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Approximate Representations and Approximate Homomorphisms
[article]
2010
arXiv
pre-print
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As an application, we bound the extent to which a function f : G -> H can be an 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. ...
arXiv:1009.6230v1
fatcat:6p46odfe45bshe4lgp6uzxfepm
On Approximate Cubic Homomorphisms
2009
Advances in Difference Equations
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On the other hand, we are looking for situations when the 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. ...
doi:10.1155/2009/618463
fatcat:xro5agjpmzcwtd6nrlun7scjgm
Approximate homomorphisms on lattices
[article]
2017
arXiv
pre-print
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One of them involves estimates by quite general error functions; the other deals with 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. ...
arXiv:1712.03513v1
fatcat:7wcxuiws55hxtanao5h3b6bsqy
On approximate cubic homomorphisms
[article]
2009
arXiv
pre-print
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In the other hand we are looking for situations when the 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. ...
arXiv:0903.1066v1
fatcat:5xrpvd2b5jhdzfyqmllzvaboti
On approximate ring homomorphisms
2002
Journal of Mathematical Analysis and Applications
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We prove the stability of a generalization of the Bourgin's result on 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. ...
doi:10.1016/s0022-247x(02)00293-7
fatcat:nprrzczcn5eijc4qpdvlqssgc4
Homomorphisms of Approximation Spaces
2012
Journal of Applied Mathematics
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The notion of the 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. ...
doi:10.1155/2012/185357
fatcat:ikwf22mc2zcmlbomjo36lgbv6i
Approximate C^*-Ternary Ring Homomorphisms
[article]
2006
arXiv
pre-print
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In this paper, we establish the generalized Hyers--Ulam--Rassias stability of C^*-ternary ring 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 ...
arXiv:math/0511539v2
fatcat:usuglgexqvhmrgdq733eicjfuq
Removal lemmas and approximate homomorphisms
[article]
2022
arXiv
pre-print
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most M vertices (here an ϵ-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. ...
arXiv:2104.11626v2
fatcat:fotjgjbczneyfplbeadibkbble
Approximation of Minimum Cost Homomorphisms
[chapter]
2012
Lecture Notes in Computer Science
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algorithm, and otherwise the minimum cost 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. ...
doi:10.1007/978-3-642-33090-2_51
fatcat:irqngj5w6zavlnnourzfqo7czq
Approximate homomorphisms on JB∗-triples
2005
Journal of Mathematical Analysis and Applications
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It is shown 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. 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. ...
doi:10.1016/j.jmaa.2004.12.043
fatcat:jf4qkzwhiveh5ipfn3gfzlb3dq
Bootstrapping for Approximate Homomorphic Encryption
[chapter]
2018
Lecture Notes in Computer Science
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This paper extends the leveled 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. ...
doi:10.1007/978-3-319-78381-9_14
fatcat:auz7y5sh7vfodh2b4f3m24i5py
Approximate Homomorphisms of Ternary Semigroups
2006
Letters in Mathematical Physics
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2005 pre-print arXiv:math-ph/0511039v1 fatcat:wbwapotg3zhj3lydcujbyjmo4e
A mapping f:(G_1,[ ]_1)→ (G_2,[ ]_2) between ternary semigroups will be called a ternary 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] . ...
doi:10.1007/s11005-005-0042-6
fatcat:kwrgpibtcvbudcja7yw6f2kwm4
Accelerating Homomorphic Encryption using Approximate Computing Techniques
2020
Proceedings of the 17th International Joint Conference on e-Business and Telecommunications
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All of the 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. ...
doi:10.5220/0009828803800387
dblp:conf/icete/KhannaR20
fatcat:oycsjlciv5bo7ewxq2plo4kf4q
Approximate -Lie Homomorphisms and Jordan -Lie Homomorphisms on -Lie Algebras
2012
Abstract and Applied Analysis
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Using fixed point methods, we establish the stability of -Lie 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. ...
doi:10.1155/2012/279632
fatcat:pgryc6blafc7halclmmvkkxgx4
Beurling moving averages and approximate homomorphisms
2016
Indagationes mathematicae
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Extensive use of group structures leads to an algebraicization not previously encountered here, and to the 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. ...
doi:10.1016/j.indag.2015.11.011
fatcat:qfy7uw7zrvgxdbskhpcglygh7e
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