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Esta ponencia muestra una unidad didáctica diseñada dentro del Proyecto Iberoamericano sobre la Naturaleza de la Ciencia y la Tecnología (EANCYT) EDU2010-16553 financiado por Plan Nacional de I+D del Ministerio de Ciencia e Innovación (España), que busca promover en futuros profesores de ciencias y de enseñanza primaria mejor comprensión de la naturaleza de la ciencia y la tecnología. Pretende que evolucionen algunas actitudes/creencias reduccionistas detectadas en el anterior Proyecto Iberoamericano de Evaluación de Actitudes Relacionadas con la Ciencia, la Tecnología y la Sociedad (PIEARCTS) respecto a las decisiones tecnológicas de un país. Plantea inicialmente la catástrofe de Fukushima, los cuestionamientos que surgen a las políticas energéticas globales relacionados con el uso de la energía nuclear versus energías mas limpias, para focalizarse finalmente en la complejidad y diversidad de condicionantes que se ponen en juego en tales decisiones. Propone actividades que desarrollan competencias cognitivo- linguísticas, metacognitivas, procedimientos y actitudes asociados a la sustentabilidad. Se evaluará el impacto de la unidad didáctica en distintos contextos/ géneros a través de un pre y post test a aplicar a dos muestras de alumnos de 18 y 22 años divididos en grupo experimental y grupo control, usando como instrumento el cuestionario estandarizado de opiniones sobre ciencia, tecnología y sociedad (COCTS).

En el marco del Proyecto EANCYT, Enseñanza y Aprendizaje de la naturaleza de la ciencia y la tecnología, el propósito del presente trabajo es presentar dos Unidades Didácticas como instrumentos de intervención en el aula, que se han diseñado para mejorar la comprensión sobre Naturaleza de la Ciencia y la Tecnología (NdCyT) en estudiantes de 12 y 15 años, que cursan los grados 6º y 9º de la básica secundaria y que serán aplicadas con una metodología explícita y reflexiva en aulas reales de Colombia y otros países que participan en el proyecto. Se muestra la necesidad de construir currículos abiertos y flexibles, que incluyan el estudio de las relaciones CTS y se articulen con los estándares de competencias para ciencias naturales del Ministerio de Educación (MEN).

Este trabalho tem por objeto apresentar as reflexões iniciais de uma pesquisa em andamento, numa escola pública do Estado do Maranhão, que visa contribuir para a produção do conhecimento em torno da formação inicial e contínua do professor de Matemática, revelando como uma formação continuada mediada pela escrita e leitura contribui para o desenvolvimento profissional do professor de matemática das Séries Finais do Ensino Fundamental. As discussões sobre a formação continuada, os grupos de trabalhos colaborativos e os processos de escrita e leitura em Educação Matemática consideram os referenciais teóricos: Gonçalves (2006), Zeichner (1998); Ferreira; Miorim (2003); Fiorentini; Nacarato (2005), Mizukami (2006), Tardif; Lessard; Gauthier (2000) e Lopes; Nacarato (2009). Apresenta alguns dados de uma pesquisa qualitativa na modalidade de estudo de caso obtidos a partir da realização de entrevistas e de observação participante, envolvendo um grupo de professores de matemática das Séries Finais do Ensino Fundamental, o qual assume a perspectiva de trabalho colaborativo.

La enseñanza de la NdCyT se constituye en un problema de investigación actualmente relevante para los procesos de formación de profesores de Ciencias. Conforme a ello, se presenta una unidad didáctica sobre el estatuto de epistemológico de la ciencia, desde un enfoque explícito reflexivo, en donde se detalla los objetivos, actividades, estrategias metodológicas y proceso de evaluación con base en cuestiones específicas del Cuestionario de opiniones de ciencia, tecnología y Sociedad (COCTS). Esta propuesta se plantea con el objetivo de aportar a la reflexión sobre proceso de intervención didáctica en el marco de la NdCyT. La unidad didáctica está en el marco del Proyecto EANCyT.

Este trabalho e um recorte de uma tese de doutorado em que se investiga o ensino e a aprendizagem de derivadas no contexto da Resolucao de Problemas. Foi realizada no 2o ano do Ensino Medio integrado ao tecnico, numa turma do curso de Eletronica. A pesquisa e qualitativa e foi desenvolvida por meio da observacao participante e analise documental. Assumimos a concepcao de resolucao de problemas como um ponto de partida para ensinar Matematica, entendida como um meio de se construir novos conhecimentos a partir de anteriores e ao longo do processo de resolucao de um ou mais problemas. Considerada, desse modo, como uma metodologia de ensino, e uma perspectiva que esta apoiada na triade ensino-aprendizagem-avaliacao e que, portanto, considera a avaliacao um processo intrinseco ao processo de ensino-aprendizagem. Apresentamos e discutimos um episodio que evidencia como essa metodologia permite ao professor e ao aluno perceberem, de forma mais clara, dificuldades no aprendizado dos conteudos, e como favorece a tomada de decisoes e mudancas de estrategias no ensino. Normal 0 21 false false false PT-BR X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabela normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman",serif; mso-fareast-language:EN-US;}

14.00 Embora sustentabilidade ambiental seja um conceito bastante discutido na literatura, torna-se cada vez mais evidente o avanco da degradacao ambiental, juntamente com o consumo excessivo de recursos naturais por consequencia do comportamento humano. A Quimica aplicada de forma inconsequente, geralmente e uma das causadoras da degradacao ambiental, mas, ao mesmo tempo, quando utilizada de forma responsavel, pode ser uma solucao, ou seja, pode ser uma aliada a sustentabilidade ambiental. Pensando na importância desse tema, foi realizada uma r evisao da literatura com o objetivo de investigar como a sustentabilidade ambiental esta sendo discutida no ensino quimica, principalmente no ensino superior. Para isso realizamos uma busca na web por Instituicoes de Ensino Superior (IES) que ofereciam cursos de quimica nas regioes sudeste e sul do pais. Selecionamos as publicas federais e estaduais mais antigas. Em algumas IES entramos em seus sites com o objetivo de verificar se essas ofereciam alguma disciplina relacionada ao meio ambiente e/ou desenvolviam em seus campi alguma acao de gerenciamento de residuos quimicos. Os resultados dessa revisao apontam que a sustentabilidade ambiental e uma das preocupacoes dos professores e pesquisadores que lecionam nos cursos de quimica de IES publicas federais e estaduais dessas regioes. Normal 0 21 false false false PT-BR X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabela normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}

Neste trabalho descreve-se e analisa-se dados de uma pesquisa referente a um programa de Alfabetização Científica e Tecnológica (ACT) de orientação Ciência, Tecnologia e Sociedade (CTS), desenvolvido com um grupo de artesãs de filé, no bairro Pontal da Barra, Maceió, Brasil, com destaque para dois tópicos: educação ambiental e educação para a saúde. A pesquisa foi realizada para tese de doutoramento em Ensino de Ciência e Matemática. Inspirando-se em Fourez e Chassot, testou possibilidades de se desenvolver este programa para adultos fora dos muros da escola, na própria comunidade, como lugar privilegiado para se fazer a análise da realidade local, a integração com os saberes populares e o levantamento de problemas ali existentes. O programa centrou-se no apropriar-se de conhecimentos científicos e tecnológicos e na mudança de atitudes que contribuíssem para a formação cidadã e a tomada de decisões conscientes, especificamente em ciência e tecnologia. As avaliações realizadas durante e ao final do programa mostraram que as artesãs conseguiram transformar algumas de suas atitudes e perceberam mudanças no seu cotidiano no que diz respeito às dimensões cognitiva, afetiva, atitudinal e cultural.

La importancia y complejidad de los temas propuestos para esta conferencia, sostenibilidad, educación y sociedad, son una oportunidad para provocar en el contexto de este evento académico sobre las actividades relacionadas con la ciencia, la tecnología y la sociedad, un diálogo crítico que aborde sus significados, las relaciones posibles y las confrontaciones que en los marcos ambiental, social, político y económico se han generado hace varias décadas.

Esta ponencia muestra una unidad didáctica diseñada dentro del Proyecto Iberoamericano sobre la Naturaleza de la Ciencia y la Tecnología (EANCYT) EDU2010-16553 financiado por Plan Nacional de I+D del Ministerio de Ciencia e Innovación (España). Busca promover en estudiantes la complejización de esas creencias reduccionistas respecto a la Tecnología detectadas en el anterior Proyecto Iberoamericano de Evaluación de Actitudes Relacionadas con la Ciencia, la Tecnología y la Sociedad (PIEARCTS). Las actividadesparten de una situación problemática contextuada que resuelven en grupo a través de la creación de un objeto tecnológico. La finalidad última es llevarlos a reflexionar sobre la tarea confrontando la propia definición inicial de Tecnología con tres tópicos/creencias dados del sentido común sobre la misma, a fin de rectificarla y ampliarla tomando conciencia de su visión también humanística y de esa interacción dialéctica que establece con la Ciencia. Se evaluará el impacto de tal unidad didáctica a travésde la aplicación de un pre y post test a dos muestras dealumnos de 12 y 15 años de un grupo experimental y de otro control,usando como instrumento cuestiones del cuestionario estandarizado de opiniones sobre ciencia, tecnología y sociedad (COCTS).

The notion of a subnexus based on ${\mathcal{N}}$-function (briefly, ${\mathcal{N}}$-subnexus) is introduced, and related properties are investigated. Also, the notions of ${\mathcal{N}}$-subnexus of type $(\alpha, \beta)$, where $(\alpha, \beta)$ is $(\in, \in)$, $(\in, q)$, $(\in, \in\! \vee \, {q})$, $(q, \in)$, $(q,q)$, $(q, \in\! \vee \, {q})$, $(\overline{\in}, \overline{\in})$ and $(\overline{\in}, \overline{\in} \vee \overline{q})$, are introduced, and their basic properties are investigated. Conditions for an ${\mathcal{N}}$-structure to be an ${\mathcal{N}}$-subnexus of type $(q, \in\! \vee \, {q})$ are given, and characterizations of ${\mathcal{N}}$-subnexus of type $(\in, \in\! \vee \, {q})$ and $(\overline{\in}, \overline{\in} \vee \overline{q})$ are provided. Homomorphic image and preimage of ${\mathcal{N}}$-subnexus are discussed.

In this paper we discuss the uniqueness property of a summation method for multiple series with respect to Vilenkin and generalized Haar systems. It is proved that if the multiple series with respect to these systems is a.e. summable by that method to an integrable function on $[0,1)^d$ and satisfies an extra condition, then it is the Fourier series of this function.

This survey article illustrates many important current trends and perspectives for the field including classification of hyperidentities, characterizations of algebras with hyperidentities, functional representations of free algebras, structure results for bilattices, categorical questions and applications. However, the paper contains new results and open problems, too.

Some Lebesgue integral inequalities of Jensen type for $\lambda$-convex functions defined on real intervals are given.

In this paper, we estimate the democratic constant for the democratic subsystems of the $d$-dimensional Haar system in $L_1[0,1]^d$.

The purpose of this paper is to establish a new result, which guarantees the asymptotic stability and boundedness of the zero solution and the square integrability of solutions and their derivatives to neutral type nonlinear differential equations of fourth-order. We illustrate our results by an example at the end of the paper.

We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.

In this paper, we study the boundedness of the fractional maximal operator and fractional integral operator on the variable exponent Morrey spaces defined over spaces $(X,d,\mu)$ of homogeneous type.

The aim of this article is to introduce the notion of almost $\alpha$-Hardy-Rogers-$F$-contractions in the partial metric space and utilize it to establish the existence of a unique fixed point. Some examples are given to demonstrate the validity of our main result. Our results generalize classical and newer results in the literature. As an application, we solve the initial value problem of damped harmonic oscillator and a nonlinear fractional differential equation satisfying periodic boundary conditions, which demonstrates the importance of our contraction and provides motivation for such investigations.

We investigate {left, right, middle} units of quasigroups and families of identities which might imply their existence. A prominent role is played by the newly introduced notion of derivative operation, generalizing Belousov's notions of left/right derivative operations for quasigroups. Partial solutions of the Belousov's Problem # 18 and its generalizations are obtained. Several related problems remain open.

The paper considers the Riemann boundary value problem in the half-plane in the class of functions that are $C(\rho)$-continuous with respect to the weight $\rho(x)$, when the weight function has infinite number of zeros. Necessary and sufficient conditions for solvability of the problem are established. If the problem is solvable, solutions are represented in an explicit form.

Penelitian ini bertujuan untuk menerapkan/kolaborasi Pendekatan Numbered Heads Together (NHT) dengan Alat Peraga Sate Bola dalam Pembelajaran Matematika sebagai upaya untuk meningkatkan pemahaman konsep peluang dan aktivitas belajar siswa kelas XI TKJ1 SMK Negeri 1 Singkep. Dalam mengukur hasil belajar penelitian ini dilakukan melalui tugas individu dan tes tindakan. Dalam aktivitas pembelajaran siswa dimotivasi dan diamati perkembangannya dalam hal keaktifan dalam kegiatan pembelajaran melalui NHT dan penggunaan sate bola melalui pengamatan dan evaluasi..Penelitian ini mengimplementasikan materi peluang melalui penemuan konsep dengan bantuan alat peraga sate bola dan pendekatan NHT sehingga siswa dapat membangun pengetahuan baru sekaligus menerapkannya dalam kehidupan sehari-hari yang menuntut siswa untuk menggali konsep peluang yang akhirnya siswa dapat meningkatkan pemahaman matematika dan aktivitas belajanya. Kata Kunci: Pendekatan NHT, Sate bola

Kemampuan komunikasi matematis merupakan salah satu kemampuan matematika yang harus dicapai oleh siswa setelah belajar matematika sehingga perlu terus dikembangkan. Penelitian ini menggunakan desain pretest-posttest control design, yang bertujuan untuk mengetahui kemampuan komunikasi matematis guru MI program DMS dengan pendekatan MEAs. Populasi dalam penelitian ini adalah seluruh guru MI program DMS Putaran III, dan pengambilan sampel penelitian dilakukan secara purposive sampling. Penelitian ini terdiri dari dua kelas pembelajaran, yaitu pembelajaran dengan pendekatan MEAs dan pembelajaran dengan pendekatan konvensional. Data penelitian dikumpulkan melalui tes kemampuan komunikasi matematis dan angket pandangan mahasiswa. Hasil dari penelitian ini menunjukan bahwa kemampuan komunikasi matematis mahasiswa yang belajar dengan menggunakan pendekatan MEAs lebih baik daripada kemampuan komunikasi matematis mahasiswa yang belajar dengan menggunakan pendekatan konvensional dan secara umum mahasiswa cenderung memiliki pandangan yang positif baik terhadap pelajaran matematika maupun terhadap pembelajaran matematika dengan pendekatan MEAs. Kata kunci: Pendekatan MEAs, Komunikasi Matematis

A numerically efficient globally averaged number density approach is used to simulate a reaction-diffusion system using a particle-based stochastic simulation algorithm called reactive multiparticle collision (RMPC) dynamics. Constant diffusivity of the particles is achieved through a time-varying rotation angle (also called collision angle). Variation in the diffusion coefficient between two different chemical species is achieved in one of two ways: (ⅰ) using a different kBT/m value for one species compared to the other, or (ⅱ) using the same kBT/m value for both species, but using a different probability to free-stream for one species compared to another. For smaller diffusivities and larger spatial inhomogeneities, bath particles were necessary for the model to agree with the PDE solution. The latter approach was further used without a bath, and shown to be capable of producing Turing patterns after long simulation times. The significance of our work is that RMPC can serve as a feasible simulation tool for both short and long-term simulations, can handle spatial inhomogeneities, can model a fairly large range of diffusivities in a reaction-diffusion scenario, and is capable of producing Turing patterns. An advantage of this method includes more detailed system information in feasible simulation times.

Let S be a complete star-omega semiring and Sigma be an alphabet. For a weighted omega-pushdown automaton P with stateset 1...n, n greater or equal to 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule pair ((S<>)^nxn, (S<>)^n) such that the behavior ||P|| of P is a component of a solution of this system. In case the basic semiring is the Boolean semiring or the semiring of natural numbers (augmented with infinity), we show that there exists a mixed context-free grammar that generates ||P||. The construction of the mixed context-free grammar from P is a generalization of the well known triple construction and is called now triple-pair construction for omega-pushdown automata., Comment: In Proceedings AFL 2017, arXiv:1708.06226. The article was prepared as a joint work with the late Zolt\'an \'Esik (1951-2016) whose definite intention was to publish the results

© 2018 by the authors. Collaboration has been common in workplaces in various engineering settings and in our daily activities. However, how to effectively engage collaborators with collaborative tasks has long been an issue due to various situational and technical constraints. The research in this paper addresses the issue in a specific scenario, which is how to enable users to interact with public information from their own perspective. We describe a 3D mobile interaction technique that allows users to collaborate with other people by creating a symmetric and collaborative ambience. This in turn can increase their engagement with public displays. In order to better understand the benefits and limitations of this technique, we conducted a usability study with a total of 40 participants. The results indicate that the 3D mobile interaction technique promotes collaboration between users and also improves their engagement with the public displays.

Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near critical temperature. Solutions are given for the changing phase of cylindrical or spherical inclusion, allowing for a “mushy” zone with a mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

In this note we investigate the general solution for the quartic functional equation of the form $\left(n\in \mathbb{N}, \, \, n > 4 \right)$ and also investigate the Hyers-Ulam stability of the quartic functional equation in random normed spaces using the direct approach and the fixed point approach.

In this paper, we introduce the notion of a modular p-metric space (an extended modular b-metric space) and establish some fixed point results for alpha-nu-Meir-Keeler contractions in this new space. Using these results, we deduce some new fixed point theorems in extended modular metric spaces endowed with a graph and in partially ordered extended modular metric spaces. Also, we develop an important relation between fuzzy-Meir-Keeler and extended fuzzy p-metric with modular p-metric and get certain new fixed point results in triangular fuzzy p-metric spaces. We provide an example and an application to support our results which generalize several well known results in the literature., Basque GovernmentBasque Government [IT1207-19]; Ege University Scientific Research Projects Coordination UnitEge University [FGA-2020-22080], The authors would like to thank the editor and the anonymous referees for their careful reading of our manuscript and their many insightful comments and suggestions. The authors thank the Basque Government for its support of this work through Grant IT1207-19. This study is supported by Ege University Scientific Research Projects Coordination Unit. Project Number FGA-2020-22080.

In recent years, the amount of available data is growing exponentially, and large-scale data is becoming ubiquitous. Machine learning is a key to deriving insight from this deluge of data. In this paper, we focus on the large-scale data analysis, especially classification data, and propose an online conjugate gradient (CG) descent algorithm. Our algorithm draws from a recent improved Fletcher-Reeves (IFR) CG method proposed in Jiang and Jian[13] as well as a recent approach to reduce variance for stochastic gradient descent from Johnson and Zhang [15]. In theory, we prove that the proposed online algorithm achieves a linear convergence rate under strong Wolfe line search when the objective function is smooth and strongly convex. Comparison results on several benchmark classification datasets demonstrate that our approach is promising in solving large-scale machine learning problems, viewed from the points of area under curve (AUC) value and convergence behavior.

We evaluate definite integrals of the form given by $\int_{0}^{\infty}R(a, x)\log (\cos (\alpha) \text{sech}(x)+1)dx$. The function $R(a, x)$ is a rational function with general complex number parameters. Definite integrals of this form yield closed forms for famous integrals in the books of Bierens de Haan [4] and Gradshteyn and Ryzhik [5].

In this paper, we introduce a class of meromorphic starlike function by subordination relationship and generalized $\lambda$-Hadamard product. We obtain the necessary and sufficient conditions and closure properties of the class. In addition, some new results of the class are given.

The iterative functional equation $ \alpha\rightarrow(\alpha\rightarrow \beta) = \alpha\rightarrow \beta $ and the law of importation $ (\alpha\wedge \beta)\rightarrow \gamma = \alpha\rightarrow (\beta\rightarrow \gamma) $ are two tautologies in classical logic. In fuzzy logics, they are two important properties, and are respectively formulated as $ I(\alpha, \beta) = I(\alpha, I(\alpha, \beta)) $ and $ I(T(\alpha, \beta), \gamma) = I(\alpha, I(\beta, \gamma)) $ where $ I $ is a fuzzy implication and $ T $ is a $ t $-norm. Over the past several years, solutions to these two functional equations involving different classes of fuzzy implications have been studied. However, there are no results about stability study of fuzzy functional equations involving fuzzy implication. This paper discusses fuzzy implications that do not strictly satisfying these equations, but approximately satisfy these equations. Then we establish the Hyers-Ulam stability of the iterative functional equation involving the $ (S, N) $-implication, where the $ (S, N) $-implication is a common class of fuzzy implications generated by a continuous $ t $-conorm $ S $ and a continuous fuzzy negation $ N $. Furthermore, given a fixed $ t $-norm (the minimum $ t $-norm or the product $ t $-norm) the Hyers-Ulam stability of the law of importation involving the $ (S, N) $-implication is studied.

Marine Predators algorithm (MPA) is a newly proposed nature-inspired metaheuristic algorithm. The main inspiration of this algorithm is based on the extensive foraging strategies of marine organisms, namely Lévy movement and Brownian movement, both of which are based on random strategies. In this paper, we combine the marine predator algorithm with Teaching-learning-based optimization algorithm, and propose a hybrid algorithm called Teaching-learning-based Marine Predator algorithm (TLMPA). Teaching-learning-based optimization (TLBO) algorithm consists of two phases: the teacher phase and the learner phase. Combining these two phases with the original MPA enables the predators to obtain prey information for foraging by learning from teachers and interactive learning, thus greatly increasing the encounter rate between predators and prey. In addition, effective mutation and crossover strategies were added to increase the diversity of predators and effectively avoid premature convergence. For performance evaluation TLMPA algorithm, it has been applied to IEEE CEC-2017 benchmark functions and four engineering design problems. The experimental results show that among the proposed TLMPA algorithm has the best comprehensive performance and has more outstanding performance than other the state-of-the-art metaheuristic algorithms in terms of the performance measures.

Grey theory is an approach that can be used to construct a model with limited samples to provide better forecasting advantage for short-term problems. In some cases, a grey forecasting model may yield unacceptable forecasting errors. In this work, a new exponential grey prediction model, which is called as EXGM (1, 1), is proposed. By using this model, new cases, deaths and recovered cases of COVID-19 in Turkey is forecast. Numerical results show that EXGM (1, 1) is a model that performs more accurately than the comparison models.

In this paper, we deal with the existence of nontrivial solutions for the following Kirchhoff-type equation where $0 < s < 1 < p < \infty$, $sp < N$, $\lambda > 0$ is a real parameter, $(-\Delta)_{p}^{s}$ is the fractional $p$-Laplacian operator, $V:\mathbb{R}^N\rightarrow\mathbb{R}^N$ is a potential function, $M$ is a Kirchhoff function, the nonlinearity $f:\mathbb{R}^N\times\mathbb{R}\rightarrow\mathbb{R}$ is a continuous function and just super-linear in a neighborhood of $u = 0$. By using an appropriate truncation argument and the mountain pass theorem, we prove the existence of nontrivial solutions for the above equation, provided that $\lambda$ is sufficiently large. Our results extend and improve the previous ones in the literature.

The fixed point results for Chatterjea type contraction in the setting of Complete metric space exists in literature. Taking this approach forward Karapinar gave the concept of cyclic Chatterjea contraction mappings. Fan also worked on these cyclic mappings in a new setting of quasi-partial b-metric space. Motivated by the work of these researchers, we have introduced the notion of $qp_{b}$-cyclic Chatterjea contractive mappings and established fixed point results on them. The aim of this paper is to use an interpolative approach in the framework of quasi-partial b-metric space and to prove existence and uniqueness of fixed point theorem for $qp_{b}$-interpolative Chatterjea contraction mappings. The results are affirmed with applications based on them.

In this work we present derivations of the formula listed in entry 4.113 in the sixth edition of Gradshteyn and Rhyzik's table of integrals. We evaluate two definite integrals of the form $ \begin{equation*} \int_{0}^{\infty}\frac{e^{-iay}(-iy+\log(z))^k+e^{iay}(iy+\log(z))^k}{\cosh(by)}dy \end{equation*} $ and $ \begin{equation*} \int_{0}^{\infty}\frac{e^{iay}(iy+\log(z))^k-e^{-iay}(-iy+\log(z))^k}{\sinh(b y)}dy \end{equation*} $ in terms of the Lerch function where $ k $, $ a $, $ z $ and $ b $ are arbitrary complex numbers. The entries in the table(s) are obtained as special cases in the paper below.

In this paper, the study of fractional order partial differential equations is made by using the reliable algorithm of the new iterative method (NIM). The fractional derivatives are considered in the Caputo sense whose order belongs to the closed interval [0, 1]. The proposed method is directly extended to study the fractional-order Roseau-Hyman and fractional order inhomogeneous partial differential equations without any transformation to convert the given problem into integer order. The obtained results are compared with those obtained by Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Laplace Variational Iteration Method (LVIM) and the Laplace Adominan Decomposition Method (LADM). The results obtained by NIM, show higher accuracy than HPM, LVIM and LADM. The accuracy of the proposed method improves by taking more iterations.

In this paper, it is explicitly determined the r-dynamic chromatic number of the direct product of any given path with either a complete graph or a wheel graph. Illustrative examples are shown for each one of the cases that are studied throughout the paper. Junta de Andalucía FQM-016

The goal of this paper is further to study a kind of generalized vector inverse quasi-variational inequality problems and to obtain error bounds in terms of the residual gap function, the regularized gap function, and the global gap function by utilizing the relaxed monotonicity and Hausdorff Lipschitz continuity. These error bounds provide effective estimated distances between an arbitrary feasible point and the solution set of generalized vector inverse quasi-variational inequality problems.

In the literature, a great number of HIV and HTLV-I mono-infection models has been formulated and analyzed. However, the within-host dynamics of HIV/HTLV-I co-infection has not been modeled. In the present paper we formulate and analyze a new HIV/HTLV-I co-infection model with latency and Cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible CD$4^{+}$T cells, latently HIV-infected cells, actively HIV-infected cells, latently HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by virus-to-cell and cell-to-cell transmissions, while the HTLV-I can only spread via cell-to-cell transmission. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We derive the threshold parameters which govern the existence and stability of all equilibria of the model. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and Lyapunov-LaSalle asymptotic stability theorem. We have presented numerical simulations to illustrate the effectiveness of our main results. In addition, we have discussed the effect of HTLV-I infection on the HIV-infected patients and vice versa. We have pointed out the influence of CTL immune response on the co-infection dynamics.

Some relations involving the qualar and null sectional curvatures for a pseudo Riemannian manifold are obtained. These curvatures are also investigated for pseudo-Riemannian submanifolds. Obtained relations are discussed for some special submanifolds of a Lorentzian manifold.

As the solutions of partial differential equations (PDEs), PDE surfaces provide an effective way for physical-based surface design in surface modeling. The bicubic B-spline surface is a useful tool for surface modeling in computer aided geometric design (CAGD). In this paper, we present a method for generating bicubic B-spline surfaces with the uniform knots and the quasi-uniform knots from the sixth order PDEs. From the given boundary condition, based on the cubic B-spline basis representation and the PDE mask, the resulting bicubic B-spline surface can be generated uniquely. The boundary condition is more flexible and can be applied for curvature-continuous surface design, surface blending and hole filling. Some representative examples show the effectiveness of the presented method.

In this paper, we develop a rumor spreading model by introducing white noise into the model. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic Lyapunov function, which provides us a good description of persistence. Finally, we provide some numerical simulations to illustrate the analytical results.

In this paper, some classes of Janowski type p-harmonic functions associated with the generalized Sǎlǎgean operator are introduced. Further, coefficient conditions, distortion estimates and the other properties of the classes are obtained. On the one hand, the results presented here generalize the results of Yaşar and Yalçin [8]. On the other hand, we obtain some new results on sufficient convolution condition of the classes.

In this paper, the boundedness and compactness of the inclusion mapping from $Q_p$ spaces into tent spaces $\mathcal{T}_{\frac{qp}{2},s}^{q}$ are completely characterized when $q>2$. As an application, the boundedness of the Volterra integral operator $T_g$ from $Q_p$ to the space $\mathcal{LF}(q,q-2,\frac{qp}{2})$ is obtained. Moreover, the essential norm and compactness of $T_g$ are also investigated.

In a graph G, the distance between two vertices is the length of the shortest path between them. The maximum distance between a vertex to any other vertex is considered as the eccentricity of the vertex. In this paper, we introduce the first general Zagreb eccentricity index and found upper and lower bounds on this index in terms of order, size and diameter. Moreover, we characterize the extremal graphs in the class of trees, trees with pendant vertices and bipartite graphs. Results on some famous topological indices can be presented as the corollaries of our main results.

By considering a weighted inner product, an adaptive generalized Arnoldi (GArnoldi) method was constructed by [ 13 ] for computing PageRank. In order to accelerate the adaptive GArnoldi method, this paper proposes a new method by using the power method with extrapolation process based on Google matrix's trace (PET) as an accelerated technique of the adaptive GArnoldi method. The new method is called as GArnoldi-PET method, whose implementation and convergence analysis are discussed in detail. Numerical experiments are used to illustrate the effectiveness of our proposed method.

We employ the multi-wavelet Galerkin method for the numerical solution of the telegraph equation with initial and boundary conditions. The problem becomes a sparse system of linear equations and the GMRES method is used to solve this system. The advantages of this scheme are complexity reduction, simplicity, and less grid selection. The convergence analysis is investigated and numerical experiments guarantee it. To show the ability of the method, we compare it with other methods and it can be confirmed that our results are better than others.

Let $G$ be a $[0, k_1+k_2+\cdots+k_m-n+1]$-digraph and $H_1, H_2, \cdots, H_r$ be $r$ vertex-disjoint $n$-subdigraphs of $G$, where $m, n, r$ and $k_i$ ($1\leq i\leq m$) are positive integers satisfying $1\leq n\leq m$ and $k_1\geq k_2\geq\cdots\geq k_m\geq r+1$. In this article, we verify that there exists a subdigraph $R$ of $G$ such that $R$ possesses a $[0, k_i]_1^{n}$-factorization orthogonal to every $H_i$ for $1\leq i\leq r$.