A homological version of the implicit function theorem

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.

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.

Alveolar process preservation at implants installed immediately into extraction sockets using deproteinized bovine bone mineral - an experimental study in dogs

Aim To evaluate the soft tissue and the dimensional changes of the alveolar bony crest at sites where deproteinized bovine bone mineral (DBBM) particles, concomitantly with the placement of a collagen membrane, were used at implants installed into sockets immediately after tooth extraction. Material and methods The pulp tissue of the mesial roots of 3P3 was removed in six Labrador dogs, and the root canals were filled. Flaps were elevated bilaterally, the premolars hemi-sectioned, and the distal roots removed. Recipient sites were prepared in the distal alveolus, and implants were placed. At the test sites, DBBM particles were placed in the residual marginal defects concomitantly with the placement of a collagen membrane. No treatment augmentation was performed at the control sites. A non-submerged healing was allowed. Impressions were obtained at baseline and at the time of sacrifice performed 4 months after surgery. The cast models obtained were analyzed using an optical system to evaluate dimensional variations. Block sections of the implant sites were obtained for histological processing and soft tissue assessments. Results After 4 months of healing, no differences in soft tissue dimensions were found between the test and control sites based on the histological assessments. The location of the soft tissue at the buccal aspect was, however, more coronal at the test compared with the control sites (1.8 +/- 0.8 and 0.9 +/- 0.8 mm, respectively). At the three-dimensional evaluation, the margin of the soft tissues at the buccal aspect appeared to be located more apically and lingually. The vertical dislocation was 1 +/- 0.6 and 2.7 +/- 0.5 mm at the test and control sites, respectively. The area of the buccal shrinkage of the alveolar crest was significantly smaller at the test sites (5.9 +/- 2.4 mm2) compared with the control sites (11.5 +/- 1.7 mm2). Conclusion The use of DBBM particles concomitantly with the application of a collagen membrane used at implants placed into sockets immediately after tooth extraction contributed to the preservation of the alveolar process.

Use of Natural Products for Post-Harvest Preservation of 'Vega' Cut Roses

Use of natural products as floral preservatives has helped to reduce the indiscriminate use of chemical products in flower preservation. In this study, we tested the ability of certain natural products to maintain the quality and to increase the commercial durability of 'Vega' cut roses. We employed a randomized factorial design with six post-harvest treatments and four evaluation dates. The following treatments were tested: 1) distilled water; 2) methyl jasmonate (350 mu M) applied in a four-hour pulse; 3) methyl jasmonate (500 mu M) spraying; 4) mint oil (100 ppm); 5) ginger oil (100 ppm); and 6) propolis (0.05%) as a maintenance solution. Flowers were kept at 20+/-2 degrees C and 67+/-3% RH. Physiological and qualitative evaluations were conducted. Natural products had a beneficial effect on the shelf life of the flowers. However, for all evaluated parameters, the methyl jasmonate spray was the most efficient treatment to maintain floral quality, resulting in less fresh-mass loss and a lower flower respiratory rate. Methyl jasmonate spray also improved the maintenance of coloration, relative water content and concentration of reducing sugars, thus extending the shelf life of roses.

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.

Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfests theorem

The electron-diffraction pattern for two slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern that is asymmetric but has a symmetric envelope. In general, both the expected displacement and the kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless, Ehrenfests theorems and the conservation of momentum are satisfied. © 1992 The American Physical Society.

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.

A refinement of the gauss-lucas theorem

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society.

Influence of different routes of flush perfusion on the distribution of lung preservation solutions in parenchyma and airways

Objective: The present study was performed to investigate the influence of different routes of perfusion on the distribution of the preservation solutions in the lung parenchyma and upper airways. Methods: Pigs were divided into four groups: control (n = 6), pulmonary artery (PA) (n = 6), simultaneous PA + bronchial artery (BA) (n = 8), and retrograde delivery (n = 6). After preparation and cannulation, cardioplegia solution and Euro- Collins solution (ECS) for lung preservation were given simultaneously. After removal of the heart, the double lung bloc was harvested. Following parameters were assessed: total and regional perfusion (dye-labeled microspheres), tissue water content, PA, aorta, left atrial and left ventricular pressures, cardiac output and lung temperature. Results: Our data show that flow of the ECS in lung parenchyma did not reach control values (9.4 ± 1.0 ml/min per g lung wet weight) regardless of the route of delivery (PA 6.3 ± 1.5, PA + BA 4.8 ± 0.9, retrograde 2.7 ± 0.9 ml/min per g lung wet weight). However, flow in the proximal and distal trachea were significantly increased by PA + BA delivery (0.970 ± 0.4, respectively, 0.380 ± 0.2 ml/min per g) in comparison with PA (0.023 ± 0.007, respectively, 0.024 ± 0.070 ml/min per g), retrograde (0.009 ± 0.003, respectively, 0.021 ± 0.006 ml/min per g) and control experiments (0.125 ± 0.0018, respectively, 0.105 ± 0.012 ml/g per min). Similarly the highest flow rates in the right main bronchus were achieved by PA + BA delivery (1.04 ± 0.4 ml/min per g) in comparison with 0.11 ± 0.03 in control, 0.033 ± 0.008 in PA, and 0.019 ± 0.005 ml/min per g in retrograde group. Flows in the left main bronchus were 0.09 ± 0.02 ml/min per g in control, 0.045 ± 0.012 ml/min per g in PA, and 0.027 ± 0.006 ml/min per g in retrograde group. The flow rates were significantly (P = 0.001) increased by PA + BA delivery of the storage solution (0.97 ± 0.3 ml/min per g). Conclusions: Our data show that the distribution of ECS for lung preservation is significantly improved in airway tissues (trachea and bronchi) if a simultaneous PA + BA delivery is used.

Invex nonsmooth alternative theorem and applications

An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion's approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

On the Optimality of Finite Constellations from Algebraic Lattices

A construction technique of finite point constellations in n-dimensional spaces from ideals in rings of algebraic integers is described. An algorithm is presented to find constellations with minimum average energy from a given lattice. For comparison, a numerical table of lattice constellations and group codes is computed for spaces of dimension two, three, and four. © 2001.