Search results for: applied algebraic topology

Authors: R. Rezaeipour, A. R. Mehrabi

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Recent increase of the DGs and microgrids in distribution systems, disturbs the tradition structure of the system. Coordination between protection devices in such a system becomes the concern of the network operators. This paper presents a new method for fault location detection in the active distribution networks, independent of the fault type or its resistance. The method uses synchronized voltage and current measurements at the interconnection of DG units and is able to adapt to changes in the topology of the system. The method has been tested on a 38-bus distribution system, with very encouraging results.

Keywords: fault location detection, active distribution system, micro grids, network operators

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Authors: Wiem Gadri

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This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral charac-teristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this new setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a novel characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, formal power series, over a finite field

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

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Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: covariation reasoning, exponential function, modeling, representations

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Mitesh Rathod, Jungho Ahn, Noo Li Jeon, Junghoon Lee

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Endothelial cells respond to cues from both biochemical as well as micro mechanical environment. Significant effort has been directed to understand the effects of biochemical signaling, however, relatively little is known about regulation of endothelial cell biology by the micro mechanical environment. Numerous studies have been performed to understand how physical forces regulate endothelial cell behavior. In this regard, past studies have majorly focused on exploring how fluid shear stress governs endothelial cell behavior. Parallel plate flow chambers and rectangular microchannels are routinely employed for applying fluid shear force on endothelial cells. However, these studies fall short in mimicking the in vivo like micro environment from topological aspects. Few studies have only used circular microchannels to replicate in vivo like condition. Seldom efforts have been directed to elucidate the combined effect of topology, substrate rigidity and fluid shear stress on endothelial cell response. In this regard, we demonstrate a facile fabrication process to develop a hybrid polydimethylsiloxane microfluidic platform to study endothelial cell biology. On a single chip microchannels with different cross sections i.e., circular, rectangular and square have been fabricated. In addition, our fabrication approach allows variation in the substrate rigidity along the channel length. Two different variants of polydimethylsiloxane, namely Sylgard 184 and Sylgard 527, were utilized to achieve the variation in rigidity. Moreover, our approach also enables in creating Y bifurcation circular microchannels. Our microfluidic platform thus facilitates for conducting studies pertaining to endothelial cell morphology with respect to change in topology, substrate rigidity and fluid flow on a single chip. The hybrid platform was tested by culturing Human Umbilical Vein Endothelial Cells in circular microchannels with varying substrate rigidity, and exposed to fluid shear stress of 12 dynes/cm² and static conditions. Results indicate the cell area response to flow induced shear stress was governed by the underlying substrate mechanics.

Keywords: hybrid, microfluidic platform, PDMS, shear flow, substrate rigidity

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Authors: Ulli Heinlein, Thomas Freimann

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Pre-applied bonded membranes are used as positive-side waterproofing on concrete basements, are installed before the concrete work, and achieve a tear-resistant and waterproof bond with the subsequently placed fresh concrete. This bond increases redundancy compared to lose waterproofing membranes by preventing lateral water migrations in the event of damage. So far, the membranes have been tested in the laboratory, but it is not yet known how they behave on construction sites in the presence of dirt, soil, cement paste or moisture. This article, therefore, conducts investigations on six construction sites using 18 test slabs where the pre-applied bonded membranes are selectively contaminated or wetted. Subsequently, cores are taken, and the influence of the contaminations on the adhesive tensile strength and waterproof bond is tested. Pre-applied bonded membranes with smooth or granular but closed surfaces show no sensitivity to wetness, whereas open-pored membranes with nonwovens do not tolerate standing water. Contaminations decline the performance of all pre-applied bonded membranes since a separating layer is formed between the bonding layer and the concrete. The influence depends on the thickness of the contamination and its mechanical properties.

Keywords: waterproofing, positive-side waterproofing, basement, pre-applied bonded waterproofing membrane, In-situ testing, lateral water migrations

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Authors: Anca Radulescu, Danae Evans

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The relationship between a network’s hardwiring and its emergent dynamics are central to neuroscience. We study the principles of this correspondence in a canonical setup (in which network nodes exhibit well-studied complex quadratic dynamics), then test their universality in biological networks. By extending methods from discrete dynamics, we study the effects of network connectivity on temporal patterns, encapsulating long-term behavior into the rich topology of network Mandelbrot sets. Then elements of fractal geometry can be used to predict and classify network behavior.

Keywords: canonical model, complex dynamics, dynamic networks, fractals, Mandelbrot set, network connectivity

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Authors: Muhammad A. Ishaq, S. U. R. Aliyu

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This paper on an exposition of Islamic fiscal policy attempts to discuss the basic principles of Islamic fiscal policy in an Islamic economy. The paper presents a number of definitions of the subject matter, its nature and its tools of application. Government spending, taxation and public borrowings were identified as the tools of the policy. The paper identifies zakat both as a veritable source of revenue and a major instrument of economic stabilization. Furthermore, the paper presents an algebraic 2-sector and 3-sector models from the basic Keynesian model. The paper posits that in view of uniqueness of its instruments, absence of interest rate in the economy and the policy’s derive towards socioeconomic justice and redistribution, Islamic fiscal policy is capable of stabilizing Islamic economy and ushering it into the path of long term economic growth and prosperity.

Keywords: automatic built-in-stabilizers, government spending, Islamic fiscal policy, taxation, zakat

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Authors: Nan Tang, Bin Wu, Cunfu He

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The trapezoid rods are widely used in civil engineering as load –carrying members. Ultrasonic guided wave is one of the most popular techniques in analyzing the propagation of elastic guided wave. The goal of this paper is to investigate the propagation of elastic waves in the isotropic bar with trapezoid cross-section. Dispersion curves that describe the relationship between the frequency and velocity provide the fundamental information to describe the propagation of elastic waves through a structure. Based on the SAFE (semi-analytical finite element) a linear algebraic system of equations is obtained. By using numerical methods, dispersion curves solved for the rods with the trapezoid cross-section. These fundamental information plays an important role in applying ultrasonic guided waves to NTD for structures with trapezoid cross section.

Keywords: guided wave, dispersion, finite element method, trapezoid rod

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Authors: A. Sardi, J. Zbitou, A. Errkik, L. El Abdellaoui, A. Tajmouati, M. Latrach

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This paper presents analysis and design of a wideband Wilkinson power divider for wireless applications. The design is accomplished by transforming the lengths and impedances of the quarter wavelength sections of the conventional Wilkinson power divider into U-shaped sections. The designed power divider is simulated by using ADS Agilent technologies and CST microwave studio software. It is shown that the proposed power divider has simple topology and good performances in terms of insertion loss, port matching and isolation at all operating frequencies (1.8 GHz, 2.45 GHz and 3.55 GHz).

Keywords: ADS agilent technologies, CST microwave studio, microstrip, wideband, wilkinson power divider

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Authors: Inayatur Rehman

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Molodtstove developed the theory of soft sets which can be seen as an effective tool to deal with uncertainties. Since the introduction of this concept, the application of soft sets has been restricted to associative algebraic structures (groups, semi groups, associative rings, semi-rings etc.). Acceptably, though the study of soft sets, where the base set of parameters is a commutative structure, has attracted the attention of many researchers for more than one decade. But on the other hand there are many sets which are naturally endowed by two compatible binary operations forming a non-associative ring and we may dig out examples which investigate a non-associative structure in the context of soft sets. Thus it seems natural to apply the concept of soft sets to non-commutative and non-associative structures. In present paper, we make a new approach to apply Molodtsoves notion of soft sets to LA-ring (a class of non-associative ring). We extend the study of soft commutative rings from theoretical aspect.

Keywords: soft sets, LA-rings, soft LA-rings, soft ideals, soft prime ideals, idealistic soft LA-rings, LA-ring homomorphism

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Authors: P. Góes, J. Manzi

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This paper focuses on the development of an energy efficiency index that will be applied to reactive systems, which is based in the First and Second Law of Thermodynamics, by giving particular consideration to the concept of maximum entropy. Among the requirements of such energy efficiency index, the practical feasibility must be essential. To illustrate the performance of the proposed index, such an index was used as decisive factor of evaluation for the optimization process of an industrial reactor. The results allow the conclusion to be drawn that the energy efficiency index applied to the reactive system is consistent because it extracts the information expected of an efficient indicator, and that it is useful as an analytical tool besides being feasible from a practical standpoint. Furthermore, it has proved to be much simpler to use than tools based on traditional methodologies.

Keywords: energy, efficiency, entropy, reactive

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Authors: Khawar Ali

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We present the numerical study of unsteady hydromagnetic (MHD) flow and heat transfer characteristics of a viscous incompressible electrically conducting water-based hybrid metallic nanofluid (containing Cu-Au/ H₂O nanoparticles) between two orthogonally moving porous coaxial disks with suction. Different from the classical shooting methodology, we employ a combination of a direct and an iterative method (SOR with optimal relaxation parameter) for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar nonlinear ODEs. Effects of the governing parameters on the flow and heat transfer are discussed and presented through tables and graphs. The findings of the present investigation may be beneficial for the electronic industry in maintaining the electronic components under effectiveand safe operational conditions.

Keywords: heat transfer enhancement, hybrid metallic nanofluid, viscous dissipation and joule heating effect , Two dimensional flow

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Authors: Hend Alrasheed

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Due to their different properties that have led to avoid several limitations of classic client/server systems, there has been a great interest in the development and the improvement of different peer to peer systems. Understanding the properties of complex peer to peer networks is essential for their future improvements. It was shown that the performances of peer to peer protocols are directly related to their underlying topologies. Therefore, multiple efforts have analyzed the topologies of different peer to peer systems. This study presents an overview of major findings of close experimental analyses to different topologies of three unstructured peer to peer systems: BitTorrent, Gnutella, and FreeNet.

Keywords: peer to peer networks, network topology, graph diameter, clustering coefficient, small-world property, random graph, degree distribution

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Authors: A. Elnady

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This paper presents an improved Direct Power Control (DPC) scheme applied to the multilevel inverter that forms a Distributed Generation Unit (DGU). This paper demonstrates the performance of active and reactive power injected by the DGU to the smart grid. The DPC is traditionally operated by the hysteresis controller with the Space Vector Modulation (SVM) which is applied on the 2-level inverters or 3-level inverters. In this paper, the DPC is operated by the PI controller with the Phase-Disposition Pulse Width Modulation (PD-PWM) applied to the 5-level diode clamped inverter. The new combination of the DPC, PI controller, PD-PWM and multilevel inverter proves that its performance is much better than the conventional hysteresis-SVM based DPC. Simulations results have been presented to validate the performance of the suggested control scheme in the grid-connected mode.

Keywords: direct power control, PI controller, PD-PWM, and power control

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Authors: Hussain Abdullah Al-Salamin, Elias Ogutu Azariah Tembe

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Supply chain (SC) is an operational research (OR) approach and technique which acts as catalyst within central nervous system of business today. Without SC, any type of business is at doldrums, hence entropy. SC is the lifeblood of business today because it is the pivotal hub which provides imperative competitive advantage. The paper present a conceptual framework dubbed as Homomorphic Conceptual Framework for Effective Supply Chain Strategy (HCEFSC).The term homomorphic is derived from abstract algebraic mathematical term homomorphism (same shape) which also embeds the following mathematical application sets: monomorphism, isomorphism, automorphisms, and endomorphism. The HCFESC is intertwined and integrated with wide and broad sets of elements.

Keywords: homomorphism, isomorphism, monomorphisms, automorphisms, epimorphisms, endomorphism, supply chain, operational research (OR)

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Authors: Davide Forcellini, James Marshal Kelly

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Seismic isolation using multi-layer elastomeric isolators has been used in the United States for more than 20 years. Although isolation bearings normally have a large factor of safety against buckling due to low shear stiffness, this phenomenon has been widely studied. In particular, the linearly elastic theory adopted to study this phenomenon is relatively accurate and adequate for most design purposes. Unfortunately it cannot consider the large deformation response of a bearing when buckling occurs and the unresolved behaviour of the stability of the post-buckled state. The study conducted in this paper may be viewed as a development of the linear theory of multi-layered elastomeric bearing, simply replacing the differential equations by algebraic equations, showing how it is possible to evaluate the post-buckling behaviour and the interactions at large deformations.

Keywords: multi-layer elastomeric isolators, large deformation, compressive load, tensile load, post-buckling behaviour

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Authors: Zhang Kehan, Du Luona

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Wireless power transfer (WPT) systems have been widely investigated for advantages of convenience and safety compared to traditional plug-in charging systems. The research contents include impedance matching, circuit topology, transfer distance et al. for improving the efficiency of WPT system, which is a decisive factor in the practical application. What is more, coil structures such as spiral circular coil and helical coil with variable distance between two turns also have indispensable effects on the efficiency of WPT systems. This paper compares the efficiency of WPT systems utilizing spiral or helical coil with variable distance between two turns, and experimental results show that efficiency of spiral circular coil with an optimum distance between two turns is the highest. According to efficiency formula of resonant WPT system with series-series topology, we introduce M²/R₋₁ to measure the efficiency of spiral circular coil and helical coil WPT system. If the distance between two turns s is too close, proximity effect theory shows that the induced current in the conductor, caused by a variable flux created by the current flows in the skin of vicinity conductor, is the opposite direction of source current and has assignable impart on coil resistance. Thus in two coil structures, s affects coil resistance. At the same time, when the distance between primary and secondary coils is not variable, s can also make the influence on M to some degrees. The aforementioned study proves that s plays an indispensable role in changing M²/R₋₁ and then can be adjusted to find the optimum value with which WPT system achieves the highest efficiency. In actual application situations of WPT systems especially in underwater vehicles, miniaturization is one vital issue in designing WPT system structures. Limited by system size, the largest external radius of spiral circular coil is 100 mm, and the largest height of helical coil is 40 mm. In other words, the turn of coil N changes with s. In spiral circular and helical structures, the distance between each two turns in secondary coil is set as a constant value 1 mm to guarantee that the R2 is not variable. Based on the analysis above, we set up spiral circular coil and helical coil model using COMSOL to analyze the value of M²/R₋₁ when the distance between each two turns in primary coil sp varies from 0 mm to 10 mm. In the two structure models, the distance between primary and secondary coils is 50 mm and wire diameter is chosen as 1.5 mm. The turn of coil in secondary coil are 27 in helical coil model and 20 in spiral circular coil model. The best value of s in helical coil structure and spiral circular coil structure are 1 mm and 2 mm respectively, in which the value of M²/R₋₁ is the largest. It is obviously to select spiral circular coil as the first choice to design the WPT system for that the value of M²/R₋₁ in spiral circular coil is larger than that in helical coil under the same condition.

Keywords: distance between two turns, helical coil, spiral circular coil, wireless power transfer

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Authors: A. Sri Janani, K. Immanuel Arokia James

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Cognitive radio ad hoc networks different unlicensed users may acquire different available channel sets. This non-uniform spectrum availability imposes special design challenges for broadcasting in CR ad hoc networks. Cognitive radio automatically detects available channels in wireless spectrum. This is a form of dynamic spectrum management. Cross-layer optimization is proposed, using this can allow far away secondary users can also involve into channel work. So it can increase the throughput and it will overcome the collision and time delay.

Keywords: cognitive radio, cross layer optimization, CR mesh network, heterogeneous spectrum, mesh topology, random routing optimization technique

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Authors: Yingxu Wang, Jianhua Lu, Jun Peng, Jiawei Zhang

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The fundamental demand in contemporary intelligent science towards Autonomous AI (AI*) is the creation of unprecedented formal means of Intelligent Mathematics (IM). It is discovered that natural intelligence is inductively created rather than exhaustively trained. Therefore, IM is a family of algebraic and denotational mathematics encompassing Inference Algebra, Real-Time Process Algebra, Concept Algebra, Semantic Algebra, Visual Frame Algebra, etc., developed in our labs. IM plays indispensable roles in training-free AI* theories and systems beyond traditional empirical data-driven technologies. A set of applications of IM-driven AI* systems will be demonstrated in contemporary intelligence science, AI*, and cognitive computers.

Keywords: intelligence mathematics, foundations of intelligent science, autonomous AI, cognitive computers, inference algebra, real-time process algebra, concept algebra, semantic algebra, applications

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Authors: R. J. Chang

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A cyclostationary Gaussian linearization method is formulated for investigating the time average response of nonlinear system under sinusoidal signal and white noise excitation. The quantitative measure of cyclostationary mean, variance, spectrum of mean amplitude, and mean power spectral density of noise is analyzed. The qualitative response behavior of stochastic jump and bifurcation are investigated. The validity of the present approach in predicting the quantitative and qualitative statistical responses is supported by utilizing Monte Carlo simulations. The present analysis without imposing restrictive analytical conditions can be directly derived by solving non-linear algebraic equations. The analytical solution gives reliable quantitative and qualitative prediction of mean and noise response for the Duffing system subjected to both sinusoidal signal and white noise excitation.

Keywords: cyclostationary, duffing system, Gaussian linearization, sinusoidal, white noise

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Authors: Amir Mahdavi

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In this paper a highly linear CMOS low noise amplifier (LNA) for ultra-wideband (UWB) applications is proposed. The proposed LNA uses a linearization technique to improve second and third-order intercept points (IIP3). The linearity is cured by repealing the common-mode section of all intermodulation components from the cascade topology current with optimization of biasing current use symmetrical and asymmetrical circuits for biasing. Simulation results show that maximum gain and noise figure are 6.9dB and 3.03-4.1dB over a 3.1–10.6 GHz, respectively. Power consumption of the LNA core and IIP3 are 2.64 mW and +4.9dBm respectively. The wideband input impedance matching of LNA is obtained by employing a degenerating inductor (|S11|<-9.1 dB). The circuit proposed UWB LNA is implemented using 0.18 μm based CMOS technology.

Keywords: highly linear LNA, low-power LNA, optimal bias techniques

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Authors: N. R. Harris, J. Curry

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This paper describes the construction and operation of an experimental LoRaWAN network surrounding the University of Southampton in the United Kingdom. Following successful installation, an experimental node design is built and characterised, with particular emphasis on radio range. Several configurations are investigated, including different data rates, and varying heights of node. It is concluded that although range can be great (over 8 km in this case), environmental topology is critical. However, shorter range implementations, up to about 2 km in an urban environment, are relatively insensitive although care is still needed. The example node and the relatively simple base station reported demonstrate that LoraWan can be a very low cost and practical solution to Internet of Things type applications for distributed monitoring systems with sensors spread over distances of several km.

Keywords: long-range, wireless, sensor, network

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Authors: Ali Asghar Memon

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A cautious and astute selection of switching devices used in power electronic converters of a switched reluctance (SR) motor is required. It is a matter of choice of best switching devices with respect to their switching ability rather than fulfilling the number of switches. This paper highlights the computational determination of switching losses comprising of switch-on, switch-off and conduction losses respectively by using experimental data in simulation model of a SR machine. The finding of this research is helpful for proper selection of electronic switches and suitable converter topology for switched reluctance motor.

Keywords: converter, operating modes, switched reluctance motor, switching losses

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Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

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We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

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Authors: Alibakhsh Kasaeian, Mohammad Sameti, Zahra Noori, Mona Rastgoo Bahambari

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Nowadays, the parabolic trough solar collector technology has become the most promising large-scale technology among various solar thermal generations. In this paper, a detailed numerical heat transfer model for a parabolic trough collector with nanofluid is presented based on the finite difference approach for which a MATLAB code was developed. The model was used to simulate the performance of a parabolic trough solar collector’s linear receiver, called a heat collector element (HCE). In this model, the heat collector element of the receiver was discretized into several segments in axial directions and energy balances were used for each control volume. All the heat transfer correlations, the thermodynamic equations and the optical properties were considered in details and the set of algebraic equations were solved simultaneously using iterative numerical solutions. The modeling assumptions and limitations are also discussed, along with recommendations for model improvement.

Keywords: heat transfer, nanofluid, numerical analysis, trough

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Authors: Alicja Starczewska, Aleksander Nawrat, Krzysztof Daniec, Jarosław Homa, Kacper Hołda

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Border Gateway Protocol is the main routing protocol that enables routing establishment between all autonomous systems, which are the basic administrative units of the internet. Due to the poor protection of BGP, it is important to use additional BGP security systems. Many solutions to this problem have been proposed over the years, but none of them have been implemented on a global scale. This article describes a system capable of building images of real-time BGP network topology in order to detect BGP anomalies. Our proposal performs a detailed analysis of BGP messages that come into local network cards supplemented by information collected by remote collectors in different localizations.

Keywords: BGP, BGP hijacking, cybersecurity, detection

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Authors: Zaouche Khelil, Talha Abdelaziz, Berkouk El Madjid

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In this paper, we present a grid-tied photovoltaic system. The studied topology is structured around a seven-level inverter, supplying a non-linear load. A three-stage step-up DC/DC converter ensures DC-link balancing. The presented system allows the extraction of all the available photovoltaic power. This extracted energy feeds the local load; the surplus energy is injected into the electrical network. During poor weather conditions, where the photovoltaic panels cannot meet the energy needs of the load, the missing power is supplied by the electrical network. At the common connexion point, the network current shows excellent spectral performances.

Keywords: seven-level inverter, multi-level DC/DC converter, photovoltaic, non-linear load

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Authors: Mourad Hrizi

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In this paper, we study the inverse problem of reconstructing an interior interface D appearing in the elliptic partial differential equation: Δu+χ(D)u=0 from the knowledge of the boundary measurements. This problem arises from a semiconductor transistor model. We propose a new shape reconstruction procedure that is based on the Kohn-Vogelius formulation and the topological sensitivity method. The inverse problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a function. The unknown subdomain D is reconstructed using a level-set curve of the topological gradient. Finally, we give several examples to show the viability of our proposed method.

Keywords: inverse problem, topological optimization, topological gradient, Kohn-Vogelius formulation

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Authors: Andrey Lebedev, Ilya Dmitrenok, JooYoung Lee, Leonard Johard

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Top-k shortest path routing problem is an extension of finding the shortest path in a given network. Shortest path is one of the most essential measures as it reveals the relations between two nodes in a network. However, in many real world networks, whose diameters are small, top-k shortest path is more interesting as it contains more information about the network topology. Many variations to compute top-k shortest paths have been studied. In this paper, we apply an efficient top-k shortest distance routing algorithm to the link prediction problem and test its efficacy. We compare the results with other base line and state-of-the-art methods as well as with the shortest path. Then, we also propose a top-k distance based graph matching algorithm.

Keywords: graph matching, link prediction, shortest path, similarity

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