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The vital signs are, by definition, the measurements of the body's
most basic functions. So far, the essential number of signs that
must be measured is not clear as some references consider that the
body temperature, blood pressure, pulse rate and breathing rate are
sufficient but other sources consider that the measurement of other
variables, such as the respiratory effort and oxygen saturation,
are also crucial to determine the health of the person. This book
is not intended to define the critical vital signs but presents the
correlation of these measurements with other variables as well as
the proposition of new methods to determine these variables. It
also proposes some innovative applications that relay on these
signs in a way to monitor and help the human being. Thus, this book
presents six chapters that deal first with the correlation between
the physical training and the blood pressure level among adults as
well as the stress effects for nurses on their vital signs. Added
to that, the influence of the vital signs to predict and detect
epileptical seizure and the analysis of neural mechanisms of major
depressive disorders will be also presented. As for the other
chapters, they go into some engineering applications related to
vital signs as the development of a smart syringe pump that
monitors the patient's crucial parameters and the introduction of a
novel system that monitors the driver's health and notifies health
care providers in case the driver has any health failure in order
to prevent cars accidents.
The first volume of this two-volume book, presents history, the
mathematical modelling and the applications of fractional order
systems, and contains mathematical and theoretical studies and
research related to this domain. This volume is made up of 11
chapters. The first chapter presents an analysis of the Caputo
derivative and the pseudo state representation with the infinite
state approach. The second chapter studies the stability of a class
of fractional Cauchy problems. The third chapter shows how to solve
fractional order differential equations and fractional order
partial differential equations using modern matrix algebraic
approaches. Following this chapter, chapter four proposes another
analytical method to solve differential equations with local
fractional derivative operators. Concerning chapter five, it
presents the extended Borel transform and its related fractional
analysis. After presenting the analytical resolution methods for
fractional calculus, chapter six shows the essentials of fractional
calculus on discrete settings. The initialisation of such systems
is shown in chapter seven. In fact, this chapter presents a
generalised application of the Hankel operator for initialisation
of fractional order systems. The last four chapters show some new
studies and applications of non-integer calculus. In fact, chapter
eight presents the fractional reaction-transport equations and
evanescent continuous time random walks. Chapter nine shows a novel
approach in the exponential integrators for fractional differential
equations. Chapter ten presents the non-fragile tuning of
fractional order PD controllers for integrating time delay systems.
At the end, chapter eleven proposes a discrete finite-dimensional
approximation of linear infinite dimensional systems. To sum up,
this volume presents a mathematical and theoretical study of
fractional calculus along with a stability study and some
applications. This volume ends up with some new techniques and
methods applied in fractional calculus. This volume will be
followed up by a second volume that focuses on the applications of
fractional calculus in several engineering domains.
After presenting the first volume of this two-volume book,
presenting a lot of mathematical and theoretical studies and
research related to non-integer calculus, the second volume
illustrates applications related to this domain. This volume is
made up of 11 chapters. The first chapter presents the heuristic
power of the non-integer differential operators in physics starting
from the chaos to the emergence, the auto-organizations and the
holistic rules. The second chapter shows the dynamics of the
fractional order chaotic systems along with some applications. The
third chapter represents the pressure control of gas engines by
non-integer order controllers by showing a novel trend in the
application of the fractional calculus to automotive systems.
Chapter 4 shows the way to model fractional order equations using
state space modeling along with some applications. Another
application related to this domain is the thermal diffusive
interface. Chapter 5 shows the analysis of a semi-infinite diffuse
plane medium along with the equations that model this medium, and
some frequency and time domain responses. However, Chapter 6 treats
this problem by controlling this plant using the well-known CRONE
controller. Chapter 8 presents the adaptive second-order fractional
sliding mode control with an application to a water tanks level
system. Chapter 9 treats the mechanical aspect by showing the
features of the fractional operators applied to this domain. Also,
Chapter Nine presents the theory of diffusive stresses based on the
fractional advection-diffusion equation. The modeling of drug
diffusion during general anesthesia using Fractional Calculus is
shown in Chapter 10 and is considered as another application
related to the biomedical field. Finally, Chapter 11 represents an
overview of the fractional fuzzy controllers by showing the
analysis, the synthesis and the implementation of this module. To
sum up, this second volume presents applications of fractional
calculus in several engineering domains as the thermal, the
automotive, the mechanical, the biomedical and much more. Note that
this volume was preceded by a first volume that focuses on the
mathematical and theoretical aspects of fractional calculus.
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