Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

Risk Aversion in a Mixed-Integer Nonlinear Approach to Support Decision-Making for a Hydro Power Producer

In this paper, a mixed-integer nonlinear approach is proposed to support decision-making for a hydro power producer, considering a head-dependent hydro chain. The aim is to maximize the profit of the hydro power producer from selling energy into the electric market. As a new contribution to earlier studies, a risk aversion criterion is taken into account, as well as head-dependency. The volatility of the expected profit is limited through the conditional value-at-risk (CVaR). The proposed approach has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems.

Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain

This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain We propose a novel mixed-integer nonlinear programming (MINLP) approach, considering hydroelectric power generation as a nonlinear function of water discharge and of the head. As a new contribution to eat her studies, we model the on-off behavior of the hydro plants using integer variables, in order to avoid water discharges at forbidden areas Thus, an enhanced STHS is provided due to the more realistic modeling presented in this paper Our approach has been applied successfully to solve a test case based on one of the Portuguese cascaded hydro systems with a negligible computational time requirement.

Nonlinear optimization method for short-term hydro scheduling considering head-dependency

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent reservoirs under competitive environment. We propose a new nonlinear optimization method to consider hydroelectric power generation as a function of water discharge and also of the head. Head-dependency is considered on short-term hydro scheduling in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems, providing a higher profit at a negligible additional computation time in comparison with a linear optimization method that ignores head-dependency.

Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations.

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Hydro energy systems management in Portugal: Profit-based evaluation of a mixed-integer nonlinear approach

In this paper, a novel mixed-integer nonlinear approach is proposed to solve the short-term hydro scheduling problem in the day-ahead electricity market, considering not only head-dependency, but also start/stop of units, discontinuous operating regions and discharge ramping constraints. Results from a case study based on one of the main Portuguese cascaded hydro energy systems are presented, showing that the proposedmixed-integer nonlinear approach is proficient. Conclusions are duly drawn. (C) 2010 Elsevier Ltd. All rights reserved.

Differential expression of the eukaryotic release factor 3 (eRF3/GSPT1) according to gastric cancer histological types

Background: There are now several lines of evidence to suggest that protein synthesis and translation factors are involved in the regulation of cell proliferation and cancer development. Aims: To investigate gene expression patterns of eukaryotic releasing factor 3 (eRF3) in gastric cancer. Methods: RNA was prepared from 25 gastric tumour biopsies and adjacent non-neoplastic mucosa. Real time TaqMan reverse transcription polymerase chain reaction (RT-PCR) was performed to measure the relative gene expression levels. DNA was isolated from tumour and normal tissues and gene dosage was determined by a quantitative real time PCR using SYBR Green dye. Results: Different histological types of gastric tumours were analysed and nine of the 25 tumours revealed eRF3/GSPT1 overexpression; moreover, eight of the 12 intestinal type carcinomas analysed overexpressed the gene, whereas eRF3/GSPT1 was overexpressed in only one of the 10 diffuse type carcinomas (Kruskal-Wallis Test; p , 0.05). No correlation was found between ploidy and transcript expression levels of eRF3/GSPT1. Overexpression of eRF3/GSPT1 was not associated with increased translation rates because the upregulation of eRF3/GSPT1 did not correlate with increased eRF1 levels. Conclusions: Overexpression of eRF3/GSPT1 in intestinal type gastric tumours may lead to an increase in the translation efficiency of specific oncogenic transcripts. Alternatively, eRF3/GSPT1 may be involved in tumorigenesis as a result of its non-translational roles, namely (dis)regulating the cell cycle, apoptosis, or transcription.

3D-2D image registration by nonlinear regression

We propose a 3D-2D image registration method that relates image features of 2D projection images to the transformation parameters of the 3D image by nonlinear regression. The method is compared with a conventional registration method based on iterative optimization. For evaluation, simulated X-ray images (DRRs) were generated from coronary artery tree models derived from 3D CTA scans. Registration of nine vessel trees was performed, and the alignment quality was measured by the mean target registration error (mTRE). The regression approach was shown to be slightly less accurate, but much more robust than the method based on an iterative optimization approach.

Differential expression of CDC25 phosphatases splice variants in human breast cancer cells

Background: CDC25 phosphatases control cell cycle progression by activating cyclin dependent kinases. The three CDC25 isoforms encoding genes are submitted to alternative splicing events which generate at least two variants for CDC25A and five for both CDC25B and CDC25C. An over-expression of CDC25 was reported in several types of cancer, including breast cancer, and is often associated with a poor prognosis. Nevertheless, most of the previous studies did not address the expression of CDC25 splice variants. Here, we evaluated CDC25 spliced transcripts expression in anti-cancerous drug-sensitive and resistant breast cancer cell lines in order to identify potential breast cancer biomarkers. Methods: CDC25 splice variants mRNA levels were evaluated by semi-quantitative RT-PCR and by an original real-time RT-PCR assay. Results: CDC25 spliced transcripts are differentially expres-sed in the breast cancer cell lines studied. An up-regulation of CDC25A2 variant and an increase of the CDC25C5/C1 ratio are associated to the multidrug-resistance in VCREMS and DOXOR breast cancer cells, compared to their sensitive counterpart cell line MCF-7. Additionally, CDC25B2 tran-script is exclusively over-expressed in VCREMS resistant cells and could therefore be involved in the development of certain type of drug resistance. Conclusions: CDC25 splice variants could represent interesting potential breast cancer prognostic biomarkers.

Differential expression of GSPT1 GGCn alleles in cancer

The human eukaryotic release factor 3a (eRF3a), encoded by the G1 to S phase transition 1 gene (GSPT1; alias eRF3a), is upregulated in various human cancers. GSPT1 contains a GGCn polymorphism in exon 1, encoding a polyglycine expansion in the N-terminal of the protein. The longer allele, GGC12, was previously shown to be associated to cancer. The GGC12 allele was present in 2.2% of colorectal cancer patients but was absent in Crohn disease patients and in the control group. Real-time quantitative RT-PCR analysis showed that the GGC12 allele was present at up to 10-fold higher transcription levels than the GGC10 allele (P < 0.001). No GSPT1 amplifications were detected, and there was no correlation between the length of the alleles and methylation levels of the CpG sites inside the GGC expansion. Using flow cytometry, we compared the levels of apoptosis and proliferation rates between cell lines with different genotypes, but detected no significant differences. Finally, we used a cytokinesis-block micronucleus assay to evaluate the frequency of micronuclei in the same cell lines. Cell lines with the longer alleles had higher frequencies of micronuclei in binucleated cells, which is probably a result of defects in mitotic spindle formation. Altogether, these findings indicate that GSPT1 should be considered a potential proto-oncogene.

Nonlinear mixture model for hyperspectral unmixing

Proceedings of International Conference - SPIE 7477, Image and Signal Processing for Remote Sensing XV - 28 September 2009

A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

Optimization of magneto-electro-elastic composite structures using differential evolution

Magneto-electro-elastic structures are built from materials that provide them the ability to convert in an interchangeable way, magnetic, electric and mechanical forms of energy. This characteristic can therefore provide an adaptive behaviour to a general configuration elastic structure, being commonly used in association with any type of composite material in an embedded or surface mounted mode, or by considering the usage of multiphase materials that enable achieving different magneto-electro-elastic properties. In a first stage of this work, a few cases studies will be considered to enable the validation of the model considered and the influence of the coupling characteristics of this type of adaptive structures. After that we consider the application of a recent computational intelligence technique, the differential evolution, in a deflection profile minimization problem. Studies on the influence of optimization parameters associated to the problem considered will be performed as well as the adoption of an adaptive scheme for the perturbation factor. Results are also compared with those obtained using an enhanced particle swarm optimization technique. (C) 2013 Elsevier Ltd. All rights reserved.