conducted in 2D, such as simple and pure shears. Besides geometric objects that are immediately available in the program window, the program can read other models from disk, thus being able to import objects created with different open-source or proprietary programs. A strain ellipsoid and a bounding box are simultaneously shown and instantly deformed with the main object. The principal axes of strain are visualized as well to provide graphical information about the orientation of the tensor's normal components. The deformed models can also be saved, retrieved later and deformed again, in order to study different steps of progressive strain, or to make this data available to other programs. The shape of stress ellipsoids and the corresponding Mohr circles defined by any stress tensor can also be represented. The application was written using the Visualization ToolKit, a powerful scientific visualization library in the public domain. This development choice, allied to the use of the Tcl/Tk programming language, which is independent on the host computational platform, makes the program a useful tool for the study of geometric deformations directly in three dimensions in teaching as well as research activities. (C) 2007 Elsevier Ltd. All rights reserved.

Refractive and geometric lens characterization through multi-wavelength digital speckle pattern interferometry

Physical parameters of different types of lenses were measured through digital speckle pattern interferometry (DSPI) using a multimode diode laser as light source. When such lasers emit two or more longitudinal modes simultaneously the speckle image of an object appears covered of contour fringes. By performing the quantitative fringe evaluation the radii of curvature as well as the refractive indexes of the lenses were determined. The fringe quantitative evaluation was carried out through the four- and the eight-stepping techniques and the branch-cut method was employed for phase unwrapping. With all these parameters the focal length was calculated. This whole-field multi-wavelength method does enable the characterization of spherical and aspherical lenses and of positive and negative ones as well. (C) 2007 Elsevier B.V. All rights reserved.

Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation

In this article we describe some qualitative and geometric aspects of nonsmooth dynamical systems theory around typical singularities. We also establish an interaction between nonsmooth systems and geometric singular perturbation theory. Such systems are represented by discontinuous vector fields on R(l), l >= 2, where their discontinuity set is a codimension one algebraic variety. By means of a regularization process proceeded by a blow-up technique we are able to bring about some results that bridge the space between discontinuous systems and singularly perturbed smooth systems. We also present an analysis of a subclass of discontinuous vector fields that present transient behavior in the 2-dimensional case, and we dedicate a section to providing sufficient conditions in order for our systems to have local asymptotic stability.

Collision and Stable Regions around Bodies with Simple Geometric Shape

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Noether theorem for geometric actions and area preserving diffeomorphisms on the torus

We find that within the formalism of coadjoint orbits of the infinite dimensional Lie group the Noether procedure leads, for a special class of transformations, to the constant of motion given by the fundamental group one-cocycle S. Use is made of the simplified formula giving the symplectic action in terms of S and the Maurer-Cartan one-form. The area preserving diffeomorphisms on the torus T2=S1⊗S1 constitute an algebra with central extension, given by the Floratos-Iliopoulos cocycle. We apply our general treatment based on the symplectic analysis of coadjoint orbits of Lie groups to write the symplectic action for this model and study its invariance. We find an interesting abelian symmetry structure of this non-linear problem.

Quantum algebraic description of the Moszkowski model

In this paper we investigate the behaviour of the Moukowski model within the mnten of quantum algebras. The Moszkwski Hamiltonian is diagonalized aractly for different numbers of panicles and for various values of the deformalion parameter of the quanlum algebra involved. We also include ranking in our system and observe its variation as a function of the deformation parameters. © 1992 IOP Publishing Ltd.

Affine Lie algebraic origin of constrained KP hierarchies

An affine sl(n + 1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (GNLS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.

Special subsets and optimum codes based on lattices and cosets

This paper introduces the concept of special subsets when applied to generator matrices based on lattices and cosets as presented by Calder-bank and Sloane. By using the special subsets we propose a non exhaustive code search for optimum codes. Although non exhaustive, the search always results in optimum codes for given (k1, V, Λ/Λ′). Tables with binary and ternary optimum codes to partitions of lattices with 8, 9 e 16 cosets, were obtained.

Construction and decoding of BCH codes over finite commutative rings

BCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, for these codes. The code construction and the decoding procedures are very similar to the BCH codes over finite integer rings. © 1999 Elsevier B.V. All rights reserved.

Variation in mandible shape in Thrichomys apereoides (Mammalia: Rodentia): Geometric analysis of a complex morphological structure

The model of development and evolution of complex morphological structures conceived by Atchley and Hall in 1991 (Biol. Rev. 66:101-157), which establishes that changes at the macroscopic, morphogenetic level can be statistically detected as variation in skeletal units at distinct scales, was applied in combination with the formalism of geometric morphometrics to study variation in mandible shape among populations of the rodent species Thrichomys apereoides. The thin-plate spline technique produced geometric descriptors of shape derived from anatomical landmarks in the mandible, which we used with graphical and inferential approaches to partition the contribution of global and localized components to the observed differentiation in mandible shape. A major pattern of morphological differentiation in T. apereoides is attributable to localized components of shape at smaller geometric scales associated with specific morphogenetic units of the mandible. On the other hand, a clinal trend of variation is associated primarily with localized components of shape at larger geometric scales. Morphogenetic mechanisms assumed to be operating to produce the observed differentiation in the specific units of the mandible include mesenchymal condensation differentiation, muscle hypertrophy, and tooth growth. Perspectives for the application of models of morphological evolution and geometric morphometrics to morphologically based systematic biology are considered.