scholarly journals Carleson’s Theorem: Proof, Complements, Variations

2004 ◽  
Vol 48 ◽  
pp. 251-307 ◽  
Author(s):  
M. T. Lacey
1969 ◽  
Vol 9 (3) ◽  
pp. 343-346 ◽  
Author(s):  
Robert E. Kuenne

The burgeoning of abstract economic analysis since about 1950 makes the need for well-conceived consolidations and codifications at the textbook level peculiarly important. The task is a challenging one, demanding the attainment of a compromise between the "mathematics for economists" catalogues of techniques and the highly specialized and formalized "theorem-proof" sequences of the high-theory journals. It requires that skilful blend of the rigorous and the heuristic, the multidimensional and the diagrammatic, the logical and the intuitive, found in the teacher-born. Lancaster has succeeded admirably in finding the optimal mixture.


2020 ◽  
Vol 20 (1) ◽  
pp. 217-226
Author(s):  
Weiqing Wan ◽  
Yongqing Yu ◽  
Qingyan Zeng ◽  
Zhicheng Wen

2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Lisong Wang ◽  
Miaofang Chen ◽  
Jun Hu

The configuration information of Integrated Modular Avionics (IMA) system includes almost all details of whole system architecture, which is used to configure the hardware interfaces, operating system, and interactions among applications to make an IMA system work correctly and reliably. It is very important to ensure the correctness and integrity of the configuration in the IMA system design phase. In this paper, we focus on modelling and verification of configuration information of IMA/ARINC653 system based on MARTE (Modelling and Analysis for Real-time and Embedded Systems). Firstly, we define semantic mapping from key concepts of configuration (such as modules, partitions, memory, process, and communications) to components of MARTE element and propose a method for model transformation between XML-formatted configuration information and MARTE models. Then we present a formal verification framework for ARINC653 system configuration based on theorem proof techniques, including construction of corresponding REAL theorems according to the semantics of those key components of configuration information and formal verification of theorems for the properties of IMA, such as time constraints, spatial isolation, and health monitoring. After that, a special issue of schedulability analysis of ARINC653 system is studied. We design a hierarchical scheduling strategy with consideration of characters of the ARINC653 system, and a scheduling analyzer MAST-2 is used to implement hierarchical schedule analysis. Lastly, we design a prototype tool, called Configuration Checker for ARINC653 (CC653), and two case studies show that the methods proposed in this paper are feasible and efficient.


Author(s):  
Pavel A. Shamanaev ◽  
Olga S. Yazovtseva

The article states the sufficient polystability conditions for part of variables for nonlinear systems of ordinary differential equations with a sufficiently smooth right-hand side. The obtained theorem proof is based on the establishment of a local componentwise Brauer asymptotic equivalence. An operator in the Banach space that connects the solutions of the nonlinear system and its linear approximation is constructed. This operator satisfies the conditions of the Schauder principle, therefore, it has at least one fixed point. Further, using the estimates of the non-zero elements of the fundamental matrix, conditions that ensure the transition of the properties of polystability are obtained, if the trivial solution of the linear approximation system to solutions of a nonlinear system that is locally componentwise asymptotically equivalent to its linear approximation. There are given examples, that illustrate the application of proven sufficient conditions to the study of polystability of zero solutions of nonlinear systems of ordinary differential equations, including in the critical case, and also in the presence of positive eigenvalues.


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