Chapter 2. Positive Systems with Retarded Delays.-
Chapter 3. Positive Systems with Distributed Delays.-
Chapter 4. Controller Synthesis of Positive Systems.-
Chapter 5. Model Reduction for Discrete-time Positive Systems with Inhomogeneous Initial Conditions.-
Chapter 6. Linear Delay Systems with Cone Invariance.-
Chapter 7. Positivity and Stability of Coupled Di erential-di erence Equations with Time-varying Delays.-
chapter 8. Conclusion and Future Work.
(source: Nielsen Book Data)
This thesis develops several systematic and unified approaches for analyzing dynamic systems with positive characteristics or a more general cone invariance property. Based on these analysis results, it uses linear programming tools to address static output feedback synthesis problems with a focus on optimal gain performances. Owing to their low computational complexity, the established controller design algorithms are applicable for large-scale systems. The theory and control strategies developed will not only be useful in handling large-scale positive delay systems with improved solvability and at lower cost, but also further our understanding of the system characteristics in other related areas, such as distributed coordination of networked multi-agent systems, formation control of multiple robots. (source: Nielsen Book Data) 9789811038792 20170612
Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Holder. In this book, Philip Isett uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself--an intricate algorithm with hidden symmetries--mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful "Main Lemma"--used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem--has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture. (source: Nielsen Book Data) 9780691174839 20170321
Book — 1 online resource () : color illustrations.
1 Introduction 1.1 Scope of the Thesis 1.2 Outline of the Thesis 1.3 Quantum Hall States 1.4 Topological Insulators 1.5 Weyl and Dirac Semimetals 1.6 -(BEDT-TTF)2I3 1.7 Topological Mott Insulators 1.8 Topological Crystalline Insulators 1.9 Classification of Topological States of Matter
2 Interacting Dirac Fermions in (3+1) Dimensions 2.1 Model 2.2 Renormalization Group Analysis 2.3 Density of States 2.4 Electromagnetic Properties 2.5 Spectral Function 2.6 Electric Conductivity 2.7 Energy Gap 2.8 Discussions and Summary
3 Tilted Dirac Cones in Two Dimensions 3.1 Model 3.2 Perturbative Renormalization Group Analysis 3.3 Spin Susceptibility 3.4 Discussions and Summary
4 Generalized Hund's Rule for Two-Atom Systems 4.1 Model 4.2 Results 4.3 Perturbative Calculation 4.4 Entanglement Entropy 4.5 Symmetry 4.6 Discussions and Summary
5 Interacting Topological Crystalline Insulators 5.1 Classification in Two Dimensions 5.2 Interacting TCIs in Three Dimensions 5.3 Discussions and Summary
6 Conclusions and Prospects.
(source: Nielsen Book Data)
This thesis elucidates electron correlation effects in topological matter whose electronic states hold nontrivial topological properties robust against small perturbations. In addition to a comprehensive introduction to topological matter, this thesis provides a new perspective on correlated topological matter. The book comprises three subjects, in which electron correlations in different forms are considered. The first focuses on Coulomb interactions for massless Dirac fermions. Using a perturbative approach, the author reveals emergent Lorentz invariance in a low-energy limit and discusses how to probe the Lorentz invariance experimentally. The second subject aims to show a principle for synthesizing topological insulators with common, light elements. The interplay between the spin-orbit interaction and electron correlation is considered, and Hund's rule and electron filling are consequently found to play a key role for a strong spin-orbit interaction important for topological insulators. The last subject is classification of topological crystalline insulators in the presence of electron correlation. Unlike non-interacting topological insulators, such two- and three-dimensional correlated insulators with mirror symmetry are demonstrated to be characterized, respectively, by the Z4 and Z8 group by using the bosonization technique and a geometrical consideration. (source: Nielsen Book Data) 9789811037429 20180730
Book — 1 online resource (xix, 350 pages) : illustrations. Digital: text file; PDF.
On the Role of Gestures in Learning Mathematics.- A Semiotic Approach and Perspectives on Learning.- Extended Methods and Methodology.- Results on the Representational and the Epistemic Functions of Gestures.- Towards the Role of Gestures: A Comparison.- Reflections, Synopsis, Perspectives.
(source: Nielsen Book Data)
In her empirical study, Christina Krause investigates how gestures can contribute to epistemic processes in social interactions. She expands the traditional speech-based approach to analyzing social processes of constructing mathematical knowledge by employing a multimodal perspective. Adopting a semiotic approach, she takes into account two functions of gestures as signs used by the participants of the social interaction: the representational function concerns the ways in which gestures take part in referring to a mathematical object in processes of knowledge construction and the epistemic function relates to the ways in which they can contribute to the performance of collective epistemic actions. The results of this study reveal that gestures influence the epistemic process significantly more than previously thought and indicate factors underlying this influence. (source: Nielsen Book Data) 9783658119478 20170313
A Model for Load Management and Response Time Prediction
The Robust Tenant Placement and Migration Problem
Algorithms for RTP
Conclusions and Perspectives.
With the proliferation of Software-as-a-Service (SaaS) offerings, it is becoming increasingly important for individual SaaS providers to operate their services at a low cost. This book investigates SaaS from the perspective of the provider and shows how operational costs can be reduced by using "multi tenancy, " a technique for consolidating a large number of customers onto a small number of servers. Specifically, the book addresses multi tenancy on the database level, focusing on in-memory column databases, which are the backbone of many important new enterprise applications. For efficiently implementing multi tenancy in a farm of databases, two fundamental challenges must be addressed, (i) workload modeling and (ii) data placement. The first involves estimating the (shared) resource consumption for multi tenancy on a single in-memory database server. The second consists in assigning tenants to servers in a way that minimizes the number of required servers (and thus costs) based on the assumed workload model. This step also entails replicating tenants for performance and high availability. This book presents novel solutions to both problems.
Introduction.- Theoretical background: non-autonomous systems and synchronization.- Inference of time-evolving coupled dynamical systems in the presence of noise.- Application to life sciences.- Analogue simulation and synchronization analysis of non-autonomous oscillators.- Conclusion.
(source: Nielsen Book Data)
This thesis presents a new method for following evolving interactions between coupled oscillatory systems of the kind that abound in nature. Examples range from the subcellular level, to ecosystems, through climate dynamics, to the movements of planets and stars. Such systems mutually interact, adjusting their internal clocks, and may correspondingly move between synchronized and non-synchronized states. The thesis describes a way of using Bayesian inference to exploit the presence of random fluctuations, thus analyzing these processes in unprecedented detail. It first develops the basic theory of interacting oscillators whose frequencies are non-constant, and then applies it to the human heart and lungs as an example. Their coupling function can be used to follow with great precision the transitions into and out of synchronization. The method described has the potential to illuminate the ageing process as well as to improve diagnostics in cardiology, anesthesiology and neuroscience, and yields insights into a wide diversity of natural processes. (source: Nielsen Book Data) 9783319007526 20160612
Maximal L p -Regularity in a Bounded Smooth Domain
Bounded Weakly Singular Domains
L p -Theory in Weakly Singular Domains.
This thesis is devoted to the study of the basic equations of fluid dynamics. First Matthias Kohne focuses on the derivation of a class of boundary conditions, which is based on energy estimates, and, thus, leads to physically relevant conditions. The derived class thereby contains many prominent artificial boundary conditions, which have proved to be suitable for direct numerical simulations involving artificial boundaries. The second part is devoted to the development of a complete Lp-theory for the resulting initial boundary value problems in bounded smooth domains, i.e. the Navier-Stokes equations complemented by one of the derived energy preserving boundary conditions. Finally, the third part of this thesis focuses on the corresponding theory for bounded, non-smooth domains, where the boundary of the domain is allowed to contain a finite number of edges, provided the smooth components of the boundary that meet at such an edge are locally orthogonal. (source: Nielsen Book Data) 9783658010515 20160615