Search results for: non-linear feed-back

Authors: Flora Babongo, Valerie Chavez

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Inferring causality from observational data is one of the fundamental subjects, especially in quantitative finance. So far most of the papers analyze additive noise models with either linearity, nonlinearity or Gaussian noise. We fill in the gap by providing a nonlinear and non-gaussian causal multiplicative noise model that aims to distinguish the cause from the effect using a two steps method based on Bayesian additive models for location, scale and shape (BAMLSS) and on causal additive models (CAM). We have tested our method on simulated and real data and we reached an accuracy of 0.86 on average. As real data, we considered the causality between financial indices such as S&P 500, Nasdaq, CAC 40 and Nikkei, and companies' log-returns. Our results can be useful in inferring causality when the data is heteroskedastic or non-injective.

Keywords: causal inference, DAGs, BAMLSS, financial index

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Authors: Mohammed Sharaf, Alireza Shokri, Adrian Small, Toby Bridges

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This paper investigates digital transformation challenges in SMEs within the automotive supply chain. A case study approach and participant observation revealed significant data management and process optimization barriers, corroborated by a conceptual model. Stakeholder feedback, visualized through a pie chart, emphasized data management and process efficiency as primary concerns. Recommended strategies include implementing advanced data systems, process simplification, and enhancing digital skills. Despite the single-case study limitation, the findings offer actionable insights for SMEs to leverage Industry 4.0 technologies effectively. This research contributes to the strategic roadmap necessary for SMEs to achieve competitive digital transformation.

Keywords: automotive supply chain, digital transformation, industry 4.0

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Authors: Craig Wight

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This presentation will identify the key findings from a recent netnographic discourse analysis of social media content generated in response to visits to three iconic European Holocaust Heritage sites: Ann Frank’s House in Amsterdam, the Netherlands, the Auschwutz-Birkenau Memorial Museum and Memorial in Poland, and the Jewish Museum in Berlin, Germany. Four major discourses are identified under the headings of Holocaust heritage as social memory, reactions to Holocaust heritage, obligation and ritual, and transgressive visitor behaviour. Together, these discourses frame the values, existential anxieties, emotions, priorities, and expectations of visitors. The findings will interest those involved in the planning and management of Holocaust heritage for tourism purposes since they provide unique access to an archive of unmediated visitor feedback on European Holocaust heritage experiences.

Keywords: foucault, european holocaust heritage, discourse analysis, netnography, social media, dark tourism

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Authors: Emma Dwi Ariyani, Dini Hadiani

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This article reports the descriptive analysis of self-compassion in polytechnic students. It has been long believed that self-compassion can improve students’ motivation in completing their studies. This research was conducted with the aim to see the degree of self-compassion in polytechnic students in Indonesia by using Neff's Self-Compassion Scale (short form) measurement tool consisting of 12 items. The research method used was descriptive study with survey technique on 255 students. The results showed that 78% of students had low self-compassion and 22% had high self-compassion. This revealed that polytechnic students still criticize themselves harshly, make a poor judgment and bad self-appraisal, and they also cannot accept their imperfection and consider it as a self-judgment. The students also tend to think that they are the only ones that experience failure and suffering. This can lead to a sense of isolation (self-isolation). Furthermore, the students are often too concerned with aspects that are not liked both in themselves and in life (over-identification). Improving the students’ level of self-compassion can be done by building an educational climate that not only criticizes the students but provides feedback as well. This should focus on the students’ real behavior rather than the students’ general character.

Keywords: descriptive study, polytechnic students, Indonesia, self-compassion

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Authors: Tushar Bhardwaj

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Internet of Things (IoT) possesses a dynamic network where the network nodes (mobile devices) are added and removed constantly and randomly, hence the traffic distribution in the network is quite variable and irregular. The basic but very important part in any network is route searching. We have many conventional route searching algorithms like link-state, and distance vector algorithms but they are restricted to the static point to point network topology. In this paper we propose a model that uses the Ant Colony Algorithm for route searching. It is dynamic in nature and has positive feedback mechanism that conforms to the route searching. We have also embedded the concept of Non-Deterministic Finite Automata [NDFA] minimization to reduce the network to increase the performance. Results show that Ant Colony Algorithm gives the shortest path from the source to destination node and NDFA minimization reduces the broadcasting storm effectively.

Keywords: routing, ant colony algorithm, NDFA, IoT

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Authors: Murtala Mohammed Alamai, Abdullahi Marshal Idris, Adama Idris

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Today, marketing does not only involve selecting target markets, but it also involves communicating with the customers through various means to put across your selling point. Modern marketing involves driving new product development based on customer needs by getting feedback from them. Utilizing the latest technology for better communication with the customers is the latest advancement in Marketing in the 21st century. The survey approach was used where a sample of tourist destinations across the six geographical zones of the country at random was done to ascertain the use of information communication systems in promoting their products and or services, the findings revealed that only a few utilize these modern advanced means in marketing and promoting their products and a need to develop effective and up to date online services for marketing was proffered as solutions to the findings observed.

Keywords: information, communication, travel, trade, promotion

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Authors: Nahid Parween Anwar, Sadia Muzaffar Bhutta, Takbir Ali

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Mentoring is a structured activity which is designed to facilitate engagement between mentor and mentee to enhance mentee’s professional capability as an effective teacher. Both mentor and mentee are important elements of the ‘mentoring equation’ and play important roles in nourishing this dynamic, collaborative and reciprocal relationship. Cluster-Based Mentoring Programme (CBMP) provides an indigenous example of a project which focused on development of primary school teachers in selected clusters with a particular focus on their classroom practice. A study was designed to examine the efficacy of CBMP as part of Strengthening Teacher Education in Pakistan (STEP) project. This paper presents results of one of the components of this study. As part of the larger study, a cross-sectional survey was employed to explore nature and patterns of mentoring process from mentees’ perspectives in the selected districts of Sindh and Balochistan. This paper focuses on the results of the study related to the question: What are mentees’ perceptions of their mentors’ support for enhancing their classroom practice during mentoring process? Data were collected from mentees (n=1148) using a 5-point scale -‘Mentoring for Effective Primary Teaching’ (MEPT). MEPT focuses on seven factors of mentoring: personal attributes, pedagogical knowledge, modelling, feedback, system requirement, development and use of material, and gender equality. Data were analysed using SPSS 20. Mentees perceptions of mentoring practice of their mentors were summarized using mean and standard deviation. Results showed that mean scale scores on mentees’ perceptions of their mentors’ practices fell between 3.58 (system requirement) and 4.55 (personal attributes). Mentees’ perceives personal attribute of the mentor as the most significant factor (M=4.55) towards streamlining mentoring process by building good relationship between mentor and mentees. Furthermore, mentees have shared positive views about their mentors efforts towards promoting gender impartiality (M=4.54) during workshop and follow up visit. Contrary to this, mentees felt that more could have been done by their mentors in sharing knowledge about system requirement (e.g. school policies, national curriculum). Furthermore, some of the aspects in high scoring factors were highlighted by the mentees as areas for further improvement (e.g. assistance in timetabling, written feedback, encouragement to develop learning corners). Mentees’ perceptions of their mentors’ practices may assist in determining mentoring needs. The results may prove useful for the professional development programme for the mentors and mentees for specific mentoring programme in order to enhance practices in primary classrooms in Pakistan. Results would contribute into the body of much-needed knowledge from developing context.

Keywords: cluster-based mentoring programme, mentoring for effective primary teaching (MEPT), professional development, survey

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Authors: Ruichong Zhang

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This study proposes a recording-based approach to characterize and quantify earthquake-induced site nonlinearity, exemplified as soil nonlinearity and/or liquefaction. Alternative to Fourier spectral analysis (FSA), the paper introduces time-frequency analysis of earthquake ground motion recordings with the aid of so-called Hilbert-Huang transform (HHT), and offers justification for the HHT in addressing the nonlinear features shown in the recordings. With the use of the 2001 Nisqually earthquake recordings, this study shows that the proposed approach is effective in characterizing site nonlinearity and quantifying the influences in seismic ground responses.

Keywords: site nonlinearity, site amplification, site damping, Hilbert-Huang Transform (HHT), liquefaction, 2001 Nisqually Earthquake

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Authors: Andrey Yatsun, Andrei Malchikov

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Exoskeletons are used to support and compensate for the load on the human musculoskeletal system. Elastomers are an important component of exoskeletons, providing additional support and compensating for the load. The algorithm of the active elastomer tension system provides the required auxiliary force depending on the angle of rotation and the tilt speed of the operator's torso. Feedback for the drive is provided by a force sensor integrated into the attachment of the exoskeleton vest. The use of direct force measurement ensures the required accuracy in all settings of the man-machine system. Non-adjustable elastic elements make it difficult to move without load, tilt forward and walk. A strategy for the organization of the auxiliary forces management system is proposed based on the allocation of 4 operating modes of the human-machine system.

Keywords: soft exoskeleton, mathematical modeling, pre-tension elastomer, human-machine interaction

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: Dong Wook Lee, Adrian Mistreanu

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The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.

Keywords: computer aided engineering, containment analysis, finite element analysis, impact analysis, penetration analysis

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Authors: Yacine Arioua

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In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: Abdelrahman Elsehsah, Hany Madkour, Khalid Farah

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This article presents a 3-D modified non-linear elastic model in the strain space. The Helmholtz free energy function is introduced with the existence of a dissipation potential surface in the space of thermodynamic conjugate forces. The constitutive equation and the damage evolution were derived as well. The modified damage has been examined to model the nonlinear behavior of reinforced concrete (RC) slabs with an opening. A parametric study with RC was carried out to investigate the impact of different factors on the behavior of RC slabs. These factors are the opening area, the opening shape, the place of opening, and the thickness of the slabs. And the numerical results have been compared with the experimental data from literature. Finally, the model showed its ability to be applied to the structural analysis of RC slabs.

Keywords: damage mechanics, 3-D numerical analysis, RC, slab with opening

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Authors: Rachid Fermous, Rima Mebrek

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Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamic multi-fluid equations, we investigated the expansion of dense plasma. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. It is shown that dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.

Keywords: plasma expansion, quantum degeneracy, weakly relativistic, under-dense plasma

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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: Chryssi Vitsilaki, Apostolos Kostas, Ilias Efthymiou

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This paper presents selected best practices on online learning and teaching derived from a novel and innovating Lifelong Learning program through e-Learning, which has during the last five years been set up at the University of the Aegean in Greece. The university, capitalizing on an award-winning, decade-long experience in e-learning and blended learning in undergraduate and postgraduate studies, recently expanded into continuous education and vocational training programs in various cutting-edge fields. So, in this article we present: (a) the academic structure/infrastructure which has been developed for the administrative, organizational and educational support of the e-Learning process, including training the trainers, (b) the mode of design and implementation based on a sound pedagogical framework of open and distance education, and (c) the key results of the assessment of the e-learning process by the participants, as they are used to feedback on continuous organizational and teaching improvement and quality control.

Keywords: distance education, e-learning, life-long programs, synchronous/asynchronous learning

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Authors: Anthony R. Hassan, Jacob A. Gbadeyan

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In this paper, the analysis of a reactive hydromagnetic Poiseuille fluid flow under each of sensitized, Arrhenius and bimolecular chemical kinetics through a channel in the presence of heat source is carried out. An exothermic reaction is assumed while the concentration of the material is neglected. Adomian Decomposition Method (ADM) together with Pade Approximation is used to obtain the solutions of the governing nonlinear non – dimensional differential equations. Effects of various physical parameters on the velocity and temperature fields of the fluid flow are investigated. The entropy generation analysis and the conditions for thermal criticality are also presented.

Keywords: chemical kinetics, entropy generation, thermal criticality, adomian decomposition method (ADM) and pade approximation

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Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

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Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: decentralized, optimal control, output, singular perturb

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Authors: Wieslaw Marszalek, Zdzislaw Trzaska

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Interesting properties of various one-period loops of singularly perturbed memristive circuits with mixed-mode oscillations (MMOs) are analyzed in this paper. The analysis is mixed, both analytical and numerical and focused on the properties of pinched hysteresis of the memristive element and other one-period loops formed by pairs of time-series solutions for various circuits' variables. The memristive element is the only nonlinear element in the two circuits. A theorem on periods of mixed-mode oscillations of the circuits is formulated and proved. Replacements of memristors by parallel G-C or series R-L circuits for a MMO response with equivalent RMS values is also discussed.

Keywords: mixed-mode oscillations, memristive circuits, pinched hysteresis, one-period loops, singularly perturbed circuits

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Authors: A. Zanj, F. He

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In the current paper, a domain independent conduction model compatible for multi-physical system dynamic investigations is suggested. By means of a port-based approach, a classical nonlinear conduction model containing physical states is first represented. A compatible discrete configuration of the thermal domain in line with the elastic domain is then generated through the enhancement of the configuration of the conventional thermal element. The presented simulation results of a sample structure indicate that the suggested conductive model can cover a wide range of dynamic behavior of the thermal domain.

Keywords: multi-physical domain, conduction model, port based modeling, dynamic interaction, physical modeling

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Authors: Denis Özdemir, Max Senges

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There are many examples of AI-supported apps for better health and wellbeing. Generally, these applications help people to achieve their goals based on scientific research and input data. Still, they do not always explain how those three are related, e.g. by making implicit assumptions about goals that hold for many but not for all. We present a seven-step method for designing health and wellbeing AIs considering goal setting, measurable results, real-time indicators, analytics, visual representations, communication, and feedback. It can help engineers as guidance in developing apps, recommendation algorithms, and interfaces that support humans in their decision-making without patronization. To illustrate the method, we create a recommender AI for tiny wellbeing habits and run a small case study, including a survey. From the results, we infer how people perceive the relationship between them and the AI and to what extent it helps them to achieve their goals. We review our seven-step engineering method and suggest modifications for the next iteration.

Keywords: recommender systems, natural language processing, health apps, engineering methods

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Authors: L. Tirabeni, K. E. Soderquist, P. Pisano

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Our purpose is to investigate how the relationship between employees and innovation management processes can drive organizations to successful innovations. This research is deeply related to a new way of thinking about human resources management practices. It’s not simply about improving the employees’ engagement, but rather about a different and more radical commitment: the employee can take on the role traditionally played by the customer, namely to become the first tester of an innovative product or service, the first user/customer and eventually the first investor in the innovation. This new perception of employees could create the basis of a novelty in the innovation process where innovation is taken to a next level when the problems with customer driven innovation on the one hand, and employees driven innovation on the other can be balanced. This research identifies an effective approach to innovation where the employees will participate throughout the whole innovation process, not only in the idea creation but also in the idea definition and development by giving feedback in parallel to that provided by customers and lead-users.

Keywords: employee-driven innovation, engagement, human resource management, innovative companies

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Authors: Shabnam Najafi, Metin Turkay

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Network design problem (NDP) is used to determine the set of optimal values for certain pre-specified decision variables such as capacity expansion of nodes and links by optimizing various system performance measures including safety, congestion, and accessibility. The designed transportation network should improve objective functions defined for the system by considering the route choice behaviors of network users at the same time. The NDP studies mostly investigated the random demand and route selection constraints separately due to computational challenges. In this work, we consider both random demand and route selection constraints simultaneously. This work presents a nonlinear stochastic model for land use and road network design problem to address the development of different functional zones in urban areas by considering both cost function and air pollution. This model minimizes cost function and air pollution simultaneously with random demand and stochastic route selection constraint that aims to optimize network performance via road capacity expansion. The Bureau of Public Roads (BPR) link impedance function is used to determine the travel time function in each link. We consider a city with origin and destination nodes which can be residential or employment or both. There are set of existing paths between origin-destination (O-D) pairs. Case of increasing employed population is analyzed to determine amount of roads and origin zones simultaneously. Minimizing travel and expansion cost of routes and origin zones in one side and minimizing CO emission in the other side is considered in this analysis at the same time. In this work demand between O-D pairs is random and also the network flow pattern is subject to stochastic user equilibrium, specifically logit route choice model. Considering both demand and route choice, random is more applicable to design urban network programs. Epsilon-constraint is one of the methods to solve both linear and nonlinear multi-objective problems. In this work epsilon-constraint method is used to solve the problem. The problem was solved by keeping first objective (cost function) as the objective function of the problem and second objective as a constraint that should be less than an epsilon, where epsilon is an upper bound of the emission function. The value of epsilon should change from the worst to the best value of the emission function to generate the family of solutions representing Pareto set. A numerical example with 2 origin zones and 2 destination zones and 7 links is solved by GAMS and the set of Pareto points is obtained. There are 15 efficient solutions. According to these solutions as cost function value increases, emission function value decreases and vice versa.

Keywords: epsilon-constraint, multi-objective, network design, stochastic

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Authors: A. Morsli, A. Tlemçani, N. Ould Cherchali, M. S. Boucherit

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This article presents two methods for the compensation of harmonics generated by a nonlinear load. The first is the classic method P-Q. The second is the controller by modern method of artificial intelligence specifically fuzzy logic. Both methods are applied to an Active Power Filter shunt (APFs) based on a three-phase voltage converter at five levels NPC topology. In calculating the harmonic currents of reference, we use the algorithm P-Q and pulse generation, we use the intersective PWM. For flexibility and dynamics, we use fuzzy logic. The results give us clear that the rate of Harmonic Distortion issued by fuzzy logic is better than P-Q.

Keywords: fuzzy logic controller, P-Q method, pulse width modulation (PWM), shunt active power filter (sAPF), total harmonic distortion (THD)

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Authors: Rasaq Kareem, Jacob Gbadeyan

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In this study, analysis of the entropy generation of an unsteady reactive hydromagnetic generalized couette fluid flow of a two-step exothermic chemical reaction through a channel with isothermal wall temperature under the influence of different chemical kinetics namely: Sensitized, Arrhenius and Bimolecular kinetics was investigated. The modelled nonlinear dimensionless equations governing the fluid flow were simplified and solved using the combined Laplace Differential Transform Method (LDTM). The effects of fluid parameters associated with the problem on the fluid temperature, entropy generation rate and Bejan number were discussed and presented through graphs.

Keywords: couette, entropy, exothermic, unsteady

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Authors: Daniel Y. Abebe, Jeonghyun Jang, Jaehyouk Choi

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This study aims to evaluate the effective size, section and structural characteristics of circular hollow steel (CHS) damper. CHS damper is among steel dampers which are used widely for seismic energy dissipation because they are easy to install, maintain and are inexpensive. CHS damper dissipates seismic energy through metallic deformation due to the geometrical elasticity of circular shape and fatigue resistance around connection part. After calculating the effective size, which is found to be height to diameter ratio of √("3"), nonlinear FE analyses were carried out to evaluate the structural characteristics and effective section (diameter-to-ratio).

Keywords: circular hollow steel damper, structural characteristics, effective size, effective section, large deformation, FE analysis

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: M-M. Mohamed Ahmed, Nacer K. M’Sirdi, Aziz Naamane

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In this paper, a longitudinal and lateral control approach based on a nonlinear observer is proposed for a convoy of autonomous vehicles to follow a desired trajectory. To authors best knowledge, this topic has not yet been sufficiently addressed in the literature for the control of multi vehicles. The modeling of the convoy of the vehicles is revisited using a robotic method for simulation purposes and control design. With these models, a sliding mode observer is proposed to estimate the states of each vehicle in the convoy from the available sensors, then a sliding mode control based on this observer is used to control the longitudinal and lateral movement. The validation and performance evaluation are done using the well-known driving simulator Scanner-Studio. The results are presented for different maneuvers of 5 vehicles.

Keywords: autonomous vehicles, convoy, non-linear control, non-linear observer, sliding mode

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Authors: Amgad Rezk, Heba Ahmed, Leslie Yeo

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Ultrasound presents a powerful means for material synthesis. In this talk, we showcase a new field demonstrating the possibility for harnessing sound energy sources at considerably higher frequencies (10 MHz to 1 GHz) compared to conventional ultrasound (kHz and up to ~2 MHz) for crystalising and manipulating a variety of nanoscale materials. At these frequencies, cavitation—which underpins most sonochemical processes—is largely absent, suggesting that altogether fundamentally different mechanisms are at dominant. Examples include the crystallization of highly oriented structures, quasi-2D metal-organic frameworks and nanocomposites. These fascinating examples reveal how the highly nonlinear electromechanical coupling associated with high-frequency surface vibration gives rise to molecular ordering and assembly on the nano and microscale.

Keywords: high-frequency acoustics, microfluidics, crystallisation, composite nanomaterials

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Authors: Leonard Kabeya Mukeba Yakasham

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The theoretical machinery from singularity theory introduced by Glolubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problem is completed and expanded wile generalized to the multiparameter context. In this setting the finite deterinancy theorem or normal forms, the stability of equivariant bifurcation problem, and the structural stability of universal unfolding are discussed. With Yakam Matrix the solutions are limited for some partial differential equations stochastic nonlinear of the open questions in singularity artificial intelligence for future.

Keywords: equivariant bifurcation, symmetry singularity, equivariant jets and transversality; normal forms, universal unfolding instability, structural stability, artificial intelligence, pdens, yakam matrix

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