Transposition Distance Based on the Algebraic Formalism

2008 ◽  
pp. 115-126 ◽  
Author(s):  
Cleber V. G. Mira ◽  
Zanoni Dias ◽  
Hederson P. Santos ◽  
Guilherme A. Pinto ◽  
Maria Emilia M. T. Walter
Keyword(s):  
Algebraic Formalism

Valence states of atoms and their conversions

1984 ◽  
Vol 49 (5) ◽  
pp. 1247-1261 ◽  
Author(s):  
Jaroslav Koča ◽  
Milan Kratochvíl ◽  
Milan Kunz ◽  
Vladimír Kvasnička
Keyword(s):  
Chemical Reactions ◽  
Computer Assisted ◽  
Efficient Tool ◽  
Common Features ◽  
Systematic Application ◽  
Organic Syntheses ◽  
Valence States ◽  
Algebraic Formalism

The algebraic formalism for the description of valence states of atoms and their interconversions is elaborated. It offers a possibility to construct and trace mechanistic paths of chemical reactions, the problem of which is of great importance in computer-assisted organic syntheses. Its systematic application gives exhaustive lists of possible mechanistic paths, and furthermore, very efficient tool to classify chemical reactions and look for their common features.

C*‐algebraic formalism for coarse graining. I. General theory

1974 ◽  
Vol 15 (8) ◽  
pp. 1343-1347 ◽  
Author(s):  
John C. Wolfe ◽  
Gérard G. Emch
Keyword(s):  
General Theory ◽  
Coarse Graining ◽  
Algebraic Formalism

Correlations in a General Theory of Quantum Measurement

2007 ◽  
Vol 14 (04) ◽  
pp. 445-458 ◽  
Author(s):  
Hanna Podsędkowska
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
General Theory ◽  
Quantum Measurement ◽  
Von Neumann Algebra ◽  
Classical Case ◽  
Von Neumann ◽  
Full Algebra ◽  
Algebraic Formalism ◽  
Algebra Of Operators

The paper investigates correlations in a general theory of quantum measurement based on the notion of instrument. The analysis is performed in the algebraic formalism of quantum theory in which the observables of a physical system are described by a von Neumann algebra, and the states — by normal positive normalized functionals on this algebra. The results extend and generalise those obtained for the classical case where one deals with the full algebra of operators on a Hilbert space.

Limit theorem and large deviation principle for the Voronoi tessellation generated by a Gibbs point process

1992 ◽  
Vol 24 (1) ◽  
pp. 45-70 ◽  
Author(s):  
Koji Kuroda ◽  
Hideki Tanemura
Keyword(s):  
Limit Theorem ◽  
Point Process ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Voronoi Tessellation ◽  
Deviation Principle ◽  
Gibbs Point Process ◽  
Polymer Expansion ◽  
Algebraic Formalism

The Voronoi tessellation generated by a Gibbs point process is considered. Using the algebraic formalism of polymer expansion, the limit theorem and the large deviation principle for the number of Voronoi vertices are proved.

AN ALGEBRAIC APPROACH TO THE KOLMOGOROV-SINAI ENTROPY

1996 ◽  
Vol 08 (02) ◽  
pp. 167-184 ◽  
Author(s):  
R. ALICKI ◽  
J. ANDRIES ◽  
M. FANNES ◽  
P. TUYLS
Keyword(s):  
Dynamical Systems ◽  
Algebraic Approach ◽  
Entropy Formula ◽  
Starting Point ◽  
Algebraic Formalism

We revisit the notion of Kolmogorov-Sinai entropy for classical dynamical systems in terms of an algebraic formalism. This is the starting point for defining the entropy for general non-commutative systems. Hereby typical quantum tools are introduced in the statistical description of classical dynamical systems. We illustrate the power of these techniques by providing a simple, self-contained proof of the entropy formula for general automorphisms of n-dimensional tori.

scholarly journals Finding formulas: Does active search facilitate appropriate generalization?

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Nicole R. Hallinen ◽  
Lauren N. Sprague ◽  
Kristen P. Blair ◽  
Rebecca M. Adler ◽  
Nora S. Newcombe
Keyword(s):  
Direct Instruction ◽  
Adaptive Learning ◽  
Original Learning ◽  
Mathematical Structure ◽  
Learning Context ◽  
Negative Effects ◽  
New Approach ◽  
Practice Activity ◽  
Algebraic Formula ◽  
Algebraic Formalism

Abstract Background One criterion of adaptive learning is appropriate generalization to new instances based on the original learning context and avoiding overgeneralization. Appropriate generalization requires understanding what features of a solution are applicable in a new context and whether the new context requires modifications or a new approach. In a series of three experiments, we investigate whether searching for an algebraic formalism before receiving direct instruction facilitates appropriate generalization. Results (1) Searching buffers against negative transfer: participants who first searched for an equation were less likely to overgeneralize compared to participants who completed a tell-and-practice activity. (2) Likelihood of creating a correct new adaptation varied by performance on the searching task. (3) Asking people to sketch alleviated some of the negative effects of tell-and-practice, but sketching did not augment the effect of searching. (4) When participants received more elaborate tell-and-practice instruction, the advantages of searching were less notable. Conclusions Searching for an algebraic formula prior to direct instruction may be a productive way to help learners connect a formula to its referent and avoid overgeneralization. Tell-and-practice instruction that only described the mathematical procedures led to the greatest levels of overgeneralization errors and worst performance. Tell-and-practice instruction that highlighted connections between the mathematical structure of the formula and the visual referent performed at similar or marginally worse levels than the search-first conditions.

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