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Page 3655 of Mathematical Reviews Vol. , Issue 99e
[page]
1999
Mathematical Reviews
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Manev (BG-AOS; Sofia)
99e:94046 94B15 Xia, Shutao (PRC-NNK;; Tianjin); Fu, Fangwei (PRC-NNK; Tianjin) Nonperiodic cyclic equivalence classes of cyclic codes and algebraic constructions of cyclically permutable ...
., 1255, Springer, Berlin, 1997 Summary: “The exact number of nonperiodic cyclic equivalence classes (NCEC) in a cyclic code is determined. ...
Page 1449 of Mathematical Reviews Vol. , Issue 99b
[page]
1991
Mathematical Reviews
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Wood, Extension theorems for linear codes over finite rings (329- 340); Shutao Xia and Fangwei Fu, Nonperiodic cyclic equivalence classes of cyclic codes and algebraic constructions of cyclically permutable ...
Potential applications of this construct in algebraic coding are discussed.” ...
Continued fraction expansions and permutative representations of the Cuntz algebra O_∞
[article]
2009
arXiv
pre-print
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We show a correspondence between simple continued fraction expansions of irrational numbers and irreducible permutative representations of the Cuntz algebra O_∞. ...
With respect to the correspondence, it is shown that the equivalence of real numbers with respect to modular transformations is equivalent to the unitary equivalence of representations. ...
We recall properties of these classes as follows: For any J, P (J) in Definition 1.2(ii) and (iii) always exists and it is a class of permutative representations, which contains only one unitary equivalence ...
arXiv:0901.2186v1
fatcat:wi5fzqj5kjgyppaf7szwtlk4yy
Multidimensional constant-length substitution sequences
2005
Topology and its Applications
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Tools such as the frequency measure, spectral measures, and the multidimensional odometer are used. We investigate several examples, among them the class of bijective substitutions. ...
Bijective substitutions are of particular interest due to their mixed dynamical spectrum and because they are skew products over multidimensional odometers. ...
The permutations p of the substitution matrix must include both of these elements to ensure that substitution is nonperiodic. ...
doi:10.1016/j.topol.2004.08.014
fatcat:aocvmpta7jcirjztrkskq7hgku
Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views?
[article]
2022
arXiv
pre-print
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Finally, we test our theory on intermediate representations of randomly initialized and fully trained convolutional neural networks and find perfect agreement. ...
Equivariance has emerged as a desirable property of representations of objects subject to identity-preserving transformations that constitute a group, such as translations and rotations. ...
Different representations of even the same group can have different coding properties, an important point for investigating biological circuits and one that we leverage to construct a new GCNN architecture ...
arXiv:2110.07472v4
fatcat:b2dn23e2hjc7tdjybwxngbhswq
Monomial algebras
1997
Journal of Mathematical Sciences
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equivalency class of the word v). ...
Let us give another (equivalent) description of automata algebras. Proof. Obviously, the set of equivalency classes is nite, if the algebra is automata. Let the number of classes is nite. ...
The method of generalization uses the passage to an associative algebra of (left) ...
doi:10.1007/bf02355446
fatcat:zt4izxi4yzhd7mx5o7lufa2ika
Rédei Actions on Finite Fields and Multiplication Map in Cyclic Group
2015
SIAM Journal on Discrete Mathematics
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Finally, we obtain some results on the length of the cycles related to Rédei permutations and we give an algorithm to construct Rédei permutations with prescribed length cycles in a geometric progression ...
In particular, we obtain two descriptions of the tree attached to the cyclic nodes in these graphs and provide period and preperiod estimates for Rédei functions. ...
Parts of this paper were written during a pleasant stay by the first author at Carleton University. He wishes to thank Carleton University for its hospitality. ...
doi:10.1137/140993338
fatcat:vw4xp2pkajbqhl4fvoafg6mym4
Iterated function systems and permutation representations of the Cuntz algebra
1999
Memoirs of the American Mathematical Society
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We have general results on a class of representations of ON on Hilbert space 1l such that the generators Si as operators permute the elements in some orthonormal basis for 1£. ...
We study a class of representations of the Cuntz algebras ON, N = 2, 3, ... , acting on L 2 (1!') where 11' = lR/27rZ. The representations arise in wavelet theory, but are of independent interest. ...
Then the new system has 2m atoms, and the number of cycles is equal to the number of m-tuples of two elements, up to cyclic permutations. ...
doi:10.1090/memo/0663
fatcat:s4v6kt6itzdlpfxtfnc6cfgsme
Profinite semigroups
[article]
2017
arXiv
pre-print
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We present a survey of results on profinite semigroups and their link with symbolic dynamics. ...
We develop a series of results, mostly due to Almeida and Costa and we also include some original results on the Sch\"utzenberger groups associated to a uniformly recurrent set. ...
One may define it equivalently as the projective limit of all cyclic groupŝ Z = n≥1 Z/nZ = {(a n ) n≥1 ∈ n≥1 Z/nZ | for all n|m, a m ≡ a n mod n} or as the projective limit of the cyclic groups Z/n! ...
arXiv:1703.10088v1
fatcat:nyslcx6iojcb5jf5jw7zrimvwq
Iterated function systems and permutation representations of the Cuntz algebra
[article]
1996
arXiv
pre-print
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We have general results on a class of representations of O_N on Hilbert space H such that the generators S_i as operators permute the elements in some orthonormal basis for H. ...
We study a class of representations of the Cuntz algebras O_N, N=2,3,..., acting on L^2(T) where T=R/2π Z. The representations arise in wavelet theory, but are of independent interest. ...
Both the statement and the proof of Proposition 10.1 are entirely due to David Handelman, and likewise the statement and proof of Lemma 3.4 are due to Helge Tverberg. ...
arXiv:funct-an/9612002v1
fatcat:obd3bx7l4bgmhh2lk6knp2ianq
Page 2377 of Mathematical Reviews Vol. 31, Issue Index
[page]
Mathematical Reviews
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Xia, Shu Tao (with Fu, Fang Wei) Nonperiodic cyclic equivalence classes of cyclic codes and algebraic constructions of cyclically permutable codes. ...
(English summary) 99e:94046
— (with Fu, Fang Wei; Yang, Yi Xian) Period distribution of generalized B-J codes and constructions of cyclically permutable (CP) codes. 99a:94052
Yang, Yi Xian see Xia, Shu ...
Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compression, and surface wave encodings
1974
Journal of combinatorial theory. Series A
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A number of special Baumert-Hall sets of units, including an infinite class, are constructed here; these give the densest known classes of Hadamard matrices. ...
The constructions relate to various topics such as pulse compression and image encodings. 313 ...
A number of such quadruples are constructed here, some possible forms are suggested, and one infinite class is presented. ...
doi:10.1016/0097-3165(74)90056-9
fatcat:w4hnqh6fmvfrvgudj7vreqkdf4
Topological chiral modes in random scattering networks
[article]
2019
arXiv
pre-print
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2020 accepted arXiv:1905.11194v2 fatcat:nhvwzbw45vdyncw72xhjvh4xrq
Using graph theory, we show the existence of interface chiral modes in random oriented scattering networks and discuss their topological nature. For particular regular networks (e.g. ...
In that case, the interface chiral modes are identified as the celebrated anomalous edge states of Floquet topological insulators and their existence is enforced by a symmetry imposed by the associated ...
One can thus choose a different origin by a cyclic permutation of the unitary steps in (5) . ...
arXiv:1905.11194v1
fatcat:iqnffy627ndptogrsn6btx63a4
Nonlinear dynamics of networks: the groupoid formalism
2006
Bulletin of the American Mathematical Society
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A formal theory of symmetries of networks of coupled dynamical systems, stated in terms of the group of permutations of the nodes that preserve the network topology, has existed for some time. ...
Now the symmetry group becomes a groupoid, which is an algebraic structure that resembles a group, except that the product of two elements may not be defined. ...
In this construction, the equivalence relation 'same phase' (or 'synchronous') is balanced. The traveling wave in a feed-forward network is an example of precisely this construction. ...
doi:10.1090/s0273-0979-06-01108-6
fatcat:pg2erwkxqfa65b27aauvxkheea
Reversing and extended symmetries of shift spaces
[article]
2017
arXiv
pre-print
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example of algebraic origin. ...
We develop their basic theory for faithful Z^d-actions, and determine the extended symmetry group of the chair tiling shift, which can be described as a model set, and of Ledrappier's shift, which is an ...
We thank an anonymous reviewer for a number of insightful suggestions that helped to improve the manuscript. ...
arXiv:1611.05756v2
fatcat:nxeafvvlyzhj5n6o2uqojemucu
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