Search results for: mixed-integer non-linear programming

Authors: Anastasiia Yu. Timofeeva

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Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: grade point average, orthogonal regression, penalized regression spline, locally weighted regression

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi

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In this paper a real-time obstacle avoidance approach for both autonomous and non-autonomous dynamical systems (DS) is presented. In this approach the original dynamics of the controller which allow us to determine safety margin can be modulated. Different common types of DS increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle especially when robot moves very fast in changeable complex environments. The method is validated by simulation and influence of different autonomous and non-autonomous DS such as important characteristics of limit cycles and unstable DS. Furthermore, the position of different obstacles in complex environment is explained. Finally, the verification of avoidance trajectories is described through different parameters such as safety factor.

Keywords: limit cycles, nonlinear dynamical system, real time obstacle avoidance, safety margin

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Authors: Khair Al-Deen Bsisu, Osama Mahmoud Abuzeid

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Significant technological advances have been achieved in the design and building construction of steel and glass in the last two decades. The metal glass support frame has been replaced by further sophisticated technological solutions, for example, the point fixed glazing systems. The minimization of the visual mass has reached extensive possibilities through the evolution of technology in glass production and the better understanding of the structural potential of glass itself, the technological development of bolted fixings, the introduction of the glazing support attachments of the glass suspension systems and the use for structural stabilization of cables that reduce to a minimum the amount of metal used. The variability of solutions of tension structures, allied to the difficulties related to geometric and material non-linear behavior, usually overrules the use of analytical solutions, letting numerical analysis as the only general approach to the design and analysis of tension structures. With the characteristics of low stiffness, lightweight, and small damping, tension structures are obviously geometrically nonlinear. In fact, analysis of cable truss is not only one of the most difficult nonlinear analyses because the analysis path may have rigid-body modes, but also a time consuming procedure. Non-linear theory allowing for large deflections is used. The flexibility of supporting members was observed to influence the stresses in the pane considerably in some cases. No other class of architectural structural systems is as dependent upon the use of digital computers as are tensile structures. Besides complexity, the process of design and analysis of tension structures presents a series of specificities, which usually lead to the use of special purpose programs, instead of general purpose programs (GPPs), such as ANSYS. In a special purpose program, part of the design know how is embedded in program routines. It is very probable that this type of program will be the option of the final user, in design offices. GPPs offer a range of types of analyses and modeling options. Besides, traditional GPPs are constantly being tested by a large number of users, and are updated according to their actual demands. This work discusses the use of ANSYS for the analysis and design of tension structures, such as cable truss structures under wind and gravity loadings. A model to describe the glass panels working in coordination with the cable truss was proposed. Under the proposed model, a FEM model of the glass panels working in coordination with the cable truss was established.

Keywords: Glass Construction material, Facades, Finite Element, Pre-Tensioned Cable Truss

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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

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Authors: O. Poleshchuk, E. Komarov

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This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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Authors: Manoj Parmar

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The article uses reflexivity as a research method to investigate and propose an architectural theory plan for climate change. It hypothecates that to discuss or formulate discourse on "Architectural Thinking in a Time of Climate Emergency," firstly, we need to understand the modes of integration that enable architectural thinking with climate change. The study intends to study the various integration modes that have evolved historically and situate them in time. Subsequently, it analyses the integration pattern, challenges the existing model, and finds a way towards climate change as central to architectural thinking. The study is fundamental on-premises that ecology and climate change scholarship has consistently out lashed the asymmetrical and nonlinear knowledge and needs approaches for architecture that are less burden to climate change to people and minimize its impact on ecology.

Keywords: climate change, architectural theory, reflexivity, modernity

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Authors: A. Chellil, A. Nour, S. Lecheb , H. Mechakra, L. Addar, H. Kebir

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This paper present a mechanical characteristics on fatigue crack propagation in Aluminium Plate based on strain and stress distribution using the abaqus software. The changes in shear strain and stress distribution during the fatigue cycle with crack growth is identified. In progressive crack in the strain distribution and the stress is increase in the critical zone. Numerical Modal analysis of the model developed, prove that the Eigen frequencies of aluminium plate were decreased after cracking, and this reduce is nonlinear. These results can provide a reference for analysts and designers of aluminium alloys in aeronautical systems. Therefore, the modal analysis is an important factor for monitoring the aeronautic structures.

Keywords: aluminum alloys, plate, crack, failure

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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: Lakshya Bhat, Anubhav Shrivastava, Shivarudraswamy

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There has been a formidable interest in the area of Distributed Generation in recent times. A wide number of loads are addressed by Distributed Generators and have better efficiency too. The major disadvantage in Distributed Generation is voltage control- is highlighted in this paper. The paper addresses voltage control at buses in IEEE 14 Bus system by regulating reactive power. An analysis is carried out by selecting the most optimum location in placing the Distributed Generators through load flow analysis and seeing where the voltage profile rises. Matlab programming is used for simulation of voltage profile in the respective buses after introduction of DG’s. A tolerance limit of +/-5% of the base value has to be maintained.To maintain the tolerance limit , 3 methods are used. Sensitivity analysis of 3 methods for voltage control is carried out to determine the priority among the methods.

Keywords: distributed generators, distributed system, reactive power, voltage control, sensitivity analysis

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Authors: Shaikh Farhad Hossain, Liakot Ali

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Technology advances accelerate the quality and type of services provided for health care and especially for monitoring health conditions. Sensors have turned out to be more effective to detect diverse physiological signs and can be worn on the human body utilizing remote correspondence modules. An assortment of programming devices have been created to help in preparing a difference rundown of essential signs by examining and envisioning information produced by different sensors. In this proposition, we presented a Health signs and Activity acknowledgment monitoring system. Utilizing off-the-rack sensors, we executed a movement location system for identifying five sorts of action: falling, lying down, sitting, standing, and walking. The framework collects and analyzes sensory data in real-time, and provides different feedback to the users. In addition, it can generate alerts based on the detected events and store the data collected to a medical server.

Keywords: ADL, SVM, TRIL , MEMS

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Authors: Mehdi Ghommem, Daniel Garcia, Nathan Collier, Victor Calo

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We develop a fast, user-friendly implementation of a potential flow solver based on the unsteady vortex lattice method (UVLM). The computational framework uses the Python programming language which has easy integration with the scripts requiring computationally-expensive operations written in Fortran. The mixed-language approach enables high performance in terms of solution time and high flexibility in terms of easiness of code adaptation to different system configurations and applications. This computational tool is intended to predict the unsteady aerodynamic behavior of multiple moving bodies (e.g., flapping wings, rotating blades, suspension bridges...) subject to an incoming air. We simulate different aerodynamic problems to validate and illustrate the usefulness and effectiveness of the developed computational tool.

Keywords: unsteady aerodynamics, numerical simulations, mixed-language approach, potential flow

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Authors: Bahram Fathi, Seyedhossein Sajadifar, Naser Khiabani

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Data envelopment analysis (DEA) has recently gained popularity in energy efficiency analysis. A common feature of the previously proposed DEA models for measuring energy efficiency performance is that they treat energy consumption as an input within a production framework without considering undesirable outputs. However, energy use results in the generation of undesirable outputs as byproducts of producing desirable outputs. Within a joint production framework of both desirable and undesirable outputs, this paper presents several DEA-type linear programming models for measuring energy efficiency performance. In addition to considering undesirable outputs, our models treat different energy sources as different inputs so that changes in energy mix could be accounted for in evaluating energy efficiency. The proposed models are applied to measure the energy efficiency performances of 12 OPEC countries and the results obtained are presented.

Keywords: energy efficiency, undesirable outputs, data envelopment analysis

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Authors: Yang-Kuei Lin, Yun-Xi Zhang

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This research focuses on the bicriteria correlated parallel machine scheduling problem. The two objective functions considered in this problem are to minimize maximum lateness and total weighted completion time. We first present a mixed integer programming (MIP) model that can find the entire efficient frontier for the studied problem. Next, we have proposed a bicriteria heuristic that can find non-dominated solutions for the studied problem. The performance of the proposed bicriteria heuristic is compared with the efficient frontier generated by solving the MIP model. Computational results indicate that the proposed bicriteria heuristic can solve the problem efficiently and find a set of diverse solutions that are uniformly distributed along the efficient frontier.

Keywords: bicriteria, correlated parallel machines, heuristic, scheduling

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Authors: Nor Sahida Ibrahim, Ruhaila Maskat, Aishah Ahmad

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Almost all tertiary-level students will undergo some form of training in organisations prior to their graduation. This practice provides the necessary exposure and experience to allow students to cope with actual working environment and culture in the future. Nevertheless, a particular degree of “matching” between what is expected and what can be offered between students and organisations underpins how effective and enriching the experience is. This matching of students and organisations is challenging when preferences from both parties must be satisfied. This work developed a web-based system, namely the OrganisationMatcher, which leverage on the use of preference weights to score each organisation and rank them based on “suitability”. OrganisationMatcher has been implemented on a relational database, designed using object-oriented methods and developed using PHP programming language for browser front-end access. We outline the challenges and limitations of our system and discuss future improvements to the system, specifically in the utilisation of intelligent methods.

Keywords: student industrial placement, information system, web-based, ranking

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Authors: Ruichong Zhang

Abstract:

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: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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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: Boris G. German, Edward Jiménez, Sebastián Espinoza, Andrés G. Chico, Ricardo A. Narváez

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The unique flora and fauna of The Galapagos Islands has leveraged a tourism-driven growth in the islands. Nonetheless, such development is energy-intensive and requires thousands of gallons of diesel each year for thermoelectric electricity generation. The needed transport of fossil fuels from the continent has generated oil spillages and affectations to the fragile ecosystem of the islands. The Zero Fossil Fuels initiative for The Galapagos proposed by the Ecuadorian government as an alternative to reduce the use of fossil fuels in the islands, considers the replacement of diesel in thermoelectric generators, by Jatropha curcas vegetable oil. However, the Jatropha oil supply cannot entirely cover yet the demand for electricity generation in Galapagos. Within this context, the present work aims to provide an optimization model that can be used as a selection criterion for approving new Jatropha Curcas collection points in rural areas of Manabi-Ecuador. For this purpose, existing Jatropha collection points in Manabi were grouped under three regions: north (7 collection points), center (4 collection points) and south (9 collection points). Field work was carried out in every region in order to characterize the collection points, to establish local Jatropha supply and to determine transportation costs. Data collection was complemented using GIS software and an objective function was defined in order to determine the profit associated to Jatropha oil production. The market price of both Jatropha oil and residual cake, were considered for the total revenue; whereas Jatropha price, transportation and oil extraction costs were considered for the total cost. The tonnes of Jatropha fruit and seed, transported from collection points to the extraction plant, were considered as variables. The maximum and minimum amount of the collected Jatropha from each region constrained the optimization problem. The supply chain was optimized using linear programming in order to maximize the profits. Finally, a sensitivity analysis was performed in order to find a profit-based criterion for the acceptance of future collection points in Manabi. The maximum profit reached a value of $ 4,616.93 per year, which represented a total Jatropha collection of 62.3 tonnes Jatropha per year. The northern region of Manabi had the biggest collection share (69%), followed by the southern region (17%). The criteria for accepting new Jatropha collection points in the rural areas of Manabi can be defined by the current maximum profit of the zone and by the variation in the profit when collection points are removed one at a time. The definition of new feasible collection points plays a key role in the supply chain associated to Jatropha oil production. Therefore, a mathematical model that assists decision makers in establishing new collection points while assuring profitability, contributes to guarantee a continued Jatropha oil supply for Galapagos and a sustained economic growth in the rural areas of Ecuador.

Keywords: collection points, Jatropha curcas, linear programming, supply chain

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Authors: Chaima Babi, Said Gadri

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The rapid increase in fake news continues to grow at a very fast rate; this requires implementing efficient techniques that allow testing the re-liability of online content. For that, the current research strives to illuminate the fake news problem using deep learning DL and machine learning ML ap-proaches. We have developed the traditional LSTM (Long short-term memory), and the bidirectional BiLSTM model. A such process is to perform a training task on almost of samples of the dataset, validate the model on a subset called the test set to provide an unbiased evaluation of the final model fit on the training dataset, then compute the accuracy of detecting classifica-tion and comparing the results. For the programming stage, we used Tensor-Flow and Keras libraries on Python to support Graphical Processing Units (GPUs) that are being used for developing deep learning applications.

Keywords: machine learning, deep learning, natural language, fake news, Bi-LSTM, LSTM, multiclass classification

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Authors: Ashwini Umale

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Trajectory planning and optimization is a fundamental problem in articulated robotics. It is often viewed as a two phase problem of initial feasible path planning around obstacles and subsequent optimization of a trajectory satisfying dynamical constraints. An optimized trajectory of multi-axis robot is important and directly influences the Performance of the executing task. Optimal is defined to be the minimum time to transition from the current speed to the set speed. In optimization of trajectory through virtual environment explores the most suitable way to represent robot motion from virtual environment to real environment. This paper aims to review the research of trajectory optimization in virtual environment using simulation software Robcad. Improvements are to be expected in trajectory optimization to generate smooth and collision free trajectories with minimization of overall robot cycle time.

Keywords: trajectory optimization, forward kinematics and reverse kinematics, dynamic constraints, robcad simulation software

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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: Jade Martínez-Llinàs, Pere Colet

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By exploring the possible dynamical regimes in a prototypical model for mutually delay-coupled OEOs, here it is shown that two mutually coupled non-identical OEOs, besides in- and out-of-phase square-waves, can generate stable square-wave pulses synchronized at a quarter of the period (T/4) in a broad parameter region. The key point to obtain T/4 solutions is that the two OEO operate with mixed feedback, namely with negative feedback in one and positive in the other. Furthermore, the coexistence of multiple solutions provides a large degree of flexibility for tuning the frequency in the GHz range without changing any parameter. As a result the two coupled OEOs system is good candidate to be implemented for information encoding as a high-capacity memory device.

Keywords: nonlinear optics, optoelectronic oscillators, square waves, synchronization

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Authors: Mami Sugiura, Shinichi Arakawa, Masayuki Murata, Satoshi Imai, Toru Katagiri, Motoyoshi Sekiya

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API (Application Programming Interface) economy, where many participants join/interact and form the economy, is expected to increase collaboration between information services through API, and thereby, it is expected to increase market value from the service collaborations. In this paper, we introduce API evaluators, which are the activator of API economy by reviewing and/or evaluating APIs, and develop a multi-sided API economy model that formulates interactions among platform provider, API developers, consumers, and API evaluators. By obtaining the equilibrium that maximizes utility of all participants, the impact of API evaluators on the utility of participants in the API economy is revealed. Numerical results show that, with the existence of API evaluators, the number of developers and consumers increase by 1.5% and the utility of platformer increases by 2.3%. We also discuss the strategies of platform provider to maximize its utility under the existence of API evaluators.

Keywords: API economy, multi-sided markets, API evaluator, platform, platform provider

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Authors: Tai-Yue Wang, Yi-Ho Chen

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In this study, we investigate a two-echelon supply chain with two suppliers and three retailers among which one retailer dominates other retailers. A price competition demand function is used to model this dominant retailer, which is leading market. The promotion strategies and negotiation schemes are integrated to form decision-making models under different scenarios. These models are then formulated into different mathematical programming models. The decision variables such as promotional costs, retailer prices, wholesale price, and order quantity are included in these models. At last, the distributions of promotion costs under different cost allocation strategies are discussed. Finally, an empirical example used to validate our models. The results from this empirical example show that the profit model will create the largest profit for the supply chain but with different profit-sharing results. At the same time, the more risk a member can take, the more profits are distributed to that member in the utility model.

Keywords: supply chain, price promotion, mathematical models, dominant retailer

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Authors: Birinderjit Singh Kalyan, Inderpreet Kaur, Balwinder Singh Sohi

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In this paper, an equivalent model for floating gate transistor has been proposed. Using the floating gate voltage value, capacitive coupling coefficients has been found at different bias conditions. The amount of charge present on the gate has been then calculated using the transient models of hot electron programming and Fowler-Nordheim Tunnelling. The proposed model can be extended to the transient conditions as well. The SPICE equivalent model is designed and current-voltage characteristics and Transfer characteristics are comparatively analysed. The dc current-voltage characteristics, as well as dc transfer characteristics, have been plotted for an FGMOS with W/L=0.25μm/0.375μm, the inter-poly capacitance of 0.8fF for both programmed and erased states. The Comparative analysis has been made between the present model and capacitive coefficient coupling methods which were already available.

Keywords: FGMOS, floating gate transistor, capacitive coupling coefficient, SPICE model

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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: 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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