Mathematical modeling and analysis of the particle interactions in the direct filtration using the colloidal theory

This work used the colloidal theory to describe forces and energy interactions of colloidal complexes in the water and those formed during filtration run in direct filtration. Many interactions of particle energy profiles between colloidal surfaces for three geometries are presented here in: spherical, plate and cylindrical; and four surface interactions arrangements: two cylinders, two spheres, two plates and a sphere and a plate. Two different situations were analyzed, before and after electrostatic destabilization by action of the alum sulfate as coagulant in water studies samples prepared with kaolin. In the case were used mathematical modeling by extended DLVO theory (from the names: Derjarguin-Landau-Verwey-Overbeek) or XDLVO, which include traditional approach of the electric double layer (EDL), surfaces attraction forces or London-van der Waals (LvdW), esteric forces and hydrophobic forces, additionally considering another forces in colloidal system, like molecular repulsion or Born Repulsion and Acid-Base (AB) chemical function forces from Lewis.

alpha,beta-Unsaturated Diazoketones as Platforms in the Asymmetric Synthesis of Hydroxylated Alkaloids. Total Synthesis of 1-Deoxy-8,8a-diepicastanospermine and 1,6-Dideoxyepicastanospermine and Formal Synthesis of Pumiliotoxin 251D

A versatile and concise approach for the stereoselective synthesis of mono-, di-, and trihydroxylated indolizidines is presented in four to six steps from Cbz-prolinal and a diazophosphonate. The key steps involved a Wolff rearrangement, followed by a stereoselective dihydroxylation/epoxidation reaction, from an alpha,beta-unsaturated diazoketone. The strategy also permits extension to the synthesis of many natural hydroxylated indolizidine alkaloids as demonstrated in the formal synthesis of pumiliotoxin 251D.

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

Alternative Tasks for the Teaching and the Learning of functions: analysis of an intervention in the High School

In this paper we focus on the application of two mathematical alternative tasks to the teaching and learning of functions with high school students. The tasks were elaborated according to the following methodological approach: (i) Problem Solving and/or mathematics investigation and (ii) a pedagogical proposal, which defends that mathematical knowledge is developed by means of a balance between logic and intuition. We employed a qualitative research approach (characterized as a case study) aimed at analyzing the didactic pedagogical potential of this type of methodology in high school. We found that tasks such as those presented and discussed in this paper provide a more significant learning for the students, allowing a better conceptual understanding, becoming still more powerful when one considers the social-cultural context of the students.

Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Hydration and anomalous solubility of the Bell-Lavis model as solvent

We address the investigation of the solvation properties of the minimal orientational model for water originally proposed by [Bell and Lavis, J. Phys. A 3, 568 (1970)]. The model presents two liquid phases separated by a critical line. The difference between the two phases is the presence of structure in the liquid of lower density, described through the orientational order of particles. We have considered the effect of a small concentration of inert solute on the solvent thermodynamic phases. Solute stabilizes the structure of solvent by the organization of solvent particles around solute particles at low temperatures. Thus, even at very high densities, the solution presents clusters of structured water particles surrounding solute inert particles, in a region in which pure solvent would be free of structure. Solute intercalates with solvent, a feature which has been suggested by experimental and atomistic simulation data. Examination of solute solubility has yielded a minimum in that property, which may be associated with the minimum found for noble gases. We have obtained a line of minimum solubility (TmS) across the phase diagram, accompanying the line of maximum density. This coincidence is easily explained for noninteracting solute and it is in agreement with earlier results in the literature. We give a simple argument which suggests that interacting solute would dislocate TmS to higher temperatures.

Mapping of risk and susceptibility of shallow-landslide in the city of Sao Paulo, Brazil

In the city of Sao Paulo, where about 11 million people live, landslides and flooding occur frequently, especially during the summer. These landslides cause the destruction of houses and urban equipment, economic damage, and the loss of lives. The number of areas threatened by landslides has been increasing each year. The objective of this article is to analyze the probability of risk and susceptibility to shallow landslides in the Limoeiro River basin, which is located at the head of the Aricanduva River basin, one of the main hydrographic basins in the city of Sao Paulo. To map areas of risk, we created a cadastral survey form to evaluate landslide risk in the field. Risk was categorized into four levels based on natural and anthropogenic factors: R1 (low risk), R2 (average risk), R3 (high risk), and R4 (very high risk). To analyze susceptibility to shallow landslides, we used the SHALSTAB (Shallow Landsliding Stability) mathematical model and calculated the Distribution Frequency (DF) of the susceptibility classes for the entire basin. Finally, we performed a joint analysis of the average Risk Concentration (RC) and Risk Potential (RP). We mapped 14 risk sectors containing approximately 685 at-risk homes, more than half of which presented a high (R3) or very high (R4) probability of risk to the population. In the susceptibility map, 41% of the area was classified as stable and 20% as unconditionally unstable. Although the latter category accounted a smaller proportion of the total area, it contained a concentration (RC) of 41% of the mapped risk areas with a risk potential (RP) of 12%. We found that the locations of areas predicted to be unstable by the model coincided with the risk areas mapped in the field. This combination of methods can be applied to evaluate the risk of shallow landslides in densely populated areas and can assist public managers in defining areas that are unstable and inappropriate for occupation. (C) 2012 Elsevier B.V. All rights reserved.

Average control of Markov decision processes with Feller transition probabilities and general action spaces

This paper studies the average control problem of discrete-time Markov Decision Processes (MDPs for short) with general state space, Feller transition probabilities, and possibly non-compact control constraint sets A(x). Two hypotheses are considered: either the cost function c is strictly unbounded or the multifunctions A(r)(x) = {a is an element of A(x) : c(x, a) <= r} are upper-semicontinuous and compact-valued for each real r. For these two cases we provide new results for the existence of a solution to the average-cost optimality equality and inequality using the vanishing discount approach. We also study the convergence of the policy iteration approach under these conditions. It should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the alpha-discounted value functions and the Poisson equations as often encountered in the literature. (C) 2012 Elsevier Inc. All rights reserved.

Existence and concentration of solutions for a class of biharmonic equations

Some superlinear fourth order elliptic equations are considered. A family of solutions is proved to exist and to concentrate at a point in the limit. The proof relies on variational methods and makes use of a weak version of the Ambrosetti-Rabinowitz condition. The existence and concentration of solutions are related to a suitable truncated equation. (C) 2012 Elsevier Inc. All rights reserved.

Fuzzy Connectedness Image Segmentation in Graph Cut Formulation: A Linear-Time Algorithm and a Comparative Analysis

A deep theoretical analysis of the graph cut image segmentation framework presented in this paper simultaneously translates into important contributions in several directions. The most important practical contribution of this work is a full theoretical description, and implementation, of a novel powerful segmentation algorithm, GC(max). The output of GC(max) coincides with a version of a segmentation algorithm known as Iterative Relative Fuzzy Connectedness, IRFC. However, GC(max) is considerably faster than the classic IRFC algorithm, which we prove theoretically and show experimentally. Specifically, we prove that, in the worst case scenario, the GC(max) algorithm runs in linear time with respect to the variable M=|C|+|Z|, where |C| is the image scene size and |Z| is the size of the allowable range, Z, of the associated weight/affinity function. For most implementations, Z is identical to the set of allowable image intensity values, and its size can be treated as small with respect to |C|, meaning that O(M)=O(|C|). In such a situation, GC(max) runs in linear time with respect to the image size |C|. We show that the output of GC(max) constitutes a solution of a graph cut energy minimization problem, in which the energy is defined as the a"" (a) norm ayenF (P) ayen(a) of the map F (P) that associates, with every element e from the boundary of an object P, its weight w(e). This formulation brings IRFC algorithms to the realm of the graph cut energy minimizers, with energy functions ayenF (P) ayen (q) for qa[1,a]. Of these, the best known minimization problem is for the energy ayenF (P) ayen(1), which is solved by the classic min-cut/max-flow algorithm, referred to often as the Graph Cut algorithm. We notice that a minimization problem for ayenF (P) ayen (q) , qa[1,a), is identical to that for ayenF (P) ayen(1), when the original weight function w is replaced by w (q) . Thus, any algorithm GC(sum) solving the ayenF (P) ayen(1) minimization problem, solves also one for ayenF (P) ayen (q) with qa[1,a), so just two algorithms, GC(sum) and GC(max), are enough to solve all ayenF (P) ayen (q) -minimization problems. We also show that, for any fixed weight assignment, the solutions of the ayenF (P) ayen (q) -minimization problems converge to a solution of the ayenF (P) ayen(a)-minimization problem (ayenF (P) ayen(a)=lim (q -> a)ayenF (P) ayen (q) is not enough to deduce that). An experimental comparison of the performance of GC(max) and GC(sum) algorithms is included. This concentrates on comparing the actual (as opposed to provable worst scenario) algorithms' running time, as well as the influence of the choice of the seeds on the output.

Modeling and simulation of severe slugging with mass transfer effects

A mathematical model and numerical simulations are presented to investigate the dynamics of gas, oil and water flow in a pipeline-riser system. The pipeline is modeled as a lumped parameter system and considers two switchable states: one in which the gas is able to penetrate into the riser and another in which there is a liquid accumulation front, preventing the gas from penetrating the riser. The riser model considers a distributed parameter system, in which movable nodes are used to evaluate local conditions along the subsystem. Mass transfer effects are modeled by using a black oil approximation. The model predicts the liquid penetration length in the pipeline and the liquid level in the riser, so it is possible to determine which type of severe slugging occurs in the system. The method of characteristics is used to simplify the differentiation of the resulting hyperbolic system of equations. The equations are discretized and integrated using an implicit method with a predictor-corrector scheme for the treatment of the nonlinearities. Simulations corresponding to severe slugging conditions are presented and compared to results obtained with OLGA computer code, showing a very good agreement. A description of the types of severe slugging for the three-phase flow of gas, oil and water in a pipeline-riser system with mass transfer effects are presented, as well as a stability map. (C) 2011 Elsevier Ltd. All rights reserved.

Multi-criteria analysis in the strategic environmental assessment of the sugar and alcohol sector

The Strategic Environmental Assessment (SEA) of the sugar and alcohol sector guides a territorial and sectoral planning that benefits most of the local society and supports this economic activity in all its stages. In this way, the present work aims to determine an index of aggregation of the indicators generated in the baseline of the SEA process, called Index of Sustainability of Expansion of the Sugar and Alcohol Sector (IScana). For this, it was used the normalization of the indicators of each city by the fuzzy logic and attribution of weights by the Analytic Hierarchy Process (AHP). Then, the IScana values had been spatialized in the region of 'Grande Dourados'-Mato Grosso do Sul State. The northern portion concentrated the highest values of IScana, 0.48 and 0.55, referring to the cities of Nova Alvorada do Sul and Rio Brilhante, while, in the central portion, the city of Dourados presented the lowest value, 0.10. The selection of the set of indicators forming the IScana, and their relative importance, was satisfactory for the application of fuzzy logic and AHP techniques. The IScana index supplies objective information regarding the diagnosis of the region for the application of SEA.

Periodontal disease and diabetes mellitus

Periodontal disease (PD) is one of the most commonly known human chronic disorders. The relationship between PD and several systemic diseases such as diabetes mellitus (DM) has been increasingly recognized over the past decades. Objective The purpose of this review is to provide the reader with knowledge concerning the relationship between PD and DM. Many articles have been published in the English and Portuguese literature over the last 50 years examining the relationship between these two chronic diseases. Data interpretation is often confounded by varying definitions of DM, PD and different clinical criteria were applied to determine the prevalence, extent and severity of PD, levels of glycemic control and diabetes-related complications. Methods This paper provides a broad overview of the predominant findings from research conducted using the BBO (Bibliografia Brasileira de Odontologia), MEDLINE, LILACS and PubMed for Controlled Trials databases, in English and Portuguese languages published from 1960 to October 2012. Primary research reports on investigations of relationships between DM/DM control, PD/periodontal treatment and PD/DM/diabetes-related complications identified relevant papers and meta-analyses published in this period. Results 7This paper describes the relationship between PD and DM and answers the following questions: 1- The effect of DM on PD, 2- The effects of glycemic control on PD and 3- The effects of PD on glycemic control and on diabetes-related complications. Conclusions The scientific evidence reviewed supports diabetes having an adverse effect on periodontal health and PD having an adverse effect on glycemic control and on diabetes-related complications. Further research is needed to clarify these relationships and larger, prospective, controlled trials with ethnically diverse populations are warranted to establish that treating PD can positively influence glycemic control and possibly reduce the burden of diabetes-related complications.

Denominal Verbs in Brazilian Portuguese: distinguishing between diachronic and synchronic structures within Distributed Morphology approach

Recent work on argument structure has shown that there must be a synchronic relation between nouns and derived verbs that can be treated in structural terms. However, a simple phonological/morphological identity or diachronic derivation between a verb and a noun cannot guarantee that there is a denominal structure in a synchronic approach. In this paper we observe the phenomenon of Denominal Verbs in Brazilian Portuguese and argue for a distinction between etymological and synchronic morphological derivation. The objectives of this paper are 1) to identify synchronic and formal criteria to define which diachronic Denominal Verbs can also be considered denominal under a synchronic analysis; and 2) to detect in which cases the label "denominal" can be justifiably abandoned. Based on results of argument structure tests submitted to the judgments of native speakers, it was possible to classify the supposed homogenous Denominal Verbs class into three major groups: Real Denominal Verbs, Root-derived Verbs, and Ambiguous Verbs. In a Distributed Morphology approach, it was possible to explain the distinction between these groups based on the ideia of phases in words and the locality of restriction in the interpretation of roots.