Search results for: applied algebraic topology

Authors: M. Khoshab, M. J. Sedigh

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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: dynamic system, lag on supply demand, market stability, supply demand model

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Authors: Ali Afaghi, Sehraneh Ghaemi

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The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications.

Keywords: fractional-order multi-agent systems, leader-following consensus, nonlinear dynamics, directed graphs

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Authors: Ladznar S. Laja, Rosalio G. Artes, Jr.

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This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established.

Keywords: convex subgraph, convex index, generating function, polynomial ring

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Authors: Adeyemo Abduljeeel Taiwo

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This research is an attempt that creates a conducive atmosphere of a phonological and morphological compendium of Arabic language in Modern Standard Arabic (MSA) for modern day communications. The research is carried out with the chief aim of grammatical analysis of the two broad fields of Arabic linguistics namely: Applied and Socio-Linguistics. It draws a pictorial record of Applied and Socio-Linguistics in Arabic phonology and morphology. Thematically, it postulates and contemplates to a large degree, the theory of concord in contemporary modern Arabic language acquisition. It utilizes an analytical method while it portrays Arabic as a Semitic language that promotes linguistics and syntax among the scholars of the fields.

Keywords: Arabic language, applied linguistics, socio-linguistics, modern communications

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Sartaj Singh, Amar Singh, Ashok Sharma, Sandeep Kaur

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With upcoming threats in a digital world, we need to work continuously in the area of security in all aspects, from hardware to software as well as data modelling. The rise in social media activities and hunger for data by various entities leads to cybercrime and more attack on the privacy and security of persons. Cryptography has always been employed to avoid access to important data by using many processes. Symmetric key and asymmetric key cryptography have been used for keeping data secrets at rest as well in transmission mode. Various cryptosystems have evolved from time to time to make the data more secure. In this research article, we are studying various cryptosystems in asymmetric cryptography and their application with usefulness, and much emphasis is given to Elliptic curve cryptography involving algebraic mathematics.

Keywords: cryptography, symmetric key cryptography, asymmetric key cryptography

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Authors: Ho-Ting Wu, Kai-Wei Ke, Bo-Yu Huang, Liang-Lin Yan, Chun-Ting Lin

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With the advances in advanced technology, wireless sensor network (WSN) has become one of the most promising candidates to implement the wireless industrial internet of things (IIOT) architecture. However, the legacy IEEE 802.15.4 based WSN technology such as Zigbee system cannot meet the stringent QoS requirement of low powered, real-time, and highly reliable transmission imposed by the IIOT environment. Recently, the IEEE society developed IEEE 802.15.4e Time Slotted Channel Hopping (TSCH) access mode to serve this purpose. Furthermore, the IETF 6TiSCH working group has proposed standards to integrate IEEE 802.15.4e with IPv6 protocol smoothly to form a complete protocol stack for IIOT. In this work, we develop key network technologies for IEEE 802.15.4e based wireless IIoT architecture, focusing on practical design and system implementation. We realize the OpenWSN-based wireless IIOT system. The system architecture is divided into three main parts: web server, network manager, and sensor nodes. The web server provides user interface, allowing the user to view the status of sensor nodes and instruct sensor nodes to follow commands via user-friendly browser. The network manager is responsible for the establishment, maintenance, and management of scheduling and topology information. It executes centralized scheduling algorithm, sends the scheduling table to each node, as well as manages the sensing tasks of each device. Sensor nodes complete the assigned tasks and sends the sensed data. Furthermore, to prevent scheduling error due to packet loss, a schedule inspection mechanism is implemented to verify the correctness of the schedule table. In addition, when network topology changes, the system will act to generate a new schedule table based on the changed topology for ensuring the proper operation of the system. To enhance the system performance of such system, we further propose dynamic bandwidth allocation and distributed scheduling mechanisms. The developed distributed scheduling mechanism enables each individual sensor node to build, maintain and manage the dedicated link bandwidth with its parent and children nodes based on locally observed information by exchanging the Add/Delete commands via two processes. The first process, termed as the schedule initialization process, allows each sensor node pair to identify the available idle slots to allocate the basic dedicated transmission bandwidth. The second process, termed as the schedule adjustment process, enables each sensor node pair to adjust their allocated bandwidth dynamically according to the measured traffic loading. Such technology can sufficiently satisfy the dynamic bandwidth requirement in the frequently changing environments. Last but not least, we propose a packet retransmission scheme to enhance the system performance of the centralized scheduling algorithm when the packet delivery rate (PDR) is low. We propose a multi-frame retransmission mechanism to allow every single network node to resend each packet for at least the predefined number of times. The multi frame architecture is built according to the number of layers of the network topology. Performance results via simulation reveal that such retransmission scheme is able to provide sufficient high transmission reliability while maintaining low packet transmission latency. Therefore, the QoS requirement of IIoT can be achieved.

Keywords: IEEE 802.15.4e, industrial internet of things (IIOT), scheduling mechanisms, wireless sensor networks (WSN)

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Authors: Serges Mendomo Meye, Li Guowei, Shen Zhenzhong

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Earthquake is one of the main loads threatening dam safety. Once the dam is damaged, it will bring huge losses of life and property to the country and people. Therefore, it is very important to research the seismic safety of the dam. Due to the complex foundation conditions, high fortification intensity, and high scientific and technological content, it is necessary to adopt reasonable methods to evaluate the seismic safety performance of concrete arch dams built and under construction in strong earthquake areas. Structural seismic vulnerability analysis can predict the probability of structural failure at all levels under different intensity earthquakes, which can provide a scientific basis for reasonable seismic safety evaluation and decision-making. In this paper, the response surface method (RSM) is applied to the seismic vulnerability analysis of arch dams, which improves the efficiency of vulnerability analysis. Based on the central composite test design method, the material-seismic intensity samples are established. The response surface model (RSM) with arch crown displacement as performance index is obtained by finite element (FE) calculation of the samples, and then the accuracy of the response surface model (RSM) is verified. To obtain the seismic vulnerability curves, the seismic intensity measure ??(?1) is chosen to be 0.1~1.2g, with an interval of 0.1g and a total of 12 intensity levels. For each seismic intensity level, the arch crown displacement corresponding to 100 sets of different material samples can be calculated by algebraic operation of the response surface model (RSM), which avoids 1200 times of nonlinear dynamic calculation of arch dam; thus, the efficiency of vulnerability analysis is improved greatly.

Keywords: high concrete arch dam, performance index, response surface method, seismic vulnerability analysis, vector-valued intensity measure

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Authors: Sana Ansari, Sirus Mohammadi

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In distribution systems, shunt capacitors are used to reduce power losses, to improve voltage profile, and to increase the maximum flow through cables and transformers. This paper presents a new method to determine the optimal locations and economical sizing of fixed and/or switched shunt capacitors with a view to power losses reduction and voltage stability enhancement. General Algebraic Modeling System (GAMS) has been used to solve the maximization modules using the MINOS optimization software with Linear Programming (LP). The proposed method is tested on 33 node distribution system and the results show that the algorithm suitable for practical implementation on real systems with any size.

Keywords: power losses, voltage stability, radial distribution systems, capacitor

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Authors: Yang Xiong, Hua Cheng

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In this paper, for the basic problem of wireless sensor network topology control and deployment, the Roesser model in rectangular grid sensor networks is presented. In addition, a general constructive realization procedure will be proposed. The procedure enables a distributed implementation of linear systems on a sensor network. A non-trivial example is illustrated.

Keywords: grid sensor networks, Roesser model, state-space realization, multidimensional systems

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Jonathan Galvan-Colin, Ariel Valladares, Renela Valladares, Alexander Valladares

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Both porous materials and bulk metallic glasses have been studied due to their potential applications and their exceptional physical and chemical properties. However, each material presents certain drawbacks which have been thought to be overcome by generating bulk metallic glass foams (BMGF). Although some experimental reports have been performed on multicomponent BMGF, still no ab initio works have been published, as far as we know. We present an approach based on the expanding lattice (EL) method to generate binary amorphous nanoporous Cu64Zr36. Starting from two different configurations: a 108-atom crystalline cubic supercell (cCu64Zr36) and a 108-atom amorphous supercell (aCu64Zr36), both with an initial density of 8.06 g/cm3, we applied EL method to halve the density and to get 50% of porosity. After the lattice expansion the supercells were subject to ab initio molecular dynamics for 500 steps at constant room temperature. Then, the samples were geometry-optimized and characterized with the pair and radial distribution functions, bond-angle distributions and a coordination number analysis. We found that pores appeared along specific spatial directions different from one to another and that they differed in size and form as well, which we think is related to the initial structure. Due to the lack of experimental counterparts our results should be considered predictive and further studies are needed in order to handle a larger number of atoms and its implication on pore topology.

Keywords: ab initio molecular dynamics, bulk mettalic glass, porous alloy

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Authors: Yen Yi Huang

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This paper aims to explore the application of strategies in applied drama to the social work education arena in order to enhance students' creativity, curiosity, and aesthetic sensitivity. Also, applied drama is used as a means to facilitate students' reflection-in-action and improve their understanding of issues on creative aging, gender equality, human rights, bullying, and prejudice. This paper mainly uses the perspective of Homi K. Bhabha's third space to explore the impact of applied drama and social work training on students. First, it focuses on how students create new understandings and insights in the third space of multidisciplinary training studies. Second, it analyzes how the hybridity and negotiation of ideas between applied drama and social work were created. Finally, it discusses the follow-up effects of the training and the factors that promote or hinder the hybridity and generation of the third space. This paper uses students' reflection papers for analysis. It is not focused on a discussion of the effectiveness of the teaching but attempts to bring new insights into the applications of applied drama to the social work education arena. The hybridity and generation of the third space require handling power strategically and looking after the emotional space of the students. Taking part in the training allows students in the third space of multidisciplinary training to reexamine the traditional framework of social work knowledge to create new ideas and possibilities.

Keywords: multidisciplinary, applied drama, social work education, third space

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Authors: Shai Sarussi

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Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. A characterization of the property of immediate neighbors in an Alexandroff topological space is given, in terms of closed and open subsets of appropriate subspaces. Moreover, two special subspaces of W are introduced, and a way in which their closed and open subsets induce W is presented.

Keywords: integral domains, Alexandroff topology, immediate neighbors, valuation domains

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Authors: Julia Langen

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This article describes the challenges of a wireless charging system for a cab waiting lane in a public space and presents a concept for solving them. In this concept, multiple cabs can be charged simultaneously and during stopping and rolling. Particular technical challenges are a coil topology that meets the EMF requirements and an intelligent control concept that allows the individual coil segments to be switched on and off. The charging concept explained here is currently being implemented as a pilot project, so that initial results on the operation can be presented.

Keywords: charge lane, inductive charging solution, smart city, wireless power transfer

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Authors: G. A. Babalola, Yusuf Muhammad

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An analysis was carried out on 19,759 citations appended to the References Section of 881 research articles published in Bayero Journal of Pure and Applied Sciences. It was found that journals publications were the most cited source of information among pure and applied sciences scientists with 12,090 (61.2%). The study also revealed that researchers in the field of pure and applied sciences used very current and up to date information sources in writing theirs articles with 10,091 (51.1%) citations and an average mean 11.1 per article in the journal.

Keywords: citation analysis, BAJOPAS, journal article, Bayero University Kano, Nigeria

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Authors: T. Asefi, J. Faiz, M. A. Khan

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This paper introduces dual rotor axial flux machines with surface mounted and spoke type ferrite permanent magnets with concentrated windings; they are introduced as alternatives to a generator with surface mounted Nd-Fe-B magnets. The output power, voltage, speed and air gap clearance for all the generators are identical. The machine designs are optimized for minimum mass using a population-based algorithm, assuming the same efficiency as the Nd-Fe-B machine. A finite element analysis (FEA) is applied to predict the performance, emf, developed torque, cogging torque, no load losses, leakage flux and efficiency of both ferrite generators and that of the Nd-Fe-B generator. To minimize cogging torque, different rotor pole topologies and different pole arc to pole pitch ratios are investigated by means of 3D FEA. It was found that the surface mounted ferrite generator topology is unable to develop the nominal electromagnetic torque, and has higher torque ripple and is heavier than the spoke type machine. Furthermore, it was shown that the spoke type ferrite permanent magnet generator has favorable performance and could be an alternative to rare-earth permanent magnet generators, particularly in wind energy applications. Finally, the analytical and numerical results are verified using experimental results.

Keywords: axial flux, permanent magnet generator, dual rotor, ferrite permanent magnet generator, finite element analysis, wind turbines, cogging torque, population-based algorithms

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Authors: Mamyrbek A. Beisenbi, Nurgul M. Kissikova, Saltanat E. Beisembina, Salamat T. Suleimenova, Samal A. Kaliyeva

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The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability

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Authors: Alessandra Rossodivita, Alexei Tikhomirov, Andrey Trufanov, Nikolay Kinash, Olga Berestneva, Svetlana Nikitina, Fabio Casati, Alessandro Visconti, Tommaso Saporito

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It is well known that world and national societies are exposed to diverse threats: anthropogenic, technological, and natural. Anthropogenic ones are of greater risks and, thus, attract special interest to researchers within wide spectrum of disciplines in efforts to lower the pertinent risks. Some researchers showed by means of multilayered, complex network models how media promotes the prevention of disease spread. To go further, not only are mass-media sources included in scope the paper suggests but also personificated social bots (socbots) linked according to reflexive theory. The novel scope considers information spread over conscious and unconscious agents while counteracting both natural and man-made threats, i.e., infections and terrorist hazards. Contrary to numerous publications on misinformation disseminated by ‘bad’ bots within social networks, this study focuses on ‘good’ bots, which should be mobilized to counter the former ones. These social bots deployed mixture with real social actors that are engaged in concerted actions at spreading, receiving and analyzing information. All the contemporary complex network platforms (multiplexes, interdependent networks, combined stem networks et al.) are comprised to describe and test socbots activities within competing information sharing tools, namely mass-media hubs, social networks, messengers, and e-mail at all phases of disasters. The scope and concomitant techniques present evidence that embedding such socbots into information sharing process crucially change the network topology of actor interactions. The change might improve or impair robustness of social network environment: it depends on who and how controls the socbots. It is demonstrated that the topological approach elucidates techno-social processes within the field and outline the roadmap to a safer world.

Keywords: complex network platform, counterterrorism, information sharing topology, social bots

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Authors: Abdelkarim Boua, Abdelhakim Chillali

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The study of non-associative structures in algebraic structures has become a separate entity; for, in the case of groups, their corresponding non-associative structure i.e. loops is dealt with separately. Similarly there is vast amount of research on the nonassociative structures of semigroups i.e. groupoids and that of rings i.e. nonassociative rings. However it is unfortunate that we do not have a parallel notions or study of non-associative near-rings. In this work we shall attempt to generalize a few known results and study the commutativity of Jordan ideal in 3-prime near-rings satisfying certain identities involving the Jordan ideal. We study the derivations satisfying certain differential identities on Jordan ideals of 3-prime near-rings. Moreover, we provide examples to show that hypothesis of our results are necessary. We give some new results and examples concerning the existence of Jordan ideal and derivations in near-rings. These near-rings can be used to build a new codes.

Keywords: 3-prime near-rings, near-rings, Jordan ideal, derivations

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Authors: Galal Elkobrosy, Amr M. Abdelrazek, Bassuny M. Elsouhily, Mohamed E. Khidr

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Crank shaft length, connecting rod length, crank angle, engine rpm, cylinder bore, mass of piston and compression ratio are the inputs that can control the performance of the slider crank mechanism and then its efficiency. Several combinations of these seven inputs are used and compared. The throughput engine torque predicted by the simulation is analyzed through two different regression models, with and without interaction terms, developed according to multi-linear regression using LU decomposition to solve system of algebraic equations. These models are validated. A regression model in seven inputs including their interaction terms lowered the polynomial degree from 3^rd degree to 1^st degree and suggested valid predictions and stable explanations.

Keywords: design of experiments, regression analysis, SI engine, statistical modeling

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Amal Ezzidani, Abdelghani Ben Tahar, Mohamed Hanini

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A sequence of finite tandem queue is considered for this study. Each one has a single server, which operates under the egalitarian processor sharing discipline. External customers arrive at each queue according to a renewal input process and having a general service times distribution. Upon completing service, customers leave the current queue and enter to the next. Under mild assumptions, including critical data, we prove the existence and the uniqueness of the fluid solution. For asymptotic behavior, we provide necessary and sufficient conditions for the invariant state and the convergence to this invariant state. In the end, we establish the convergence of a correctly normalized state process to a fluid limit characterized by a system of algebraic and integral equations.

Keywords: fluid limit, fluid model, measure valued process, processor sharing, tandem queue

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Authors: Qingying Liu, S. Liu, L. Hao, B. Zhang, J. D. Yan

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HVDC technology is becoming increasingly popular due to its simplicity in topology and less power loss over long distance of power transmission, in comparison with HVAC technology. However, the dielectric behavior of insulators in the long term under HVDC stress is completely different from that under HVAC stress as a result of charge accumulation in a constant electric field. Insulators used in practical systems are never perfect in their structural conditions. Over time shallow cracks may develop on their surface. The presence of defects can lead to drastic change in their dielectric behaviour and thus increase the probability of surface flashover. In this contribution, experimental investigations have been carried out on the charge accumulation phenomenon on the surface of a rod insulator made of epoxy that is placed between two disk shaped electrodes at different voltage levels and in different gases (SF6, CO2 and N2). Many results obtained, such as, the two-dimensional electrostatic potential distribution along the insulator surface after the removal of the power source following a pre-defined period of application. The probe has been carefully calibrated before each test. Results show that surface charge distribution near the two disk shaped electrodes is not uniform in the circumferential direction, possibly due to the imperfect electrical connections between the embeded conductor in the insulator and the disk shaped electrodes. The axial length of this non-uniform region is experimentally determined, which provides useful information for shielding design. A charge transport model is also used to explain the formation of the long term electrostatic potential distribution under a constant applied voltage.

Keywords: HVDC, power systems, dielectric behavior, insulation, charge accumulation

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Authors: Jin Xu

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5G network developers need to satisfy the necessary requirements of additional capacity from massive users and spectrally efficient wireless technologies. Therefore, the significant amount of underutilized spectrum in network is motivating operators to combine long-term evolution (LTE) with intelligent spectrum management technology. This new LTE intelligent spectrum management in unlicensed band (LTE-U) has the physical layer topology to access spectrum, specifically the 5-GHz band. We proposed a new intelligent cloud RAN for 5G.

Keywords: cloud radio access network, wireless network, cloud computing, multi-agent

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

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Authors: Vishal H. Shukla, Sanjay B. Deshmukh

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Traffic engineering, at its center, is the ability of moving traffic approximately so that traffic from a congested link is moved onto the unused capacity on another link. Traffic Engineering ensures the best possible use of the resources. Now to support traffic engineering in the today’s network, Multiprotocol Label Switching (MPLS) is being used which is very helpful for reliable packets delivery in an ongoing internet services. Here a topology is been implemented on GNS3 to focus on the analysis of the communication take place from one site to other through the ISP. The comparison is made between the IP network & MPLS network based on Bandwidth & Jitter which are one of the performance parameters using JPERF simulator.

Keywords: GNS3, JPERF, MPLS, traffic engineering, VMware

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Authors: Joao Fialho

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The mathematical modelling of idiopathic scoliosis has been studied throughout the years. The models presented on those papers are based on the orthotic stabilization of the idiopathic scoliosis, which are based on a transversal force being applied to the human spine on a continuous form. When considering the ATT (Antalgic-Trak Technology) device, the existent models cannot be used, as the type of forces applied are no longer transversal nor applied in a continuous manner. In this device, vertical traction is applied. In this study we propose to model the idiopathic scoliosis, using the ATT (Antalgic-Trak Technology) device, and with the parameters obtained from the mathematical modeling, set up a case-by-case individualized therapy plan, for each patient.

Keywords: idiopathic scoliosis, mathematical modelling, human spine, Antalgic-Trak technology

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Authors: Abdi Ammar, Ouazir Youcef, Laissaoui Abdelmalek

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In this work, an approach based on transmission lines theory is presented. It is exploited for the calculation of overvoltage created by direct impacts of lightning waves on a guard cable of an overhead high-voltage line. First, we show the theoretical developments leading to the propagation equation, its discretization by finite difference time domain method (FDTD), and the resulting linear algebraic equations, followed by the calculation of the linear parameters of the line. The second step consists of solving the transmission lines system of equations by the FDTD method. This enabled us to determine the spatio-temporal evolution of the induced overvoltage.

Keywords: lightning surge, transient overvoltage, eddy current, FDTD, electromagnetic compatibility, ground wire

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Authors: Radoslaw Pytlak, Damian Suski

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The aim of the paper is to provide a computational tool for planning a haemodialysis process. It is shown that optimization methods can be used to obtain the most effective treatment focused on removing both urea and phosphorus during the process. In order to achieve that, the IV–compartment model of phosphorus kinetics is applied. This kinetics model takes into account a rebound phenomenon that can occur during haemodialysis and results in a hybrid model of the process. Furthermore, vector fields associated with the model equations are such that it is very likely that using the most intuitive objective functions in the planning problem could lead to solutions which include sliding motions. Therefore, building computational tools for solving the problem of planning a haemodialysis process has required constructing numerical algorithms for solving optimal control problems with hybrid systems. The paper concentrates on minimum time control of hybrid systems since this control objective is the most suitable for the haemodialysis process considered in the paper. The presented approach to optimal control problems with hybrid systems is different from the others in several aspects. First of all, it is assumed that a hybrid system can exhibit sliding modes. Secondly, the system’s motion on the switching surface is described by index 2 differential–algebraic equations, and that guarantees accurate tracking of the sliding motion surface. Thirdly, the gradients of the problem’s functionals are evaluated with the help of adjoint equations. The adjoint equations presented in the paper take into account sliding motion and exhibit jump conditions at transition times. The optimality conditions in the form of the weak maximum principle for optimal control problems with hybrid systems exhibiting sliding modes and with piecewise constant controls are stated. The presented sensitivity analysis can be used to construct globally convergent algorithms for solving considered problems. The paper presents numerical results of solving the haemodialysis planning problem.

Keywords: haemodialysis planning process, hybrid systems, optimal control, sliding motion

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