Aqueous solution behavior of thermosensitive (N-isopropylacrylamide-acrylic acid-ethyl methacrylate) terpolymers

A series of N-isopropylacrylamide (NIPAM)-acrylic acid-ethyl methacrylate terpolymers with varied monomer compositions was prepared by radical polymerization. The solution behavior of these polymers was studied in dilute aqueous solution using spectrophotometry, fluorescence spectroscopy and high-sensitivity differential scanning calorimetry. The results obtained revealed that the lower critical solution temperatures depend strongly on the copolymer composition, solution pH and ionic strength. At a high pH, the ionization of acrylic acid (AA) units leads to an increase in solution cloud points (T-c). Solutions of polymers containing 10% or less of AA display a constant T-c for pH above 5.5, with 15% there is a continuous increase in T-c with pH and, for higher AA contents, no clouding was observed within the studied temperature range. Fluorescence probe studies were conducted by following the I (1)/I (3) ratio of pyrene vibronic bands and the emission of anilinonaphtalene sulfonic acid, sodium salt (ANS), both approaches revealing the existence of hydrophobic domains for polymers with higher ethyl methacrylate content at temperatures lower than T-c, suggesting some extent of aggregation and/or a coil-to-globule transition. Scanning calorimetry measurements showed an endothermic transition at temperatures agreeing with the previously detected cloud points. Moreover, the transition curves became broader and with a smaller transition enthalpy, as both the AA content and the solution pH were increased. These broader transitions were interpreted to be the result of a wider molecular distribution upon polymer ionization, hence, displaying varied solution properties. The decrease in transition enthalpy was rationalized as a consequence of reminiscent hydration of NIPAM units, even after phase separation, owing to the presence of electric charges along the polymer chain.

Integrability and conformal symmetry in higher dimensions: A model with exact hopfion solutions

We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two-dimensional target space. Requiring the existence of lagrangean and the stability of static solutions singles out a class of models which have an additional conformal symmetry. That is used to explain the existence of an ansatz leading to solutions with non-trivial Hopf charges. © SISSA/ISAS 2002.

Classes of exact wave functions for general time-dependent Dirac Hamiltonians in 1+1 dimensions

The construction of two classes of exact solutions for the most general time-dependent Dirac Hamiltonian in 1+1 dimensions was discussed. The extension of solutions by introduction of a time-dependent mass was elaborated. The possibility of existence of a generalized Lewis-Riesenfeld invariant connected with such solutions was also analyzed.

On stability of differential equations with piecewise constant argument using dichotomic maps

This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.

On a model for the growth of an invasive avascular tumor

This paper is devoted to study the 1D model of invasive avascular tumor growth, which takes into account cell division, death, and motility, proposed by Kolobov and collaborators in 2009. First, we examine the existence and uniqueness of the solution to this model. Second, we studied qualitatively and numerically the traveling wave solutions. Finally, we show some numerical simulations for the cell density and nutrient concentration. © 2013 NSP Natural Sciences Publishing Cor.

Identifying problems for choosing suitable areas for installation of a new landfill through GIS technology: A case study

Selecting a suitable place to install a new landfill is a hard work. Bauru is a Brazilian municipality where the local landfill currently in use has a life span that is almost over, and the selection of a new area for a future landfill is crucial and urgent. Here we use a geographic information system (GIS) approach to indicate possible suitable areas for installing the landfill. The considered criteria were: river network and the respective buffer zone, relief, urban areas and their respective buffer zone, existence of Areas for Environmental Protection (AEPs), occurrence of wells and their respective buffer zones, existence of airports and their buffer zones, wind direction, and the road network and its respective buffer zone. Due the facts that (1) Bauru has an urban area relatively large in relation to whole municipal area, (2) Bauru has two airports, and (3) this area encompasses parts of three AEPs, the model showed that there are few areas suitable and moderately suitable in Bauru, and the greater part of the municipality is unsuitable to install a new landfill. Due to this important finding reported here, the local policymakers should consider the suitable or even moderately suitable areas for analysis in situ or look for other creative solutions for destination of the solid waste. We highly encourage the use of GIS in studies that seek suitable areas for future landfills, having found that SIG was a tool that allowed fast and precise work and generated an outcome sufficiently clear of interpretation.Implications: Solid waste (SW) management is one of the main environmental concerns nowadays. Landfilling SW is still the main practice to disposal of such material. However, for many regions, suitable places for landfilling are getting scarce. This study proved this situation for a populous place in a southeastern Brazilian region. This study also showed how the decision makers should manage the problem in order to minimize the amount of SW generated and delivered for the landfill. Massive investment in education is a critical issue to reach the proposed aim.

Positive Solution for a Class of Degenerate Quasilinear Elliptic Equations in R-N

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On symmetries of singular implicit ODEs

We study implicit ODEs, cubic in derivative, with infinitesimal symmetry at singular points. Cartan showed that even at regular points the existence of nontrivial symmetry imposes restrictions on the ODE. Namely, this algebra has the maximal possible dimension 3 iff the web of solutions is flat. For cubic ODEs with flat 3-web of solutions we establish sufficient conditions for the existence of nontrivial symmetries at singular points and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling is some coordinates. We use this symmetry to find first integrals of the ODE.

Local classification of singular hexagonal 3-webs with holomorphic Chern connection form and infinitesimal symmetries

Implicit ODE, cubic in derivative, generically has no infinitesimal symmetries even at regular points with distinct roots. Cartan showed that at regular points, ODEs with hexagonal 3-web of solutions have symmetry algebras of the maximal possible dimension 3. At singular points such a web can lose all its symmetries. In this paper we study hexagonal 3-webs having at least one infinitesimal symmetry at singular points. In particular, we establish sufficient conditions for the existence of non-trivial symmetries and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling in some coordinates. Using the obtained results, we provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection form is holomorphic at the singular point, 2) the web admits at least one infinitesimal symmetry at this point. As a by-product, a classification of hexagonal weighted homogeneous 3-webs is obtained.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.

On some extension of optimal control theory

Some problems of Calculus of Variations do not have solutions in the class of classic continuous and smooth arcs. This suggests the need of a relaxation or extension of the problem ensuring the existence of a solution in some enlarged class of arcs. This work aims at the development of an extension for a more general optimal control problem with nonlinear control dynamics in which the control function takes values in some closed, but not necessarily bounded, set. To achieve this goal, we exploit the approach of R.V. Gamkrelidze based on the generalized controls, but related to discontinuous arcs. This leads to the notion of generalized impulsive control. The proposed extension links various approaches on the issue of extension found in the literature.

Transmission coefficient and two-fold degenerate discrete spectrum of spin-1 bosons in a double-step potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The subdomain structure of human serum albumin in solution under different pH conditions studied by small angle X-ray scattering

Small-angle X-ray scattering (SAXS) was used to study structural characteristics of human serum albumin (HSA) in solution under different pH conditions. Guinier analysis of SAXS results yielded values of the molecular radius of gyration ranging from 26.7 Å to 34.5 Å for pH varying from 2.5 to 7.0. This suggests the existence of significant differences in the overall shape of the molecule at different pH. Molecular models based on subdomains with different spatial configurations were proposed. The distance distribution functions associated with these models were calculated and compared with those determined from the experimental SAXS intensity functions. The conclusion of this SAXS study is that the arrangement of molecular subdomains is clearly pH dependent; the molecule adopting more or less compact configuration for different pH conditions. The conclusions of this systematic study on the modification in molecular shape of HSA as a response to pH changes is consistent with those of previous investigations performed for particular pH conditions.