Search results for: complement order

Authors: Mahdi Shamsi, Tohid Yousefi Rezaii, Siavash Eftekharifar

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Compressed sensing (CS) is a new powerful mathematical theory concentrating on sparse signals which is widely used in signal processing. The main idea is to sense sparse signals by far fewer measurements than the Nyquist sampling rate, but the reconstruction process becomes nonlinear and more complicated. Common dilemma in sparse signal recovery in CS is the lack of knowledge about sparsity order of the signal, which can be viewed as model order selection procedure. In this paper, we address the problem of sparsity order estimation in sparse signal recovery. This is of main interest in situations where the signal sparsity is unknown or the signal to be recovered is approximately sparse. It is shown that the proposed method also leads to some kind of signal denoising, where the observations are contaminated with noise. Finally, the performance of the proposed approach is evaluated in different scenarios and compared to an existing method, which shows the effectiveness of the proposed method in terms of order selection as well as denoising.

Keywords: compressed sensing, data denoising, model order selection, sparse representation

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Authors: Herbert Ntuli, Edwin Muchapondwa

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This study used a sample of 336 households and community level data from 30 communities around the Gonarezhou National Park in Zimbabwe to analyse the association between ability to self-organize or cooperation and institutions on one hand and the relationship between success of biodiversity outcomes and cooperation on the other hand. Using both the ordinary least squares and instrumental variables estimation with heteroskedasticity-based instruments, our results confirmed that sound institutions are indeed an important ingredient for cooperation in the respective communities and cooperation positively and significantly affects biodiversity outcomes. Group size, community level trust, the number of stakeholders and punishment were found to be important variables explaining cooperation. From a policy perspective, our results show that external enforcement of rules and regulations does not necessarily translate into sound ecological outcomes but better outcomes are attainable when punishment is rather endogenized by local communities. This seems to suggest that communities should rather be supported in such a way that robust institutions that are tailor made to suit the needs of local condition will emerge that will in turn facilitate good environmental husbandry. Cooperation, training, benefits, distance from the nearest urban canter, distance from the fence, social capital average age of household head, fence and information sharing were found to be very important variables explaining the success of biodiversity outcomes ceteris paribus. Government programmes should target capacity building in terms of institutional capacity and skills development in order to have a positive impact on biodiversity. Hence, the role of stakeholders (e.g., NGOs) in capacity building and government effort should complement each other to ensure that the necessary resources are mobilized and all communities receive the necessary training and resources.

Keywords: institutions, self-organize, common pool resources, wildlife, conservation, Zimbabwe

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Sonto Maputle

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Background: Support during labour increase women's chances of having positive childbirth experiences as well as childbirth outcomes. The purpose of this study was to determine the support provided by midwives to women during labour at the public hospital in Limpopo Province. The study was conducted at the Tertiary hospital in Limpopo Province. Methods: A qualitative, participant observation approach was used. Population consisted of all women that were admitted to deliver their babies and the midwives who provided midwifery care in the obstetric unit of one tertiary public hospital in Limpopo Province. Non-probability, purposive and convenience sampling were used to sample 24 women and 12 midwives. Data were collected through participant observations which included unstructured conversations with the use of observational guide, field notes of events and conversations that occurred when women interact with midwives were recorded verbatim and a Visual Analog Scale to complement the observations. Data was analysed qualitatively but were presented in the tables and bar graphs. Results: Five themes emerged as support provided by midwives during labour, namely; communication between women and midwives, informational support, emotional support activities, interpretation of the experienced labour pain and supportive care activities during labour. Conclusion: The communication was occurring when the midwife was rendering midwifery care and very limited for empowering. The information sharing focused on the assistive actions rather than on the activities that would promote mothers’ participation. The emotional support activities indicated lack of respect and disregard cultural preferences and this contributed to inability to exercise choices in decision-making. The study recommended the implementation of Batho Pele principles in order to provide woman-centred care during labour.

Keywords: communication between women and midwives, labour pains, informational and emotional support, physical comforting measures

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Authors: María-Dolores Olvera-Lobo, Bryan John Robinson, Juncal Gutierrez-Artacho

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Graduates are equipped with a wide range of generic competencies which complement solid curricular competencies and facilitate their access to the labour market in diverse fields and careers. However, some generic competencies such as instrumental, personal and systemic competencies related to teamwork and interpersonal communication skills, decision-making and organization skills are seldom taught explicitly and even less often assessed. In this context, translator training has embraced a broad range of competencies specified in the undergraduate program currently taught at universities and opens up the learning experience to cover areas often ignored due to the difficulties inherent in both teaching and assessment. In practice, translator training combines two well-established approaches to teaching/learning: project-based learning and genuinely cooperative – or merely collaborative – learning. Our professional approach to translator training is a model focused on and adapted to the teleworking context of professional translation and presented through the medium of blended e-learning. Teamwork-related competencies are extremely relevant, and they require explicit and implicit teaching so that graduates can be confident about their capacity to make their way in professional contexts. In order to highlight the importance of teamwork and intra-team relationships beyond the classroom, we aim to raise awareness of teamwork processes so as to empower translation students in managing their interaction and ensure that they gain valuable pre-professional experience. With these objectives, at the University of Granada (Spain) we have developed a range of classroom activities and assessment tools. The results of their application are summarized in this study.

Keywords: blended learning, collaborative teamwork, cross-curricular competencies, higher education, intra-team relationships, students’ perceptions, translator training

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: George Hadjinicola, Andreas Soteriou

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This paper examines the relationship between the number of price promotions that a firm should conduct per year and the level of safety stocks that the firm should maintain. Price promotions result in temporary sales increases, which affect the operations function through (1) an increase in the quantities demanded and (2) an increase in safety stocks required to maintain the desired service level. We propose a modeling framework where both price promotions and improved service levels, operationalized through higher safety stocks, can affect sales. We treat the annual number of promotions as a decision variable. We identify market conditions where the operations function, through improved safety stocks, can complement price promotions or even play the leading role in sales increases.

Keywords: price promotions, safety stocks, marketing/operations interface, mathematical model

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

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Authors: L. C. Ansanelli, P. Alfredini

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The article presents the evaluation of the effectiveness of two groins located at Gonzaguinha and Milionários Beaches, situated on the southeast coast of Brazil. The effectiveness of these coastal defense structures is evaluated in terms of sedimentary dynamics, which is one of the most important environmental processes to be assessed in coastal engineering studies. The applied method is based on the implementation of the Delft3D numerical model system tools. Delft3D-WAVE module was used for waves modelling, Delft3D-FLOW for hydrodynamic modelling and Delft3D-SED for sediment transport modelling. The calibration of the models was carried out in a way that the simulations adequately represent the region studied, evaluating improvements in the model elements with the use of statistical comparisons of similarity between the results and waves, currents and tides data recorded in the study area. Analysis of the maximum wave heights was carried to select the months with higher accumulated energy to implement these conditions in the engineering scenarios. The engineering studies were performed for two scenarios: 1) numerical simulation of the area considering only the two existing groins; 2) conception of breakwaters coupled at the ends of the existing groins, resulting in two “T” shaped structures. The sediment model showed that, for the simulated period, the area is affected by erosive processes and that the existing groins have little effectiveness in defending the coast in question. The implemented T structures showed some effectiveness in protecting the beaches against erosion and provided the recovery of the portion directly covered by it on the Milionários Beach. In order to complement this study, it is suggested the conception of further engineering scenarios that might recover other areas of the studied region.

Keywords: coastal engineering, coastal erosion, Sao Vicente bay, Delft3D, coastal engineering works

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Authors: Ying Yi Wu

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The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Moh'd Alodat

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In this paper, we discuss the power function distribution and derive the maximum likelihood estimator of its parameter as well as the reliability parameter. We derive the large sample properties of the estimators based on the selective order statistic scheme. We conduct simulation studies to investigate the significance of the selective order statistic scheme in our setup and to compare the efficiency of the new proposed estimators.

Keywords: fisher information, maximum likelihood estimator, power function distribution, ranked set sampling, selective order statistics sampling

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Authors: Jabulani Sibanda, Clemence Chikiwa

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This paper traces diverse language practices representative of equally diverse conceptions of language. To be dynamic with languaging practices, one needs to appreciate nuanced languaging practices, their challenges, prospects, and opportunities. The paper presents what we envision as three major conceptions of language that give impetus to diverse language practices. It examines theoretical models of the bilingual mental lexicon and how they inform language practices. The paper explores classroom languaging practices that have been promulgated and experimented with. The paper advocates the deployment of multisensory semiotic systems to complement linguistic classroom communication and the acknowledgement of learners’ linguistic and semiotic resources as valid in the learning enterprise. It recommends the enactment of specific clauses on language in education policies and curriculum documents that empower classroom interactants to exercise discretion in languaging practices.

Keywords: languaging, monolingual, multilingual, semiotic and linguistic repertoire

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, analog control

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, and analog control

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Authors: Jabulani Sibanda, Clemence Chikiwa

Abstract:

This paper traces diverse language practices representative of equally diverse conceptions of language. To be dynamic with languaging practices, one needs to appreciate nuanced languaging practices, their challenges, prospects, and opportunities. The paper presents what we envision as three major conceptions of language that give impetus to diverse language practices. It examines theoretical models of the bilingual mental lexicon and how they inform language practices. The paper explores classroom languaging practices that have been promulgated and experimented with. The paper advocates the deployment of multisensory semiotic systems to complement linguistic classroom communication and the acknowledgement of learners’ linguistic and semiotic resources as valid in the learning enterprise. It recommends the enactment of specific clauses on language in education policies and curriculum documents that empower classroom interactants to exercise discretion in languaging practices.

Keywords: languaging, monolingual, multilingual, semiotic and linguistic repertoire

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Authors: Amenador Kate Benedicta, Wang Zhiwei

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Since the later parts of the 20th century, the notion of equivalence continues to be a central and critical concept in the development of translation theory. After decades of arguments over word-for-word and free translations methods, scholars attempting to develop more systematic and efficient translation theories began to focus on fundamental translation concepts such as equivalence. Although the concept of equivalence has piqued the interest of many scholars, its definition, scope, and applicability have sparked contentious arguments within the discipline. As a result, several distinct theories and explanations on the concept of equivalence have been put forward over the last half-century. Thus, this study explores and discusses the evolution of the critical concept of equivalence in translation studies through a bibliometric method of investigation of manual and digital books and articles by analyzing different scholars' key contributions and limitations on equivalence from various theoretical perspectives. While analyzing them, emphasis is placed on the innovations that each theory has brought to the comprehension of equivalence. In order to achieve the aim of the study, the article began by discussing the contributions of linguistically motivated theories to the notion of equivalence in translation, followed by functionalist-oriented contributions, before moving on to more recent advancements in translation studies on the concept. Because equivalence is such a broad notion, it is impossible to discuss each researcher in depth. As a result, the most well-known names and their equivalent theories are compared and contrasted in this research. The study emphasizes the developmental progression in our comprehension of the equivalence concept and equivalent effect. It concluded that the various theoretical perspective's contributions to the notion of equivalence rather complement and make up for the limitations of each other. The study also highlighted how troublesome the equivalent concept might become in terms of identifying the nature of translation and how central and unavoidable the concept is in every translation action, despite its limitations. The significance of the study lies in its synthesis of the different contributions and limitations of the various theories offered by scholars on the notion of equivalence, lending literature to both student and scholars in the field, and providing insight on future theoretical development

Keywords: equivalence, functionalist translation theories, linguistic translation approaches, translation theories, Skopos

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Authors: Huei Chu Weng

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This paper presents a study on the effect of second-order slip on forced convection through a long isoflux heated or cooled planar microchannel. The fully developed solutions of flow and thermal fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and local heat flux boundary conditions. Results reveal that when the average flow velocity increases or the wall heat flux amount decreases, the role of thermal creep becomes more insignificant, while the effect of second-order slip becomes larger. The second-order term in the Deissler slip boundary condition is found to contribute a positive velocity slip and then to lead to a lower pressure drop as well as a lower temperature rise for the heated-wall case or to a higher temperature rise for the cooled-wall case. These findings are contrary to predictions made by the Karniadakis slip model.

Keywords: microfluidics, forced convection, thermal creep, second-order boundary conditions

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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: Xiaoyang Zhao, Kaiying Wang

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The choice of stocking density in poultry farming is a potential way for determining welfare level of poultry. However, it is difficult to measure stocking densities in poultry farming because of a lot of variables such as species, age and weight, feeding way, house structure and geographical location in different broiler houses. A method was proposed in this paper to measure the differences of young broilers reared under different stocking densities by sound analysis. Vocalisations of broilers were recorded and analysed under different stocking densities to identify the relationship between sounds and stocking densities. Recordings were made continuously for three-week-old chickens in order to evaluate the variation of sounds emitted by the animals at the beginning. The experimental trial was carried out in an indoor reared broiler farm; the audio recording procedures lasted for 5 days. Broilers were divided into 5 groups, stocking density treatments were 8/m², 10/m², 12/m² (96birds/pen), 14/m² and 16/m², all conditions including ventilation and feed conditions were kept same except from stocking densities in every group. The recordings and analysis of sounds of chickens were made noninvasively. Sound recordings were manually analysed and labelled using sound analysis software: GoldWave Digital Audio Editor. After sound acquisition process, the Mel Frequency Cepstrum Coefficients (MFCC) was extracted from sound data, and the Support Vector Machine (SVM) was used as an early detector and classifier. This preliminary study, conducted in an indoor reared broiler farm shows that this method can be used to classify sounds of chickens under different densities economically (only a cheap microphone and recorder can be used), the classification accuracy is 85.7%. This method can predict the optimum stocking density of broilers with the complement of animal welfare indicators, animal productive indicators and so on.

Keywords: broiler, stocking density, poultry farming, sound monitoring, Mel Frequency Cepstrum Coefficients (MFCC), Support Vector Machine (SVM)

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Authors: Sara Mota Carmo

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Nowadays, there is an increasing demand for buildings to be energetically autonomous through energy generation systems from renewable sources, according to the concept of a net zero energy building (NZEB). In this sense, the present study aims to study the integration of wind energy through piezoelectricity applied to the building skin. As a methodology, a reduced-scale prototype of a building was developed and tested in a wind tunnel, with the four façades monitored by recording the energy produced by each. The applied wind intensities varied between 2m/s and 8m/s and the four façades were compared with each other regarding the energy produced according to the intensity of wind and position in the wind. The results obtained concluded that it was not a sufficient system to generate sources to cover family residential buildings' energy needs. However, piezoelectricity is expanding and can be a promising path for a wind energy system in architecture as a complement to other renewable energy sources.

Keywords: adaptative building skin, kinetic façade, wind energy in architecture, NZEB

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Authors: Adriano Pinargote, Josue Mosquera, Eduardo Montero, Dalton Noboa, Jenny Venegas, Genesis Vasquez Escuela

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In the framework of Pre University learning of the Polytechnic School of the Litoral, Guayaquil, Ecuador, the methodology of Active Learning (Flipped Classroom) has been implemented for applicants who wish to obtain a quota within the university. To complement the Active Learning cycle, it has been proposed that the respective students influence the qualification of their work groups, for which a web platform has been created that allows them to evaluate the performance of their peers through a digital coevaluation that measures through statistical methods, the group and individual performance score that can reflect in numbers a weighting score corresponding to the grade of each student. Their feedback provided by the group help to improve the performance of the activities carried out in classes because the note reflects the commitment with their classmates shown in the class, within this analysis we will determine if this implementation directly influences the performance of the grades obtained by the student.

Keywords: active learning, coevaluation, flipped classroom, pre university

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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Authors: Brando Vagenende, Marie-Anne Guerry

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For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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Authors: Fouzi Aboura

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The fractional order proportional-integral-derivative (FOPID) controller or fractional order (PIλDµ) is a proportional-integral-derivative (PID) controller where integral order (λ) and derivative order (µ) are fractional, one of the important application of classical PID is the Automatic Voltage Regulator (AVR).The FOPID controller needs five parameters optimization while the design of conventional PID controller needs only three parameters to be optimized. In our paper we have proposed a comparison between algorithms Differential Evolution (DE) and Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) ,we have studied theirs characteristics and performance analysis to find an optimum parameters of the FOPID controller, a new objective function is also proposed to take into account the relation between the performance criteria’s.

Keywords: FOPID controller, fractional order, AVR system, objective function, optimization, GA, PSO, HGAPSO

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: S. Takaidza, M. Pillay, F. Mtunzi

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Since time immemorial, plants have been used by several communities to treat a large number of diseases. Numerous studies on the pharmacology of medicinal plants have been done. Medicinal plants constitute a potential source for the production of new medicines and may complement conventional antimicrobials and probably decrease health costs. Phytochemical compounds in plants are known to be biologically active aiding, for example, as antioxidants and antimicrobials. The overwhelming challenge of drug resistance has resulted in an increasing trend towards using medicinal plants to treat various diseases, especially in developing countries. Species of the genus Tulbaghia has been widely used in traditional medicine to treat various ailments such rheumatism, fits, fever, earache, tuberculosis etc. It is believed that the species possess several therapeutic properties. This paper evaluates some of the biological activities of the genus Tulbaghia. It is evident from current literature that T. violacea is the most promising species. The other species of Tulbaghia still require further studies to ascertain their medicinal potential.

Keywords: biological activities, antimicrobial, antioxidant, phytochemicals, tulbaghia

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Matthew C. Best

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Linear Multi-Input Multi-Output (MIMO) dynamic models can be identified, with no a priori knowledge of model structure or order, using a new Generalised Identifying Filter (GIF). Based on an Extended Kalman Filter, the new filter identifies the model iteratively, in a continuous modal canonical form, using only input and output time histories. The filter’s self-propagating state error covariance matrix allows easy determination of convergence and conditioning, and by progressively increasing model order, the best fitting reduced-order model can be identified. The method is shown to be resistant to noise and can easily be extended to identification of smoothly nonlinear systems.

Keywords: system identification, Kalman filter, linear model, MIMO, model order reduction

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