scholarly journals Defect Effect of Bi-infinite Words in the Two-element Case

2001 ◽  
Vol Vol. 4 no. 2 ◽  
Author(s):  
Ján Maňuch
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Alphabet ◽  
Infinite Words ◽  
Infinite Word ◽  
The Family ◽  
International Audience ◽  
Necessary And Sufficient ◽  
Primitive Roots ◽  
Element Set

International audience Let X be a two-element set of words over a finite alphabet. If a bi-infinite word possesses two X-factorizations which are not shiftequivalent, then the primitive roots of the words in X are conjugates. Note, that this is a strict sharpening of a defect theorem for bi-infinite words stated in \emphKMP. Moreover, we prove that there is at most one bi-infinite word possessing two different X-factorizations and give a necessary and sufficient conditions on X for the existence of such a word. Finally, we prove that the family of sets X for which such a word exists is parameterizable.

Using binary operations to construct a transitive set of block transformations

2020 ◽  
Vol 30 (6) ◽  
pp. 375-389
Author(s):  
Igor V. Cherednik
Keyword(s):  
Binary Operation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Binary Operations ◽  
The Family ◽  
Transitive Set ◽  
Necessary And Sufficient

AbstractWe study the set of transformations {ΣF : F∈ 𝓑∗(Ω)} implemented by a network Σ with a single binary operation F, where 𝓑∗(Ω) is the set of all binary operations on Ω that are invertible as function of the second variable. We state a criterion of bijectivity of all transformations from the family {ΣF : F∈ 𝓑∗(Ω)} in terms of the structure of the network Σ, identify necessary and sufficient conditions of transitivity of the set of transformations {ΣF : F∈ 𝓑∗(Ω)}, and propose an efficient way of verifying these conditions. We also describe an algorithm for construction of networks Σ with transitive sets of transformations {ΣF : F∈ 𝓑∗(Ω)}.

scholarly journals A natural representation of partitions as terms of a universal algebra

1993 ◽  
Vol 55 (3) ◽  
pp. 311-324
Author(s):  
Harry Lakser
Keyword(s):  
Universal Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Variety Of Algebras ◽  
Natural Representation ◽  
Necessary And Sufficient ◽  
Element Set

AbstractWe consider a variety of algebras with two binary commutative and associative operations. For each integer n ≥ 0, we represent the partitions on an n-element set as n-ary terms in the variety. We determine necessary and sufficient conditions on the variety ensuring that, for each n, these representing terms be all the essentially n-ary terms and moreover that distinct partitions yield distinct terms.

scholarly journals The distribution of prime ideals of a Dedekind domain

1974 ◽  
Vol 11 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Anne P. Grams
Keyword(s):  
Class Group ◽  
Sufficient Conditions ◽  
Torsion Group ◽  
Dedekind Domain ◽  
Necessary And Sufficient Conditions ◽  
Prime Ideals ◽  
Class Groups ◽  
Maximal Ideals ◽  
The Family ◽  
Necessary And Sufficient

Let G be an abelian group, and let S be a subset of G. Necessary and sufficient conditions on G and S are given in order that there should exist a Dedekind domain D with class group G with the property that S is the set of classes that contain maximal ideals of D. If G is a torsion group, then S is the set of classes containing the maximal ideals of D if and only if S generates G. These results are used to determine necessary and sufficient conditions on a family {Hλ} of subgroups of G in order that there should exist a Dedekind domain D with class group G such that {G/Hλ} is the family of class groups of the set of overrings of D. Several applications are given.

scholarly journals Regular formal modules in local fields and irregularly degree

2020 ◽  
Vol 65 (4) ◽  
pp. 588-596
Author(s):  
Natalya K. Vlaskina ◽  
◽  
Sergei V. Vostokov ◽  
Petr N. Pital’ ◽  
Aleksey E. Tsybyshiev ◽  
...  
Keyword(s):  
Positive Integer ◽  
Local Field ◽  
Sufficient Conditions ◽  
Formal Group ◽  
Necessary And Sufficient Conditions ◽  
Local Fields ◽  
Ramification Index ◽  
Necessary And Sufficient ◽  
Primitive Roots

In this paper we investigate the irregular degree of finite not ramified local field extantions with respect to a polynomial formal group and in the multiplicative case. There was found necessary and sufficient conditions for the existence of primitive roots of ps power from 1 and (endomorphism [ps]Fm) in L-th unramified extension of the local field K (for all positive integer s). These conditions depend only on the ramification index of the maximal abelian subextension of the field K Ka/Qp.

scholarly journals Equicontinuity of iterates of circle maps

1998 ◽  
Vol 21 (3) ◽  
pp. 453-458 ◽  
Author(s):  
Antonios Valaristos
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Circle Maps ◽  
Continuous Map ◽  
The Family ◽  
Necessary And Sufficient

Letfbe a continuous map of the circle to itself. Necessary and sufficient conditions are given for the family ofiterates{fn}n=1∞to be equicontinuous.

scholarly journals Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space

2016 ◽  
Vol 34 (1) ◽  
pp. 187-202 ◽  
Author(s):  
Gulnur Saffak Atalay ◽  
Emin Kasap
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bishop Frame ◽  
The Family ◽  
Necessary And Sufficient

In this paper, we analyzed the problem of constructing a family of surfaces from a given some special Smarandache curves in  Euclidean 3-space. Using the Bishop frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficients to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache asymptotic curve.

scholarly journals Surfaces family with common Smarandache asymptotic curve

2016 ◽  
Vol 34 (1) ◽  
pp. 9-20
Author(s):  
Gulnur Saffak Atalay ◽  
Emin Kasap
Keyword(s):  
Linear Combination ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Frenet Frame ◽  
The Family ◽  
Necessary And Sufficient

In this paper, we analyzed the problem of constructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficients to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache curve.

scholarly journals Darboux Iso-Geodesic Special Curve in Euclidean Space

2019 ◽  
Vol 13 (9) ◽  
pp. 98
Author(s):  
M. M. Wageeda ◽  
E. M. Solouma ◽  
M. Bary
Keyword(s):  
Euclidean Space ◽  
Linear Combination ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Family ◽  
Darboux Frame ◽  
Necessary And Sufficient ◽  
Special Curve

In this paper, by using Darboux frame we scrutinize the issues of reconstructing surfaces with given some unusual Smarandache curves in Euclidean 3-space, we make manifest the family of surfaces as a linear combination of the components of this frame and derive the necessary and sufficient conditions for coefficients to satisfy both the iso-geodesic and iso-parametric requirements.

scholarly journals The game chromatic number of trees and forests

2015 ◽  
Vol Vol. 17 no.2 (Graph Theory) ◽  
Author(s):  
Charles Dunn ◽  
Victor Larsen ◽  
Kira Lindke ◽  
Troy Retter ◽  
Dustin Toci
Keyword(s):  
Computational Complexity ◽  
Chromatic Number ◽  
Polynomial Time ◽  
Maximum Degree ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Game Chromatic Number ◽  
International Audience ◽  
Necessary And Sufficient ◽  
Open Question

International audience While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and then investigate the differences between forests with game chromatic number 3 and 4. In doing so, we present a minimal example of a forest with game chromatic number 4, criteria for determining in polynomial time the game chromatic number of a forest without vertices of degree 3, and an example of a forest with maximum degree 3 and game chromatic number 4. This gives partial progress on the open question of the computational complexity of the game chromatic number of a forest.

scholarly journals Multigraph decomposition into multigraphs with two underlying edges

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Miri Priesler ◽  
Michael Tarsi
Keyword(s):  
Decision Problem ◽  
Sufficient Conditions ◽  
Simple Graph ◽  
Necessary And Sufficient Conditions ◽  
International Audience ◽  
Necessary And Sufficient ◽  
The Given

International audience Due to some intractability considerations, reasonable formulation of necessary and sufficient conditions for decomposability of a general multigraph G into a fixed connected multigraph H, is probably not feasible if the underlying simple graph of H has three or more edges. We study the case where H consists of two underlying edges. We present necessary and sufficient conditions for H-decomposability of G, which hold when certain size parameters of G lies within some bounds which depends on the multiplicities of the two edges of H. We also show this result to be "tight" in the sense that even a slight deviation of these size parameters from the given bounds results intractability of the corresponding decision problem.

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