Axiomatization of local-global principles for pp-formulas in spaces of orderings

2004 ◽  
Vol 44 (1) ◽  
pp. 77-95 ◽  
Author(s):  
V. Astier ◽  
M. Tressl
Keyword(s):  
Spaces Of Orderings ◽  
Global Principles

Identifying Product Scaling Principles: A Tool for Bioinspired Design and Beyond

2011 ◽  
Author(s):  
Angel G. Perez ◽  
Julie S. Linsey
Keyword(s):  
Scaling Laws ◽  
Initial Step ◽  
Nano Scale ◽  
Bioinspired Design ◽  
Macro Scale ◽  
Design By Analogy ◽  
Global Principles ◽  
Physical Principles

There are countless products that perform the same function but are engineered to suit a different scale. Designers are often faced with the problem of taking a solution at one scale and mapping it to another. This frequently happens with design-by-analogy and bioinspired design. Despite various scaling laws for specific systems, there are no global principles for scaling systems, for example from a biological nano-scale to macro-scale. This is likely one of the reasons bioinspired design is difficult. Very often scaling laws assume the same physical principles are being used, but this study of products indicates that a variety of changes occur as scale changes, including changing the physical principles to meet a particular function. Empirical product research was used to determine a set of principles by observing and understanding numerous products to unearth new generalizations. The function a product performs is examined in various scales to view subtle and blatant differences. Principles are then determined. This study provides an initial step in creating new innovative designs based on existing solutions in nature or other products that occur at very different scales. Much further work is needed by studying additional products and bioinspired examples.

scholarly journals Direct limits of finite spaces of orderings

1984 ◽  
Vol 112 (2) ◽  
pp. 391-406 ◽  
Author(s):  
Mieczysław Kula ◽  
Murray Marshall ◽  
Andrzej Sładek
Keyword(s):  
Spaces Of Orderings ◽  
Direct Limits ◽  
Finite Spaces

scholarly journals A comparison between obstructions to local-global principles over semi-global fields

2021 ◽  
pp. 135-146
Author(s):  
David Harbater ◽  
Julia Hartmann ◽  
Valentijn Karemaker ◽  
Florian Pop
Keyword(s):  
Global Fields ◽  
Global Principles

Some Local-Global Principles for Formally Real Fields

1977 ◽  
Vol 29 (3) ◽  
pp. 606-614 ◽  
Author(s):  
M. Marshall
Keyword(s):  
Real Field ◽  
Global Principles

Let F be a formally real field, and let A be a preordering of F; that is, a subset of F satisfying Δ + Δ = Δ, Δ Δ = Δ, F2 ⊆ Δ. Denote by X Δ the set of all orderings P of F satisfying P ⊇ Δ. Thus Δ = ⋂ p ∈xΔP. This result is well known. It was first proved by Artin [3, Satz 1] in the case Δ = ∑ F2.

Quotients and Inverse Limits of Spaces of Orderings

1979 ◽  
Vol 31 (3) ◽  
pp. 604-616 ◽  
Author(s):  
Murray A. Marshall
Keyword(s):  
Quadratic Forms ◽  
Sums Of Squares ◽  
Inverse Limits ◽  
Witt Ring ◽  
Spaces Of Orderings ◽  
Image Position

A connection between the theory of quadratic forms defined over a given field F, and the space XF of all orderings of F is developed by A. Pfister in [12]. XF can be viewed as a set of characters acting on the group F×/ΣF×2, where ΣF×2 denotes the subgroup of F× consisting of sums of squares. Namely, each ordering P ∈ XF can be identified with the characterdefined byIt follows from Pfister's result that the Witt ring of F modulo its radical is completely determined by the pair (XF, F×/ΣF×2).

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