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Approximate Representations and Approximate Homomorphisms
[article]

2010
*
arXiv
*
pre-print

As an application, we bound the extent to which a function f : G -> H can be an

arXiv:1009.6230v1
fatcat:6p46odfe45bshe4lgp6uzxfepm
*approximate**homomorphism*where H is another finite group. ... We show that if H's representations are significantly smaller than G's, no such f can be much more*homomorphic*than a random function. ...*Approximate**homomorphisms*In this section we prove Theorems 2 and 3, bounding the extent to which a function from one finite group to another can act like a*homomorphism*. Proof of Theorem 2. ...##
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On Approximate Cubic Homomorphisms

2009
*
Advances in Difference Equations
*

On the other hand, we are looking for situations when the

doi:10.1155/2009/618463
fatcat:xro5agjpmzcwtd6nrlun7scjgm
*homomorphisms*are stable, that is, if a mapping is an*approximate**homomorphism*, then there exists an exact*homomorphism*near it. ... The topic of*approximate**homomorphisms*was studied by a number of mathematicians, see 15-22 and references therein. Jun and Kim 1 introduced the following functional equation: for all a, b ∈ R. ... Advances in Difference Equations Furthermore, 2.47 Hence T is cubic*homomorphism*. ...##
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Approximate homomorphisms on lattices
[article]

2017
*
arXiv
*
pre-print

One of them involves estimates by quite general error functions; the other deals with

arXiv:1712.03513v1
fatcat:7wcxuiws55hxtanao5h3b6bsqy
*approximate*(join)*homomorphisms*in terms of certain systems of lattice neighborhoods. ... As a corollary, we obtain a stability result for*approximately*monotone functions. ... We will see that this theorem can be easily derived from our results on*approximate*lattice*homomorphisms*. ...##
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On approximate cubic homomorphisms
[article]

2009
*
arXiv
*
pre-print

In the other hand we are looking for situations when the

arXiv:0903.1066v1
fatcat:5xrpvd2b5jhdzfyqmllzvaboti
*homomorphisms*are stable, i.e., if a mapping is an*approximate**homomorphism*, then there exists an exact*homomorphism*near it. ... The topic of*approximate**homomorphisms*was studied by a number of mathematicians, see [2, 3, 10, 14, 15, 19] and references therein. ...##
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On approximate ring homomorphisms

2002
*
Journal of Mathematical Analysis and Applications
*

We prove the stability of a generalization of the Bourgin's result on

doi:10.1016/s0022-247x(02)00293-7
fatcat:nprrzczcn5eijc4qpdvlqssgc4
*approximate*ring*homomorphisms*. ... For ring*homomorphisms*Bourgin (see [2] ) proved the following. Theorem B. Let ε and δ be nonnegative real numbers. ... To prove the uniqueness property of h, assume that h * is another ring*homomorphism*with f (x)−h * (x) ε, x ∈ R. ...##
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Homomorphisms of Approximation Spaces

2012
*
Journal of Applied Mathematics
*

The notion of the

doi:10.1155/2012/185357
fatcat:ikwf22mc2zcmlbomjo36lgbv6i
*homomorphism*of*approximation*spaces is introduced. Some properties of*homomorphism*are investigated, and some characterizations of*homomorphism*are given. ... Furthermore, the notion of*approximation*subspace of*approximation*spaces is introduced. The relations between*approximation*subspaces and*homomorphisms*are studied. ... Conclusions In this paper, we present the notion of the*homomorphism*of*approximation*spaces. A*homomorphism*may be viewed as a special mapping between two*approximation*spaces. ...##
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Approximate C^*-Ternary Ring Homomorphisms
[article]

2006
*
arXiv
*
pre-print

In this paper, we establish the generalized Hyers--Ulam--Rassias stability of C^*-ternary ring

arXiv:math/0511539v2
fatcat:usuglgexqvhmrgdq733eicjfuq
*homomorphisms*associated to the Trif functional equation d · C_d-2^l-2 f(x_1+... ... By an*approximate*C * -ternary ring*homomorphism*associated to the Trif equation we mean a mapping f : A → B for which there exists a certain control function ϕ : A d+3 → [0, ∞) such that if D µ f (x 1 ... Therefore q n T ([xyz]) = T ([xy(q n z)]) = [T (x)T (y)f (q n z)], and so T [xyz]) = lim n→∞ 1 q n [T (x)T (y)f (q n z)] = T (x)T (Suppose that f : A → B is an*approximate*C * -ternary ring*homomorphism*...##
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Removal lemmas and approximate homomorphisms
[article]

2022
*
arXiv
*
pre-print

most M vertices (here an ϵ-

arXiv:2104.11626v2
fatcat:fotjgjbczneyfplbeadibkbble
*approximate**homomorphism*is a map V(G) → V(F) where all but at most ϵ |V(G)|^2 edges of G are mapped to edges of F). ... One such variant, which we call the triangle-free lemma, states that for each ϵ>0 there exists M such that every triangle-free graph G has an ϵ-*approximate**homomorphism*to a triangle-free graph F on at ... Suppose φ : V (G ′ ) → V (F ) is an ǫ-*approximate**homomorphism*and F is H-*homomorphism*-free. ...##
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Approximation of Minimum Cost Homomorphisms
[chapter]

2012
*
Lecture Notes in Computer Science
*

algorithm, and otherwise the minimum cost

doi:10.1007/978-3-642-33090-2_51
fatcat:irqngj5w6zavlnnourzfqo7czq
*homomorphism*problem to H is not*approximable*. ... We prove that if H is a co-circular arc bigraph then the minimum cost*homomorphism*problem to H admits a polynomial time constant ratio*approximation*algorithm; otherwise the minimum cost*homomorphism*... Introduction We study the*approximability*of the minimum cost*homomorphism*problem, introduced below. A c-*approximation*algorithm produces a solution of cost at most c times the minimum cost. ...##
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Approximate homomorphisms on JB∗-triples

2005
*
Journal of Mathematical Analysis and Applications
*

It is shown that for an

doi:10.1016/j.jmaa.2004.12.043
fatcat:jf4qkzwhiveh5ipfn3gfzlb3dq
*approximate**homomorphism*f : J → B of a JB * -triple J into a JB * -triple B, there exists a unique * -*homomorphism*H : J → B near the*approximate**homomorphism*. 2004 Elsevier ... In this paper, we prove that for an*approximate**homomorphism*f : J → B of a JB *triple J into a JB * -triple B, there exists a unique * -*homomorphism*H : J → B near the*approximate**homomorphism*. ... We are going to show the Cauchy-Rassias stability of * -*homomorphisms*on JB * -triples. ...##
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Bootstrapping for Approximate Homomorphic Encryption
[chapter]

2018
*
Lecture Notes in Computer Science
*

This paper extends the leveled

doi:10.1007/978-3-319-78381-9_14
fatcat:auz7y5sh7vfodh2b4f3m24i5py
*homomorphic*encryption scheme for an*approximate*arithmetic of Cheon et al. ... We exploit a scaled sine function as an*approximation*of the modular reduction operation and present an efficient evaluation strategy. ... In the EvalExp step, we take two ciphertexts to be*homomorphically*evaluated by the*approximate*polynomial P r (·) of the complex exponential polynomial. ...##
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Approximate Homomorphisms of Ternary Semigroups

2006
*
Letters in Mathematical Physics
*

A mapping f:(G_1,[ ]_1)→ (G_2,[ ]_2) between ternary semigroups will be called a ternary

doi:10.1007/s11005-005-0042-6
fatcat:kwrgpibtcvbudcja7yw6f2kwm4
*homomorphism*if f([xyz]_1)=[f(x)f(y)f(z)]_2. ... In addition, we establish the superstability of ternary*homomorphisms*into Banach algebras endowed with multiplicative norms. ... For an extensive account on*approximately**homomorphisms*in the binary mode we refer the reader to [19] . ...##
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Accelerating Homomorphic Encryption using Approximate Computing Techniques

2020
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Proceedings of the 17th International Joint Conference on e-Business and Telecommunications
*

All of the

doi:10.5220/0009828803800387
dblp:conf/icete/KhannaR20
fatcat:oycsjlciv5bo7ewxq2plo4kf4q
*approximate*functions, as given in Equations (1-8) , (11), (13) and (14) , are*homomorphically*evaluated. ... Here SEAL is used to measure the effect the proposed*approximations*have on*homomorphic*evaluations. Further generic software optimisations could improve performance. ...##
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Approximate -Lie Homomorphisms and Jordan -Lie Homomorphisms on -Lie Algebras

2012
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Abstract and Applied Analysis
*

Using fixed point methods, we establish the stability of -Lie

doi:10.1155/2012/279632
fatcat:pgryc6blafc7halclmmvkkxgx4
*homomorphisms*and Jordan -Lie*homomorphisms*on -Lie algebras associated to the following generalized Jensen functional equation . ... Under what condition does there exist a*homomorphism*near an*approximate**homomorphism*? ... A generalized version of the theorem of Hyers for*approximately*linear mappings was presented by Rassias 12 in 1978 by considering the case when inequality 1.4 is unbounded. ...##
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Beurling moving averages and approximate homomorphisms

2016
*
Indagationes mathematicae
*

Extensive use of group structures leads to an algebraicization not previously encountered here, and to the

doi:10.1016/j.indag.2015.11.011
fatcat:qfy7uw7zrvgxdbskhpcglygh7e
*approximate**homomorphisms*of the title. ... The theory of regular variation, in its Karamata and Bojani\'c-Karamata/de Haan forms, is long established and makes essential use of*homomorphisms*. ... 1 a F (x)= (x) (a 2 A); (ker) hence we refer to K F here and above as the regular kernel of F -the*homomorphism**approximating*F of our title. ...
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