116 research outputs found
Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems
This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.The authors are very grateful to the Spanish Government for Grant DPI2012-30651 and to the Basque Government and UPV/EHU for Grants IT378-10, SAIOTEK S-PE13UN039 and UFI 2011/07. The authors are also grateful to the referees for their suggestions
Theory and Application of Fixed Point
In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications
A Weak Tripled Contraction for Solving a Fuzzy Global Optimization Problem in Fuzzy Metric Spaces
In the setting of fuzzy metric spaces (FMSs), a global optimization problem (GOP) obtaining the distance between two subsets of an FMS is solved by a tripled fixed-point (FP) technique here. Also, fuzzy weak tripled contractions (WTCs) for that are given. This problem was known before in metric space (MS) as a proximity point problem (PPP). The result is correct for each continuous τ
—norms related to the FMS. Furthermore, a non-trivial example to illustrate the main theorem is discussed.This work was supported in part by the Basque Government under Grant IT1207-19
On the UC and UC* properties and the existence of best proximity points in metric spaces
We investigate the connections between UC and UC* properties for ordered
pairs of subsets (A,B) in metric spaces, which are involved in the study of
existence and uniqueness of best proximity points. We show that the
property is included into the UC property. We introduce some new notions:
bounded UC (BUC) property and uniformly convex set about a function. We prove
that these new notions are generalizations of the property and that both
of them are sufficient for to ensure existence and uniqueness of best proximity
points. We show that these two new notions are different from a uniform
convexity and even from a strict convexity. If we consider the underlying space
to be a Banach space we find a sufficient condition which ensures that from the
UC property it follows the uniform convexity of the underlying Banach space. We
illustrate the new notions with examples. We present an example of a cyclic
contraction T in a space, which is not even strictly convex and the ordered
pair (A,B) has not the UC property, but has the property and thus there
is a unique best proximity point of T in A.Comment: 22 page, 2 figure
Nonlinear Analysis and Optimization with Applications
Nonlinear analysis has wide and significant applications in many areas of mathematics, including functional analysis, variational analysis, nonlinear optimization, convex analysis, nonlinear ordinary and partial differential equations, dynamical system theory, mathematical economics, game theory, signal processing, control theory, data mining, and so forth. Optimization problems have been intensively investigated, and various feasible methods in analyzing convergence of algorithms have been developed over the last half century. In this Special Issue, we will focus on the connection between nonlinear analysis and optimization as well as their applications to integrate basic science into the real world
Characterisation of ground thermal and thermo-mechanical behaviour for shallow geothermal energy applications
Increasing use of the ground as a thermal reservoir is expected in the near future. Shallow geothermal energy (SGE) systems have proved to be sustainable alternative solutions for buildings and infrastructure conditioning in many areas across the globe in the past decades. Recently novel solutions, including energy geostructures, where SGE systems are coupled with foundation heat exchangers, have also been developed. The performance of these systems is dependent on a series of factors, among which the thermal properties of the soil play one of major roles. The purpose of this paper is to present, in an integrated manner, the main methods and procedures to assess ground thermal properties for SGE systems and to carry out a critical review of the methods. In particular, laboratory testing through either steady-state or transient methods are discussed and a new synthesis comparing results for different techniques is presented. In-situ testing including all variations of the thermal response test is presented in detail, including a first comparison between new and traditional approaches. The issue of different scales between laboratory and in-situ measurements is then analysed in detail. Finally, thermo-hydro-mechanical behaviour of soil is introduced and discussed. These coupled processes are important for confirming the structural integrity of energy geostructures, but routine methods for parameter determination are still lacking
Cone Penetration Testing 2022
This volume contains the proceedings of the 5th International Symposium on Cone Penetration Testing (CPT’22), held in Bologna, Italy, 8-10 June 2022. More than 500 authors - academics, researchers, practitioners and manufacturers – contributed to the peer-reviewed papers included in this book, which includes three keynote lectures, four invited lectures and 169 technical papers. The contributions provide a full picture of the current knowledge and major trends in CPT research and development, with respect to innovations in instrumentation, latest advances in data interpretation, and emerging fields of CPT application. The paper topics encompass three well-established topic categories typically addressed in CPT events: - Equipment and Procedures - Data Interpretation - Applications. Emphasis is placed on the use of statistical approaches and innovative numerical strategies for CPT data interpretation, liquefaction studies, application of CPT to offshore engineering, comparative studies between CPT and other in-situ tests. Cone Penetration Testing 2022 contains a wealth of information that could be useful for researchers, practitioners and all those working in the broad and dynamic field of cone penetration testing
Heterogeneity of the Attractor of the Lorenz '96 Model: Lyapunov Analysis, Unstable Periodic Orbits, and Shadowing Properties
The predictability of weather and climate is strongly state-dependent:
special and extremely relevant atmospheric states like blockings are associated
with anomalous instability. Indeed, typically, the instability of a chaotic
dynamical system can vary considerably across its attractor. Such an attractor
is in general densely populated by unstable periodic orbits that can be used to
approximate any forward trajectory through the so-called shadowing. Dynamical
heterogeneity can lead to the presence of unstable periodic orbits with
different number of unstable dimensions. This phenomenon - unstable dimensions
variability - implies a serious breakdown of hyperbolicity and has considerable
implications in terms of the structural stability of the system and of the
possibility to describe accurately its behaviour through numerical models. As a
step in the direction of better understanding the properties of
high-dimensional chaotic systems, we provide here an extensive numerical study
of the dynamical heterogeneity of the Lorenz '96 model in a parametric
configuration leading to chaotic dynamics. We show that the detected
variability in the number of unstable dimensions is associated with the
presence of many finite-time Lyapunov exponents that fluctuate about zero also
when very long averaging times are considered. The transition between regions
of the attractor with different degrees of instability comes with a significant
drop of the quality of the shadowing. By performing a coarse graining based on
the shadowing unstable periodic orbits, we can characterize the slow
fluctuations of the system between regions featuring, on the average,
anomalously high and anomalously low instability. In turn, such regions are
associated, respectively, with states of anomalously high and low energy, thus
providing a clear link between the microscopic and thermodynamical properties
of the system.Comment: 28 pages, 11 figures, final accepted versio
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