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The Banach Fixed Point Theorem: selected topics from its hundred-year history
On June 24, 1920 Stefan Banach presented his doctoral dissertation titled O operacjach na zbiorach abstrakcyjnych i ich zastosowaniach do równañ...
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Quantum Harmonic Oscillator in a Time Dependent Noncommutative Background
This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in Dey and Fring...
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Evolution of the Internet Topology and Traffic Dynamics of Data Packets
In recent years, the Internet has become one of the most influential media in our daily life, going beyond in its role as the basic infrastructure in...
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9 The Goldstone Theorem
The mechanism of SSB does not only provide a general strategy for unifying the description of apparently different systems, but it also provide...
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Orbit Dynamics, Stability and Chaos in Planetary Systems
Let us start with a problem of dynamical biology, which was posed about 800 years ago by Fibonacci1
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Introduction to Part II
These notes arose from courses given at the International School for Advanced Studies (Trieste) and at the Scuola Normale Superiore (Pisa) in various...
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6 Sectors with Energy-Momentum Density
We shall now discuss the requirement III of finite energy-momentum, briefly mentioned in the previous section. Clearly, the possibility of using...
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A Homotopy Continuation Solution of the Covariance Extension Equation
Algebraic geometry plays an important role in the theory of linear systems for (at least) three reasons. First, the Laplace transform turns...
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On Existence and Nonexistence of Limit Cycles for FitzHugh-Nagumo Class Models
In this paper we discuss the existence and non-existence of limit cycles of FitzHugh-Nagumo class models. The purpose is to clarify some unclear...
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From Empirical Data to Multi-Modal Control Procedures
In this paper we study the problem of generating control programs, i.e. strings of symbolic descriptions of control-interrupt pairs (or modes) from...
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The Kernel Memory Concept – A Paradigm Shift from Conventional Connectionism
In this chapter, the general concept of kernel memory (KM) is described, which is given as the basis for not only representing the general notion of...
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Modelling Abstract Notions Relevant to the Mind and the Associated Modules
This chapter is devoted to the remaining four modules within the AMS, i.e. 1) attention, 2) emotion, 3) intention, and 4) intuition module, and their...
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5. Nonlinear Systems with Autonomous Linear Parts
Denote $\displaystyle \Omega(r) = \{h \in C^n : \vert\vert h \vert\vert \leq...
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11. Input-to-State Stability
Let us consider a system described by the following equation in a Euclidean space C n :...
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Existence of Steady States. Positive and Nontrivial Steady States
Let us consider in C n the nonlinear equation...
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9. Lur’e Type Systems
In the present chapter we investigate the asymptotic stability of the system...
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Coupled Map Lattices: at the Age of Maturity
Coupled Map Lattices (CML) were simultaneously and independently introduced by K. Kaneko, R. Kapral and S. Kuznetsov in 1983–84 [1, 2, 3, 4, 5, 6]....
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Deterministic Control Theory
In this chapter we focus our attention on the open loop control of deterministic problems. We will see that the language of deterministic control...
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Optimization Problems
Several problems, for example Pontryagin’s maximum principle or the minimax problems of game theoretical approaches, require the determination of an...
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The Four–Dimensional Spacetime
Physics theories are made by building mathematical models that correspond to physical systems. General Relativity, the physical theory of...