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Systems Biology: necessary developments and trends
At the end of this definition of Systems Biology through exampling, we discuss ambitions, goals, and challenges relating to this new discipline. We... -
Method of Invariant Grids
The method of invariant grids is developed for a grid-based computation of invariant manifolds. -
Mathematical Notation and Some Terminology
– The operator L from space W to space E: L : W → E -
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Invariance Equation in Differential Form
Definition of invariance in terms of motions and trajectories assumes, at least, existence and uniqueness theorems for solutions of the original... -
Entropy, Quasiequilibrium, and Projectors Field
Projection operators Py contribute both to the invariance equation (3.2), and to the film extension of the dynamics (4.5). Limiting results, exact... -
1 Introduction
The class of block-oriented nonlinear models includes complex models which are composed of linear dynamic systems and nonlinear static elements.... -
Results for Sr2RuO4
In this chapter, we focus on our results for the elementary excitations and Cooper pairing in strontium ruthenate (... -
10. Main sychronization
It was made clear in Chapter 9 that the second order type-II loop operates either in saturated or in unsaturated mode. In this chapter, only the main... -
4. Main synchronization
In this chapter the main synchronization of the first order PLL is discussed. At first, we perform the local stability analysis of the main... -
8. Main synchronization
In the present chapter the main synchronization of the second order type-I loop is treated. At first, the local stability analysis is presented and... -
Optimal stabilization of linear stochastic systems
Having introduced and motivated our concepts of stochastic control systems in the previous chapter we now turn to optimal and suboptimal... -
Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method
We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e.... -
11. Third harmonic synchronization
In this chapter, a brief analysis of the synchronization at the third harmonic of the center VCO frequency is given. The relatively large width of... -
6. Introduction to second order type – I PLL
From the analysis of the first order loop, presented in Part I, it becomes evident that the presence of the ripple in the output of the phase... -
12. Introduction to third order type – II PLL
According to the analysis presented in Part IV, the presence of ripple makes the performance of the second order type-II loop problematic. Therefore,... -
Theory of Cooper Pairing Due to Exchange of Spin Fluctuations
It is of general interest whether singlet high- \(T_{\rm c}\)... -
14. Third harmonic sychronization
In this chapter we will present a brief analysis of the synchronization at the third harmonic of the center VCO frequency for the third order type-II... -
9. Introduction to second order type – II PLL
In the second order type-II loop the filter is active and specifically a PI controller. This loop is considered superior to the second order type-I... -
Linear map**s on ordered vector spaces
Before we can start to analyze the generalized Riccati operators derived in the previous chapter, we have to deal with generalized Lyapunov operators...