A primer of simple theories

2002 ◽  
Vol 41 (6) ◽  
pp. 541-580 ◽  
Author(s):  
Rami Grossberg ◽  
José Iovino ◽  
Olivier Lessmann
Keyword(s):  
1974 ◽  
Vol 16 (6) ◽  
pp. 391-401 ◽  
Author(s):  
P. M. Came ◽  
H. Marsh

By considering a many-bladed cascade, two simple theories are developed for secondary flow in cascades. Following the work of Hawthorne (1)†, three components of vorticity are identified at exit from the cascade. An expression is obtained for the difference in the time taken for fluid particles to travel over the two surfaces of the blade, and this is used to derive the governing equations for the distributed secondary, trailing filament and trailing shed vorticities. It is shown that, for a many-bladed cascade, the total secondary circulation in the downstream flow is zero. The calculation of secondary flow for a real cascade is discussed, and it is shown that earlier calculations of secondary flow at exit from cascades are consistent with this new approach.


2005 ◽  
Vol 70 (2) ◽  
pp. 460-472 ◽  
Author(s):  
David Lippel

AbstractLet F be the class of complete, finitely axiomatizable ω-categorical theories. It is not known whether there are simple theories in F. We prove three results of the form: if T ∈ F has a sufficently well-behaved definable set J, then T is not simple. (In one case, we actually prove that T has the strict order property.) All of our arguments assume that the definable set J satisfies the Mazoyer hypothesis, which controls how an element of J can be algebraic over a subset of the model. For every known example in F, there is a definable set satisfying the Mazoyer hypothesis.


Author(s):  
Roald Hoffmann

The theory of theories goes like this: A theory will be accepted by a scientific community if it explains better (or more of) what is known, fits at its fringes with what is known in other parts of our universe, and makes verifiable, preferably risky, predictions. Sometimes it does go like that. So the theory that made my name (and added to the already recognized greatness of the man with whom I collaborated, the synthetic chemist of the 20th century, R. B. Woodward) did make sense of many disparate and puzzling observations in organic chemistry. And “orbital symmetry control,” as our complex of ideas came to be called, made some risky predictions. I remember well the day that Jerry Berson sent us his remarkable experimental results on the stereochemistry of the so- called 1,3-sigmatropic shift . It should proceed in a certain way, he reasoned from our theory—a non-intuitive way. And it did. But much that goes into the acceptance of theories has little to do with rationalization and prediction. Instead, I will claim, what matters is a heady mix of factors in which psychological attitudes figure prominently. A simple equation describing a physical phenomenon (better still, many), the molecule shaped like a Platonic solid with regular geometry, the simple mechanism (A→B, in one step)—these have tremendous aesthetic appeal, a direct beeline into our soul. They are beautifully simple, and simply beautiful. Theories of this type are awesome in the original sense of the word—who would deny this of the theory of evolution, the Dirac equation or general relativity? A little caution might be suggested from pondering the fact that political ads patently cater to our psychobiological predilection for simplicity. Is the world simple? Or do we just want it to be such? In the dreams of some, the beauty and simplicity of equations becomes a criterion for their truth. Simple theories seem to validate that idol of science, Ockham’s Razor. In preaching the poetic conciseness and generality of orbital explanations, I have succumbed to this, too.


Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4190 ◽  
Author(s):  
Eric Chaidez ◽  
Shankar P. Bhattacharyya ◽  
Adonios N. Karpetis

The Hyperloop system offers the promise of transportation over distances of 1000 km or more, at speeds approaching the speed of sound, without the complexity and cost of high-speed trains or commercial aviation. Two crucial technological issues must be addressed before a practical system can become operational: air resistance, and contact/levitation friction must both be minimized in order to minimize power requirements and system size. The present work addresses the second issue by estimating the power requirements for each of the three major modes of Hyperloop operation: rolling wheels, sliding air bearings, and levitating magnetic suspension systems. The salient features of each approach are examined using simple theories and a comparison is made of power consumption necessary in each case.


2001 ◽  
Vol 66 (1) ◽  
pp. 127-143 ◽  
Author(s):  
D. Lascar ◽  
A. Pillay

A hyperimaginary is an equivalence class of a type-definable equivalence relation on tuples of possibly infinite length. The notion was recently introduced in [1], mainly with reference to simple theories. It was pointed out there how hyperimaginaries still remain in a sense within the domain of first order logic. In this paper we are concerned with several issues: on the one hand, various levels of complexity of hyperimaginaries, and when hyperimaginaries can be reduced to simpler hyperimaginaries. On the other hand the issue of what information about hyperimaginaries in a saturated structure M can be obtained from the abstract group Aut(M).In Section 2 we show that if T is simple and canonical bases of Lascar strong types exist in Meq then hyperimaginaries can be eliminated in favour of sequences of ordinary imaginaries. In Section 3, given a type-definable equivalence relation with a bounded number of classes, we show how the quotient space can be equipped with a certain compact topology. In Section 4 we study a certain group introduced in [5], which we call the Galois group of T, develop a Galois theory and make the connection with the ideas in Section 3. We also give some applications, making use of the structure of compact groups. One of these applications states roughly that bounded hyperimaginaries can be eliminated in favour of sequences of finitary hyperimaginaries. In Sections 3 and 4 there is some overlap with parts of Hrushovski's paper [2].


2002 ◽  
Vol 8 (4) ◽  
pp. 522
Author(s):  
Bradd Hart ◽  
Frank O. Wagner
Keyword(s):  

2017 ◽  
pp. 440-467 ◽  
Author(s):  
Frank Wagner
Keyword(s):  

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