scholarly journals Stability implications of delay distribution for first-order and second-order systems

2010 ◽  
Vol 13 (2) ◽  
pp. 327-345 ◽  
Author(s):  
Gábor Kiss ◽  
◽  
Bernd Krauskopf ◽  
Keyword(s):  
Second Order ◽  
First Order ◽  
Delay Distribution ◽  
Second Order Systems

A second order version of S2i and U21

1991 ◽  
Vol 56 (3) ◽  
pp. 1038-1063 ◽  
Author(s):  
Gaisi Takeuti
Keyword(s):  
Second Order ◽  
The Other ◽  
Polynomial Hierarchy ◽  
Bounded Arithmetic ◽  
Conservative Extension ◽  
First Order ◽  
Second Order Systems ◽  
Separation Problems

In [1] S. Buss introduced systems of bounded arithmetic , , , (i = 1, 2, 3, …). and are first order systems and and are second order systems. and are closely related to and respectively in the polynomial hierarchy, and and are closely related to PSPACE and EXPTIME respectively. One of the most important problems in bounded arithmetic is whether the hierarchy of bounded arithmetic collapses, i.e. whether = or = for some i, or whether = , or whether is a conservative extension of S2 = ⋃i. These problems are relevant to the problems whether the polynomial hierarchy PH collapses or whether PSPACE = PH or whether PSPACE = EXPTIME. It was shown in [4] that = implies and consequently the collapse of the polynomial hierarchy. We believe that the separation problems of bounded arithmetic and the separation problems of computational complexities are essentially the same problem, and the solution of one of them will lead to the solution of the other.

scholarly journals Extracting second-order system matrices from state space system

2006 ◽  
Vol 220 (8) ◽  
pp. 1147-1149 ◽  
Author(s):  
P R Houlston
Keyword(s):  
Technical Note ◽  
Second Order ◽  
Order System ◽  
System Modelling ◽  
Direct Control ◽  
Space System ◽  
First Order ◽  
The Reformation ◽  
State Space System ◽  
Second Order Systems

This technical note concerns the reformation of a second-order system from an arbitrary first-order system. At present, the majority of control literature is concerned with controlling systems within the first-order linearization of a system. The author is part of a growing community looking to expand the direct control of second-order systems and the benefits associated in doing so. However, there are potential stages of system modelling that may result in it being necessary to form the first-order form of the system, such as model reduction. This may have the effect of destroying the second-order notion of the system. The purpose of this note is to regain the structure of the second-order system and thus enable the benefits of direct second-order control to be realized. Although the problem itself has been previously resolved, the author proposes the virtue of a simpler method.

Research on Realization Methods of Gaussian System

2012 ◽  
Vol 241-244 ◽  
pp. 104-113
Author(s):  
Lian Hu Xu ◽  
Yi Bao Yuan ◽  
Wei Ying Piao
Keyword(s):  
Theoretical Analysis ◽  
Finite Number ◽  
Gaussian Approximation ◽  
Second Order ◽  
Maximum Deviation ◽  
First Order ◽  
Displacement Sensors ◽  
Gaussian System ◽  
Second Order Systems ◽  
Mixed Systems

The approximate realization methods of system with Gaussian characteristics for inductive micro-displacement sensors were studied in this paper. It was assumed that the sensors used were the first-order systems, for such sensors, it was first proved that cascaded systems formed by an infinite number of first-order systems, its characteristics will infinitely approximate to be those of the Gaussian system. In other words, the cascaded system of a finite number of the first-order systems which have the same characteristics is a Gaussian approximation system. This law can also be applied to the second-order systems, and to the first-order and second-order mixed systems. Theoretical analysis shows that the maximum deviation of Gaussian approximation that 16 cascaded first-order systems is 1.4%, and the maximum deviation of the Gaussian approximation that 16 cascaded second-order systems is 0.1%. This law provided a theoretical guidance for the design of the Gaussian system, which makes the application of the Gaussian system for the geometric multi-probe measurement system to be easy and possible.

scholarly journals Gaia Theory: Between Autopoiesis and Sympoiesis

Problemos ◽  
2020 ◽  
Vol 98 ◽  
pp. 141-153
Author(s):  
Audronė Žukauskaitė
Keyword(s):  
Systems Theory ◽  
Systems Thinking ◽  
Second Order ◽  
Specific Kind ◽  
First Order ◽  
Gaia Hypothesis ◽  
Lynn Margulis ◽  
James Lovelock ◽  
Gaia Theory ◽  
Second Order Systems

The article discusses the development of the Gaia Hypothesis as it was defined by James Lovelock in the 1970s and later elaborated in his collaboration with biologist Lynn Margulis. Margulis’s research in symbiogenesis and her interest in Maturana and Varela’s theory of autopoiesis helped to reshape the Gaia theory from a first-order systems theory to second-order systems theory. In contrast to the first-order systems theory, which is concerned with the processes of homeostasis, second-order systems incorporate emergence, complexity and contingency. In this respect Latour’s and Stengers’s takes on Gaia, even defining it as an “outlaw” or an anti-system, can be interpreted as specific kind of systems thinking. The article also discusses Haraway’s interpretation of Gaia in terms of sympoiesis and argues that it presents a major reconceptualization of systems theory.

scholarly journals A phase semantics for polarized linear logic and second order conservativity

2010 ◽  
Vol 75 (1) ◽  
pp. 77-102 ◽  
Author(s):  
Masahiro Hamano ◽  
Ryo Takemura
Keyword(s):  
Topological Structure ◽  
Linear Logic ◽  
Second Order ◽  
Order Linear ◽  
First Order ◽  
Counter Model ◽  
Linear Fragment ◽  
Phase Semantics ◽  
Second Order Systems ◽  
Completeness Theorems

AbstractThis paper presents a polarized phase semantics, with respect to which the linear fragment of second order polarized linear logic of Laurent [15] is complete. This is done by adding a topological structure to Girard's phase semantics [9], The topological structure results naturally from the categorical construction developed by Hamano–Scott [12]. The polarity shifting operator ↓ (resp. ↑) is interpreted as an interior (resp. closure) operator in such a manner that positive (resp. negative) formulas correspond to open (resp. closed) facts. By accommodating the exponentials of linear logic, our model is extended to the polarized fragment of the second order linear logic. Strong forms of completeness theorems are given to yield cut-eliminations for the both second order systems. As an application of our semantics, the first order conservativity of linear logic is studied over its polarized fragment of Laurent [16]. Using a counter model construction, the extension of this conservativity is shown to fail into the second order, whose solution is posed as an open problem in [16]. After this negative result, a second order conservativity theorem is proved for an eta expanded fragment of the second order linear logic, which fragment retains a focalized sequent property of [3].

Limit-point criteria for systems of differential equations

1980 ◽  
Vol 85 (3-4) ◽  
pp. 233-245 ◽  
Author(s):  
Hilbert Frentzen
Keyword(s):  
Differential Equations ◽  
Limit Point ◽  
Sufficient Conditions ◽  
Second Order ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Sesquilinear Form ◽  
Second Order Systems ◽  
Complex Coefficients ◽  
Second Order Equations

SYNOPSISFor a certain class of first order systems of differential equations several theorems are derived which give sufficient conditions for an appropriate sesquilinear form to be identically zero on suitable spaces of solutions of the system. As a consequence for second order systems limit-point criteria are obtained which include rather general criteria in the case of second order equations. The method used involves sequences of auxiliary functions and is most expedient for the proof of interval limit-point criteria. The theory is also applicable to second order equations with complex coefficients yielding sufficient conditions for the existence of solutions which are not of integrable square.

scholarly journals Non-linear oscillations in first order systems with delay. II. Non-autonomous case

1990 ◽  
Vol 12 (3) ◽  
pp. 1-7
Author(s):  
Nguyen Dong Anh ◽  
Nguyen Tien Khiem
Keyword(s):  
Asymptotic Method ◽  
Second Order ◽  
Van Der Pol ◽  
Periodic Force ◽  
First Order ◽  
Autonomous Case ◽  
Non Linear ◽  
Second Order Systems

The influence of the periodic force on the nonlinear first order systems with delay is investigated by the asymptotic method Crulov-Bogoliubov-Mitropolski. A detailed research of the response of Duffing and Van der Pol systems to external periodic force is given. The obtained results are compared with well-known ones in such second order systems without delay.

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