Characterization of Easily Controllable Plants Based on the Finite Frequency Phase/Gain Property: A Magic Number √͞4͞+͞2͞√͞2 in ℋ∞Loop Shaping Design

2007 ◽  
Author(s):  
Masaaki Kanno ◽  
Shinji Hara ◽  
Masahiko Onishi
Keyword(s):  
Magic Number ◽  
Finite Frequency ◽  
Property A ◽  
Loop Shaping ◽  
Frequency Phase

scholarly journals Isothermic surfaces in sphere geometries as Moutard nets

2007 ◽  
Vol 463 (2088) ◽  
pp. 3171-3193 ◽  
Author(s):  
Alexander I Bobenko ◽  
Yuri B Suris
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauss Map ◽  
Point Property ◽  
Property A ◽  
Lie Geometry ◽  
Möbius Geometry ◽  
Isothermic Surfaces ◽  
Three Dimensional Space

We give an elaborated treatment of discrete isothermic surfaces and their analogues in different geometries (projective, Möbius, Laguerre and Lie). We find the core of the theory to be a novel characterization of discrete isothermic nets as Moutard nets. The latter are characterized by the existence of representatives in the space of homogeneous coordinates satisfying the discrete Moutard equation. Moutard nets admit also a projective geometric characterization as nets with planar faces with a five-point property: a vertex and its four diagonal neighbours span a three-dimensional space. Restricting the projective theory to quadrics, we obtain Moutard nets in sphere geometries. In particular, Moutard nets in Möbius geometry are shown to coincide with discrete isothermic nets. The five-point property, in this particular case, states that a vertex and its four diagonal neighbours lie on a common sphere, which is a novel characterization of discrete isothermic surfaces. Discrete Laguerre isothermic surfaces are defined through the corresponding five-plane property, which requires that a plane and its four diagonal neighbours share a common touching sphere. Equivalently, Laguerre isothermic surfaces are characterized by having an isothermic Gauss map. S-isothermic surfaces as an instance of Moutard nets in Lie geometry are also discussed.

Logical constants

2018 ◽  
Author(s):  
Timothy McCarthy
Keyword(s):  
Fundamental Problem ◽  
Logical Consequence ◽  
Logical Form ◽  
Logical Truth ◽  
Semantic Property ◽  
Truth Conditions ◽  
Property A ◽  
Logical Constants ◽  
Language L

A fundamental problem in the philosophy of logic is to characterize the concepts of ‘logical consequence’ and ‘logical truth’ in such a way as to explain what is semantically, metaphysically or epistemologically distinctive about them. One traditionally says that a sentence p is a logical consequence of a set S of sentences in a language L if and only if (1) the truth of the sentences of S in L guarantees the truth of p and (2) this guarantee is due to the ‘logical form’ of the sentences of S and the sentence p. A sentence is said to be logically true if its truth is guaranteed by its logical form (for example, ‘2 is even or 2 is not even’). There are three problems presented by this picture: to explicate the notion of logical form or structure; to explain how the logical forms of sentences give rise to the fact that the truth of certain sentences guarantees the truth of others; and to explain what such a guarantee consists in. The logical form of a sentence may be exhibited by replacing nonlogical expressions with a schematic letter. Two sentences have the same logical form when they can be mapped onto the same schema using this procedure (‘2 is even or 2 is not even’ and ‘3 is prime or 3 is not prime’ have the same logical form: ‘p or not-p’). If a sentence is logically true then each sentence sharing its logical form is true. Any characterization of logical consequence, then, presupposes a conception of logical form, which in turn assumes a prior demarcation of the logical constants. Such a demarcation yields an answer to the first problem above; the goal is to generate the demarcation in such a way as to enable a solution of the remaining two. Approaches to the characterization of logical constants and logical consequence are affected by developments in mathematical logic. One way of viewing logical constanthood is as a semantic property; a property that an expression possesses by virtue of the sort of contribution it makes to determining the truth conditions of sentences containing it. Another way is proof-theoretical: appealing to aspects of cognitive or operational role as the defining characteristics of logical expressions. Broadly, proof-theoretic accounts go naturally with the conception of logic as a theory of formal deductive inference; model-theoretic accounts complement a conception of logic as an instrument for the characterization of structure.

scholarly journals Remarks on the range of a vector measure

1994 ◽  
Vol 36 (2) ◽  
pp. 157-161 ◽  
Author(s):  
Jesús M. F. Castilo ◽  
Fernando Sánchez
Keyword(s):  
Vector Measure ◽  
Null Sequence ◽  
Property A ◽  
Weakly Compact ◽  
Countably Additive Vector Measure ◽  
Additive Vector ◽  
Standing Problem ◽  
Additive Vector Measure

A long-standing problem is the characterization of subsets of the range of a vector measure. It is known that the range of a countably additive vector measure is relatively weakly compact and, in addition, possesses several interesting properties (see [2]). In [6] it is proved that if m: Σ → Χ is a countably additive vector measure, then the range of m has not only the Banach–Saks property, but even the alternate Banach-Saks property. A tantalizing conjecture, which we shall disprove in this article, is that the range of m has to have, for some p > 1, the p-Banach–Saks property. Another conjecture, which has been around for some time (see [2]) and is also disproved in this paper, is that weakly null sequences in the range of a vector measure admit weakly-2-summable sub-sequences. In fact, we shall show a weakly null sequence in the range of a countably additive vector measure having, for every p < ∞, no weakly-p-summable sub-sequences.

Distributed parameter modeling and finite-frequency loop-shaping of electromagnetic molding machine

2013 ◽  
Vol 21 (12) ◽  
pp. 1735-1743 ◽  
Author(s):  
Takayuki Ishizaki ◽  
Kenji Kashima ◽  
Jun-ichi Imura ◽  
Atsushi Katoh ◽  
Hiroshi Morita ◽  
...  
Keyword(s):  
Distributed Parameter ◽  
Finite Frequency ◽  
Molding Machine ◽  
Loop Shaping ◽  
Distributed Parameter Modeling

scholarly journals Factorizations in preduals associated to ρ-contractions

2015 ◽  
Vol 53 (1) ◽  
pp. 3-17
Author(s):  
Bernard Chevreau ◽  
Aurelian Crăciunescu
Keyword(s):  
Functional Calculus ◽  
Property A ◽  
Absolutely Continuous ◽  
The Way

Abstract We establish directly factorization results for classes of ρ-contractions, corresponding to those obtained for certain classes of contractions. As an example of result which is not an immediate consequence of the fact that any ρ-contraction is similar to an ordinary contraction we give an "optimal" characterization of absolutely continuous ρ-contractions whose associated functional calculus has Property (Aא₀). Along the way we show that a ρ-contraction is absolutely continuous if and only if it admits an absolutely continuous unitary ρ-dilation generalizing a well- known result for usual contractions.

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