A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

Correlation between metal-ceramic bond strength and coefficient of linear thermal expansion difference

The purpose of this study was to evaluate the metal-ceramic bond strength (MCBS) of 6 metal-ceramic pairs (2 Ni-Cr alloys and 1 Pd-Ag alloy with 2 dental ceramics) and correlate the MCBS values with the differences between the coefficients of linear thermal expansion (CTEs) of the metals and ceramics. Verabond (VB) Ni-Cr-Be alloy, Verabond II (VB2), Ni-Cr alloy, Pors-on 4 (P), Pd-Ag alloy, and IPS (I) and Duceram (D) ceramics were used for the MCBS test and dilatometric test. Forty-eight ceramic rings were built around metallic rods (3.0 mm in diameter and 70.0 mm in length) made from the evaluated alloys. The rods were subsequently embedded in gypsum cast in order to perform a tensile load test, which enabled calculating the CMBS. Five specimens (2.0 mm in diameter and 12.0 mm in length) of each material were made for the dilatometric test. The chromel-alumel thermocouple required for the test was welded into the metal test specimens and inserted into the ceramics. ANOVA and Tukey's test revealed significant differences (p=0.01) for the MCBS test results (MPa), with PI showing higher MCBS (67.72) than the other pairs, which did not present any significant differences. The CTE (10-6 oC-1) differences were: VBI (0.54), VBD (1.33), VB2I (-0.14), VB2D (0.63), PI (1.84) and PD (2.62). Pearson's correlation test (r=0.17) was performed to evaluate of correlation between MCBS and CTE differences. Within the limitations of this study and based on the obtained results, there was no correlation between MCBS and CTE differences for the evaluated metal-ceramic pairs.

COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

The game inside the school: a representation of 5(th) graders physical education classes

Since the beginning of Physical Education entrance in the brazilin public schools, the game has been frequently used as content, and in the course of time that practice seems to be intensified. In spite of many approaches of different purposes to justify its pedagogic usefulness, the game has been used as an indiscriminate way due to the fascination that it provides to the students. The present study searches for a description and analysis of children`s (10-12 years old) attitudes behaviors in games, on Physical Education classes, inside a public school. The study was accomplished with the researcher also attending as a teacher (action research). For the accomplishment of the study 55 children were filmed in four different games, of different kinds (exposed, transformed, and spontaneous). The classes` description and analysis were focused in the attitude axis and it was defined four topics for the discussion: Conflicts, Respect of rules, Expressiveness, and Competitiveness. The relationship between the individual with the game and its culture were pointed as the main characteristics in the configuration of the ludicrous activity atmosphere. It was also possible to observe specific situations of this relationship, once the games were limited to the social games (Piaget category), in a school atmosphere where children have students roles. Due to the obtained results, the study proposes a reflexive practice in which the students notice their own attitudes and try to adapt the game to their needs and not he other way around. In this perspective, the teacher has an important mediator roll, once he will be responsible to point out the students` difficulties and promote discussions in favor to provide teamwork.

Anaerobic degradation of linear alkylbenzene sulfonate (LAS) in fluidized bed reactor by microbial consortia in different support materials

Four anaerobic fluidized bed reactors filled with activated carbon (R1), expanded clay (R2), glass beads (R3) and sand (R4) were tested for anaerobic degradation of LAS. All reactors were inoculated with sludge from a UASB reactor treating swine wastewater and were fed with a synthetic substrate supplemented with approximately 20 mg l(-1) of LAS, on average. To 560 mg l(-1) COD influent, the maximum COD and LAS removal efficiencies were mean values of 97 +/- 2% and 99 +/- 2%, respectively, to all reactors demonstrating the potential applicability of this reactor configuration for treating LAS. The reactors were kept at 30 degrees C and operated with a hydraulic retention time (HRT) of 18 h. The use of glass beads and sand appear attractive because they favor the development of biofilms capable of supporting LAS degradation. Subsequent 16S rRNA gene sequencing and phylogenetic analysis of samples from reactors R3 and R4 revealed that these reactors gave rise to broad microbial diversity, with microorganisms belonging to the phyla Bacteroidetes, Firmicutes, Actinobacteria and Proteobacteria, indicating the role of microbial consortia in degrading the surfactant LAS. (C) 2010 Elsevier Ltd. All rights reserved.

Treatment of linear alkylbenzene sulfonate in a horizontal anaerobic immobilized biomass reactor

Linear alkylbenzene sulfonate (LAS) is an anionic surfactant widely used to manufacture detergents and found in domestic and industrial wastewater. LAS removal was evaluated in a horizontal anaerobic immobilized biomass reactor. The system was filled with polyurethane foam and inoculated with sludge that was withdrawn from an up flow anaerobic sludge blanket reactor that is used to treat swine wastewater. The reactor was fed with easily degradable substrates and a solution of commercial LAS for 313 days. The hydraulic retention time applied was 12 h. The system was initially operated without detergent and resulted to 94% reduction of demand. The mass balance in the system indicated that the LAS removal efficiency was 45% after 180 days. From the 109th day to the 254th day, a removal efficiency of 32% was observed. The removal of LAS was approximately 40% when 1500 mg of LAS were applied in the absence of co-substrates suggesting that the LAS molecules were used selectively. Microscopic analyses of the biofilm revealed diverse microbial morphologies and denaturing gradient gel electrophoresis profiling showed variations in the total bacteria and sulfate-reducing bacteria populations. 16S rRNA sequencing and phylogenetic analyses demonstrated that members of the order Clostridiales were the major components of the bacterial community in the last step of the reactor operation. (c) 2009 Elsevier Ltd. All rights reserved.

Influence of support material on the immobilization of biomass for the degradation of linear alkylbenzene sulfonate in anaerobic reactors

Two horizontal-flow anaerobic immobilized biomass reactors (HAIB) were used to study the degradation of the LAS surfactant: one filled with charcoal (HAIB1) and the other with a mixed bed of expanded clay and polyurethane foam (HAIB2). The reactors were fed with synthetic substrate supplemented with 14 mg l(-1) of LAS, kept at 30 +/- 2 degrees C and operated with a hydraulic retention time (HRT) of 12 h. The surfactant was quantified by HPLC. Spatial variation analyses were done to quantify organic matter and LAS consumption along the reactor length. The presence of the surfactant in the load did not affect the removal of organic matter (COD), which was close to 90% in both reactors for an influent COD of 550 ring l(-1). The results of a mass balance indicated that 28% of all LAS added to HAIB1 was removed by degradation. HAIB2 presented 27% degradation. Molecular biology techniques revealed microorgan isms belonging the uncultured Holophaga sp., uncultured delta Proteobacterium, uncultured Verrucomicrobium sp., Bacteroides sp. and uncultured gamma Proteobacterium sp. The reactor with biomass immobilized on charcoal presented lower adsorption and a higher kinetic degradation coefficient. So, it was the most suitable support for LAS anaerobic treatment. (c) 2008 Elsevier Ltd. All rights reserved.

MODELING THE UNVOICED COMPONENT IN THE CANONICAL REPRESENTATION OF SPEECH

The canonical representation of speech constitutes a perfect reconstruction (PR) analysis-synthesis system. Its parameters are the autoregressive (AR) model coefficients, the pitch period and the voiced and unvoiced components of the excitation represented as transform coefficients. Each set of parameters may be operated on independently. A time-frequency unvoiced excitation (TFUNEX) model is proposed that has high time resolution and selective frequency resolution. Improved time-frequency fit is obtained by using for antialiasing cancellation the clustering of pitch-synchronous transform tracks defined in the modulation transform domain. The TFUNEX model delivers high-quality speech while compressing the unvoiced excitation representation about 13 times over its raw transform coefficient representation for wideband speech.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Distinct conformational properties determined by implicit and explicit representation of protein-solvent interactions. An analytical and computer simulation study

In the protein folding problem, solvent-mediated forces are commonly represented by intra-chain pairwise contact energy. Although this approximation has proven to be useful in several circumstances, it is limited in some other aspects of the problem. Here we show that it is possible to achieve two models to represent the chain-solvent system. one of them with implicit and other with explicit solvent, such that both reproduce the same thermodynamic results. Firstly, lattice models treated by analytical methods, were used to show that the implicit and explicitly representation of solvent effects can be energetically equivalent only if local solvent properties are time and spatially invariant. Following, applying the same reasoning Used for the lattice models, two inter-consistent Monte Carlo off-lattice models for implicit and explicit solvent are constructed, being that now in the latter the solvent properties are allowed to fluctuate. Then, it is shown that the chain configurational evolution as well as the globule equilibrium conformation are significantly distinct for implicit and explicit solvent systems. Actually, strongly contrasting with the implicit solvent version, the explicit solvent model predicts: (i) a malleable globule, in agreement with the estimated large protein-volume fluctuations; (ii) thermal conformational stability, resembling the conformational hear resistance of globular proteins, in which radii of gyration are practically insensitive to thermal effects over a relatively wide range of temperatures; and (iii) smaller radii of gyration at higher temperatures, indicating that the chain conformational entropy in the unfolded state is significantly smaller than that estimated from random coil configurations. Finally, we comment on the meaning of these results with respect to the understanding of the folding process. (C) 2009 Elsevier B.V. All rights reserved.

Assessment of linear measurements of bone for implant sites in the presence of metallic artefacts using cone beam computed tomography and multislice computed tomography

The objective was to evaluate the influence of dental metallic artefacts on implant sites using multislice and cone-beam computed tomography techniques. Ten dried human mandibles were scanned twice by each technique, with and without dental metallic artefacts. Metallic restorations were placed at the top of the alveolar ridge adjacent to the mental foramen region for the second scanning. Linear measurements (thickness and height) for each cross-section were performed by a single examiner using computer software. All mandibles were analysed at both the right and the left mental foramen regions. For the multislice technique, dental metallic artefact produced an increase of 5% in bone thickness and a reduction of 6% in bone height; no significant differences (p > 0.05) were detected when comparing measurements performed with and without metallic artefacts. With respect to the cone-beam technique, dental metallic artefact produced an increase of 6% in bone thickness and a reduction of 0.68% in bone height. No significant differences (p > 0.05) were observed when comparing measurements performed with and without metallic artefacts. The presence of dental metallic artefacts did not alter the linear measurements obtained with both techniques, although its presence made the location of the alveolar bone crest more difficult.