Limitations of the classical phase-locked loop analysis

Nonlinear analysis of the classical phase-locked loop (PLL) is a challenging task. In classical engineering literature simplified mathematical models and simulation are widely used for its study. In this work the limitations of classical engineering phase-locked loop analysis are demonstrated, e.g., hidden oscillations, which can not be found by simulation, are discussed. It is shown that the use of simplified dynamical models and the application of simulation may lead to wrong conclusions concerning the operability of PLL-based circuits

Approximating optimal control problems governed by variational inequalities

It is proposed an approximating method for optimal control problems governed by elliptic variational inequalities. Some applications and numerical examples are treated

Stochastic Galerkin Method for Optimal Control Problem Governed by Random Elliptic PDE with State Constraints

In this paper, we investigate a stochastic Galerkin approximation scheme for an optimal control problem governed by an elliptic PDE with random field in its coefficients. The optimal control minimizes the expectation of a cost functional with mean-state constraints. We first represent the stochastic elliptic PDE in terms of the generalized polynomial chaos expansion and obtain the parameterized optimal control problems. By applying the Slater condition in the subdifferential calculus, we obtain the necessary and sufficient optimality conditions for the state-constrained stochastic optimal control problem for the first time in the literature. We then establish a stochastic Galerkin scheme to approximate the optimality system in the spatial space and the probability space. Then the a priori error estimates are derived for the state, the co-state and the control variables. A projection algorithm is proposed and analyzed. Numerical examples are presented to illustrate our theoretical results

Dependency on un-captured GDP as a source of resilience beyond economic value in countries with advanced ICT infrastructure: Similarities and disparities between Finland and Singapore

The majority of countries with advanced information and communication technology (ICT) infrastructure have been experiencing extended stagnation due to an "embedded" trap in ICT advancement. However, certain countries have been able to sustain a high level of ICT- diven global competitiveness. This suggests that in these contexts there is resilience beyond economic value. Finland and Singapore can be considered coutries of resilience with respect to ICT-driven global competitiveness because of their continued GDP growth despite the recession. While both countries share significant similarities including institutional strength in ICT, they demonstrate noteworthy disparities in their development trajectories: Singapore is growth-oriented based on captured GDP while Finland seeks happiness by shifting to un-captured GDP. This contrast can be attributed to their distinct co-evolution with their institutional systems characterized by government/business initiatives in ICT usage for economic efficiency and differences in the new economic index referred to as "happiness seeking". Given the increasing significance of un-captured GDP derived from the dramatic advancement of the Internet, this paper, will use a comparative analysis of ICT-driven development trajectories in six leading countries in the field over the last two decades. This analyss reveals the different option for maintaining economic resilience. A new method for measuring un-captured GDP was developed to assess the consequences and state of un-captured GDP in six countries. Institutional sources leading to this state were analyzed and a source of resilience beyond economic value was conceptualized and articulated

Existence For Shape Optimization Problems in Arbitrary Dimension

We discuss some existence results for optimal design problems governed by second order elliptic equations with the homogeneous Neumann boundary conditions or with the interior transmission conditions. We show that our continuity hypotheses for the unknown boundaries yield the compactness of the associated characteristic functions, which, in turn, guarantees convergence of any minimizing sequences for the first problem. In the second case, weaker assumptions of measurability type are shown to be sufficient for the existence of the optimal material distribution. We impose no restriction on the dimension of the underlying Euclidean space

On the structural optimization problems

We discuss existence theorems for shape optimization and material distribution problems. The conditions that we impose on the unknown sets are continuity of the boundary, respectively a certain measurability hypothesis