Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Can power laws help us understand gene and proteome information?

Proteins are biochemical entities consisting of one or more blocks typically folded in a 3D pattern. Each block (a polypeptide) is a single linear sequence of amino acids that are biochemically bonded together. The amino acid sequence in a protein is defined by the sequence of a gene or several genes encoded in the DNA-based genetic code. This genetic code typically uses twenty amino acids, but in certain organisms the genetic code can also include two other amino acids. After linking the amino acids during protein synthesis, each amino acid becomes a residue in a protein, which is then chemically modified, ultimately changing and defining the protein function. In this study, the authors analyze the amino acid sequence using alignment-free methods, aiming to identify structural patterns in sets of proteins and in the proteome, without any other previous assumptions. The paper starts by analyzing amino acid sequence data by means of histograms using fixed length amino acid words (tuples). After creating the initial relative frequency histograms, they are transformed and processed in order to generate quantitative results for information extraction and graphical visualization. Selected samples from two reference datasets are used, and results reveal that the proposed method is able to generate relevant outputs in accordance with current scientific knowledge in domains like protein sequence/proteome analysis.

A Review of Definitions for Fractional Derivatives and Integral

This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.

Fractional Order Junctions

Gottfried Leibniz generalized the derivation and integration, extending the operators from integer up to real, or even complex, orders. It is presently recognized that the resulting models capture long term memory effects difficult to describe by classical tools. Leon Chua generalized the set of lumped electrical elements that provide the building blocks in mathematical models. His proposal of the memristor and of higher order elements broadened the scope of variables and relationships embedded in the development of models. This paper follows the two directions and proposes a new logical step, by generalizing the concept of junction. Classical junctions interconnect system elements using simple algebraic restrictions. Nevertheless, this simplistic approach may be misleading in the presence of unexpected dynamical phenomena and requires including additional “parasitic” elements. The novel γ-junction includes, as special cases, the standard series and parallel connections and allows a new degree of freedom when building models. The proposal motivates the search for experimental and real world manifestations of the abstract conjectures.

Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

Sectors and routes in solid waste collection

Collecting and transporting solid waste is a constant problem for municipalities and populations in general. Waste management should take into account the preservation of the environment and the reduction of costs. The goal with this paper is to address a real-life solid waste problem. The case reveals some general and specific characteristics which are not rare, but are not widely addressed in the literature. Furthermore, new methods and models to deal with sectorization and routing are introduced, which can be extended to other applications. Sectorization and routing are tackled following a two-phase approach. In the first phase, a new method is described for sectorization based on electromagnetism and Coulomb’s Law. The second phase addresses the routing problems in each sector. The paper addresses not only territorial division, but also the frequency with which waste is collected, which is a critical issue in these types of applications. Special characteristics related to the number and type of deposition points were also a motivation for this work. A new model for a Mixed Capacitated Arc Routing Problem with Limited Multi-Landfills is proposed and tested in real instances. The computational results achieved confirm the effectiveness of the entire approach.

Modelos Teóricos de Difusão Dérmica: abordagens matemáticas e computacionais para terapias transdérmicas da Obesidade

É de senso comum que os nutrientes são fundamentais à vida e que a subnutrição leva à acumulação de gorduras que pode chegar a casos de obesidade, tendo como consequência inúmeras complicações de saúde. Diferentes estruturas neuroanatómicas do cérebro têm um papel essencial no comportamento digestivo. A ação de várias moléculas de sinalização (hormonas, neurotransmissores e neuropéptidos) resulta na regulação da ingestão de alimentos, sendo que, por exemplo, algumas hormonas podem aumentar a sensação de saciedade podendo diminuir o apetite e a ingestão calórica. A descoberta de hormonas envolvidas no balanço energético proporcionou novas oportunidades para desenvolver meios para o tratamento da obesidade. A transferência de medicação antiobesidade por via tópica ou transdérmica é um desafio pois a pele funciona como uma barreira natural e protetora. Sendo uma barreira com uma grande área de superfície e de fácil acessibilidade, a pele tem potencial interesse na libertação de fármacos específicos a cada terapia. Vários métodos têm sido estudados de modo a permitir um aumento da permeabilidade de moléculas terapêuticas para o interior da pele e através da pele. As biotecnologias transdérmicas são um campo de interesse cada vez maior, devido as aplicações dérmicas e farmacêuticas que lhes estão subjacentes. Existem vários modelos computacionais e matemáticos em uso que permite uma visão mais abrangente de puros dados experimentais e até mesmo permite a extrapolação prática de novas metodologias de difusão dérmica. Contudo, eles compreendem uma complexa variedade de teorias e suposições que atribuem a sua utilização para situações específicas. Este trabalho, primeiramente analisa, de forma extensiva, as várias metodologias teóricas para o estudo da difusão dérmica e sistematiza as suas características, realizando depois a fase prévia duma nova abordagem computacional para o estudo da difusão dérmica, que determina características microscópicas de moléculas capazes de provocar a perda de peso, tais como a Leptina e/ou os seus agonistas.