46 research outputs found

    Electronic Journal of Qualitative Theory of Differential Equations 2021

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    Time-Delay Switch Attack on Networked Control Systems, Effects and Countermeasures

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    In recent years, the security of networked control systems (NCSs) has been an important challenge for many researchers. Although the security schemes for networked control systems have advanced in the past several years, there have been many acknowledged cyber attacks. As a result, this dissertation proposes the use of a novel time-delay switch (TDS) attack by introducing time delays into the dynamics of NCSs. Such an attack has devastating effects on NCSs if prevention techniques and countermeasures are not considered in the design of these systems. To overcome the stability issue caused by TDS attacks, this dissertation proposes a new detector to track TDS attacks in real time. This method relies on an estimator that will estimate and track time delays introduced by a hacker. Once a detector obtains the maximum tolerable time delay of a plant’s optimal controller (for which the plant remains secure and stable), it issues an alarm signal and directs the system to its alarm state. In the alarm state, the plant operates under the control of an emergency controller that can be local or networked to the plant and remains in this stable mode until the networked control system state is restored. In another effort, this dissertation evaluates different control methods to find out which one is more stable when under a TDS attack than others. Also, a novel, simple and effective controller is proposed to thwart TDS attacks on the sensing loop (SL). The modified controller controls the system under a TDS attack. Also, the time-delay estimator will track time delays introduced by a hacker using a modified model reference-based control with an indirect supervisor and a modified least mean square (LMS) minimization technique. Furthermore, here, the demonstration proves that the cryptographic solutions are ineffective in the recovery from TDS attacks. A cryptography-free TDS recovery (CF-TDSR) communication protocol enhancement is introduced to leverage the adaptive channel redundancy techniques, along with a novel state estimator to detect and assist in the recovery of the destabilizing effects of TDS attacks. The conclusion shows how the CF-TDSR ensures the control stability of linear time invariant systems

    AnĂĄlisis de sistemas dinĂĄmicos infinito-dimensionales asociados a ecuaciones en derivadas parciales funcionales.

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    Based on the theory of functional diferential equations, theory of semigroup, theory of random dynamical systems and theory of in nite dimensional dynamical systems, this thesis studies the long time behavior of several kinds of in nite dimensional dynamical systems associated to partial diferential equations containing some kinds of hereditary characteristics (such as variable delay, distributed delay or memory, etc), including existence and upper semicontinuity of pullback/random attractors and the stability analysis of stationary (steady-state) solutions. Three important mathematical-phyiscal models are considered, namely, reaction-di usion equation, 2D-Navier-Stokes equation as well as in-compressible non-Newtonian uids. Chapter 1 is devoted to the dynamics of an integer order stochastic reaction-difusion equation with thermal memory when the nonlinear term is subcritical or critical. Notice that our model contains not only memory but also white noise, which means it is not easy to prove the existence and uniqueness of solutions directly. In order to deal with this problem, we need introduce a new variable to transform our model into a system with two equations, and we use the Ornstein-Uhlenbeck to transfer this system into a deterministic ones only with random parameter. Then a semigroup method together with the Lax-Milgram theorem is applied to prove the existence, uniqueness and continuity of mild solutions. Next, the dynamics of solutions is analyzed by a priori estimates, and the existence of pullback random attractors is established. Besides, we prove that this pullback random attractors cannot explode, a property known as upper semicontinuity. But the dimension of the random attractor is still unknown. On the other hand, it has been proved that sometimes, especially when self-orgnization phenomena, anisotropic di usion, anomalous difusion occurs, a fractional order diferential equation can model this phenomena more precisely than a integer one. Hence, in Chapter 2, we focus on the asymptotical behavior of a fractional stochastic reaction-difusion equation with memory, which is also called fractional integro-diferential equation. First of all, the Ornstein-Uhlenbeck is applied to change the stochastic reaction-difusion equation into a deterministic ones, which makes it more convenient to solve. Then existence and uniqueness of mild solutions is proved by using the Lumer-Phillips theorem. Next, under appropriate assumptions on the memory kernel and on the magnitude of the nonlinearity, the existence of random attractor is achieved by obtaining some uniform estimates and solutions decomposition. Moreover, the random attractor is shown to have nite Hausdorf dimension, which means the asymptotic behavior of the system is determined by only a nite number of degrees of freedom, though the random attractor is a subset of an in nite-dimensional phase space. But we still wonder whether this random attractor has inertial manifolds, which means this random attractor needs to be exponentially attracting. Besides, the long time behavior of time-fractional reaction-difusion equation and fractional Brownian motion are still unknown. The rst two chapters consider an important partial function diferential equations with in nite distributed delay. However, partial functional diferential equations include more than only distributed delays; for instance, also variable delay terms can be considered. Therefore, in the next chapter, we consider another signi cant partial functional diferential equation but with variable delay. In Chapter 3, we discuss the stability of stationary solutions to 2D Navier-Stokes equations when the external force contains unbounded variable delay. Notice that the classic phase space C which is used to deal with diferential equations with in nite delay does not work well for our unbounded variable delay case. Instead, we choose the phase space of continuous bounded functions with limits at1. Then the existence and uni- queness of solutions is proved by Galerkin approximations and the energy method. The existence of stationary solutions is established by means of the Lax-Milgram theorem and the Schauder xed point theorem. Afterward, the local stability analysis of stationary solutions is carried out by three diferent approaches: the classical Lyapunov function method, the Razumikhin-Lyapunov technique and by constructing appropriate Lyapunov functionals. It worths mentioning that the classical Lyapunov function method requires diferentiability of delay term, which in some extent is restrictive. Fortunately, we could utilize Razumikhin-Lyapunov argument to weak this condition, and only requires continuity of every operators of this equation but allows more general delay. Neverheless, by these methods, the best result we can obtain is the asymptotical stability of stationary solutions by constructing a suitable Lyapunov functionals. Fortunately, we could obtain polynomial stability of the steady-state in a particular case of unbounded variable delay, namely, the proportional delay. However, the exponential stability of stationary solutions to Navier-Stokes equation with unbounded variable delay still seems an open problem. We can also wonder about the stability of stationary solutions to 2D Navier-Stokes equations with unbounded delay when it is perturbed by random noise. Therefore, in Chapter 4, a stochastic 2D Navier-Stokes equation with unbounded delay is analyzed in the phase space of continuous bounded functions with limits at1. Because of the perturbation of random noise, the classical Galerkin approximations alone is not enough to prove the existence and uniqueness of weak solutions. By combing a technical lemma and Faedo-Galerkin approach, the existence and uniqueness of weak solutions is obtained. Next, the local stability analysis of constant solutions (equilibria) is carried out by exploiting two methods. Namely, the Lyapunov function method and by constructing appropriate Lyapunov functionals. Although it is not possible, in general, to establish the exponential convergence of the stationary solutions, the polynomial convergence towards the stationary solutions, in a particular case of unbounded variable delay can be proved. We would like to point out that the Razumikhin argument cannot be applied to analyze directly the stability of stationary solutions to stochastic equations as we did to deterministic equations. Actually, we need more technical, and this will be our forthcoming paper. We also would like to mention that exponential stability of other special cases of in nite delay remains as an open problem for both the deterministic and stochastic cases. Especially, we are interested in the pantograph equation, which is a typical but simple unbounded variable delayed diferential equation.We believe that the study of pantograph equation can help us to improve our knowledge about 2D{Navier-Stokes equations with unbounded delay. Notice that Chapter 3 and Chapter 4 are both concerned with delayed Navier-Stokes equations, which is a very important Newtonian uids, and it is extensively applied in physics, chemistry, medicine, etc. However, there are also many important uids, such as blood, polymer solutions, and biological uids, etc, whose motion cannot be modeled pre- cisely by Newtonian uids but by non-Newtonian uids. Hence, in the next two chapters, we are interested in the long time behavior of an incompressible non-Newtonian uids ith delay. In Chapter 5, we study the dynamics of non-autonomous incompressible non-Newtonian uids with nite delay. The existence of global solution is showed by classical Galerkin approximations and the energy method. Actually, we also prove the uniqueness of solutions as well as the continuous dependence of solutions on the initial value. Then, the existence of pullback attractors for the non-autonomous dynamical system associated to this problem is established under a weaker condition in space C([h; 0];H2) rather than space C([h; 0];L2), and this improves the available results that worked on non-Newtonian uids. However, we still would like to analyze the Hausdor dimension or fractal dimension of the pullback attractor, as well as the existence of inertial manifolds and morsedecomposition. Finally, in Chapter 6, we consider the exponential stability of an incompressible non Newtonian uids with nite delay. The existence and uniqueness of stationary solutions are rst established, and this is not an obvious and straightforward work because of the nonlinearity and the complexity of the term N(u). The exponential stability of steady state solutions is then analyzed by means of four diferent approaches. The rst one is the classical Lyapunov function method, which requires the diferentiability of the delay term. But this may seem a very restrictive condition. Luckily, we could use a Razumikhin type argument to weaken this condition, but allow for more general types of delay. In fact, we could obtain a better stability result by this technique. Then, a method relying on the construction of Lyapunov functionals and another one using a Gronwall-like lemma are also exploited to study the stability, respectively. We would like to emphasize that by using a Gronwall-like lemma, only the measurability of delay term is demanded, but still ensure the exponential stability. Furthermore, we also would like to discuss the dynamics of stochastic non-Newtonian uids with both nite delay and in nite delay. All the problems deserve our attraction, and actually, these are our forthcoming work

    On the electromagnetic field of a proton beam as a basis for range verification in particle therapy

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    Targeting tumor cells with ionizing radiation in an effort to eliminate them is a mainstay of cancer treatment. External beams of heavy charged particles, such as protons, are applied for such purposes and have the potential to enable highly conformal dose delivery due to their favorable depth dose profile, i.e. the so-called Bragg peak. This allows an effective sparing of healthy tissues and organs at risk, especially when compared to the conventional approach with x-rays. The finite penetration depth of protons within the patient, known as the range, is however subject to uncertainties, which can lead to significant underdosage in the tumor and excessive dose to critical structures. Inaccuracies can originate from imaging, anatomical changes, patient positioning, just to name a few. Such risk factors limit the full potential of proton therapy and necessitate the utilization of safety margins around the tumor volume, which increases the overall dose to healthy tissue. Hence, the development of methodologies to verify the proton range in vivo is an active field of research. The most prominent candidates rely on positron emission tomography (PET), prompt gamma (PG) imaging or the detection of thermoacoustic waves. These methods, however, are limited in several aspects, such as low signal-to-noise ratios or challenging detection, leaving room for new ideas and methods to be developed. Recently, it has been suggested to use the electric field of the primary protons as a basis for an alternative range verification method. The present work aims to investigate the possibilities and limitations of such an approach. The first part is concerned with an exhaustive analytical characterization of the electromagnetic field that originates from a proton pencil beam and how it is affected by biological tissues. The impact of the beam pulse shape, permittivity, conductivity and tissue boundaries are considered. Contradictory to previous results, it has been found that the charge relaxation, which originates from the ionic conductivity of biological tissues, has a huge impact on the electric field, causing it to diminish in a nanosecond time scale. The electric field is thus not suitable as a basis for range verification, considering also the washout effect, that the rapid redistribution of charges creates. The magnetic field, on the other hand, is not affected by the latter and benefits from the approximate constancy of the current density. It does not drop together with the decreasing particle velocity, but is upheld due to the equally increasing charge density towards the range. The associated magnetic field does not show a distinctive peak at the range but follows a smooth yet characteristic profile along the beam axis, from which the range could be determined. Finally, an in-depth analysis of the frequency spectrum has been carried out, separating it into well-known constituents. The second part aimed to lift some of the simplifying assumptions, investigating the impact of nuclear reactions, energy and range straggling, lateral scattering, beam spot size and secondary particles. With an emphasis on the secondary electrons, dedicated Monte Carlo (MC) simulations were conducted, tracking them down to 10 eV. Despite being significantly more numerous than the primary protons, they reduce the overall current density by only 10%. The main reasons are their mostly isotropic flow and short lifetimes, which followed from a thorough phase space analysis. The current density extracted from the MC simulations served as an input for a numerical magnetic field estimation via finite element analysis. Thereby, it has been found that the loss of intensity from nuclear reactions, the electron current and the radial proton current introduce a small but non-negligible longitudinal shift with respect to the analytical result from the first part. In addition, the random current density fluctuations were quantified and deemed negligible in the context of a measurement. Finally, it has been shown that the beam spot size has no impact on the detectable magnetic field. In summary, barring minor deviations, the findings from the first part have been confirmed under more realistic assumptions. The last part expand the applicability of the analytical approach to simple inhomogeneous targets. Through a Green's function approach, the impact of boundaries for a more realistic beam, which includes the RF structure from the accelerator, has been examined. Also, the possibility to modulate the beam intensity artificially in an effort to separate the sought signal from ambient noise (bioelectricity) can be investigated with the same method. Preliminary results indicated that the boundaries cannot be neglected causing an overall reduction of the transmitted signal due to the comparatively large reflection coefficients. Also, the longitudinal magnetic field profile depends on the modulation frequency. Finally, the potential of the range verification method under consideration has been evaluated with respect to current technological capabilities.Die Bestrahlung von Tumorzellen mit ionisierenden Strahlen mit dem Ziel sie unschädlich zu machen gehört zu den Hauptpfeilern der Krebsbehandlung. Zu diesem Zweck werden externe Strahlen bestehend aus schweren geladenen Teilchen wie Protonen eingesetzt, die aufgrund ihres vorteilhaften Tiefendosisprofils, des so genannten Bragg-Peaks, eine sehr konforme Dosisabgabe ermöglichen. Dies gestattet eine effektive Schonung von gesundem Gewebe und gefährdeten Organen, insbesondere im Vergleich zum konventionellen Ansatz mit Röntgenstrahlen. Die endliche Eindringtiefe der Protonen in den Patienten, die so genannte Reichweite, ist jedoch mit Unsicherheiten behaftet, die zu einer erheblichen Unterdosierung im Tumor und einer übermäßigen Dosis in lebensnotwendigen Organen führen können. Ungenauigkeiten können von der Bildgebung, anatomischen Veränderungen, der Positionierung des Patienten, um nur einige zu nennen, herrühren. Solche Risikofaktoren schränken das volle Potenzial der Protonentherapie ein und machen die Verwendung von Sicherheitsmargen um das Tumorvolumen herum erforderlich, was die Gesamtdosis für das gesunde Gewebe erhöht. Daher ist die Entwicklung von Methoden zur Überprüfung der Protonenreichweite in vivo ein aktives Forschungsgebiet. Die bekann-testen Herangehensweisen stützen sich auf die Positronen-Emissions-Tomographie (PET), die prompt gamma (PG) Bildgebung oder die Messung von thermoakustischen Wellen. Diese Methoden sind jedoch in vielerlei Hinsicht eingeschränkt, z. B. durch ein geringes Signal-Rausch-Verhältnis oder eine schwierige Detektion, was Raum für die Entwicklung neuer Ideen und Methoden lässt. Kürzlich wurde vorgeschlagen, das elektrische Feld der Primärprotonen als Grundlage für eine alternative Methode zur Überprüfung der Reichweite zu verwenden. Die vorliegende Arbeit zielt darauf ab, die Möglichkeiten und Grenzen eines solchen Ansatzes zu untersuchen. Der erste Teil befasst sich mit einer umfassenden analytischen Charakterisierung des elektromagnetischen Feldes, das von einem Protonenstrahl ausgeht und wie es von biologischem Gewebe beeinflusst wird. Dabei werden die Auswirkungen der Form des Strahlpulses, der Permittivität, der Leitfähigkeit und der Gewebegrenzen berücksichtigt. Im Gegensatz zu bisherigen Ergebnissen wurde festgestellt, dass die Ladungsrelaxation, die auf die Ionenleitfähigkeit von biologischem Gewebe zurückzuführen ist, einen enormen Einfluss auf das elektrische Feld hat, so dass es sich innerhalb von Nanosekunden abschwächt. Das elektrische Feld eignet sich daher nicht als Grundlage für die Reichwei-tenüberprüfung, auch unter Berücksichtigung des Auswascheffekts, der durch die schnelle Umverteilung der Ladungen entsteht. Das magnetische Feld hingegen wird davon nicht beeinflusst und profitiert von der annähernd konstanten Stromdichte. Sie nimmt nicht mit der abnehmenden Teilchengeschwindigkeit ab, sondern wird aufgrund der ebenfalls zunehmenden Ladungsdichte zur Reichweite hin aufrechterhalten. Das zugehörige Magnetfeld weist keinen ausgeprägten Peak im Bereich der Reichweite auf, sondern folgt einem flachem, aber charakteristischen Profil entlang der Strahlachse, aus dem die Reichweite be- stimmt werden könnte. Schließlich wurde eine eingehende Analyse des Frequenzspektrums durchgeführt, wobei es in die bekannten Bestandteile zerlegt wurde. Der zweite Teil zielte darauf ab, einige der vereinfachenden Annahmen aufzuheben und die Auswirkungen von Kernreaktionen, Energie- und Reichweitenstreuung, lateraler Streuung, Strahldurchmesser und Sekundärteilchen zu untersuchen. Mit Schwerpunkt auf den Sekundärelektronen wurden speziell dafür vorgesehene Monte-Carlo-Simulationen (MC) durchgeführt, bei denen die Elektronen bis hinunter zu 10 eV nachverfolgt wurden. Obwohl sie wesentlich zahlreicher sind als die primären Protonen, reduzieren sie die Gesamtstromdichte nur um 10%. Die Hauptgründe dafür sind ihr überwiegend isotroper Fluss und ihre kurze Lebensdauer, was sich aus einer eingehenden Phasenraumanalyse ergeben hat. Die aus den MC-Simulationen extrahierte Stromdichte diente als Ausgangspunkt für eine numerische Magnetfeldbestimmung mittels Finite-Elemente-Analyse. Dabei wurde festgestellt, dass der Intensitätsverlust aus Kernreaktionen, der Elektronenstrom und der radiale Protonenstrom eine kleine, aber nicht vernachlässigbare Längsverschiebung gegenüber dem analytischen Ergebnis aus dem ersten Teil verursachen. Darüber hinaus wurden die Zufallsschwankungen der Stromdichte quantifiziert und im Rahmen einer Messung als vernachlässigbar eingestuft. Schließlich wurde gezeigt, dass der Strahldurchmesser keinen Einfluss auf das messbare Magnetfeld hat. Zusammenfassend kann gesagt werden, dass die Ergebnisse des ersten Teils, abgesehen von geringfügigen Abweichungen, unter realistischeren Annahmen bestätigt werden konnten. Im letzten Teil wird die Anwendbarkeit des analytischen Ansatzes auf einfache inhomogene Targets erweitert. Mit Hilfe eines Green'schen Funktionsansatzes wurden die Auswirkungen von Gewebegrenzen für einen realistischeren Strahl, der die HF-Struktur des Beschleunigers einschließt, untersucht. Auch die Möglichkeit, die Strahlintensität künst-lich zu modulieren, um das gesuchte Signal vom Umgebungsrauschen (Bioelektrizität) zu trennen, kann mit der gleichen Methode untersucht werden. Vorläufige Ergebnisse zeigten, dass die Grenzflächen nicht vernachlässigt werden können, was aufgrund der vergleichsweise großen Reflexionskoeffizienten zu einer Gesamtverringerung des transmittierten Signals führt. Außerdem hängt das longitudinale Profil des magnetischen Feldes von der Modulationsfrequenz ab. Schließlich wurde das Potenzial der untersuchten Methode zur Reichweitenverifizierung im Hinblick auf die derzeitigen technischen Möglichkeiten evaluiert

    Energy-Efficient and Reliable Computing in Dark Silicon Era

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    Dark silicon denotes the phenomenon that, due to thermal and power constraints, the fraction of transistors that can operate at full frequency is decreasing in each technology generation. Moore’s law and Dennard scaling had been backed and coupled appropriately for five decades to bring commensurate exponential performance via single core and later muti-core design. However, recalculating Dennard scaling for recent small technology sizes shows that current ongoing multi-core growth is demanding exponential thermal design power to achieve linear performance increase. This process hits a power wall where raises the amount of dark or dim silicon on future multi/many-core chips more and more. Furthermore, from another perspective, by increasing the number of transistors on the area of a single chip and susceptibility to internal defects alongside aging phenomena, which also is exacerbated by high chip thermal density, monitoring and managing the chip reliability before and after its activation is becoming a necessity. The proposed approaches and experimental investigations in this thesis focus on two main tracks: 1) power awareness and 2) reliability awareness in dark silicon era, where later these two tracks will combine together. In the first track, the main goal is to increase the level of returns in terms of main important features in chip design, such as performance and throughput, while maximum power limit is honored. In fact, we show that by managing the power while having dark silicon, all the traditional benefits that could be achieved by proceeding in Moore’s law can be also achieved in the dark silicon era, however, with a lower amount. Via the track of reliability awareness in dark silicon era, we show that dark silicon can be considered as an opportunity to be exploited for different instances of benefits, namely life-time increase and online testing. We discuss how dark silicon can be exploited to guarantee the system lifetime to be above a certain target value and, furthermore, how dark silicon can be exploited to apply low cost non-intrusive online testing on the cores. After the demonstration of power and reliability awareness while having dark silicon, two approaches will be discussed as the case study where the power and reliability awareness are combined together. The first approach demonstrates how chip reliability can be used as a supplementary metric for power-reliability management. While the second approach provides a trade-off between workload performance and system reliability by simultaneously honoring the given power budget and target reliability

    Cooperative Radio Communications for Green Smart Environments

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    The demand for mobile connectivity is continuously increasing, and by 2020 Mobile and Wireless Communications will serve not only very dense populations of mobile phones and nomadic computers, but also the expected multiplicity of devices and sensors located in machines, vehicles, health systems and city infrastructures. Future Mobile Networks are then faced with many new scenarios and use cases, which will load the networks with different data traffic patterns, in new or shared spectrum bands, creating new specific requirements. This book addresses both the techniques to model, analyse and optimise the radio links and transmission systems in such scenarios, together with the most advanced radio access, resource management and mobile networking technologies. This text summarises the work performed by more than 500 researchers from more than 120 institutions in Europe, America and Asia, from both academia and industries, within the framework of the COST IC1004 Action on "Cooperative Radio Communications for Green and Smart Environments". The book will have appeal to graduates and researchers in the Radio Communications area, and also to engineers working in the Wireless industry. Topics discussed in this book include: • Radio waves propagation phenomena in diverse urban, indoor, vehicular and body environments• Measurements, characterization, and modelling of radio channels beyond 4G networks• Key issues in Vehicle (V2X) communication• Wireless Body Area Networks, including specific Radio Channel Models for WBANs• Energy efficiency and resource management enhancements in Radio Access Networks• Definitions and models for the virtualised and cloud RAN architectures• Advances on feasible indoor localization and tracking techniques• Recent findings and innovations in antenna systems for communications• Physical Layer Network Coding for next generation wireless systems• Methods and techniques for MIMO Over the Air (OTA) testin

    Simulation and measurement of the dynamics of ultra-short electron bunch profiles for the generation of coherent THz radiation

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    The shape of an electron bunch has a tremendous impact on its emission of synchrotron radiation. Especially the formation of sub-structures can increase the yield in the THz region. This thesis investigates the micro-bunching instability, a mechanism where structures form due to self-interaction of the electrons with their own wake-field. The methods include simulation and measurements. On the simulation side, the thesis describes the optimization of simulation algorithms to increase numerical stability as well as computational performance. On the experimental side, an optimized monitor for single-shot bunch profile measurements was designed to allow continuous bunch profile measurements with high signal-to-noise ratio and a sub-ps resolution at 2.7 MHz repetition rate

    Cooperative Radio Communications for Green Smart Environments

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    The demand for mobile connectivity is continuously increasing, and by 2020 Mobile and Wireless Communications will serve not only very dense populations of mobile phones and nomadic computers, but also the expected multiplicity of devices and sensors located in machines, vehicles, health systems and city infrastructures. Future Mobile Networks are then faced with many new scenarios and use cases, which will load the networks with different data traffic patterns, in new or shared spectrum bands, creating new specific requirements. This book addresses both the techniques to model, analyse and optimise the radio links and transmission systems in such scenarios, together with the most advanced radio access, resource management and mobile networking technologies. This text summarises the work performed by more than 500 researchers from more than 120 institutions in Europe, America and Asia, from both academia and industries, within the framework of the COST IC1004 Action on "Cooperative Radio Communications for Green and Smart Environments". The book will have appeal to graduates and researchers in the Radio Communications area, and also to engineers working in the Wireless industry. Topics discussed in this book include: • Radio waves propagation phenomena in diverse urban, indoor, vehicular and body environments• Measurements, characterization, and modelling of radio channels beyond 4G networks• Key issues in Vehicle (V2X) communication• Wireless Body Area Networks, including specific Radio Channel Models for WBANs• Energy efficiency and resource management enhancements in Radio Access Networks• Definitions and models for the virtualised and cloud RAN architectures• Advances on feasible indoor localization and tracking techniques• Recent findings and innovations in antenna systems for communications• Physical Layer Network Coding for next generation wireless systems• Methods and techniques for MIMO Over the Air (OTA) testin

    Electronic Journal of Qualitative Theory of Differential Equations 2022

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