Search results for: semantic differential scale

Authors: A. Elsehemy, M. Abdeen , T. Nazmy

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Since the appearance of the Semantic web, many semantic search techniques and models were proposed to exploit the information in ontology to enhance the traditional keyword-based search. Many advances were made in languages such as English, German, French and Spanish. However, other languages such as Arabic are not fully supported yet. In this paper we present a framework for ontology based information retrieval for Arabic language. Our system consists of four main modules, namely query parser, indexer, search and a ranking module. Our approach includes building a semantic index by linking ontology concepts to documents, including an annotation weight for each link, to be used in ranking the results. We also augmented the framework with an automatic document categorizer, which enhances the overall document ranking. We have built three Arabic domain ontologies: Sports, Economic and Politics as example for the Arabic language. We built a knowledge base that consists of 79 classes and more than 1456 instances. The system is evaluated using the precision and recall metrics. We have done many retrieval operations on a sample of 40,316 documents with a size 320 MB of pure text. The results show that the semantic search enhanced with text classification gives better performance results than the system without classification.

Keywords: Arabic text classification, ontology based retrieval, Arabic semantic web, information retrieval, Arabic ontology

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Authors: Xiaocong Liu, Huazhen Wang, Ting He, Xiaozheng Li, Weihan Zhang, Jian Chen

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The utilization of electronic medical record (EMR) data to establish the disease diagnosis model has become an important research content of biomedical informatics. Deep learning can automatically extract features from the massive data, which brings about breakthroughs in the study of EMR data. The challenge is that deep learning lacks semantic knowledge, which leads to impracticability in medical science. This research proposes a method of incorporating lexical-semantic knowledge from abundant entities into a convolutional neural network (CNN) framework for pediatric disease diagnosis. Firstly, medical terms are vectorized into Lexical Semantic Vectors (LSV), which are concatenated with the embedded word vectors of word2vec to enrich the feature representation. Secondly, the semantic distribution of medical terms serves as Semantic Decision Guide (SDG) for the optimization of deep learning models. The study evaluate the performance of LSV-SDG-CNN model on four kinds of Chinese EMR datasets. Additionally, CNN, LSV-CNN, and SDG-CNN are designed as baseline models for comparison. The experimental results show that LSV-SDG-CNN model outperforms baseline models on four kinds of Chinese EMR datasets. The best configuration of the model yielded an F1 score of 86.20%. The results clearly demonstrate that CNN has been effectively guided and optimized by lexical-semantic knowledge, and LSV-SDG-CNN model improves the disease classification accuracy with a clear margin.

Keywords: convolutional neural network, electronic medical record, feature representation, lexical semantics, semantic decision

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Authors: Ganfeng Yu, Yuefeng Ma, Shanliang Yang

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The word discovery is a key problem in text information retrieval technology. Methods in new word discovery tend to be closely related to words because they generally obtain new word results by analyzing words. With the popularity of social networks, individual netizens and online self-media have generated various network texts for the convenience of online life, including network words that are far from standard Chinese expression. How detect network words is one of the important goals in the field of text information retrieval today. In this paper, we integrate the word embedding model and clustering methods to propose a network word discovery framework based on sentence semantic similarity (S³-NWD) to detect network words effectively from the corpus. This framework constructs sentence semantic vectors through a distributed representation model, uses the similarity of sentence semantic vectors to determine the semantic relationship between sentences, and finally realizes network word discovery by the meaning of semantic replacement between sentences. The experiment verifies that the framework not only completes the rapid discovery of network words but also realizes the standard word meaning of the discovery of network words, which reflects the effectiveness of our work.

Keywords: text information retrieval, natural language processing, new word discovery, information extraction

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Authors: Montaceur Zaghdoud, Mohamed Moussaoui, Jalel Akaichi

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Frequent subgraph mining refers usually to graph matching and it is widely used in when analyzing big data with large graphs. A lot of research works dealt with structural exact or inexact graph matching but a little attention is paid to semantic matching when graph vertices and/or edges are attributed and typed. Therefore, it seems very interesting to integrate background knowledge into the analysis and that extracted frequent subgraphs should become more pruned by applying a new semantic filter instead of using only structural similarity in graph matching process. Consequently, this paper focuses on developing a new hybrid approximate structuralsemantic graph matching to discover a set of frequent subgraphs. It uses simultaneously an approximate structural similarity function based on graph edit distance function and a possibilistic vertices similarity function based on affinity function. Both structural and semantic filters contribute together to prune extracted frequent set. Indeed, new hybrid structural-semantic frequent subgraph mining approach searches will be suitable to be applied to several application such as community detection in social networks.

Keywords: approximate graph matching, hybrid frequent subgraph mining, graph mining, possibility theory

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Authors: Fatima Al-Aswadi, Chan Yong

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With the large volume of unstructured data that increases day by day on the web, the motivation of representing the knowledge in this data in the machine processable form is increased. Ontology is one of the major cornerstones of representing the information in a more meaningful way on the semantic Web. The goal of Ontology learning from text is to elicit and represent domain knowledge in the machine readable form. This paper aims to give a follow-up review on the ontology learning systems from text and some of their defects. Furthermore, it discusses how far the ontology learning process will enhance in the future.

Keywords: concept discovery, deep learning, ontology learning, semantic relation, semantic web

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Authors: Oliwia Bator

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The subject of this description is phraseologisms with the component “spices and food additives component" in Polish and Russian. The purpose of the study is to analyze the phraseologisms from the point of view of lexis and semantics. The material for analysis was extracted from Phraseological Dictionaries of Polish and Russian. The phraseologisms were considered from the lexical point of view, taking into account the name of the " spices and food additives" component, which forms them. From the semantic point of view, 12 semantic groups of phraseologisms were separated in Polish, while 9 semantic groups were separated in Russian. In addition is shown their functioning in the contexts of contemporary Polish and Russian. The contexts were taken from the National Corpus of the Polish Language and the National Corpus of the Russian Language.

Keywords: phraseology, language, slavic studies, linguistics

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Authors: Firas A. Al Laban, Mohamed Chabi, Sammani Danwawu Abdullahi

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There are a real needs to integrate types of Open Educational Resources (OER) with an intelligent system to extract information and knowledge in the semantic searching level. Those needs raised because most of current learning standard adopted web based learning and the e-learning systems does not always serve all educational goals. Semantic Web systems provide educators, students, and researchers with intelligent queries based on a semantic knowledge management learning system. An ontology-based learning system is an advanced system, where ontology plays the core of the semantic web in a smart learning environment. The objective of this paper is to discuss the potentials of ontologies and mapping different kinds of ontologies; heterogeneous or homogenous to manage and control different types of Open Educational Resources. The important contribution of this research is to approach a methodology uses logical rules and conceptual relations to map between ontologies of different educational resources. We expect from this methodology to establish for an intelligent educational system supporting student tutoring, self and lifelong learning system.

Keywords: knowledge management systems, ontologies, semantic web, open educational resources

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: Tamás Matuszka, Attila Kiss

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Due the proliferation of smartphones in everyday use, several different outdoor navigation systems have become available. Since these smartphones are able to connect to the Internet, the users can obtain location-based information during the navigation as well. The users could interactively get to know the specifics of a particular area (for instance, ancient cultural area, Statue Park, cemetery) with the help of thus obtained information. In this paper, we present an Augmented Reality system which uses Semantic Web technologies and is based on the interaction between the user and the smartphone. The system allows navigating through a specific area and provides information and details about the sight an interactive manner.

Keywords: augmented reality, semantic web, human computer interaction, mobile application

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Authors: Marina Fomina

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The paper focuses on the category of semantic subject within the framework of a functional approach to linguistics. The semantic subject is related to similar notions such as the grammatical subject and the bearer of predicative feature. It is the multifaceted nature of the category of subject that 1) triggers a number of issues that, syntax-wise, remain to be dealt with (cf. semantic vs. syntactic functions / sentence parts vs. parts of speech issues, etc.); 2) results in a variety of approaches to the category of subject, such as formal grammatical, semantic/syntactic (functional), communicative approaches, etc. Many linguists consider the prototypical approach to the category of subject to be the most instrumental as it reveals the integrity of denotative and linguistic components of the conceptual category. This approach relates to subject as a source of non-passive predicative feature, an element of subject-predicate-object situation that can take on a variety of semantic roles, cf.: 1) an agent (He carefully surveyed the valley stretching before him), 2) an experiencer (I feel very bitter about this), 3) a recipient (I received this book as a gift), 4) a causee (The plane broke into three pieces), 5) a patient (This stove cleans easily), etc. It is believed that the variety of roles stems from the radial (prototypical) structure of the category with some members more central than others. Translation-wise, the most “treacherous” subject types are the peripheral ones. The paper 1) features a peripheral status of spatial impersonal sentence models such as U menia v ukhe zvenit (lit. I-Gen. in ear buzzes) within the category of semantic subject, 2) makes a structural and semantic analysis of the models, 3) focuses on their Russian-English translation patterns, 4) reveals non-prototypical features of subjects in the English equivalents.

Keywords: bearer of predicative feature, grammatical subject, impersonal sentence model, semantic subject

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Authors: Mahya Naghipoor

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Purpose: Non-small cell lung cancer (NSCLC) is the most common lung cancer type. Epidermal growth factor receptor (EGFR) mutation is the main reason which causes NSCLC. Computed tomography (CT) is used for diagnosis and prognosis of lung cancers because of low price and little invasion. Semantic analyses of qualitative CT features are based on visual evaluation by radiologist. However, the naked eye ability may not assess all image features. On the other hand, radiomics provides the opportunity of quantitative analyses for CT images features. The aim of this review study was comparing accuracy of semantic and radiomics features in prognosis of EGFR mutation in NSCLC. Methods: For this purpose, the keywords including: non-small cell lung cancer, epidermal growth factor receptor mutation, semantic, radiomics, feature, receiver operating characteristics curve (ROC) and area under curve (AUC) were searched in PubMed and Google Scholar. Totally 29 papers were reviewed and the AUC of ROC analyses for semantic and radiomics features were compared. Results: The results showed that the reported AUC amounts for semantic features (ground glass opacity, shape, margins, lesion density and presence or absence of air bronchogram, emphysema and pleural effusion) were %41-%79. For radiomics features (kurtosis, skewness, entropy, texture, standard deviation (SD) and wavelet) the AUC values were found %50-%86. Conclusions: In conclusion, the accuracy of radiomics analysis is a little higher than semantic in prognosis of EGFR mutation in NSCLC.

Keywords: lung cancer, radiomics, computer tomography, mutation

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Authors: Tiexin Wang, Sebastien Truptil, Frederick Benaben

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Model transformation, as a pivotal aspect of Model-driven engineering, attracts more and more attentions both from researchers and practitioners. Many domains (enterprise engineering, software engineering, knowledge engineering, etc.) use model transformation principles and practices to serve to their domain specific problems; furthermore, model transformation could also be used to fulfill the gap between different domains: by sharing and exchanging knowledge. Since model transformation has been widely used, there comes new requirement on it: effectively and efficiently define the transformation process and reduce manual effort that involved in. This paper presents an automatic model transformation methodology based on semantic and syntactic comparisons, and focuses particularly on granularity issue that existed in transformation process. Comparing to the traditional model transformation methodologies, this methodology serves to a general purpose: cross-domain methodology. Semantic and syntactic checking measurements are combined into a refined transformation process, which solves the granularity issue. Moreover, semantic and syntactic comparisons are supported by software tool; manual effort is replaced in this way.

Keywords: automatic model transformation, granularity issue, model-driven engineering, semantic and syntactic comparisons

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: F. Lhafiane, A. Elbyed, M. Bouchoum

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Reverse Logistics (RL) Process is considered as complex and dynamic network that involves many stakeholders such as: suppliers, manufactures, warehouse, retails, and costumers, this complexity is inherent in such process due to lack of perfect knowledge or conflicting information. Ontologies, on the other hand, can be considered as an approach to overcome the problem of sharing knowledge and communication among the various reverse logistics partners. In this paper, we propose a semantic representation based on hybrid architecture for building the Ontologies in an ascendant way, this method facilitates the semantic reconciliation between the heterogeneous information systems (ICT) that support reverse logistics Processes and product data.

Keywords: Reverse Logistics, information management, heterogeneity, ontologies, semantic web

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Anam Bhatti, Sumbal Arif, Mariam Mehar, Sohail Younas

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CSR has become one of the imperative implements in satisfying customers. The impartial of this research is to calculate CSR, relationship marketing, and customer satisfaction. In Pakistan, there is not enough research work on the effect of CSR and relationship marketing on relationship maintainer and customer loyalty. To find out deductive approach and survey method is used as research approach and research strategy respectively. This research design is descriptive and quantitative study. For data, collection questionnaire method with semantic differential scale and seven point scales are adopted. Data has been collected by adopting the non-probability convenience technique as sampling technique and the sample size is 400. For factor confirmatory factor analysis, structure equation modeling and medication analysis, regression analysis Amos software were used. Strong empirical evidence supports that the customer’s perception of CSR performance is highly influenced by the values.

Keywords: CSR, Relationship marketing, Relationship maintainer, Customer loyalty, Customer satisfaction

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Authors: Imen Elleuch, Wael Ouarda, Gargouri Bilel

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We proposes in this paper a Deep Learning based approach to classify text in order to enrich an Arabic ontology based on the objects classes of Gaston Gross. Those object classes are defined by taking into account the syntactic and semantic features of the treated language. Thus, our proposed approach is a hybrid one. In fact, it is based on the one hand on the object classes that represents a knowledge based-approach on classification of text and in the other hand it uses the deep learning approach that use the word embedding-based-approach to classify text. We have applied our proposed approach on a corpus constructed from an Arabic dictionary. The obtained semantic classification of text will enrich the Arabic objects classes ontology. In fact, new classes can be added to the ontology or an expansion of the features that characterizes each object class can be updated. The obtained results are compared to a similar work that treats the same object with a classical linguistic approach for the semantic classification of text. This comparison highlight our hybrid proposed approach that can be ameliorated by broaden the dataset used in the deep learning process.

Keywords: deep-learning approach, object-classes, semantic classification, Arabic

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Abderrahmane Khiat, Moussa Benaissa

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Due to the increasing number of sources of information available on the web and their distribution and heterogeneity, ontology alignment became a very important and inevitable problem to ensure semantic interoperability. Instance-based ontology alignment is based on the comparison of the extensions of concepts; and represents a very promising technique to find semantic correspondences between entities of different ontologies. In practice, two situations may arise: ontologies that share many common instances and ontologies that share few or do not share common instances. In this paper, we describe an approach to manage the latter case. This approach exploits the reasoning on ontologies in order to create a corpus of common instances. We show that it is theoretically powerful because it is based on description logics and very useful in practice. We present the experimental results obtained by running our approach on ontologies of OAEI 2012 benchmark test. The results show the performance of our approach.

Keywords: description logic inference, instance-based ontology alignment, semantic interoperability, semantic web

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Valdênia Carvalho e Almeida

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The goal of the present study is to investigate the semantic preference of the most frequent adjectives in research articles through a corpus-based analysis of texts published in journals in Applied Linguistics (AL). The corpus used in this study contains texts published in the period from 2014 to 2018 in the three journals: Language Learning and Technology; English for Academic Purposes, and TESOL Quaterly, totaling more than one million words. A corpus-based analysis was carried out on the corpus to identify the most frequent adjectives that co-occurred in the three journals. By observing the concordance lines of the adjectives and analyzing the words they associated with, the semantic preferences of each adjective were determined. Later, the AL corpus analysis was compared to the investigation of the same adjectives in a corpus of Chemistry. This second part of the study aimed to identify possible differences and similarities between the two corpora in relation to the use of the adjectives in research articles from both areas. The results show that there are some preferences which seem to be closely related not only to the academic genre of the texts but also to the specific domain of the discipline and, to a lesser extent, to the context of research in each journal. This research illustrates a possible contribution of Corpus Linguistics to explore the concept of semantic preference in more detail, considering the complex nature of the phenomenon.

Keywords: applied linguistics, corpus linguistics, chemistry, research article, semantic preference

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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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: Zhan Chen, Wenquan Bi

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This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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