Boolean algebras, splitting theorems, and sets
Michael Morley, Robert Soare (1975)
Fundamenta Mathematicae
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Michael Morley, Robert Soare (1975)
Fundamenta Mathematicae
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Jan Waszkiewicz (1974)
Colloquium Mathematicae
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T. Traczyk, W. Zarębski (1976)
Colloquium Mathematicae
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Jerzy Płonka (2001)
Discussiones Mathematicae - General Algebra and Applications
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Let τ: F → N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of all positive integers. An identity φ ≈ ψ is called biregular if it has the same variables in each of it sides and it has the same fundamental operation symbols in each of it sides. For a variety V of type τ we denote by the biregularization of V, i.e. the variety of type τ defined by all biregular identities from Id(V). Let B be the variety of Boolean algebras of type , where...
W. Zarębski (1977)
Colloquium Mathematicae
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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 . Only 64 Boolean functions f can produce different classes , special cases...
W. B. Vasantha Kandasamy (1992)
Publications du Département de mathématiques (Lyon)
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Piotr Nayar (2014)
Colloquium Mathematicae
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We consider Boolean functions defined on the discrete cube equipped with a product probability measure , where and γ = √(α/β). This normalization ensures that the coordinate functions are orthonormal in . 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,...
Scott Duke Kominers, Zachary Abel (2008)
Journal de Théorie des Nombres de Bordeaux
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We show that if is an extremal even unimodular lattice of rank with , then is generated by its vectors of norms and . Our result is an extension of Ozeki’s result for the case .
Ivan Chajda, Filip Švrček (2011)
Discussiones Mathematicae - General Algebra and Applications
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We study unitary rings of characteristic 2 satisfying identity 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 or or for a suitable natural number n. Some other (more general) cases are solved for p expressed in the form or where q is a natural number and .
Wolfgang Rump (2001)
Colloquium Mathematicae
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We extend our module-theoretic approach to Zavadskiĭ’s differentiation techniques in representation theory. Let R be a complete discrete valuation domain with quotient field K, and Λ an R-order in a finite-dimensional K-algebra. For a hereditary monomorphism u: P ↪ I of Λ-lattices we have an equivalence of quotient categories which generalizes Zavadskiĭ’s algorithms for posets and tiled orders, and Simson’s reduction algorithm for vector space categories. In this article we replace...
Rostislav Černý (2006)
Kybernetika
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Consider a stationary Boolean model with convex grains in and let any exposed lower tangent point of be shifted towards the hyperplane by the length of the part of the segment between the point and its projection onto the covered by . The resulting point process in the halfspace (the Laslett’s transform of ) is known to be stationary Poisson and of the same intensity as the original Boolean model. This result was first formulated for the planar Boolean model (see N. Cressie...
Zenobia Anusiak (1971)
Colloquium Mathematicae
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Helena Rasiowa
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Contents Introduction.................................................................................................................................................. 3 § 1. System of a propositional calculus...................................................................... 4 § 2. System ..................................................................................................................... 5 § 3. -algebras.....................................................................................................................