Formalismo de Hamilton-Jacobi à la Carathéodory

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

Some account of the Jacotot system of universal instruction with a preliminary reference to the systems of Lancaster, Fellenburgh, and Pestalozzi, read before the Albany Institute at its last regular meeting, in April 1831.

Mode of access: Internet.

Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

Simultaneous X-ray imaging of plant root growth and water uptake in thin-slab systems

Direct and simultaneous observation of root growth and plant water uptake is difficult because soils are opaque. X-ray imaging techniques such as projection radiography or Computer Tomography (CT) offer a partial alternative to such limitations. Nevertheless, there is a trade-off between resolution, large field-of-view and 3-dimensionality: With the current state of the technology, it is possible to have any two. In this study, we used X-ray transmission through thin-slab systems to monitor transient saturation fields that develop around roots as plants grow. Although restricted to 2-dimensions, this approach offers a large field-of-view together with high spatial and dynamic resolutions. To illustrate the potential of this technology, we grew peas in 1 cm thick containers filled with soil and imaged them at regular intervals. The dynamics of both the root growth and the water content field that developed around the roots could be conveniently monitored. Compared to other techniques such as X-ray CT, our system is relatively inexpensive and easy to implement. It can potentially be applied to study many agronomic problems, such as issues related to the impact of soil constraints (physical, chemical or biological) on root development.

Micromorphology of Resin-Dentin Interfaces Using One-Bottle Etch&Rinse and Self-Etching Adhesive Systems on Laser-Treated Dentin Surfaces: A Confocal Laser Scanning Microscope Analysis

Background and Objectives: This study evaluated the hybrid layer (HL) morphology created by three adhesive systems (AS) on dentin surfaces treated with Er:YAG laser using two irradiation parameters. Study Design: Occlusal flat dentin surfaces of 36 human third molars were assigned into nine groups (n = 4) according to the following ASs: one bottle etch&rinse Single Bond Plus (3M ESPE), two-step Clearfil Protect Bond (Kuraray), and all-in-one S3 Bond (Kuraray) self-etching, which were labeled with rhodamine B or fluorescein isothiocyanate dextran and were applied to dentin surfaces that were irradiated with Er:YAG laser at either 120 (38.7 J/cm(2)) or 200 mJ/pulse (64.5 J/cm(2)), or were applied to untreated dentin surfaces (control group). The ASs were light-activated following MI and the bonded surfaces were restored with resin composite Z250 (3M ESPE). After 24 hours of storage in vegetable oil, the restored teeth were vertically, serially sectioned into 1-mm thick slabs, which had the adhesive interfaces analyzed with confocal laser microscope (CLSM-LSM 510 Meta). CLSM images were recorded in the fluorescent mode from three different regions along each bonded interface. Results: Non-uniform HL was created on laser-irradiated dentin surfaces regardless of laser irradiation protocol for all AS, while regular and uniform HL was observed in the control groups. ""Stretch mark""-like red lines were found within the HL as a result of resin infiltration into dentin microfissures, which were predominantly observed in 200 mJ/pulse groups regardless of AS. Poor resin infiltration into peritubular dentin was observed in most regions of adhesive interfaces created by all ASs on laser-irradiated dentin, resulting in thin resin tags with neither funnel-shaped morphology nor lateral resin projections. Conclusion: Laser irradiation of dentin surfaces at 120 or 200 mJ/pulse resulted in morphological changes in HL and resin tags for all ASs evaluated in the study. Lasers Surg. Med. 42:662-670, 2010. (C) 2010 Wiley-Liss, Inc.

Shear Bond Strength and Ultrastructural Interface Analysis of Different Adhesive Systems to Bleached Dentin

Background: It remains unclear as to whether or not dental bleaching affects the bond strength of dentin/resin restoration. Purpose: To evaluated the bond strength of adhesive systems to dentin submitted to bleaching with 38% hydrogen peroxide (HP) activated by LED-laser and to assess the adhesive/dentin interfaces by means of SEM. Study design: Sixty fragments of dentin (25 mm(2)) were included and divided into two groups: bleached and unbleached. HP was applied for 20 s and photoactivated for 45 s. Groups were subdivided according to the adhesive systems (n = 10): (1) two-steps conventional system (Adper Single Bond), (2) two-steps self-etching system (Clearfil standard error (SE) Bond), and (3) one-step self-etching system (Prompt L-Pop). The specimens received the Z250 resin and, after 24 h, were submitted to the bond strength test. Additional 30 dentin fragments (n = 5) received the same surface treatments and were prepared for SEM. Data were analyzed by ANOVA and Tukey`s test (alpha = 0.05). Results: There was significant strength reduction in bleached group when compared to unbleached group (P < 0.05). Higher bond strength was observed for Prompt. Single Bond and Clearfil presented the smallest values when used in bleached dentin. SEM analysis of the unbleached specimens revealed long tags and uniform hybrid layer for all adhesives. In bleached dentin, Single Bond provided open tubules and with few tags, Clearfil determined the absence of tags and hybrid layer, and Prompt promoted a regular hybrid layer with some tags. Conclusions: Prompt promoted higher shear bond strength, regardless of the bleaching treatment and allowed the formation of a regular and fine hybrid layer with less deep tags, when compared to Single Bond and Clearfil. Microsc. Res. Tech. 74:244-250, 2011. (C) 2010 Wiley-Liss, Inc.

Perp-systems and partial geometries

A perp-system R(r) is a maximal set of r-dimensional subspaces of PG(N,q) equipped with a polarity rho, such that the tangent space of an element of R(r) does not intersect any element of R(r). We prove that a perp-system yields partial geometries, strongly regular graphs, two-weight codes, maximal arcs and k-ovoids. We also give some examples, one of them yielding a new pg(8,20,2).

Shopping for apparel: how can kiosk systems help?

When shopping for apparel, many consumers seek advice from friends and family or store personnel. In-store kiosk systems might serve as an alternative decision support system. In the present study we address the key question of how such kiosk systems are evaluated by consumers. We conducted three focus group discussions with regular apparel shoppers aged between 23 and 39 years. In sum, qualitative information from 15 participants was subject to a qualitative content analysis with the aim of gaining a more comprehensive understanding of how apparel shoppers experience the shopping process. Getting a more in-depth understanding of the needs and wishes associated with the apparel shopping process gives a basis for evaluating the potential acceptance of electronic decision support systems in apparel shopping. Although our study is exploratory in nature, we are able to draw an initial picture of how kiosk systems could be used in apparel shopping.

A framework for semantic checking of information systems

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Towards robust network based complex systems : from evolutionary cellular automata to biological models

Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

Canonical transformations theory for presymplectic systems

We develop a theory of canonical transformations for presymplectic systems, reducing this concept to that of canonical transformations for regular coisotropic canonical systems. In this way we can also link these with the usual canonical transformations for the symplectic reduced phase space. Furthermore, the concept of a generating function arises in a natural way as well as that of gauge group.

Central configurations of nested regular polyhedra for the spatial 2n–body problem

We consider 2n masses located at the vertices of two nested regular polyhedra with the same number of vertices. Assuming that the masses in each polyhedron are equal, we prove that for each ratio of the masses of the inner and the outer polyhedron there exists a unique ratio of the length of the edges of the inner and the outer polyhedron such that the configuration is central.