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Page 3655 of Mathematical Reviews Vol. , Issue 99e
[page]

1999
*
Mathematical Reviews
*

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. ...##
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Page 1449 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

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.” ...##
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Continued fraction expansions and permutative representations of the Cuntz algebra O_∞
[article]

2009
*
arXiv
*
pre-print

We show a correspondence between simple continued fraction expansions

arXiv:0901.2186v1
fatcat:wi5fzqj5kjgyppaf7szwtlk4yy
*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*...##
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Multidimensional constant-length substitution sequences

2005
*
Topology and its Applications
*

Tools such as the frequency measure, spectral measures,

doi:10.1016/j.topol.2004.08.014
fatcat:aocvmpta7jcirjztrkskq7hgku
*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*. ...##
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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

Finally, we test our theory on intermediate representations

arXiv:2110.07472v4
fatcat:b2dn23e2hjc7tdjybwxngbhswq
*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 ...##
###
Monomial algebras

1997
*
Journal of Mathematical Sciences
*

*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) ...

##
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Rédei Actions on Finite Fields and Multiplication Map in Cyclic Group

2015
*
SIAM Journal on Discrete Mathematics
*

Finally, we obtain some results on the length

doi:10.1137/140993338
fatcat:vw4xp2pkajbqhl4fvoafg6mym4
*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. ...##
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Iterated function systems and permutation representations of the Cuntz algebra

1999
*
Memoirs of the American Mathematical Society
*

We have general results on a

doi:10.1090/memo/0663
fatcat:s4v6kt6itzdlpfxtfnc6cfgsme
*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*. ...##
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Profinite semigroups
[article]

2017
*
arXiv
*
pre-print

We present a survey

arXiv:1703.10088v1
fatcat:nyslcx6iojcb5jf5jw7zrimvwq
*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! ...##
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Iterated function systems and permutation representations of the Cuntz algebra
[article]

1996
*
arXiv
*
pre-print

We have general results on a

arXiv:funct-an/9612002v1
fatcat:obd3bx7l4bgmhh2lk6knp2ianq
*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. ...##
###
Page 2377 of Mathematical Reviews Vol. 31, Issue Index
[page]

*
Mathematical Reviews
*

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
*

A number

doi:10.1016/0097-3165(74)90056-9
fatcat:w4hnqh6fmvfrvgudj7vreqkdf4
*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. ...##
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Topological chiral modes in random scattering networks
[article]

2019
*
arXiv
*
pre-print

Using graph theory, we show the existence

arXiv:1905.11194v1
fatcat:iqnffy627ndptogrsn6btx63a4
*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) . ...##
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Nonlinear dynamics of networks: the groupoid formalism

2006
*
Bulletin of the American Mathematical Society
*

A formal theory

doi:10.1090/s0273-0979-06-01108-6
fatcat:pg2erwkxqfa65b27aauvxkheea
*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*. ...##
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Reversing and extended symmetries of shift spaces
[article]

2017
*
arXiv
*
pre-print

example

arXiv:1611.05756v2
fatcat:nxeafvvlyzhj5n6o2uqojemucu
*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. ...
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