Search results for: thread lift method

Authors: David C. Ni

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The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: general relativity, quantum mechanics, string theory, duality, symmetry, correspondence, algebra, momentum-angular-momentum

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Authors: Dingyang Hu, Dan Liu

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DNN (Deep Neural Network) deep learning models are widely used in classification, prediction, and other task scenarios. To address the difficulties of generic adversarial perturbation generation for deep learning models under black-box conditions, a generic adversarial ingestion generation method based on a saliency map (CJsp) is proposed to obtain salient image regions by counting the factors that influence the input features of an image on the output results. This method can be understood as a saliency map attack algorithm to obtain false classification results by reducing the weights of salient feature points. Experiments also demonstrate that this method can obtain a high success rate of migration attacks and is a batch adversarial sample generation method.

Keywords: adversarial sample, gradient, probability, black box

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Authors: Nizar Tayem, AbuMuhammad Moinuddeen, Ahmed A. Hussain, Redha M. Radaydeh

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This research paper introduces an approach for estimating the direction of arrival (DOA) of multiple RF noncoherent sources in a uniform linear array (ULA). The proposed method utilizes a Capon-like estimation algorithm and incorporates LU decomposition to enhance the accuracy of DOA estimation while significantly reducing computational complexity compared to existing methods like the Capon method. Notably, the proposed method does not require prior knowledge of the number of sources. To validate its effectiveness, the proposed method undergoes validation through both software simulations and practical experimentation on a prototype testbed constructed using a software-defined radio (SDR) platform and GNU Radio software. The results obtained from MATLAB simulations and real-time experiments provide compelling evidence of the proposed method's efficacy.

Keywords: DOA estimation, real-time validation, software defined radio, computational complexity, Capon's method, GNU radio

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Authors: Young Hee Geum

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We propose the numerical method defined by xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N, and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: asymptotic error constant, iterative method, multiple root, root-finding

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Authors: Marcin Sowa

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The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions.

Keywords: numerical method, SubIval, fractional calculus, numerical solver, circuit analysis

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

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

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Aymen Laadhari

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We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framework and the membrane motion is tracked using the level set method. The resulting nonlinear problem is solved by a Newton-Raphson strategy, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the proposed method. We show that stability is maintained for significantly larger time steps with respect to an explicit decoupling method.

Keywords: finite element method, level set, Newton, membrane

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Authors: Atilla Bayram

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This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: computed force method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss

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Authors: Yael Dubinsky, Orit Hazzan

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There is a constant need for hi-tech innovation to be decentralized to peripheral regions. This work describes how we applied design science research (DSR) principles to define what we refer to as the Sea of Galilee (SoG) method. The goal of the SoG method is to harness existing and new technological initiatives in peripheral regions to create a socio-technological network that can initiate and maintain hi-tech activities. The SoG method consists of a set of principles, a stakeholder network, and actual hi-tech business initiatives, including their infrastructure and practices. The three cycles of DSR, the Relevance, Design, and Rigor cycles, layout a research framework to sharpen the requirements, collect data from case studies, and iteratively refine the SoG method based on the existing knowledge base. We propose that the SoG method can be deployed by regional authorities that wish to be considered smart regions (an extension of the notion of smart cities).

Keywords: design science research, socio-technological initiatives, Sea of Galilee method, periphery stakeholder network, hi-tech initiatieves

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Authors: M. S. Annie Christi

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Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Keywords: best candidate method, centroid ranking technique, fuzzy transportation problem, robust ranking technique, transportation problem

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Authors: Blanco T. F., Fernández-López A.

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Nowadays, education, motivated by the new demands of the 21st century, acquires a dimension that converts the skills that new generations may need into a huge and uncertain set of knowledge too broad to be entirety covered. Within this set, and as tools to reach them, we find Learning and Knowledge Technologies (LKT). Thus, in order to prepare students for an everchanging society in which the technological boom involves everything, it is essential to develop digital competence. Nevertheless LKT seems not to have found their place in the educational system. This work is aimed to go a step further in the research of the most appropriate procedures and resources for technological integration in the classroom. The main objective of this exploratory study is to analyze the didactic suitability (epistemic, cognitive, affective, interactional, mediational and ecological) for teaching and learning processes of mathematics with robotics and 3D printing. The analysis carried out is drawn from a STEAM (Science, Technology, Engineering, Art and Mathematics) project that has the Pilgrimage way to Santiago de Compostela as a common thread. The sample is made up of 25 Primary Education students (10 and 11 years old). A qualitative design research methodology has been followed, the sessions have been distributed according to the type of technology applied. Robotics has been focused towards learning two-dimensional mathematical notions while 3D design and printing have been oriented towards three-dimensional concepts. The data collection instruments used are evaluation rubrics, recordings, field notebooks and participant observation. Indicators of didactic suitability proposed by Godino (2013) have been used for the analysis of the data. In general, the results show a medium-high level of didactic suitability. Above these, a high mediational and cognitive suitability stands out, which led to a better understanding of the positions and relationships of three-dimensional bodies in space and the concept of angle. With regard to the other indicators of the didactic suitability, it should be noted that the interactional suitability would require more attention and the affective suitability a deeper study. In conclusion, the research has revealed great expectations around the combination of teaching-learning processes of mathematics and LKT. Although there is still a long way to go in terms of the provision of means and teacher training.

Keywords: 3D printing, didactic suitability, educational design, robotics

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Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Nopsarun Vannasirikul

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The purposes of this research paper were to study the current situations of community development, women’s potentials, women’s participation, network, and government policy as well as to study the factors influencing women’s potentials, women’s participation, network, and government policy that have on the community development. The population included the women age of 18 years old who were living in the communities of Bangkok areas. This study was a mix research method of quantitative and qualitative method. A simple random sampling method was utilized to obtain 400 sample groups from 50 districts of Bangkok and to perform data collection by using questionnaire. Also, a purposive sampling method was utilized to obtain 12 informants for an in-depth interview to gain an in-sight information for quantitative method.

Keywords: community development, participation, network, women’s right, management

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Authors: Andrey V. Timofeev

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A method is proposed for stable detection of seismoacoustic sources in C-OTDR systems that guarantee given upper bounds for probabilities of type I and type II errors. Properties of the proposed method are rigorously proved. The results of practical applications of the proposed method in a real C-OTDR-system are presented in this.

Keywords: guaranteed detection, C-OTDR systems, change point, interval estimation

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Authors: W. S. Lawal, T. A. Akande

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Four (4) different methods were employed to detoxified jatropha caucas, they are physical method (if include soaking and drying) chemical method (use of methylated spirit, hexane and methene) biological method,(use of Aspergillus niger and Sunday for 7 days and then baccillus lichifarming) and finally combined method (combination of all these methods). Phobol esther andysis was carried out after the detoxification and was found that combined method is better off (P>0.05). 100 broiler birds was used to further test the effect of detoxified Jatropha by combined method, 50 birds for Jatropha made feed at 10 birds per treatment and was replicated five times, this was also repeated for another 50 birds fed conventional feed, Jatropha made feed was compranded at 8% inclusion level. At the end of the 8th weeks, 8 birds were sacrificed each from each treatment and one bird each was fry, roast, boil and grilled from both conventional and Jatropha fed birds and panelist were served for evaluation. It was found that feeding Jatropha to poultry birds has no effect on the taste of the meat.

Keywords: phobol esther, inclusion level, tolerance level, Jatropha carcass

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Authors: Kuo-Teng Tsai, You-Min Huang

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In this study, the problem of a spiral fin with a period base temperature is analyzed by using the Adomian decomposition method. The Adomian decomposition method is a useful and practice method to solve the nonlinear energy equation which are associated with the heat radiation. The period base temperature is around a mean value. The results including the temperature distribution and the heat flux from the spiral fin base can be calculated directly. The results also discussed the effects of the dimensionless variables for the temperature variations and the total energy transferred from the spiral fin base.

Keywords: spiral fin, period, adomian decomposition method, nonlinear

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Authors: Bogusław Schreyer

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The paper enquires on the two methods of the wheeled robot braking torque control. Those two methods are applied when the adhesion coefficient under left side wheels is different from the adhesion coefficient under the right side wheels. In case of the select-low (SL) method the braking torque on both wheels is controlled by the signals originating from the wheels on the side of the lower adhesion. In the select-high (SH) method the torque is controlled by the signals originating from the wheels on the side of the higher adhesion. The SL method is securing stable and secure robot behaviors during the braking process. However, the efficiency of this method is relatively low. The SH method is more efficient in terms of time and braking distance but in some situations may cause wheels blocking. It is important to monitor the velocity of all wheels and then take a decision about the braking torque distribution accordingly. In case of the SH method the braking torque slope may require significant decrease in order to avoid wheel blocking.

Keywords: select-high, select-low, torque distribution, wheeled robots

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Authors: Allen A. Espinosa, Larkins A. Trinidad

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The present study investigated collegiate students’ problem solving strategies and misconceptions in solving stoichiometric problems and later on formulate a teaching framework from the result of the study. The study found out that the most prominent strategies among students are the mole method and the proportionality method, which are both algorithmic by nature. Misconception was also noted as some students rely on Avogadro’s number in converting between moles. It is suggested therefore that the teaching of stoichiometry should not be confined to demonstration. Students should be involved in the process of thinking of ways to solve the problem.

Keywords: stoichiometry, Svogadro’s number, mole method, proportionality method

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Authors: M. A. Sedghamiz, S. Raeissi

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This study presents three different approaches to estimate bubble point pressures for the binary system of CO2 and ethyl palmitate fatty acid ethyl ester. The first method involves the Peng-Robinson (PR) Equation of State (EoS) with the conventional mixing rule of Van der Waals. The second approach involves the PR EOS together with the Wong Sandler (WS) mixing rule, coupled with the Uniquac Ge model. In order to model the bubble point pressures with this approach, the volume and area parameter for ethyl palmitate were estimated by the Hansen group contribution method. The last method involved the Peng-Robinson, combined with the Wong-Sandler Method, but using NRTL as the GE model. Results using the Van der Waals mixing rule clearly indicated that this method has the largest errors among all three methods, with errors in the range of 3.96–6.22 %. The Pr-Ws-Uniquac method exhibited small errors, with average absolute deviations between 0.95 to 1.97 percent. The Pr-Ws-Nrtl method led to the least errors where average absolute deviations ranged between 0.65-1.7%.

Keywords: bubble pressure, Gibbs excess energy model, mixing rule, CO2 solubility, ethyl palmitate

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Authors: Gianna Zou

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Propensity score matching (PSM), introduced by Paul R. Rosenbaum and Donald Rubin in 1983, is a popular statistical matching technique which tries to estimate the treatment effects by taking into account covariates that could impact the efficacy of study medication in clinical trials. PSM can be used to reduce the bias due to confounding variables. However, PSM assumes that the response values are normally distributed. In some cases, this assumption may not be held. In this paper, a machine learning method - Bayesian Additive Regression Tree (BART), is used as a more robust method of matching. BART can work well when models are misspecified since it can be used to model heterogeneous treatment effects. Moreover, it has the capability to handle non-linear main effects and multiway interactions. In this research, a BART Matching Method (BMM) is proposed to provide a more reliable matching method over PSM. By comparing the analysis results from PSM and BMM, BMM can perform well and has better prediction capability when the response values are not normally distributed.

Keywords: BART, Bayesian, matching, regression

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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: Sendi Zohra, Belhadjsalah Hedi, Labergere Carl, Saanouni Khemais

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The modeling of mechanical problems including both material and geometric nonlinearities with Finite Element Method (FEM) remains challenging. Meshless methods offer special properties to get rid of well-known drawbacks of the FEM. The main objective of Meshless Methods is to eliminate the difficulty of meshing and remeshing the entire structure by simply insertion or deletion of nodes, and alleviate other problems associated with the FEM, such as element distortion, locking and others. In this study, a robust numerical implementation of an Element Free Galerkin Method for an elastoplastic coupled to damage problem is presented. Several results issued from the numerical simulations by a DynamicExplicit resolution scheme are analyzed and critically compared with Element Finite Method results. Finally, different numerical examples are carried out to demonstrate the efficiency of this method.

Keywords: damage, dynamic explicit, elastoplasticity, isotropic hardening, meshless

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Authors: Safia Hocine, Zina Benouaret, Djamil A¨ıssani

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In this paper, we study the performance of the strong stability method of the univariate classical risk model. We interest to the stability bounds established using two approaches. The first based on the strong stability method developed for a general Markov chains. The second approach based on the regenerative processes theory . By adopting an algorithmic procedure, we study the performance of the stability method in the case of exponential distribution claim amounts. After presenting numerically and graphically the stability bounds, an interpretation and comparison of the results have been done.

Keywords: Marcov chain, regenerative process, risk model, ruin probability, strong stability

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Authors: Michaela Vašková

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The paper is focused on the application of the security audit method on the selected objects of the critical infrastructure. The emphasis is put on security audit method to find gaps in the critical infrastructure security. The theoretical part describes objects of the critical infrastructure. The practical part describes using the security audit method. The main emphasis was put on the protection of the critical infrastructure in the Czech Republic.

Keywords: crisis management, critical infrastructure, object of critical infrastructure, security audit, extraordinary event

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The aim of this paper is to examine the behavior of elastic stability of reinforced and composite concrete struts with axial loads. The objective of this study is to verify the ability of the Modified Newmark Method to include geometric non-linearity in addition to non-linearity due to cracking, and also to show the advantage of the established method to reconsider an ignored minor parameter in mathematical modeling, such as the effect of the cracking by extra geometric bending moment Ny on cross-section properties. The purpose of this investigation is not to present some new results for the instability of reinforced or composite concrete columns. Therefore, no kinds of non-linearity involved in the problem are considered here. Only as mentioned, it is a part of the verification of the new established method to solve two kinds of non-linearity P- δ effect and cracking together simultaneously. However, the Modified Newmark Method can be used to solve non-linearity of materials and time-dependent behavior of concrete. However, since it is out of the scope of this article, it is not considered.

Keywords: stability, buckling, modified newmark method, reinforced

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Authors: Zhai Yuan, Wu Xueqing

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This article statistics the technology which used by Chinese and foreign excellent players in the game, including types and serves areas,receive technology and effect and utilization ratio receiving and losing points. The sample is che videos which is world's top matches of excellent badminton athletes of che single, including Chinese players’ 43 games and foreign players’ 38 games. Conclusion: For the serving, Chinese and foreign single players are to give priority to forehand short-low serve and the long-high serve. And Chinese and foreign players in using forehand short-low serve and drive server exist significant differences; For the serves areas, Chinese and foreign players serve area is concentrated in area 1,5,6. Area 6 has the highest rate of all the district areas, following by the area 1and area 5. Among the 2ed serve area Sino-foreign player, there exist significant differences; In the receiver, when returning the frontcourt shutter, players is given priority to net lift and push. When returning the backcourt shutter, receiver's the best ball is smash, followed by clear and drop shot. Foreign players have higher utilization rate in smash than Chinese players in the backcourt; In the receiver result, Chinese players give priority to actively and equally situation than foreign players, but in negatively receiving is just opposite.

Keywords: badminton, woman’s singles, technique and tactics, comparative analysis

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Authors: Bulcha Belay Etana

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Electromyography is used to measure the electrical activity of muscles for various health monitoring applications using surface electrodes or needle electrodes. Recent developments in electromyogram signal acquisition using textile electrodes open the door for wearable health monitoring which enables patients to monitor and control their health issues outside of traditional healthcare facilities. The aim of this research is therefore to develop and analyze wearable textile electrodes for the acquisition of electromyography signals for Parkinson’s patients and apply an appropriate thermal stimulus to relieve muscle cramping. In order to achieve this, textile electrodes are sewn with a silver-coated thread in an overlapping zigzag pattern into an inextensible fabric, and stainless steel knitted textile electrodes attached to a sleeve were prepared and its electrical characteristics including signal to noise ratio were compared with traditional electrodes. To relieve muscle cramping, a heating element using stainless steel conductive yarn Sewn onto a cotton fabric, coupled with a vibration system were developed. The system was integrated using a microcontroller and a Myoware muscle sensor so that when muscle cramping occurs, measured by the system activates the heating elements and vibration motors. The optimum temperature considered for treatment was 35.50c, so a Temperature measurement system was incorporated to deactivate the heating system when the temperature reaches this threshold, and the signals indicating muscle cramping have subsided. The textile electrode exhibited a signal to noise ratio of 6.38dB while the signal to noise ratio of the traditional electrode was 7.05dB. The rise time of the developed heating element was about 6 minutes to reach the optimum temperature using a 9volt power supply. The treatment of muscle cramping in Parkinson's patients using heat and muscle vibration simultaneously with a wearable electromyography signal acquisition system will improve patients’ livelihoods and enable better chronic pain management.

Keywords: electromyography, heating textile, vibration therapy, parkinson’s disease, wearable electronic textile

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Authors: Siti Noor Farwina Anwar, Hailiza Kamarulhaili

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In this paper, we present the idea of implementing the Integer Sub-Decomposition (ISD) method on elliptic curves with j-invariant 1728. The ISD method was proposed in 2013 to compute scalar multiplication in elliptic curves, which remains to be the most expensive operation in Elliptic Curve Cryptography (ECC). However, the original ISD method only works on integer number field and solve integer scalar multiplication. By extending the method into the complex quadratic field, we are able to solve complex multiplication and implement the ISD method on elliptic curves with j-invariant 1728. The curve with j-invariant 1728 has a unique discriminant of the imaginary quadratic field. This unique discriminant of quadratic field yields a unique efficiently computable endomorphism, which later able to speed up the computations on this curve. However, the ISD method needs three endomorphisms to be accomplished. Hence, we choose all three endomorphisms to be from the same imaginary quadratic field as the curve itself, where the first endomorphism is the unique endomorphism yield from the discriminant of the imaginary quadratic field.

Keywords: efficiently computable endomorphism, elliptic scalar multiplication, j-invariant 1728, quadratic field

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Authors: Robert Ogbanje Okwori

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The research studied expository and simulation method of teaching woodwork at Federal University of Technology, Minna, Niger State, Nigeria. The purpose of the study was to compare expository and simulation method of teaching woodwork and determine the method that is more effective in improving performance of students in woodwork. Two research questions and two hypotheses were formulated to guide the study. Fifteen objective questions and two theory questions were used for data collection. The questions set were on structure of timber. The study used the quasi experimental design. The population of the study consisted of 25 woodwork students of Federal University of Technology, Minna, Niger State, Nigeria and three hundred (300) level students were used for the study. The lesson plans for expository method and questions were validated by three lecturers in the Department of Industrial and Technology Education, Federal University of Technology, Minna, Nigeria. The validators checked the appropriates of test items and all the corrections and inputs were effected before administration of the instrument. Data obtained were analyzed using mean, standard deviation and t-test statistical tool. The null hypotheses were formulated and tested using t-test statistics at 0.05 level of significance. The findings of the study showed that simulation method of teaching has improved students’ performance in woodwork and the performance of the students was not influenced by gender. Based on the findings of the study, it was concluded that there was a significant difference in the mean achievement scores of students taught woodwork using simulation method. This implies that simulation method is more effective than expository method of teaching woodwork. Therefore, woodwork teachers should adopt simulation method of teaching woodwork towards better performance. It was recommended that simulation method should be used by woodwork lecturers to teach woodwork since students perform better using the method and also the teachers needs to be trained and re-trained in using simulation method for teaching woodwork. Teachers should be encouraged to use simulation method for their instructional delivery because it will allow them to identify their areas of strength and weakness when imparting knowledge to woodwork students. Government and different agencies should assist in procuring materials and equipment for wood workshops to enable students effectively practice what they have been taught using simulation method.

Keywords: comparative, expository, simulation, woodwork

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