Search results for: explicit representation of solutions

Authors: A. Giniatoulline

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A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid

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Authors: Ang Ling Weay, Mona Masood

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This paper discusses the potential benefits of an interactive multimedia information representation in enhancing students’ critical thinking aligned with history reasoning in learning history between Secondary School students in Malaysia. Two modes of multimedia information representation implemented which are chronological and thematic information representation. A qualitative study of an unstructured interview was conducted among two history teachers, one history education lecturer, two i-think expert and program trainers and five form 4 secondary school students. The interview was to elicit their opinions on the implementation of thinking maps and interactive multimedia information representation in history learning. The key elements of interactive multimedia (e.g. multiple media, user control, interactivity, and use of timelines and concept maps) were then considered to improve the learning process. Findings of the preliminary investigation reveal that the interactive multimedia information representations have the potential benefits to be implemented as instructional resource in enhancing students’ higher order thinking skills (HOTs). This paper concludes by giving suggestions for future work.

Keywords: multimedia information representation, critical thinking, history reasoning, chronological and thematic information representation

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Authors: Samai'la Abdullahi

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A graph is a pair of two set and so that a graph is a pictorial representation of a system using two basic element nodes and edges. A node is represented by a circle (either hallo shade) and edge is represented by a line segment connecting two nodes together. In this paper, we present a circuit network in the concept of graph theory application and also circuit models of graph are represented in logical connection method were we formulate matrix method of adjacency and incidence of matrix and application of truth table.

Keywords: euler circuit and path, graph representation of circuit networks, representation of graph models, representation of circuit network using logical truth table

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Zainab Al-Maamari, Yassir Dinar

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The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds.

Keywords: invariant ring, Frobenius manifold, inversion, representation theory

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: Edamana Krishnan, Khalil Al-Ghafri

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In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

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Authors: B. A. A. Paixão, J. V. B. Gomide

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This work aims to analyze the locative structure used by the locative games of the company Niantic. To fulfill this objective, a literature review on the representation and simulation of cities was developed; interviews with Ingress players and playing Ingress. Relating these data, it was possible to deepen the relationship between the virtual and the real to create the simulation of cities and their cultural objects in locative games. Cities representation associates geo-location provided by the Global Positioning System (GPS), with augmented reality and digital image, and provides a new paradigm in the city interaction with its parts and real and virtual world elements, homeomorphic to real world. Bibliographic review of papers related to the representation and simulation study and their application in locative games was carried out and is presented in the present paper. The cities representation and simulation concepts in locative games, and how this setting enables the flow and immersion in urban space, are analyzed. Some examples of games are discussed for this new setting development, which is a mix of real and virtual world. Finally, it was proposed a Locative Structure for electronic games using the concepts of heterotrophic representations and isotropic representations conjoined with immediacy and hypermediacy.

Keywords: cities representation, cities simulation, games simulation, immersion, locative games

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Authors: Saeid Haghjoo, Ebrahim Reyhani, Fahimeh Kolahdouz

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The present study aimed to evaluate the understanding of the students in Tehran universities (Iran) about the numerical representation of the average rate of change based on the Structure of Observed Learning Outcomes (SOLO). In the present descriptive-survey research, the statistical population included undergraduate students (basic sciences and engineering) in the universities of Tehran. The samples were 604 students selected by random multi-stage clustering. The measurement tool was a task whose face and content validity was confirmed by math and mathematics education professors. Using Cronbach's Alpha criterion, the reliability coefficient of the task was obtained 0.95, which verified its reliability. The collected data were analyzed by descriptive statistics and inferential statistics (chi-squared and independent t-tests) under SPSS-24 software. According to the SOLO model in the prestructural, unistructural, and multistructural levels, basic science students had a higher percentage of understanding than that of engineering students, although the outcome was inverse at the relational level. However, there was no significant difference in the average understanding of both groups. The results indicated that students failed to have a proper understanding of the numerical representation of the average rate of change, in addition to missconceptions when using physics formulas in solving the problem. In addition, multiple solutions were derived along with their dominant methods during the qualitative analysis. The current research proposed to focus on the context problems with approximate calculations and numerical representation, using software and connection common relations between math and physics in the teaching process of teachers and professors.

Keywords: average rate of change, context problems, derivative, numerical representation, SOLO taxonomy

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Authors: Kamel Al-Khaled

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Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

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Authors: Yuanchao Sang, Zhihao Gong, Longsheng Chen, Long Chen

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Clothing fashion represents a human’s aesthetic appreciation towards everyday outfits and appetite for fashion, and it reflects the development of status in society, humanity, and economics. However, modelling fashion by machine is extremely challenging because fashion is too abstract to be efficiently described by machines. Even human beings can hardly reach a consensus about fashion. In this paper, we are dedicated to answering a fundamental fashion-related problem: what image feature best describes clothing fashion? To address this issue, we have designed and evaluated various image features, ranging from traditional low-level hand-crafted features to mid-level style awareness features to various current popular deep neural network-based features, which have shown state-of-the-art performance in various vision tasks. In summary, we tested the following 9 feature representations: color, texture, shape, style, convolutional neural networks (CNNs), CNNs with distance metric learning (CNNs&DML), AutoEncoder, CNNs with multiple layer combination (CNNs&MLC) and CNNs with dynamic feature clustering (CNNs&DFC). Finally, we validated the performance of these features on two publicly available datasets. Quantitative and qualitative experimental results on both intra-domain and inter-domain fashion clothing image retrieval showed that deep learning based feature representations far outweigh traditional hand-crafted feature representation. Additionally, among all deep learning based methods, CNNs with explicit feature clustering performs best, which shows feature clustering is essential for discriminative fashion feature representation.

Keywords: convolutional neural network, feature representation, image processing, machine modelling

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Authors: Firmansyah David

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This paper aims to investigate factors that drive individuals to transfer their knowledge in the context of online communities. By revisiting tacit-to-explicit knowledge creation, this research attempts to contribute empirically using three online forums (1) Software Engineering; (2) Aerospace Simulator; (3) Health Insurance System. A qualitative approach was deployed to map and recognize the pattern of users ‘Knowledge Transfer (KT), particularly from expert to novice. The findings suggest a common form on how experts give their effort to formulate ‘explicit’ knowledge and how novices ‘understand’ such knowledge. This research underlines that skill; intuition, judgment; value and belief are the prominent factors, both for experts and novice. Further, this research has recognized the groups of expert and novice by their ability to transfer and to ‘adopt’ new knowledge. Future research infers to triangulate the method in which the quantitative study is needed to measure the level of adoption of (new) knowledge by individuals.

Keywords: explicit, expert, knowledge, online community

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Authors: Fan Wei, Tang Yipeng

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Knowledge sharing is of great value to organizational performance and innovation ability. However, the mainstream research has focused largely on the impact of knowledge sharing at the team level on individuals and teams. There is a lack of empirical studies on how employees interact in the exchange of knowledge and its effect on employees’ own creative performance. Based on communication accommodation theory and social exchange theory, this article explores the construction of an employee knowledge interaction mechanism under the moderating of social status and introduces the leader's creativity expectation as a moderating variable to explore its cross-level moderating effect on employee knowledge sharing and their own creative performance. An empirical test was conducted on 36 teaching and research teams in the two primary schools, and the results showed that: (1) Explicit/tacit knowledge of employees is positively correlated with acquisition of explicit/tacit knowledge; (2) Colleagues’ evaluations of employees’ social status play a moderating role between the employees’ explicit/tacit knowledge and the acquisition of explicit/tacit knowledge. (3) The leadership creativity expectation positively regulates the relationship between the employees' explicit knowledge acquisition and creative performance. This research helps to open the "black box" of the interpersonal interaction mechanism of knowledge sharing and also provides an important theoretical basis and practical guidance for organizational managers to effectively stimulate employee knowledge sharing and creative performance.

Keywords: knowledge sharing, knowledge interaction, social status, leadership creativity expectations, creative performance

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Authors: Siqi Qiu, Yijian Zheng, Xin Guo Ming

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In many reliability and risk analysis, failures of components are supposed to be independent. However, in reality, the ignorance of failure dependencies among components may render the results of reliability and risk analysis incorrect. There are two principal ways to incorporate failure dependencies in system reliability and risk analysis: implicit and explicit methods. In the implicit method, failure dependencies can be modeled by joint probabilities, correlation values or conditional probabilities. In the explicit method, certain types of dependencies can be modeled in a fault tree as mutually independent basic events for specific component failures. In this paper, explicit and implicit methods based on BDD will be proposed to evaluate the reliability of systems considering failure dependencies. The obtained results prove the equivalence of the proposed implicit and explicit methods. It is found that the consideration of failure dependencies decreases the reliability of systems. This observation is intuitive, because more components fail due to failure dependencies. The consideration of failure dependencies helps designers to reduce the dependencies between components during the design phase to make the system more reliable.

Keywords: reliability assessment, risk assessment, failure dependencies, binary decision diagram

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Authors: Chetna Jaswal, Nishi Srivastava, Ahammedul Kabeer AP, Puja Prasad

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We are a culture of mass media consumers and cinema as its integral part has high visibility and potential influence on public attitude towards disability which maintains no sociocultural boundaries but experiences substantial social marginalization. Given the lack of awareness and direct experience with disability, on-screen or film representations can give powerful and memorable definitions for the public that can contribute to framing the perception and attitude change. Social representation refers to common ways of thinking, conceiving about and evaluating social reality. It is a product of collective cognition, common sense and thought system. This study aims at analyzing the representations and narratives of disability in Indian cinema and Hollywood with the help of a conceptual understanding of social representation and its theoretical framework.

Keywords: disability, social representation, mainstream cinema, diversity

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Lee Myung-Won, Kwak Keun-Chang

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This paper is concerned with knowledge representation and extraction of fuzzy if-then rules using Interval Type-2 Context-based Fuzzy C-Means clustering (IT2-CFCM) with the aid of fuzzy granulation. This proposed clustering algorithm is based on information granulation in the form of IT2 based Fuzzy C-Means (IT2-FCM) clustering and estimates the cluster centers by preserving the homogeneity between the clustered patterns from the IT2 contexts produced in the output space. Furthermore, we can obtain the automatic knowledge representation in the design of Radial Basis Function Networks (RBFN), Linguistic Model (LM), and Adaptive Neuro-Fuzzy Networks (ANFN) from the numerical input-output data pairs. We shall focus on a design of ANFN in this paper. The experimental results on an estimation problem of energy performance reveal that the proposed method showed a good knowledge representation and performance in comparison with the previous works.

Keywords: IT2-FCM, IT2-CFCM, context-based fuzzy clustering, adaptive neuro-fuzzy network, knowledge representation

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Authors: D. R. Ambika, K. R. Radhika, D. Seshachalam

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Unconstrained authentication is an important component for personal automated systems and human-computer interfaces. Existing solutions mostly use face as the primary object of analysis. The performance of face-based systems is largely determined by the extent of deformation caused in the facial region and amount of useful information available in occluded face images. Periocular region is a useful portion of face with discriminative ability coupled with resistance to deformation. A reliable portion of periocular area is available for occluded images. The present work demonstrates that joint representation of periocular texture and periocular structure provides an effective expression and poses invariant representation. The proposed methodology provides an effective and compact description of periocular texture and shape. The method is tested over four benchmark datasets exhibiting varied acquisition conditions.

Keywords: periocular authentication, Zernike moments, LBP variance, shape and texture fusion

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Authors: Safia Hocine, Djamil Aïssani

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Risk models, recently studied in the literature, are becoming increasingly complex. It is rare to find explicit analytical relations to calculate the ruin probability. Indeed, the stability issue occurs naturally in ruin theory, when parameters in risk cannot be estimated than with uncertainty. However, in most cases, there are no explicit formulas for the ruin probability. Hence, the interest to obtain explicit stability bounds for these probabilities in different risk models. In this paper, we interest to the stability bounds of the univariate classical risk model established using the regenerative processes approach. By adopting an algorithmic approach, we implement this approximation and determine numerically the bounds of ruin probability in the case of large claims (heavy-tailed distribution).

Keywords: heavy-tailed distribution, large claims, regenerative process, risk model, ruin probability, stability

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Authors: Jawad Abuhlail, Hamza Hroub

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Let R be a commutative ring. Representation theory studies the representation of R-modules as (possibly finite) sums of special types of R-submodules. Here we are interested in a class of R-modules between the class of semisimple R-modules and the class of R-modules that can be written as (possibly finite) sums of secondary R-submodules (we know that every simple R-submodule is secondary). We investigate R-modules which can be written as (possibly finite) sums of second R-submodules (we call those modules second representable). Moreover, we investigate the class of (main) second attached prime ideals related to a module with such representation. We provide sufficient conditions for an R-module M to get a (minimal) second representation. We also found the collection of second attached prime ideals for some types of second representable R-modules, in particular within the class of injective R-modules. As we know that every simple R-submodule is second and every second R-submodule is secondary, we can see the importance of the second representable R-module.

Keywords: lifting modules, second attached prime ideals, second representations, secondary representations, semisimple modules, second submodules

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Authors: A. Hidalgo, A. Desportes, E. Bonin, A. Kadaoui, T. Bouaricha

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Present paper is concerned with portfolio management with Black-Litterman (B-L) model. Considered stocks are exclusively limited to large companies stocks on US market. Results obtained by application of the model are presented. From analysis of collected Dow Jones stock data, remarkable explicit analytical expression of optimal B-L parameter τ, which scales dispersion of normal distribution of assets mean return, is proposed in terms of standard deviation of covariance matrix. Implementation has been developed in Matlab environment to split optimization in Markovitz sense from specific elements related to B-L representation.

Keywords: Black-Litterman, Markowitz, market data, portfolio manager opinion

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Authors: Revytia Tanera

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This research is a pilot study to examine the rise of selfie trend in dealing with individual self representation and identity building in social media. The symbolic interactionism theory is used as the concept of the desired self image, and Cooley’s looking glass-self concept is used to analyze the mechanical reflection of ourselves; how do people perform their “digital self” in social media. In-depth interviews were conducted in the study with a non-random sample who owns a smartphone with a front camera feature and are active in social media. This research is trying to find out whether the selfie trend brings any influence on identity building on each individual. Through analysis of interview results, it can be concluded that people take selfie photos in order to express themselves and to boost their confidence. This study suggests a follow up and more in depth analysis on identity and self representation from various age groups.

Keywords: self representation, selfie, social media, symbolic interaction, looking glass-self

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Authors: Amanda Julia Binay, Patricia Elise Suarez

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Female representation in media is an important subject in the discussion of gender equality, especially in impactful and influential media like film. As the Filipino film industry continues to grow and evolve, the need for analysis on Filipino female representation on screen is imperative. Additionally, there has been limited research made on female representation in the Philippine film scene. Thus, the paper aims to analyze the presence and evolution of female representation in Philippine cinema and compare the findings with that of American films to see how Filipino filmmakers hold their own against the standards of international movements that call for more and better female representation, especially in Hollywood. The participants selected were Filipino and American films released within the years 1975 to 2020 in five (5) year intervals. Twenty (20) critically acclaimed and highest-grossing Filipino films and twenty (20) critically acclaimed and highest-grossing Hollywood films were then subject to the Bechdel and Peirce tests to obtain statistical measures of their female representation. The findings of the study reveal that the presence of female representation in Philippine film history has been consistent and has continued to grow and evolve throughout the years, with strong female leads with vibrant characteristics and diverse stories. However, analysis of female representation regarding American films has shown an extreme lack thereof with more misogynistic, sexist, and limiting ideals. Thus, the study concludes that the state of female representation in Philippine cinema and film industry holds its own when compared to American cinema and film industry and even outperforms it in many aspects of female representation, such as consistent inclusion and depiction of multi-dimensional female leads and female relationships. Hence, the study implies that women’s consistent presence in Philippine cinema mirrors Filipino women’s prominent role in Philippine society and that American cinema must continue to make efforts to change their portrayals of female characters, leads, and relationships to make them more grounded in reality.

Keywords: female representation, gender studies, feminism, philippine cinema, American cinema, bechdel test, peirce test, comparative analysis

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Authors: Francesco Arese Visconti

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The purpose of this paper is to question the methodological challenges that practice-based research on recent Italian migrants in Switzerland can pose. The entire development of the work has moved from the theorization to the production and back in a continuous exchange which is at the base of failures and successful results. The theoretical background leads to reflect on practical solutions to produce photographic portraits in the attempt to depict the cultural identity of a specific population. Thus, a series of key points of this challenging, visual, and intimate journey are discussed and developed. While analyzing, in the first stance, the psychological challenges resulting from the encounter of the photographer, the sitter, and the spectator, the challenges of the representation of a group of people with individual photographic portraits will secondly be highlighted. The paper underlines how previous work can be precursory of subsequent research and why the inclusion of the landscape versus maintaining a neutral background has links with paintings from the Italian Renaissance.

Keywords: photography, migration, Italians, Switzerland

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Authors: M. H. Kazemi, D. Salac

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A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method

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Authors: Zainab Abdulkarim

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Literature is the study of life, a source of knowledge. It involves the truth about many things in life. Most of these creative artistes most especially the poets are representatives of the voices of the people. These set of artistes have been the critics to all involved in the development of their nation. This paper will examine how Nigerian Poets goes further not just by writing but by showing the different ways the country has been convoluted. This paper intends to show the power and ability literature has in representation. The power is to represent the important values of life. There is no doubt that literature asserts truth. Through the various poems examined in this paper, Nigerian Poets have proved to portray the realities of the nation.

Keywords: literature, poets, reality, representation

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Adel Ebrahimpourtaher, Saeede Eisaie

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This study was an attempt to investigate the types of feedback most frequently provided to the students and their effectiveness based on the students’ preferences established through the interview conducted after the treatment. For this purpose, some class sessions of the students of the institute who were studying general English (pre-intermediate level) were recorded by the teacher for the analysis of the feed backs. The results of the analysis and transcriptions indicated that recast is the most frequent feedback type used by the teacher. In addition, the interview indicated that most of the students prefer recast as well as elicitation and explicit correction to some extent.

Keywords: EFL, elicitation, explicit, recast, feedback

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Authors: E. V. Krishnan

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In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.

Keywords: travelling wave solutions, Jacobi elliptic functions, solitary wave solutions, Korteweg-de Vries equation

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Authors: Janis Matvejs

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Visual representation of a city creates unique perspectives that allow to interpret the urban environment and enable to understand a space that is culturally created and territorially organized. Residential complexes are an essential part of cities and cinema is a specific representation form of these areas. There has been very little research done on exploring how these areas are depicted in the Thai movies. The aim of this research is to interpret the discourse of residential areas of Bangkok throughout the 20th and 21st centuries and to examine essential changes in the residential structure. Specific cinematic formal techniques in relation to the urban image were used. The movie review results were compared with changes in Bangkok’s residential development. Movie analysis displayed that residential areas are frequently used in Thai cinematography and they make up an integral part of the urban visual perception.

Keywords: Bangkok, cinema, residential area, representation, visual perception

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