Local fractional variational iteration and decomposition methods for wave equation on cantor sets within local fractional operators

We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

Multidimensional scaling analysis of the dynamics of a country economy

This paper analyzes the Portuguese short-run business cycles over the last 150 years and presents the multidimensional scaling (MDS) for visualizing the results. The analytical and numerical assessment of this long-run perspective reveals periods with close connections between the macroeconomic variables related to government accounts equilibrium, balance of payments equilibrium, and economic growth. The MDS method is adopted for a quantitative statistical analysis. In this way, similarity clusters of several historical periods emerge in the MDS maps, namely, in identifying similarities and dissimilarities that identify periods of prosperity and crises, growth, and stagnation. Such features are major aspects of collective national achievement, to which can be associated the impact of international problems such as the World Wars, the Great Depression, or the current global financial crisis, as well as national events in the context of broad political blueprints for the Portuguese society in the rising globalization process.

Systems of Navier-Stokes equations on cantor sets

We present systems of Navier-Stokes equations on Cantor sets, which are described by the local fractional vector calculus. It is shown that the results for Navier-Stokes equations in a fractal bounded domain are efficient and accurate for describing fluid flow in fractal media.

Fractional dynamics of genetic algorithms using hexagonal space tessellation

The paper formulates a genetic algorithm that evolves two types of objects in a plane. The fitness function promotes a relationship between the objects that is optimal when some kind of interface between them occurs. Furthermore, the algorithm adopts an hexagonal tessellation of the two-dimensional space for promoting an efficient method of the neighbour modelling. The genetic algorithm produces special patterns with resemblances to those revealed in percolation phenomena or in the symbiosis found in lichens. Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions.

Observability of nonlinear fractional dynamical systems

We study the observability of linear and nonlinear fractional differential systems of order 0 < α < 1 by using the Mittag-Leffler matrix function and the application of Banach’s contraction mapping theorem. Several examples illustrate the concepts.

Root-locus practical sketching rules for fractional-order system

For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

Multidimensional scaling for orthodontic root resorption

The paper investigates the risk factors for the severity of orthodontic root resorption. The multidimensional scaling (MDS) visualization method is used to investigate the experimental data from patients who received orthodontic treatment at the Department of Orthodontics and Dentofacial Orthopedics, Faculty of Dentistry, “Carol Davila” University of Medicine and Pharmacy, during a period of 4 years. The clusters emerging in the MDS plots reveal features and properties not easily captured by classical statistical tools. The results support the adoption of MDS for tackling the dentistry information and overcoming noise embedded into the data. The method introduced in this paper is rapid, efficient, and very useful for treating the risk factors for the severity of orthodontic root resorption.

Fractional coins and fractional derivatives

This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. Based on the new conceptual perspective, some experiments are performed shading new light into possible future progress.

Stability of fractional order systems

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Hydroxycinnamic acid antioxidants: an electrochemical overview

Hydroxycinnamic acids (such as ferulic, caffeic, sinapic, and p-coumaric acids) are a group of compounds highly abundant in food that may account for about one-third of the phenolic compounds in our diet. Hydroxycinnamic acids have gained an increasing interest in health because they are known to be potent antioxidants. These compounds have been described as chain-breaking antioxidants acting through radical scavenging activity, that is related to their hydrogen or electron donating capacity and to the ability to delocalize/stabilize the resulting phenoxyl radical within their structure.The free radical scavenger ability of antioxidants can be predicted from standard one-electron potentials. Thus, voltammetric methods have often been applied to characterize a diversity of natural and synthetic antioxidants essentially to get an insight into their mechanism and also as an important tool for the rational design of new and potent antioxidants.The structure-property-activity relationships (SPARs) correlations already established for this type of compounds suggest that redox potentials could be considered a good measure of antioxidant activity and an accurate guideline on the drug discovery and development process. Due to its magnitude in the antioxidant field, the electrochemistry of hydroxycinnamic acid-based antioxidants is reviewed highlighting the structure-property-activity relationships (SPARs) obtained so far.

Photostabilization of phenoxyacetic acid herbicides MCPA and mecoprop by hydroxypropyl-β-cyclodextrin

New strategies to reduce the environmental and economic costs of pesticides use are currently under study. Microencapsulation has been used as a versatile tool for the production of controlled release agricultural formulations. In this study, the photochemical degradation of the herbicides MCPA and mecoprop has been investigated in different aqueous media such as ultrapure and river water under simulated solar irradiation. To explore the possibility of introducing cyclodextrins in the herbicide formulations, the photodegradation study of the inclusion complexes of MCPA and mecoprop with (2-hydroxypropyl)-β-cyclodextrin (HP-β-CD) was also performed. The half-lives of MCPA and mecoprop inclusion complexes were increased approximately by a factor of three related to the free molecules. Additionally, it has been shown that the photodegradation of MCPA and mecoprop is influenced by their structural features. The additional methyl group existing in mecoprop molecular structure has a positive influence on the stabilization of the radical intermediate formed in the first stage of photodegradation of both herbicides. The results found indicated that MCPA and mecoprop form inclusion complexes with HP-β-CD showing higher photostability compared to free herbicides indicating that HP-β-CD may serve as ingredient in these herbicide formulations.

Host-Guest interaction between herbicide oxadiargyl and hydroxypropyl-β-cyclodextrin

In the face of a growing human population and increased urbanization, the demand for pesticides will simply rise. Farmers must escalate yields on increasingly fewer farm acres. However, the risks of pesticides, whether real or perceived, may force changes in the way these chemicals are used. Scientists are working toward pest control plans that are environmentally sound, effective, and profitable. In this context the development of new pesticide formulations which may improve application effectiveness, safety, handling, and storage can be pointed out as a solution. As a contribution to the area, the microencapsulation of the herbicide oxadiargyl (OXA) in (2-hydroxypropyl)-β-cyclodextrin (HP-β-CD) was performed. The study was conducted in different aqueous media (ultrapure water and in different pH buffer solutions). In all cases an increment of the oxadiargyl solubility as a function of the HP-β-CD concentration that has been related to the formation of an inclusion complex was verified. UV-Vis and NMR experiments allowed concluding that the stoichiometry of the OXA/HP-β-CD complex formed is 1 : 1. The gathered results can be regarded as an important step for its removal from industrial effluents and/or to increase the stabilizing action, encapsulation, and adsorption in water treatment plants.

Does Pro12Ala polymorphism enhance the physiological role of PPARy2?

Obesity and type 2 diabetes mellitus (T2D) are two major public health problems that have motivated the scientific community to investigate the high contribution of genetic factors to these disorders. The peroxisome proliferator activated by gamma 2 (PPARy2) plays an important role in the lipid metabolism. Since PPARy2 is expressed mainly in adipose tissue, a moderate reduction of its activity influences the sensitivity to insulin, diabetes, and other metabolic parameters. The present study aims to contribute to the elucidation of the impact of the Pro12Ala polymorphism associated with T2D and obesity through a meta-analysis study of the literature that included approximately 11500 individuals, from which 3870 were obese and 7625 were diabetic. Statistical evidence supports protective effect in T2D of polymorphism Pro12Ala of PPARy2 (OR = 0.702 with 95% CI: 0.622; 0.791, P<0.01). Conversely the same polymorphism Pro12Ala of PPARy2 seems to favor obesity since 1.196 more chance than nonobese was found (OR = 1.196 with 95% CI: 1.009; 1.417,P<0.004). Our results suggest that Pro12Ala polymorphism enhances both adipogenic and antidiabetogenic physiological role of PPARy. Does Pro12Ala polymorphism represent an evolutionary step towards the stabilization of the molecular function of PPARy transcription factor signaling pathway?

On a generalized Laguerre operational matrix of fractional integration

A new operationalmatrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived.The fractional integration is described in the Riemann-Liouville sense.This operational matrix is applied together with generalized Laguerre tau method for solving general linearmultitermfractional differential equations (FDEs).Themethod has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposedmethod is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.

Dynamical analysis of the global warming

Global warming is a major concern nowadays. Weather conditions are changing, and it seems that human activity is one of the main causes. In fact, since the beginning of the industrial revolution, the burning of fossil fuels has increased the nonnatural emissions of carbon dioxide to the atmosphere. Carbon dioxide is a greenhouse gas that absorbs the infrared radiation produced by the reflection of the sunlight on the Earth’s surface, trapping the heat in the atmosphere. Global warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic, and health aspects of human life. This paper studies the global warming trend in the perspective of dynamical systems and fractional calculus, which is a new standpoint in this context. Worldwide distributed meteorological stations and temperature records for the last 100 years are analysed. It is shown that the application of Fourier transforms and power law trend lines leads to an assertive representation of the global warming dynamics and a simpler analysis of its characteristics.