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.

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.

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 Note on Legendre's and Bertrand's Proofs of the Parallel-Postulate by Infinite Areas

1911 ◽  
Vol 30 ◽  
pp. 31-36
Author(s):  
D. M. Y. Sommerville
Keyword(s):  
Finite Number ◽  
Plane Surface ◽  
Second Order ◽  
The Other ◽  
Linear Segment ◽  
First Order ◽  
Other Hand ◽  
Straight Lines

One of the most plausible of the host of “proofs” that have ever been offered for Euclid's parallel-postulate is that known as Bertrand's, which is based upon a consideration of infinite areas. The area of the whole plane being regarded as an infinity of the second order, the area of a strip of plane surface bounded by a linear segment AB and the rays AA′, BB perpendicular to AB is an infinity of the first order, since a single infinity of such strips is required to cover the plane. On the other hand, the area contained between two intersecting straight lines is an infinity of the same order as the plane, since the plane can be covered by a finite number of such sectors. Hence if AP is drawn making any angle, however small, with AA′, the area A′AP, an infinity of the second order, cannot be contained within the area A′ABB′, an infinity of the first order, and therefore AP must cut BB′. And this is just Euclid's postulate.

scholarly journals Cascadable Current-Mode First-Order and Second-Order Multifunction Filters Employing Grounded Capacitors

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Jiun-Wei Horng ◽  
Chun-Li Hou ◽  
Ching-Yao Tseng ◽  
Ryan Chang ◽  
Dun-Yih Yang
Keyword(s):  
Theoretical Analysis ◽  
Second Generation ◽  
Current Mode ◽  
Bandpass Filters ◽  
Second Order ◽  
Current Conveyors ◽  
First Order ◽  
Simulation Results ◽  
Circuit Configuration ◽  
High Output

A configuration for realizing low input and high output impedances current-mode multifunction filters using multiple output second-generation current conveyors (MOCCIIs) is presented. From the proposed circuit configuration, first-order allpass, highpass, lowpass and second-order allpass, notch, bandpass filters can be obtained. The simulation results confirm the theoretical analysis.

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