Search results for: Vekua integral operator

Authors: Fl. Loury, P. Sablonière

Abstract:

In this paper a stochastic scenario-based model predictive control applied to molten salt storage systems in concentrated solar tower power plant is presented. The main goal of this study is to build up a tool to analyze current and expected future resources for evaluating the weekly power to be advertised on electricity secondary market. This tool will allow plant operator to maximize profits while hedging the impact on the system of stochastic variables such as resources or sunlight shortage.

Solving the problem first requires a mixed logic dynamic modeling of the plant. The two stochastic variables, respectively the sunlight incoming energy and electricity demands from secondary market, are modeled by least square regression. Robustness is achieved by drawing a certain number of random variables realizations and applying the most restrictive one to the system. This scenario approach control technique provides the plant operator a confidence interval containing a given percentage of possible stochastic variable realizations in such a way that robust control is always achieved within its bounds. The results obtained from many trajectory simulations show the existence of a ‘’reliable’’ interval, which experimentally confirms the algorithm robustness.

Keywords: Molten Salt Storage System, Concentrated Solar Tower Power Plant, Robust Stochastic Model Predictive Control.

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Authors: V. Masilamani, C. Vanniarajan, Kamala Krithivasan

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As the Computed Tomography(CT) requires normally hundreds of projections to reconstruct the image, patients are exposed to more X-ray energy, which may cause side effects such as cancer. Even when the variability of the particles in the object is very less, Computed Tomography requires many projections for good quality reconstruction. In this paper, less variability of the particles in an object has been exploited to obtain good quality reconstruction. Though the reconstructed image and the original image have same projections, in general, they need not be the same. In addition to projections, if a priori information about the image is known, it is possible to obtain good quality reconstructed image. In this paper, it has been shown by experimental results why conventional algorithms fail to reconstruct from a few projections, and an efficient polynomial time algorithm has been given to reconstruct a bi-level image from its projections along row and column, and a known sub image of unknown image with smoothness constraints by reducing the reconstruction problem to integral max flow problem. This paper also discusses the necessary and sufficient conditions for uniqueness and extension of 2D-bi-level image reconstruction to 3D-bi-level image reconstruction.

Keywords: Discrete Tomography, Image Reconstruction, Projection, Computed Tomography, Integral Max Flow Problem, Smooth Binary Image.

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

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Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: Fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization.

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Authors: Kalyan Chatterjee

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The optimal design of PI controller for Automatic Generation Control in two area is presented in this paper. The concept of Dual mode control is applied in the PI controller, such that the proportional mode is made active when the rate of change of the error is sufficiently larger than a specified limit otherwise switched to the integral mode. A digital simulation is used in conjunction with the Hooke-Jeeve’s optimization technique to determine the optimum parameters (individual gain of proportional and integral controller) of the PI controller. Integrated Square of the Error (ISE), Integrated Time multiplied by Absolute Error(ITAE) , and Integrated Absolute Error(IAE) performance indices are considered to measure the appropriateness of the designed controller.  The proposed controller are tested for a two area single nonreheat thermal system considering the practical aspect of the problem such as Deadband and Generation Rate Constraint(GRC). Simulation results show that  dual mode with optimized values of the gains improved the control performance than the commonly used Variable Structure .

Keywords: Load Frequency Control, Area Control Error(ACE), Dual Mode PI Controller, Performance Index

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Authors: S. Panda, S. K. Tomar, R. Prasad, C. Ardil

Abstract:

Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.

Keywords: Model Order Reduction, Markov Parameters, Routh Approximation, Particle Swarm Optimization, Integral Squared Error, Steady State Stability.

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Authors: Shang-En Yu

Abstract:

Human society, there are many uncertainties, such as economic growth rate forecast of the financial crisis, many scholars have, since the the Song Chissom two scholars in 1993 the concept of the so-called fuzzy time series (Fuzzy Time Series)different mode to deal with these problems, a previous study, however, usually does not consider the relevant variables selected and fuzzy process based solely on subjective opinions the fuzzy semantic discrete, so can not objectively reflect the characteristics of the data set, in addition to carrying outforecasts are often fuzzy rules as equally important, failed to consider the importance of each fuzzy rule. For these reasons, the variable selection (Factor Selection) through self-organizing map (Self-Organizing Map, SOM) and proposed high-end weighted multivariate fuzzy time series model based on fuzzy neural network (Fuzzy-BPN), and using the the sequential weighted average operator (Ordered Weighted Averaging operator, OWA) weighted prediction. Therefore, in order to verify the proposed method, the Taiwan stock exchange (Taiwan Stock Exchange Corporation) Taiwan Weighted Stock Index (Taiwan Stock Exchange Capitalization Weighted Stock Index, TAIEX) as experimental forecast target, in order to filter the appropriate variables in the experiment Finally, included in other studies in recent years mode in conjunction with this study, the results showed that the predictive ability of this study further improve.

Keywords: Heterogeneity, residential mortgage loans, foreclosure.

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Authors: S. Panda, S. K. Tomar, R. Prasad, C. Ardil

Abstract:

Reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM), using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Mihailov stability criterion and continued fraction expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. In the evolutionary technique method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.

Keywords: Reduced Order Modeling, Stability, Continued Fraction Expansions, Mihailov Stability Criterion, Particle Swarm Optimization, Integral Squared Error.

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Authors: Sidhartha Panda, N. P. Padhy, R.N.Patel

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In this paper, genetic algorithm (GA) opmization technique is applied to design Flexible AC Transmission System (FACTS)-based damping controllers. Two types of controller structures, namely a proportional-integral (PI) and a lead-lag (LL) are considered. The design problem of the proposed controllers is formulated as an optimization problem and GA is employed to search for optimal controller parameters. By minimizing the time-domain based objective function, in which the deviation in the oscillatory rotor speed of the generator is involved; stability performance of the system is improved. The proposed controllers are tested on a weakly connected power system subjected to different disturbances. The non-linear simulation results are presented to show the effectiveness of the proposed controller and their ability to provide efficient damping of low frequency oscillations. It is also observed that the proposed SSSC-based controllers improve greatly the voltage profile of the system under severe disturbances. Further, the dynamic performances of both the PI and LL structured FACTS-controller are analyzed at different loading conditions and under various disturbance condition as well as under unbalanced fault conditions..

Keywords: Genetic algorithm, proportional-integral controller, lead-lag controller, power system stability, FACTS.

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Authors: Consalva J. Msigwa, Beda J. Kundy, Bakari M. M. Mwinyiwiwa,

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This paper presents a method for obtaining the desired reference current for Voltage Source Converter (VSC) of the Shunt Active Power Filter (SAPF) using Synchronous Reference Frame Theory. The method relies on the performance of the Proportional-Integral (PI) controller for obtaining the best control performance of the SAPF. To improve the performance of the PI controller, the feedback path to the integral term is introduced to compensate the winding up phenomenon due to integrator. Using Reference Frame Transformation, reference signals are transformed from a - b - c stationery frame to 0 - d - q rotating frame. Using the PI controller, the reference signals in the 0 - d - q rotating frame are controlled to get the desired reference signals for the Pulse Width Modulation. The synchronizer, the Phase Locked Loop (PLL) with PI filter is used for synchronization, with much emphasis on minimizing delays. The system performance is examined with Shunt Active Power Filter simulation model.

Keywords: Phase Locked Loop (PLL), Voltage Source Converter (VSC), Shunt Active Power Filter (SAPF), PI, Pulse Width Modulation (PWM)

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Authors: Rafal Stegierski, Krzysztof Dmitruk

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The paper focus on robotic telepresence system build around humanoid robot operated with controller-less Wizard of Oz technique. Proposed solution gives possibility to quick start acting as a operator with short, if any, initial training.

Keywords: Robotics, Motion Capture, Wizard of Oz, Humanoid Robots, Human Robot Interaction.

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Authors: Mehtap Dursun, E. Ertugrul Karsak, Melis Almula Karadayi

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The management of the health-care wastes is one of the most important problems in Istanbul, a city with more than 12 million inhabitants, as it is in most of the developing countries. Negligence in appropriate treatment and final disposal of the healthcare wastes can lead to adverse impacts to public health and to the environment. This paper employs a fuzzy multi-criteria group decision making approach, which is based on the principles of fusion of fuzzy information, 2-tuple linguistic representation model, and technique for order preference by similarity to ideal solution (TOPSIS), to evaluate health-care waste (HCW) treatment alternatives for Istanbul. The evaluation criteria are determined employing nominal group technique (NGT), which is a method of systematically developing a consensus of group opinion. The employed method is apt to manage information assessed using multigranularity linguistic information in a decision making problem with multiple information sources. The decision making framework employs ordered weighted averaging (OWA) operator that encompasses several operators as the aggregation operator since it can implement different aggregation rules by changing the order weights. The aggregation process is based on the unification of information by means of fuzzy sets on a basic linguistic term set (BLTS). Then, the unified information is transformed into linguistic 2-tuples in a way to rectify the problem of loss information of other fuzzy linguistic approaches.

Keywords: Group decision making, health care waste management, multi-criteria decision making, OWA, TOPSIS, 2-tuple linguistic representation

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Authors: Cheng Zhang, James Marco, Walid Allafi, Truong Q. Dinh, W. D. Widanage

Abstract:

Equivalent circuit models (ECMs) are widely used in battery management systems in electric vehicles and other battery energy storage systems. The battery dynamics and the model parameters vary under different working conditions, such as different temperature and state of charge (SOC) levels, and therefore online parameter identification can improve the modelling accuracy. This paper presents a way of online ECM parameter identification using a continuous time (CT) estimation method. The CT estimation method has several advantages over discrete time (DT) estimation methods for ECM parameter identification due to the widely separated battery dynamic modes and fast sampling. The presented method can be used for online SOC estimation. Test data are collected using a lithium ion cell, and the experimental results show that the presented CT method achieves better modelling accuracy compared with the conventional DT recursive least square method. The effectiveness of the presented method for online SOC estimation is also verified on test data.

Keywords: Equivalent circuit model, continuous time domain estimation, linear integral filter method, parameter and SOC estimation, recursive least square.

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Authors: M. H. M. Rashid

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Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.

Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge Transformation.

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Authors: Ziraguen O. Williams, Shield B. Lin, Fouad N. Matari, Leslie J. Quiocho

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Simulation for seated row exercise was a continued task to assist NASA in analyzing a one-dimensional vibration isolation and stabilization system for astronaut’s exercise platform. Feedback delay and signal noise were added to the simulation model. Simulation runs for this study were conducted in two software simulation tools, Trick and MBDyn, software simulation environments developed at the NASA Johnson Space Center. The exciter force in the simulation was calculated from motion capture of an exerciser during a seated aerobic row exercise. The simulation runs include passive control, active control using a Proportional, Integral, Derivative (PID) controller, and active control using a Piecewise Linear Integral Derivative (PWLID) controller. Output parameters include displacements of the exercise platform, the exerciser, and the counterweight; transmitted force to the wall of spacecraft; and actuator force to the platform. The simulation results showed excellent force reduction in the active controlled system compared to the passive controlled system, which showed less force reduction.

Keywords: Simulation, counterweight, exercise, vibration.

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Authors: András Szekrényes

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Delamination is one of the major failure modes in laminated composite structures. Delamination tips are mostly captured by spatial numerical models in order to predict crack growth. This paper presents some mechanical models of delaminated composite shells based on shallow shell theories. The mechanical fields are based on a third-order displacement field in terms of the through-thickness coordinate of the laminated shell. The undelaminated and delaminated parts are captured by separate models and the continuity and boundary conditions are also formulated in a general way providing a large size boundary value problem. The system of differential equations is solved by the state space method for an elliptic delaminated shell having simply supported edges. The comparison of the proposed and a numerical model indicates that the primary indicator of the model is the deflection, the secondary is the widthwise distribution of the energy release rate. The model is promising and suitable to determine accurately the J-integral distribution along the delamination front. Based on the proposed model it is also possible to develop finite elements which are able to replace the computationally expensive spatial models of delaminated structures.

Keywords: J-integral, Lévy method, third-order shell theory, state space solution.

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Authors: Yung-Tien Liu, Chun-Chao Wang

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This paper presents the control performance of a high-precision positioning device using the hybrid actuator composed of a piezoelectric (PZT) actuator and a voice-coil motor (VCM). The combined piezo-VCM actuator features two main characteristics: a large operation range due to long stroke of the VCM, and high precision and heavy load positioning ability due to PZT impact force. A one-degree-of-freedom (DOF) experimental setup was configured to examine the fundamental characteristics, and the control performance was effectively demonstrated by using a switching controller. In rough positioning state, an integral variable structure controller (IVSC) was used for the VCM to conduct long range of operation; in precision positioning state, an impact force controller (IFC) for the PZT actuator coupled with presliding states of the sliding table was used to obtain high-precision position control and achieve both forward and backward actuations. The experimental results showed that the sliding table having a mass of 881g and with a preload of 10 N was successfully positioned within the positioning accuracy of 10 nm in both forward and backward position controls.

Keywords: Integral variable structure controller (IVSC), impact force, precision positioning, presliding, PZT actuator, voice-coil motor (VCM).

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Authors: M. Salmani Jelodar, M.J. Fadaeieslam, N. Mozayani, M. Fazeli

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Optical Character Recognition (OCR) is a very old and of great interest in pattern recognition field. In this paper we introduce a very powerful approach to recognize Persian text. We have used morphological operators, especially Hit/Miss operator to descript each sub-word and by using a template matching approach we have tried to classify generated description. We used just one font in two different sizes to verify our approach. We achieved a very good rate, up to 99.9%.

Keywords: A Persian Optical Character Recognition.

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Authors: S. Panda, J. S. Yadav, N. P. Patidar, C. Ardil

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Recently, genetic algorithms (GA) and particle swarm optimization (PSO) technique have attracted considerable attention among various modern heuristic optimization techniques. The GA has been popular in academia and the industry mainly because of its intuitiveness, ease of implementation, and the ability to effectively solve highly non-linear, mixed integer optimization problems that are typical of complex engineering systems. PSO technique is a relatively recent heuristic search method whose mechanics are inspired by the swarming or collaborative behavior of biological populations. In this paper both PSO and GA optimization are employed for finding stable reduced order models of single-input- single-output large-scale linear systems. Both the techniques guarantee stability of reduced order model if the original high order model is stable. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example from literature and the results are compared with recently published conventional model reduction technique.

Keywords: Genetic Algorithm, Particle Swarm Optimization, Order Reduction, Stability, Transfer Function, Integral Squared Error.

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Authors: Ali Essam El Shazly

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The Haussmannization plan of Cairo in 1867 formed a regular network of roundabout spaces, though deteriorated at present. The method of identifying the spatial structure of roundabout Cairo for conservation matches the voronoi diagram with the space syntax through their geometrical property of spatial convexity. In this initiative, the primary convex hull of first-order voronoi adopts the integral and control measurements of space syntax on Cairo’s roundabout generators. The functional essence of royal palaces optimizes the roundabout structure in terms of spatial measurements and the symbolic voronoi projection of 'Tahrir Roundabout' over the Giza Nile and Pyramids. Some roundabouts of major public and commercial landmarks surround the pole of 'Ezbekia Garden' with a higher control than integral measurements, which filter the new spatial structure from the adjacent traditional town. Nevertheless, the least integral and control measures correspond to the voronoi contents of pollutant workshops and the plateau of old Cairo Citadel with the visual compensation of new royal landmarks on top. Meanwhile, the extended suburbs of infinite voronoi polygons arrange high control generators of chateaux housing in 'garden city' environs. The point pattern of roundabouts determines the geometrical characteristics of voronoi polygons. The measured lengths of voronoi edges alternate between the zoned short range at the new poles of Cairo and the distributed structure of longer range. Nevertheless, the shortest range of generator-vertex geometry concentrates at 'Ezbekia Garden' where the crossways of vast Cairo intersect, which maximizes the variety of choice at different spatial resolutions. However, the symbolic 'Hippodrome' which is the largest public landmark forms exclusive geometrical measurements, while structuring a most integrative roundabout to parallel the royal syntax. Overview of the symbolic convex hull of voronoi with space syntax interconnects Parisian Cairo with the spatial chronology of scattered monuments to conceive one universal Cairo structure. Accordingly, the approached methodology of 'voronoi-syntax' prospects the future conservation of roundabout Cairo at the inferred city-level concept.

Keywords: Roundabout Cairo, first-order Voronoi, space syntax, spatial structure.

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Authors: N. Khelil. L. Djerou , A. Zerarka, M. Batouche

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Consider the Gregory integration (G) formula with end corrections where h Δ is the forward difference operator with step size h. In this study we prove that can be optimized by minimizing some of the coefficient k a in the remainder term by particle swarm optimization. Experimental tests prove that can be rendered a powerful formula for library use.

Keywords: Numerical integration, Gregory Formula, Particle Swarm optimization.

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Authors: Mohammad Fuad Mohammad Naser, Faycal Ikhouane

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LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.

Keywords: Hysteresis, LuGre model, operator, (strong) consistency.

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Authors: J. S. Yadav, N. P. Patidar, J. Singhai, S. Panda, C. Ardil

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In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.

Keywords: Reduced Order Modeling, Stability, Mihailov Stability Criterion, Continued Fraction Expansions, Differential Evolution, Integral Squared Error.

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Authors: Rami Darwish

Abstract:

The transport industry is transitioning to sustainable industrial systems to meet its environmental targets. At the heart of this transition lies the electrification of bus systems, which involves the introduction and testing of sustainable technologies in protected environments for customer evaluation. While the transition necessitates business-model innovation, practical implementation has proven to be complex. This article delves into efforts to present the business model of a bus operator engaged in public procurement with the goal of facilitating the industry's shift towards electrification. Through an in-depth case study, the influence of public contracts’ design on the evolution of a technology and the operator's business model for electrification is explored. While the extant literature suggests that public procurement can facilitate business-model innovation and sustainable development, the findings reveal that public-contract design can limit value creation and value capture in potential business models, locking organizations into existing business models and hindering the socio-technical transition to sustainability. Interestingly, public-procurement contract design can play a pivotal role in preventing sustainable innovations from breaking through. This highlights the importance of contract design as a vehicle for dialogue between businesses and authorities that can enable systemic change. The case study also illuminates a paradoxical scenario in which the transport authority was required to reconcile the efficiency and stability required for bus transport with the potential benefits of electrification technologies promising sustainability. Finally, recommendations for navigating and addressing this tension are provided. The implications of these findings extend to the literature on discontinuous innovation and business-model innovation.

Keywords: Sustainable transition, public procurement, business-model innovation, discontinuous innovation, lock-in.

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Authors: Chuang-Hung Lin, Cheng-Yuan Hsu, Jia-Yan Lin

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It is an indispensible strategy to adopt greenery approach on architectural bases so as to improve ecological habitats, decrease heat-island effect, purify air quality, and relieve surface runoff as well as noise pollution, all of which are done in an attempt to achieve sustainable environment. How we can do with plant design to attain the best visual quality and ideal carbon dioxide fixation depends on whether or not we can appropriately make use of greenery according to the nature of architectural bases. To achieve the goal, it is a need that architects and landscape architects should be provided with sufficient local references. Current greenery studies focus mainly on the heat-island effect of urban with large scale. Most of the architects still rely on people with years of expertise regarding the adoption and disposition of plantation in connection with microclimate scale. Therefore, environmental design, which integrates science and aesthetics, requires fundamental research on landscape environment technology divided from building environment technology. By doing so, we can create mutual benefits between green building and the environment. This issue is extremely important for the greening design of the bases of green buildings in cities and various open spaces. The purpose of this study is to establish plant selection and allocation strategies under different building sunshade levels. Initially, with the shading of sunshine on the greening bases as the starting point, the effects of the shades produced by different building types on the greening strategies were analyzed. Then, by measuring the PAR (photosynthetic active radiation), the relative DLI (daily light integral) was calculated, while the DLI Map was established in order to evaluate the effects of the building shading on the established environmental greening, thereby serving as a reference for plant selection and allocation. The discussion results were to be applied in the evaluation of environment greening of greening buildings and establish the “right plant, right place” design strategy of multi-level ecological greening for application in urban design and landscape design development, as well as the greening criteria to feedback to the eco-city greening buildings.

Keywords: Daily light integral, plant design, urban open space.

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Authors: A. Basit, M. Y. Javed, M. A. Anjum

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In this paper, an efficient method for personal identification based on the pattern of human iris is proposed. It is composed of image acquisition, image preprocessing to make a flat iris then it is converted into eigeniris and decision is carried out using only reduction of iris in one dimension. By comparing the eigenirises it is determined whether two irises are similar. The results show that proposed method is quite effective.

Keywords: Biometrics, Canny Operator, Eigeniris, Iris Recognition.

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Authors: Inese Bula

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Symbolic dynamics studies dynamical systems on the basis of the symbol sequences obtained for a suitable partition of the state space. This approach exploits the property that system dynamics reduce to a shift operation in symbol space. This shift operator is a chaotic mapping. In this article we show that in the symbol space exist other chaotic mappings.

Keywords: Infinite symbol space, prefix metric, chaotic mapping, generator function, jump mapping.

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Authors: Safeer Hussain Khan

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In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves andgeneralizes corresponding results in the literature in two ways: iterativeprocess is faster, operators are more general. At the end, we indicatethat the results can also be proved with the iterative process witherror terms.

Keywords: Contractive-like operator, iterative process, fixed point, strong convergence.

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Authors: Nidhal Jamia, Sami El-Borgi

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In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: Functionally graded piezoelectric material, mixed-mode crack, non-local theory, Schmidt method.

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Authors: Amnah E. Shammahy

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In this paper, we study the boundedness and compactness of the weighted composition operator W_u,φ, which is induced by an holomorphic function u and holomorphic self-map φ, acting between the N_K-space and the Bers-type space H^∞_α on the unit disk.

Keywords: Weighted composition operators, NK-space, Bers-type space.

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Authors: Consalva J. Msigwa, Beda J. Kundy, Bakari M. M. Mwinyiwiwa

Abstract:

In this paper the reference current for Voltage Source Converter (VSC) of the Shunt Active Power Filter (SAPF) is generated using Synchronous Reference Frame method, incorporating the PI controller with anti-windup scheme. The proposed method improves the harmonic filtering by compensating the winding up phenomenon caused by the integral term of the PI controller. Using Reference Frame Transformation, the current is transformed from om a - b - c stationery frame to rotating 0 - d - q frame. Using the PI controller, the current in the 0 - d - q frame is controlled to get the desired reference signal. A controller with integral action combined with an actuator that becomes saturated can give some undesirable effects. If the control error is so large that the integrator saturates the actuator, the feedback path becomes ineffective because the actuator will remain saturated even if the process output changes. The integrator being an unstable system may then integrate to a very large value, the phenomenon known as integrator windup. Implementing the integrator anti-windup circuit turns off the integrator action when the actuator saturates, hence improving the performance of the SAPF and dynamically compensating harmonics in the power network. In this paper the system performance is examined with Shunt Active Power Filter simulation model.

Keywords: Phase Locked Loop (PLL), Voltage SourceConverter (VSC), Shunt Active Power Filter (SAPF), PI, Pulse WidthModulation (PWM).

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