scholarly journals Dissipative extension theory for linear relations

2020 ◽  
Vol 38 (1) ◽  
pp. 60-90 ◽  
Author(s):  
Josué I. Rios-Cangas ◽  
Luis O. Silva
Keyword(s):  
Extension Theory ◽  
Linear Relations ◽  
Dissipative Extension

scholarly journals Stability of deficiency indices for discrete Hamiltonian systems under bounded perturbations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yan Liu ◽  
Meiru Xu
Keyword(s):  
Perturbation Theory ◽  
Hamiltonian Systems ◽  
Limit Point ◽  
Limit Circle ◽  
Linear Relations ◽  
Deficiency Indices ◽  
Bounded Perturbations

AbstractThis paper is concerned with stability of deficiency indices for discrete Hamiltonian systems under perturbations. By applying the perturbation theory of Hermitian linear relations we establish the invariance of deficiency indices for discrete Hamiltonian systems under bounded perturbations. As a consequence, we obtain the invariance of limit types for the systems under bounded perturbations. In particular, we build several criteria of the invariance of the limit circle and limit point cases for the systems. Some of these results improve and extend some previous results.

scholarly journals Assessing the Manuscripts of Sefer Ḥasidim

2021 ◽  
Author(s):  
Saskia Dönitz
Keyword(s):  
Linear Relations ◽  
Gradual Process

AbstractThis article examines the content and structure of the manuscripts of Sefer Ḥasidim, engaging with ideas concerning its production addressed in Ivan Marcus’s recently published book on Sefer Ḥasidim. Marcus has argued that the book was written piece by piece and not as an integral book and further suggested that each and every manuscript of Sefer Ḥasidim should be taken as a distinct edition of the book prepared by Judah he-Ḥasid. The present study demonstrates that, notwithstanding the gradual process in which Sefer Ḥasidim was written and the great variations among the manuscripts, it is possible to reconstruct a textual process that led to the larger compilations found in the three well-known text editions of Sefer Ḥasidim, represented by MS Parma 3280, MS JTS Boesky 45, and the edition printed in Bologna in 1538. The analysis focuses on the distribution of the text in the manuscripts. While it is difficult to show linear relations among them, the different versions demonstrate a gradual process of growth and enlargement of the material around topical structures. Since most of the material is transmitted in more than one exemplar and few passages appear in one manuscript alone, it is argued that the manuscripts can be linked to show how the material grew from random collections of single paragraphs to topically ordered clusters and into the larger compilations of Sefer Ḥasidim.

scholarly journals A Novel Extension Decision-Making Method for Selecting Solar Power Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Meng-Hui Wang
Keyword(s):  
Decision Making ◽  
Solar System ◽  
Power Systems ◽  
Power System ◽  
Solar Power ◽  
Important Task ◽  
Extension Theory ◽  
Solar Systems ◽  
Load Demand ◽  
Generating Capacity

Due to the complex parameters of a solar power system, the designer not only must think about the load demand but also needs to consider the price, weight, and annual power generating capacity (APGC) and maximum power of the solar system. It is an important task to find the optimal solar power system with many parameters. Therefore, this paper presents a novel decision-making method based on the extension theory; we call it extension decision-making method (EDMM). Using the EDMM can make it quick to select the optimal solar power system. The paper proposed this method not only to provide a useful estimated tool for the solar system engineers but also to supply the important reference with the installation of solar systems to the consumer.

Linear relations in microbial reaction systems: A general overview of their origin, form, and use

1991 ◽  
Vol 38 (6) ◽  
pp. 603-618 ◽  
Author(s):  
H. J. Noorman ◽  
J. J. Heijnen ◽  
K. Ch. A. M. Luyben
Keyword(s):  
Reaction Systems ◽  
Linear Relations ◽  
General Overview
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