scholarly journals The classification of abelian groups generated by time-varying automata and by Mealy automata over the binary alphabet

2016 ◽  
Vol 249 ◽  
pp. 18-27 ◽  
Author(s):  
Adam Woryna
Keyword(s):  
Abelian Groups ◽  
Time Varying ◽  
Binary Alphabet ◽  
Mealy Automata

scholarly journals ABELIAN GROUPS WITH A p2-BOUNDED SUBGROUP, REVISITED

2011 ◽  
Vol 10 (03) ◽  
pp. 377-389
Author(s):  
CARLA PETRORO ◽  
MARKUS SCHMIDMEIER
Keyword(s):  
Abelian Group ◽  
Prime Number ◽  
Maximal Ideal ◽  
Abelian Groups ◽  
Finitely Generated ◽  
Uniserial Ring

Let Λ be a commutative local uniserial ring of length n, p be a generator of the maximal ideal, and k be the radical factor field. The pairs (B, A) where B is a finitely generated Λ-module and A ⊆B a submodule of B such that pmA = 0 form the objects in the category [Formula: see text]. We show that in case m = 2 the categories [Formula: see text] are in fact quite similar to each other: If also Δ is a commutative local uniserial ring of length n and with radical factor field k, then the categories [Formula: see text] and [Formula: see text] are equivalent for certain nilpotent categorical ideals [Formula: see text] and [Formula: see text]. As an application, we recover the known classification of all pairs (B, A) where B is a finitely generated abelian group and A ⊆ B a subgroup of B which is p2-bounded for a given prime number p.

Some results on the classification of expansive automorphisms of compact abelian groups

1996 ◽  
Vol 16 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Fabio Fagnani
Keyword(s):  
Finite Group ◽  
Topological Entropy ◽  
Abelian Groups ◽  
Topological Classification ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compact Abelian Groups ◽  
A Finite Group ◽  
Necessary And Sufficient

AbstractIn this paper we study expansive automorphisms of compact 0-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements isp2for a primep. This yields a classification of the transitive expansive automorphisms with topological entropy logp2. Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.

Analysis and classification of time-varying signals with multiple time-frequency structures

2002 ◽  
Vol 9 (3) ◽  
pp. 92-95 ◽  
Author(s):  
A. Papandreou-Suppappola ◽  
S.B. Suppappola
Keyword(s):  
Multiple Time ◽  
Time Varying ◽  
Time Frequency

Visual Classification of Formula One Races by Events, Drivers, and Time Periods

2020 ◽  
pp. 101-114
Author(s):  
Tobias Lampprecht ◽  
David Salb ◽  
Marek Mauser ◽  
Huub van de Wetering ◽  
Michael Burch ◽  
...  
Keyword(s):  
Time Series Data ◽  
Series Data ◽  
Time Varying ◽  
Visual Metaphor ◽  
Web Based ◽  
Visual Classification ◽  
Formula One ◽  
Data Worth ◽  
Time Periods

Formula One races provide a wealth of data worth investigating. Although the time-varying data has a clear structure, it is pretty challenging to analyze it for further properties. Here the focus is on a visual classification for events, drivers, as well as time periods. As a first step, the Formula One data is visually encoded based on a line plot visual metaphor reflecting the dynamic lap times, and finally, a classification of the races based on the visual outcomes gained from these line plots is presented. The visualization tool is web-based and provides several interactively linked views on the data; however, it starts with a calendar-based overview representation. To illustrate the usefulness of the approach, the provided Formula One data from several years is visually explored while the races took place in different locations. The chapter discusses algorithmic, visual, and perceptual limitations that might occur during the visual classification of time-series data such as Formula One races.

scholarly journals Joint Tracking and Classification of Extended Targets Using Random Matrix and Bernoulli Filter for Time-Varying Scenarios

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 129584-129603 ◽  
Author(s):  
Liping Wang ◽  
Yuan Huang ◽  
Ronghui Zhan ◽  
Jun Zhang
Keyword(s):  
Random Matrix ◽  
Time Varying ◽  
Bernoulli Filter ◽  
Joint Tracking

Reduction of Arbitrary Dynamical Systems by Wavelet Bases

2001 ◽  
Author(s):  
Roger Ghanem ◽  
Francesco Romeo
Keyword(s):  
Dynamical Systems ◽  
Reduction Process ◽  
Inner Product ◽  
Scaling Functions ◽  
Time Varying ◽  
Governing Equations ◽  
Wavelet Bases ◽  
Input And Output ◽  
Analytical Expressions

Abstract A procedure is developed for the identification and classification of nonlinear and time-varying dynamical systems based on measurements of their input and output. The procedure consists of reducing the governing equations with respect to a basis of scaling functions. Given the localizing properties of wavelets, the reduced system is well adapted to predicting local changes in time as well as changes that are localized to particular components of the system. The reduction process relies on traditional Galerkin techniques and recent analytical expressions for evaluating the inner product between scaling functions and their derivatives. Examples from a variety of dynamical systems are used to demonstrate the scope and limitations of the proposed method.

A Classification Of n-Abelian Groups

1969 ◽  
Vol 21 ◽  
pp. 1238-1244 ◽  
Author(s):  
J. L. Alperin
Keyword(s):  
Group Theory ◽  
Abelian Group ◽  
Recent Result ◽  
Abelian Groups ◽  
The Way

The concept of an abelian group is central to group theory. For that reason many generalizations have been considered and exploited. One, in particular, is the idea of an n-abelian group (6). If n is an integer and n > 1, then a group G is n-abelian if, and only if,(xy)n = xnynfor all elements x and y of G. Thus, a group is 2-abelian if, and only if, it is abelian, while non-abelian n-abelian groups do exist for every n > 2.Many results pertaining to the way in which groups can be constructed from abelian groups can be generalized to theorems on n-abelian groups (1; 2). Moreover, the case of n = p, a prime, is useful in the study of finite p-groups (3; 4; 5). Moreover, a recent result of Weichsel (9) gives a description of all p-abelian finite p-groups.

EQUIVALENT AUTOMATIC STRUCTURES AND THEIR BOUNDARIES

1992 ◽  
Vol 02 (04) ◽  
pp. 443-469 ◽  
Author(s):  
WALTER D. NEUMANN ◽  
MICHAEL SHAPIRO
Keyword(s):  
Equivalence Class ◽  
Abelian Groups ◽  
Automatic Structures ◽  
Automatic Structure

Two (synchronous, asynchronous, or non-deterministic asynchronous) automatic structures on a group G are “equivalent” if their union is a non-deterministic asynchronous automatic structure. We discuss this relation, giving a classification of structures up to equivalence for abelian groups and partial results in some other cases. We also discuss a “boundary” of an asynchronous automatic structure. We show that it is an invariant of the equivalence class of the structure, and describe other properties. We describe a “rehabilitated boundary” which yields Sn−1 for any automatic structure on ℤn.

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