Elastoplastic invariant relation for deformation of solids

2013 ◽  
Vol 54 (1) ◽  
pp. 108-115
Author(s):  
L. B. Zuev
Keyword(s):  
Invariant Relation

scholarly journals The Double Six of Lines and a Theorem in Euclidean Plane Geometry

1952 ◽  
Vol 1 (1) ◽  
pp. 1-7 ◽  
Author(s):  
John Dougall
Keyword(s):  
Projective Space ◽  
Euclidean Plane ◽  
Natural Extension ◽  
Plane Geometry ◽  
Three Dimensions ◽  
Classical Theorem ◽  
Invariant Relation ◽  
Geometrical Form

The object of the present paper is to establish the equivalence of the well-known theorem of the double-six of lines in projective space of three dimensions and a certain theorem in Euclidean plane geometry. The latter theorem is of considerable interest in itself for two reasons. In the first place, it is a natural extension of Euler's classical theorem connecting the radii of the circumscribed and the inscribed (or the escribed) circles of a triangle with the distance between their centres. Secondly, it gives in a geometrical form the invariant relation between the circle circumscribed to a triangle and a conic inscribed in the triangle. For a statement of the theorem, see § 13 (4).

On an extension of Mycielski’s theorem and invariant scrambled sets

2014 ◽  
Vol 36 (2) ◽  
pp. 632-648 ◽  
Author(s):  
FENG TAN
Keyword(s):  
Dynamical System ◽  
Polish Space ◽  
Invariant Relation ◽  
Invariant Subset ◽  
Residual Subset ◽  
Continuous Map ◽  
Dynamical Properties ◽  
Do So

Let $(X,f)$ be a dynamical system, where $X$ is a perfect Polish space and $f:X\rightarrow X$ is a continuous map. In this paper we study the invariant dependent sets of a given relation string ${\it\alpha}=\{R_{1},R_{2},\ldots \}$ on $X$. To do so, we need the relation string ${\it\alpha}$ to satisfy some dynamical properties, and we say that ${\it\alpha}$ is $f$-invariant (see Definition 3.1). We show that if ${\it\alpha}=\{R_{1},R_{2},\ldots \}$ is an $f$-invariant relation string and $R_{n}\subset X^{n}$ is a residual subset for each $n\geq 1$, then there exists a dense Mycielski subset $B\subset X$ such that the invariant subset $\bigcup _{i=0}^{\infty }f^{i}B$ is a dependent set of $R_{n}$ for each $n\geq 1$ (see Theorems 5.4 and 5.5). This result extends Mycielski’s theorem (see Theorem A) when $X$ is a perfect Polish space (see Corollary 5.6). Furthermore, in two applications of the main results, we simplify the proofs of known results on chaotic sets in an elegant way.

scholarly journals AN INVARIANT RELATION BETWEEN CHANGING OVER AND REINFORCEMENT

1982 ◽  
Vol 38 (3) ◽  
pp. 327-338 ◽  
Author(s):  
L. R. Dreyfus ◽  
L. G. Dorman ◽  
J. G. Fetterman ◽  
D. A. Stubbs
Keyword(s):  
Invariant Relation

scholarly journals Automated Conjecturing II: Chomp and Reasoned Game Play

2020 ◽  
Vol 68 ◽  
pp. 447-461
Author(s):  
Alexander Bradford ◽  
J. Kain Day ◽  
Laura Hutchinson ◽  
Bryan Kaperick ◽  
Craig Larson ◽  
...  
Keyword(s):  
General Purpose ◽  
Invariant Relation ◽  
Game Play ◽  
Combinatorial Game

We demonstrate the use of a program that generates conjectures about positions of the combinatorial game Chomp—explanations of why certain moves are bad. These could be used in the design of a Chomp-playing program that gives reasons for its moves. We prove one of these Chomp conjectures—demonstrating that our conjecturing program can produce genuine Chomp knowledge. The conjectures are generated by a general purpose conjecturing program that was previously and successfully used to generate mathematical conjectures. Our program is initialized with Chomp invariants and example game boards—the conjectures take the form of invariant-relation statements interpreted to be true for all board positions of a certain kind. The conjectures describe a theory of Chomp positions. The program uses limited, natural input and suggests how theories generated on-the-fly might be used in a variety of situations where decisions—based on reasons—are required.

scholarly journals A Denotational Account of Untyped Normalization by Evaluation

2003 ◽  
Vol 10 (40) ◽  
Author(s):  
Andrzej Filinski ◽  
Henning Korsholm Rohde
Keyword(s):  
Normal Forms ◽  
Logical Relation ◽  
Invariant Relation ◽  
Correctness Proof ◽  
Functional Program ◽  
Central Type ◽  
Natural Counterpart ◽  
The Senses ◽  
Normalization Function

We show that the standard normalization-by-evaluation construction for the simply-typed lambda_{beta eta}-calculus has a natural counterpart for the untyped lambda_beta-calculus, with the central type-indexed logical relation replaced by a "recursively defined'' <em>invariant relation</em>, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.<br /> <br />In the untyped setting, not all terms have normal forms, so the normalization function is necessarily partial. We establish its correctness in the senses of <em>soundness</em> (the output term, if any, is beta-equivalent to the input term); <em>standardization</em> ( beta-equivalent terms are mapped to the same result); and <em>completeness</em> (the function is defined for all terms that do have normal forms). We also show how the semantic construction enables a simple yet formal correctness proof for the normalization algorithm, expressed as a functional program in an ML-like call-by-value language.

Invariant relation between total acid secretion and secretagogue exposure: secretory dynamics in bullfrog

1984 ◽  
Vol 246 (4) ◽  
pp. G325-G330 ◽  
Author(s):  
E. B. Ekblad ◽  
V. Licko
Keyword(s):  
Acid Secretion ◽  
Response Curve ◽  
Limited Range ◽  
Secretion Rate ◽  
Invariant Relation ◽  
Total Acid ◽  
Time Integral ◽  
Ph Stat ◽  
Concentration Response Curve ◽  
Stimulation By Histamine

Using a continuous recording of acid secretion in frog gastric mucosa by pH-stat interfaced with a microcomputer, the pattern of secretion rate was studied under variable concentrations and durations of stimulation by histamine and forskolin. This tissue can respond with only a limited range of secretory rates. Larger concentrations and/or longer durations of stimulation may result in a secretion rate pattern prolonged far beyond the duration of stimulation. Although for the concentration-response curve the steady-state or peak acid secretion varies with the duration of stimulation, total acid secreted as a function of exposure to stimulator (time integral of the stimulatory pattern) is independent of the stimulatory pattern.

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