Displaying similar documents to “Laslett’s transform for the Boolean model in ℝ d ”

Generalised irredundance in graphs: Nordhaus-Gaddum bounds

Ernest J. Cockayne, Stephen Finbow (2004)

Discussiones Mathematicae Graph Theory

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For each vertex s of the vertex subset S of a simple graph G, we define Boolean variables p = p(s,S), q = q(s,S) and r = r(s,S) which measure existence of three kinds of S-private neighbours (S-pns) of s. A 3-variable Boolean function f = f(p,q,r) may be considered as a compound existence property of S-pns. The subset S is called an f-set of G if f = 1 for all s ∈ S and the class of f-sets of G is denoted by Ω f ( G ) . Only 64 Boolean functions f can produce different classes Ω f ( G ) , special cases...

Generic extensions of models of ZFC

Lev Bukovský (2017)

Commentationes Mathematicae Universitatis Carolinae

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The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35–46, saying that for models M ⊆ N of ZFC with same ordinals, the condition A p r M , N ( κ ) implies that N is a κ -C.C. generic extension of M .

Linear preserver of n × 1 Ferrers vectors

Leila Fazlpar, Ali Armandnejad (2023)

Czechoslovak Mathematical Journal

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Let A = [ a i j ] m × n be an m × n matrix of zeros and ones. The matrix A is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero ( 1 , 1 ) -entry. We characterize all linear maps perserving the set of n × 1 Ferrers vectors over the binary Boolean semiring and over the Boolean ring ℤ 2 . Also, we have achieved the number of these linear maps in each case.

FKN Theorem on the biased cube

Piotr Nayar (2014)

Colloquium Mathematicae

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We consider Boolean functions defined on the discrete cube - γ , γ - 1 ⁿ equipped with a product probability measure μ ⊗ n , where μ = β δ - γ + α δ γ - 1 and γ = √(α/β). This normalization ensures that the coordinate functions ( x i ) i = 1 , . . . , n are orthonormal in L ₂ ( - γ , γ - 1 ⁿ , μ ⊗ n ) . We prove that if the spectrum of a Boolean function is concentrated on the first two Fourier levels, then the function is close to a certain function of one variable. Our theorem strengthens the non-symmetric FKN Theorem due to Jendrej, Oleszkiewicz and Wojtaszczyk. Moreover,...

The rings which are Boolean

Ivan Chajda, Filip Švrček (2011)

Discussiones Mathematicae - General Algebra and Applications

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We study unitary rings of characteristic 2 satisfying identity x p = x for some natural number p. We characterize several infinite families of these rings which are Boolean, i.e., every element is idempotent. For example, it is in the case if p = 2 n - 2 or p = 2 n - 5 or p = 2 n + 1 for a suitable natural number n. Some other (more general) cases are solved for p expressed in the form 2 q + 2 m + 1 or 2 q + 2 m where q is a natural number and m ∈ 1 , 2 , . . . , 2 q - 1 .

Coherent ultrafilters and nonhomogeneity

Jan Starý (2015)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the notion of a coherent P -ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a P -point on ω , and show that these ultrafilters exist generically under 𝔠 = 𝔡 . This improves the known existence result of Ketonen [On the existence of P -points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), 91–94]. Similarly, the existence theorem of Canjar [On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1,...

Distributivity of strong implications over conjunctive and disjunctive uninorms

Daniel Ruiz-Aguilera, Joan Torrens (2006)

Kybernetika

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This paper deals with implications defined from disjunctive uninorms U by the expression I ( x , y ) = U ( N ( x ) , y ) where N is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a t -norm or a t -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works...