Search results for: chebyshev collocation method(CCA)

Authors: Soroush Hooshyar, Mohamadali Masoudian, Natalie Germann

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Many soft materials such as polymer solutions can develop localized bands with different shear rates, which are known as shear bands. Using the generalized bracket approach of nonequilibrium thermodynamics, we recently developed a new two-fluid model to study shear banding for semi-dilute polymer solutions. The two-fluid approach is an appropriate means for describing diffusion processes such as Fickian diffusion and stress-induced migration. In this approach, it is assumed that the local gradients in concentration and, if accounted for, also stress generate a nontrivial velocity difference between the components. Since the differential velocity is treated as a state variable in our model, the implementation of the boundary conditions arising from the derivative diffusive terms is straightforward. Our model is a good candidate for benchmark simulations because of its simplicity. We analyzed its behavior in cylindrical Couette flow, a rectilinear channel flow, and a 4:1 planar contraction flow. The latter problem was solved using the OpenFOAM finite volume package and the impact of shear banding on the lip and salient vortices was investigated. For the other smooth geometries, we employed a standard Chebyshev pseudospectral collocation method. The results showed that the steady-state solution is unique with respect to initial conditions, deformation history, and the value of the diffusivity constant. However, smaller the value of the diffusivity constant is, the more time it takes to reach the steady state.

Keywords: nonequilibrium thermodynamics, planar contraction, polymer solutions, shear banding, two-fluid approach

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Authors: Amirreza Kosari, Hossein Maghsoudi, Malahat Givar

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In this study, the three-dimensional optimal path planning of a flying robot for Terrain Following / Terrain Avoidance (TF/TA) purposes using Direct Collocation has been investigated. To this purpose, firstly, the appropriate equations of motion representing the flying robot translational movement have been described. The three-dimensional optimal path planning of the flying vehicle in terrain following/terrain avoidance maneuver is formulated as an optimal control problem. The terrain profile, as the main allowable height constraint has been modeled using Fractal Generation Method. The resulting optimal control problem is discretized by applying Direct Collocation numerical technique, and then transformed into a Nonlinear Programming Problem (NLP). The efficacy of the proposed method is demonstrated by extensive simulations, and in particular, it is verified that this approach could produce a solution satisfying almost all performance and environmental constraints encountering a low-level flying maneuver

Keywords: path planning, terrain following, optimal control, nonlinear programming

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Authors: Hanwei Gao, Louis Jezequel, Eric Cabrol, Bernard Vitry

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The chassis system is composed of complex elements that take up all the loads from the tire-ground contact area and thus it plays an important role in numerous specifications such as durability, comfort, crash, etc. During the development of new vehicle projects in Renault, durability validation is always the main focus while deployment of comfort comes later in the project. Therefore, sometimes design choices have to be reconsidered because of the natural incompatibility between these two specifications. Besides, robustness is also an important point of concern as it is related to manufacturing costs as well as the performance after the ageing of components like shock absorbers. In this paper an approach is proposed aiming to realize a multi-objective optimization between chassis endurance and comfort while taking the random factors into consideration. The adaptive-sparse polynomial chaos expansion method (PCE) with Chebyshev polynomial series has been applied to predict responses’ uncertainty intervals of a system according to its uncertain-but-bounded parameters. The approach can be divided into three steps. First an initial design of experiments is realized to build the response surfaces which represent statistically a black-box system. Secondly within several iterations an optimum set is proposed and validated which will form a Pareto front. At the same time the robustness of each response, served as additional objectives, is calculated from the pre-defined parameter intervals and the response surfaces obtained in the first step. Finally an inverse strategy is carried out to determine the parameters’ tolerance combination with a maximally acceptable degradation of the responses in terms of manufacturing costs. A quarter car model has been tested as an example by applying the road excitations from the actual road measurements for both endurance and comfort calculations. One indicator based on the Basquin’s law is defined to compare the global chassis durability of different parameter settings. Another indicator related to comfort is obtained from the vertical acceleration of the sprung mass. An optimum set with best robustness has been finally obtained and the reference tests prove a good robustness prediction of Chebyshev PCE method. This example demonstrates the effectiveness and reliability of the approach, in particular its ability to save computational costs for a complex system.

Keywords: chassis durability, Chebyshev polynomials, multi-objective optimization, polynomial chaos expansion, ride comfort, robust design

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Yaser Mohammed Altameemi

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This research looks at the representation of the social media for the Saudi Government decrees regarding the developmental projects of the Saudi 2030 vision. The paper analyses a television interview with the Crown Prince Mohammed Bin Salman who talks about the progress of the Saudi vision of 2030, and how the government had acted as response to the COVID-19 pandemic. The interview was on 28/4/2021. The paper analyses the tweets on Twitter that cover the interview for the purpose of investigating the development of concepts and meanings regarding the Saudi peoples’ orientations towards the Saudi projects. The data include all related tweets from the day of the interview and the following seven days after the interview. The finding of the collocation analysis suggests that nationalism notion is explicitly expressed by users in Twitter. The main finding of this paper suggests the importance of further analyses for the concordance lines. However, the collocation network suggests that there is a clear highlight for nationalism.

Keywords: social media, twitter, political interview, prince Mohammed Bin Salman, Saudi vision 2030

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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: Mohamed S. Negm, Waleed S. Mandour

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The present study aims primarily at investigating words of peace (lexemes of peace) in the formal speeches of the Egyptian president Abdulfattah El-Sisi in a two-year span of time, from 2018 to 2019. This paper attempts to shed light not only on the contextual use of the antonyms, war and peace, but also it underpins quantitative analysis through the current methods of corpus linguistics. As such, the researchers have deployed a corpus-based approach in collecting, encoding, and processing 30 presidential speeches over the stated period (23,411 words and 25,541 tokens in total). Further, semantic fields and collocational networkzs are identified and compared statistically. Results have shown a significant propensity of adopting peace, including its relevant collocation network, textually and therefore, ideationally, at the expense of war concept which in most cases surfaces euphemistically through the noun conflict. The president has not justified the action of war with an honorable cause or a valid reason. Such results, so far, have indicated a positive sociopolitical mindset the Egyptian president possesses and moreover, reveal national and international fair dealing on arising issues.

Keywords: CADS, collocation network, corpus linguistics, critical discourse analysis

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Authors: Ngan Nguyen

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The study analyses adjectives collocating with the word ‘education’ in the American language of the Corpus of Global Web-based English using a combination of corpus linguistic and discourse analytical methods to examine not only language patterns but also social political ideologies around the topic. Significant conclusions are deduced: (1) there are a large number of adjectival collocates of the word education which have been identified and classified into four categories representing four different aspects of education: level, quality, forms and types of education; (2) education, as in combination with three first categories, carries the meaning as the act and process of teaching and learning while with the last category having the meaning of a particular kind of teaching or training; (3) higher education is the topic that gains most concerns from the American public; (4) five most significant ideologies are discovered from the corpus: higher education associates with financial affairs, higher education is an industry, monetary policy of the government on higher education, people require greater accessibility to higher education and people value higher education. The study contributes to the field of developing meanings of words through corpus analysis and the field of discourse analysis.

Keywords: adjectival collocation, American context, corpus linguistics, discourse analysis, education

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Authors: Hashem Sazegar

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Legendre’s conjecture states that there is a prime number between n^2 and (n + 1)^2 for every positive integer n. In this paper we prove that every composite number between n2 and (n + 1)2 can be written u^2 − v^2 or u^2 − v^2 + u − v that u > 0 and v ≥ 0. Using these result as well as induction and residues (modq) we prove Legendre’s conjecture.

Keywords: bertrand-chebyshev theorem, landau’s problems, goldbach’s conjecture, twin prime, ramanujan proof

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Authors: Badr Alkahtani

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In this poster, numerical solutions of two-dimensional and three-dimensional lid driven cavity are presented by solving the steady Navier-Stokes equations at high Reynolds numbers where it becomes difficult. Lid driven cavity is where the a fluid contained in a cube and the upper wall is moving. In two dimensions, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to Re=20000 on a fine grid of 131 * 131. Also in this presentation, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations (which is the first time that this has been simulated with special boundary conditions) for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and a finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200. , The work prepared here is to show the efficiency of methods used to simulate the physical problem where accurate simulations of lid driven cavity are obtained at high Reynolds number as mentioned above. The result for the two dimensional problem is far from the previous researcher result.

Keywords: lid driven cavity, navier-stokes, simulation, Reynolds number

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Authors: Prashant Pandey

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In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

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Authors: Navdeep Goel, Salvador Gabarda

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Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Multiplexing involves packing signals together whose representations are compact in the working domain. In order to optimize transmission resources each 4x4 pixel block of the image is transformed by a suitable polynomial approximation, into a minimal number of coefficients. Less than 4*4 coefficients in one block spares a significant amount of transmitted information, but some information is lost. Different approximations for image transformation have been evaluated as polynomial representation (Vandermonde matrix), least squares + gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev polynomials or singular value decomposition (SVD). Results have been compared in terms of nominal compression rate (NCR), compression ratio (CR) and peak signal-to-noise ratio (PSNR) in order to minimize the error function defined as the difference between the original pixel gray levels and the approximated polynomial output. Polynomial coefficients have been later encoded and handled for generating chirps in a target rate of about two chirps per 4*4 pixel block and then submitted to a transmission multiplexing operation in the time-frequency domain.

Keywords: chirp signals, image multiplexing, image transformation, linear canonical transform, polynomial approximation

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Authors: K. Godazandeh, K. Sadeghy

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In the present study, the effect of magnetic field on the hydrodynamic instability of Taylor-Couette flow between two concentric rotating cylinders has been numerically investigated. At the beginning the basic flow has been solved using continuity, Cauchy equations (with regards to Lorentz force) and the constitutive equations of a viscoelastic model called "Giesekus" model. Small perturbations, considered to be normal mode, have been superimposed to the basic flow and the unsteady perturbation equations have been derived consequently. Neglecting non-linear terms, the general eigenvalue problem obtained has been solved using pseudo spectral method (combination of Chebyshev polynomials). The objective of the calculations is to study the effect of magnetic fields on the onset of first mode of instability (axisymmetric mode) for different dimensionless parameters of the flow. The results show that the stability picture is highly influenced by the magnetic field. When magnetic field increases, it first has a destabilization effect which changes to stabilization effect due to more increase of magnetic fields. Therefor there is a critical magnetic number (Hartmann number) for instability of Taylor-Couette flow. Also, the effect of magnetic field is more dominant in large gaps. Also based on the results obtained, magnetic field shows a more considerable effect on the stability at higher Weissenberg numbers (at higher elasticity), while the "mobility factor" changes show no dominant role on the intense of suction and injection effect on the flow's instability.

Keywords: magnetic field, Taylor-Couette flow, Giesekus model, pseudo spectral method, Chebyshev polynomials, Hartmann number, Weissenberg number, mobility factor

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Authors: Shubham Jaiswal

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During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

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Authors: Samuel Ahamefula Mba

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Fluid turbulence is a complex and nonlinear phenomenon that occurs in various natural and industrial processes. Understanding turbulence remains a challenging task due to its intricate nature. One approach to gain insights into turbulence is through the study of entropy, which quantifies the disorder or randomness of a system. This research presents a numerical investigation of entropy signatures in fluid turbulence. The work is to develop a numerical framework to describe and analyse fluid turbulence in terms of entropy. This decomposes the turbulent flow field into different scales, ranging from large energy-containing eddies to small dissipative structures, thus establishing a correlation between entropy and other turbulence statistics. This entropy-based framework provides a powerful tool for understanding the underlying mechanisms driving turbulence and its impact on various phenomena. This work necessitates the derivation of the Poisson equation for pressure transformation of Navier-Stokes equation and using Chebyshev-Finite Difference techniques to effectively resolve it. To carry out the mathematical analysis, consider bounded domains with smooth solutions and non-periodic boundary conditions. To address this, a hybrid computational approach combining direct numerical simulation (DNS) and Large Eddy Simulation with Wall Models (LES-WM) is utilized to perform extensive simulations of turbulent flows. The potential impact ranges from industrial process optimization and improved prediction of weather patterns.

Keywords: turbulence, Navier-Stokes equation, Poisson pressure equation, numerical investigation, Chebyshev-finite difference, hybrid computational approach, large Eddy simulation with wall models, direct numerical simulation

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Authors: Ravi Kiran Jaladi, Ezz I. El-Masry

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Emerging technologies such as ultra-wide band wireless access technology that operate at ultra-low power present several challenges due to their inherent design that limits the use of voltage-mode filters. Therefore, Continuous-time current-mode (CTCM) filters have become very popular in recent times due to the fact they have a wider dynamic range, improved linearity, and extended bandwidth compared to their voltage-mode counterparts. The goal of this research is to develop analog filters which are suitable for the current scaling CMOS technologies. Bulk-driven MOSFET is one of the most popular low power design technique for the existing challenges, while other techniques have obvious shortcomings. In this work, a CTCM Gate-driven (GD) differentiator has been presented with a frequency range from dc to 100MHz which operates at very low supply voltage of 0.7 volts. A novel CTCM Bulk-driven (BD) differentiator has been designed for the first time which reduces the power consumption multiple times that of GD differentiator. These GD and BD differentiator has been simulated using CADENCE TSMC 65nm technology for all the bilinear and biquadratic band-pass frequency responses. These basic building blocks can be used to implement the higher order filters. A 6th order cascade CTCM Chebyshev band-pass filter has been designed using the GD and BD techniques. As a conclusion, a low power GD and BD 6th order chebyshev stagger-tuned band-pass filter was simulated and all the parameters obtained from all the resulting realizations are analyzed and compared. Monte Carlo analysis is performed for both the 6th order filters and the results of sensitivity analysis are presented.

Keywords: bulk-driven (BD), continuous-time current-mode filters (CTCM), gate-driven (GD)

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Authors: Manal Mohammed Hisham Said Najjar

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The Arab Grammarians shed light on the redundant kana (was) and gave it a considerable attention. However, their considerations and interpretations pertaining to using this verb varied: is it used to determine tense? Or used for further emphasis or for another function? Does it have a syntactic function? Morphologically, could it be used in other forms than the past? In addition, Arab Grammarians discussed the possibility of using kana to locate itself in between the syntactic constructs of a sentence, a phrase, or a collocation. Others questioned its position whether it is in initial or final. This study found out that the redundant kana (was) is cited in Quran and was used by the Arabs in their speech and poetry. This redundant kana, whether used in initial position or in a final position, or in between the constructs of a sentence, a phrase, or a collocation, implies pragmatic meanings intended by the speaker or the poet to serve different functions, such as to indicate the past tense, to provide emphasis, and to refer to the continuity of the effect and meaning of a verb or adjective. The study concludes that this verb kana can be utilized in different contexts to achieve a specific effect as did the old Arabs who used it to add specific shades of meanings. Kana as a redundant word could be added to further highlight the meaning aimed at in a specific utterance. In addition, this verb can be used in both the past and the present morphological form; and its availability in an utterance could be functional and could not be. In other words, the study found out that the redundant kana can be used in various positions in an utterance, initial, final, or in between a syntactic structure, provided that this use is pragmatically functional. In conclusion, this paper seeks to invite the scholars of the Arabic language to coin a new term which is the “pragmatic kana” to replace the term “kana alzae’da (redundant kana)” which might mean that its use is redundant and void of significance – a fact that is illogical due to its recurrent use in the Holy Quran. NOTE: Please take this study not the other one (sent by mistake) and titled kana alnaqisa

Keywords: redundan, kana, grammarians, quran

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Authors: Janaina Camile Pasqual Lofhagen, David Savarese, Veronika Vazhnik

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The urgency of the climate crisis requires both innovation and practicality. The energy transition framework allows industry to deliver resilient cities, enhance adaptability to change, pursue energy objectives such as growth or efficiencies, and increase renewable energy. This paper investigates a real-world application perspective for the use of biogas in Brazil and the U.S.. It will examine interventions to provide a foundation of infrastructure, as well as the tangible benefits for policy-makers crafting law and providing incentives.

Keywords: resilience, vulnerability, risks, biogas, sustainability.

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Authors: Shuaili Ji

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The correct use of verbs is an important element of high-quality research articles, and thus for Chinese EFL learners, it is significant to master characteristics of verbs and to precisely use verbs. However, some researches have shown that there are differences in using verbs between learners and native speakers and learners have difficulty in using English verbs. This corpus-based quantitative research can enhance learners’ knowledge of English verbs and promote the quality of research article abstracts even of the whole academic writing. The aim of this study is to find the differences between learners’ and native speakers’ use of verbs and to study the factors that contribute to those differences. To this end, the research question is as follows: What are the differences between most frequently used verbs by learners and those by native speakers? The research question is answered through a study that uses corpus-based data-driven approach to analyze the verbs used by learners in their abstract writings in terms of collocation, colligation and semantic prosody. The results show that: (1) EFL learners obviously overused ‘be, can, find, make’ and underused ‘investigate, examine, may’. As to modal verbs, learners obviously overused ‘can’ while underused ‘may’. (2) Learners obviously overused ‘we find + object clauses’ while underused ‘nouns (results, findings, data) + suggest/indicate/reveal + object clauses’ when expressing research results. (3) Learners tended to transfer the collocation, colligation and semantic prosody of shǐ and zuò to make. (4) Learners obviously overused ‘BE+V-ed’ and used BE as the main verb. They also obviously overused the basic forms of BE such as be, is, are, while obviously underused its inflections (was, were). These results manifested learners’ lack of accuracy and idiomatic property in verb usage. Due to the influence of the concept transfer of Chinese, the verbs in learners’ abstracts showed obvious transfer of mother language. In addition, learners have not fully mastered the use of verbs, avoiding using complex colligations to prevent errors. Based on these findings, the present study has implications for English teaching, seeking to have implications for English academic abstract writing in China. Further research could be undertaken to study the use of verbs in the whole dissertation to find out whether the characteristic of the verbs in abstracts can apply in the whole dissertation or not.

Keywords: academic writing abstracts, Chinese EFL learners, corpus-based, data-driven, verbs

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Authors: Asabe Ahmad Tijani, Y. A. Yahaya

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The paper considers the derivation of implicit Adams-Moulton type method, with k=4 and 5. We adopted the method of interpolation and collocation of power series approximation to generate the continuous formula which was evaluated at off-grid and some grid points within the step length to generate the proposed block schemes, the schemes were investigated and found to be consistent and zero stable. Finally, the methods were tested with numerical experiments to ascertain their level of accuracy.

Keywords: Adam-Moulton Type (AMT), off-grid, block method, consistent and zero stable

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Authors: Fatima Muhammad Shitu

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In language learning, Second language learners like their native speaker counter parts, commit errors in their attempt to achieve competence in the target language. The realm of Collocation has to do with meaning relation between lexical items. In all human language, there is a kind of ‘natural order’ in which words are arranged or relate to one another in sentences so much so that when a word occurs in a given context, the related or naturally co -occurring word will automatically come to the mind. It becomes an error, therefore, if students inappropriately pair or arrange such ‘naturally’ co – occurring lexical items in a text. It has been observed that most of the second language learners in this research group commit collocational errors. A study of this kind is very significant as it gives insight into the kinds of errors committed by learners. This will help the language teacher to be able to identify the sources and causes of such errors as well as correct them thereby guiding, helping and leading the learners towards achieving some level of competence in the language. The aim of the study is to understand the nature of these errors as stumbling blocks to effective essay writing. The objective of the study is to identify the errors, analyse their structural compositions so as to determine whether there are similarities between students in this regard and to find out whether there are patterns to these kinds of errors which will enable the researcher to understand their sources and causes. As a descriptive research, the researcher samples some nine hundred essays collected from three hundred undergraduate learners of English as a second language in the Federal College of Education, Kano, North- West Nigeria, i.e. three essays per each student. The essays which were given on three different lecture times were of similar thematic preoccupations (i.e. same topics) and length (i.e. same number of words). The essays were written during the lecture hour at three different lecture occasions. The errors were identified in a systematic manner whereby errors so identified were recorded only once even if they occur severally in students’ essays. The data was collated using percentages in which the identified number of occurrences were converted accordingly in percentages. The findings from the study indicates that there are similarities as well as regular and repeated errors which provided a pattern. Based on the pattern identified, the conclusion is that students’ collocational errors are attributable to poor teaching and learning which resulted in wrong generalisation of rules.

Keywords: collocations, errors, second language learning, ESL students

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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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: Gennady M. Kulikov, Svetlana V. Plotnikova

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This paper focuses on implementation of the sampling surfaces (SaS) method for the three-dimensional (3D) stress analysis of functionally graded (FG) laminated elastic and piezoelectric shells. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the electric potentials and displacements of these surfaces as basic shell variables. Such choice of unknowns permits the presentation of the proposed FG piezoelectric shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that improves the convergence of the SaS method significantly. As a result, the SaS formulation can be applied efficiently to 3D solutions for FG piezoelectric laminated shells, which asymptotically approach the exact solutions of piezoelectricity as the number of SaS In goes to infinity.

Keywords: electroelasticity, functionally graded material, laminated piezoelectric shell, sampling surfaces method

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Authors: Raja Rajeswari K

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Orthogonal Frequency Division Multiplexing (OFDM), a multi Carrier transmission technique that has been used in implementing the majority of wireless applications like Wireless Network Protocol Standards (like IEEE 802.11a, IEEE 802.11n), in telecommunications (like LTE, LTE-Advanced) and also in Digital Audio & Video Broadcast standards. The latest research and development in the area of orthogonal frequency division multiplexing, Universal Filtered Multi Carrier (UFMC) & Filtered OFDM (F-OFDM) has attracted lots of attention for wideband wireless communications. In this paper UFMC & F-OFDM system are implemented and comparative analysis are carried out in terms of M-ary QAM modulation scheme over Dolph-chebyshev filter & rectangular window filter and to estimate Bit Error Rate (BER) over Rayleigh fading channel.

Keywords: UFMC, F-OFDM, BER, M-ary QAM

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Authors: Martina Katalin Szabó, István Üveges

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In this paper, the usage of negative emotive words is examined on the basis of a large Hungarian twitter-database via NLP methods. The data is analysed from a gender point of view, as well as changes in language usage over time. The term negative emotive word refers to those words that, on their own, without context, have semantic content that can be associated with negative emotion, but in particular cases, they may function as intensifiers (e.g. rohadt jó ’damn good’) or a sentiment expression with positive polarity despite their negative prior polarity (e.g. brutális, ahogy ez a férfi rajzol ’it’s awesome (lit. brutal) how this guy draws’. Based on the findings of several authors, the same phenomenon can be found in other languages, so it is probably a language-independent feature. For the recent analysis, 67783 tweets were collected: 37818 tweets (19580 tweets written by females and 18238 tweets written by males) in 2016 and 48344 (18379 tweets written by females and 29965 tweets written by males) in 2021. The goal of the research was to make up two datasets comparable from the viewpoint of semantic changes, as well as from gender specificities. An exhaustive lexicon of Hungarian negative emotive intensifiers was also compiled (containing 214 words). After basic preprocessing steps, tweets were processed by ‘magyarlanc’, a toolkit is written in JAVA for the linguistic processing of Hungarian texts. Then, the frequency and collocation features of all these words in our corpus were automatically analyzed (via the analysis of parts-of-speech and sentiment values of the co-occurring words). Finally, the results of all four subcorpora were compared. Here some of the main outcomes of our analyses are provided: There are almost four times fewer cases in the male corpus compared to the female corpus when the negative emotive intensifier modified a negative polarity word in the tweet (e.g., damn bad). At the same time, male authors used these intensifiers more frequently, modifying a positive polarity or a neutral word (e.g., damn good and damn big). Results also pointed out that, in contrast to female authors, male authors used these words much more frequently as a positive polarity word as well (e.g., brutális, ahogy ez a férfi rajzol ’it’s awesome (lit. brutal) how this guy draws’). We also observed that male authors use significantly fewer types of emotive intensifiers than female authors, and the frequency proportion of the words is more balanced in the female corpus. As for changes in language usage over time, some notable differences in the frequency and collocation features of the words examined were identified: some of the words collocate with more positive words in the 2nd subcorpora than in the 1st, which points to the semantic change of these words over time.

Keywords: gender differences, negative emotive words, semantic changes over time, twitter

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Authors: Sobia Rana

Abstract:

The study intends to explain the problems of English collocational use faced by college students in Rawalpindi, Pakistan and recommends some authentic ways that will help in removing the learning barriers in light of the concerning methodological issues. It will not only help the students to improve their knowledge of the phenomena but will also enlighten the target teachers about the significance of authentic collocational use and how it naturalizes both written and spoken expressions. Data from both the students and teachers have been collected with the help of open/close-ended questionnaires to unearth the genuine cause/s and supplement them with the required solutions rooted in the actual problems. The students fail to use authentic collocations owing to multiple reasons: lack of awareness about English collocational use, improper teaching methodologies, and inexpert teachers.

Keywords: English collocational use, teaching methodologies, English learning barriers, vocabulary acquisition, college students of Rawalpindi

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

Abstract:

This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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Authors: Aichun Feng, Zhi-Min Chen, Jing Tang Xing

Abstract:

A two-dimensional linear wave-body interaction problem can be solved using a desingularized integral method by placing free surface Rankine sources over calm water surface and satisfying boundary conditions at prescribed collocation points on the calm water surface. A new free-surface Rankine source distribution scheme, determined by the intersection points of free surface and body surface, is developed to reduce numerical computation cost. Associated with this, a new treatment is given to the intersection point. The present scheme results are in good agreement with traditional numerical results and measurements.

Keywords: source point distribution, panel method, Rankine source, desingularized algorithm

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