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Z specification of object oriented constraint programs.

Laurent Henocque (2004)

RACSAM

Object oriented constraint programs (OOCPs) emerge as a leading evolution of constraint programming and artificial intelligence, first applied to a range of industrial applications called configuration problems. The rich variety of technical approaches to solving configuration problems (CLP(FD), CC(FD), DCSP, Terminological systems, constraint programs with set variables, . . . ) is a source of difficulty. No universally accepted formal language exists for communicating about OOCPs, which makes...

Základové arithmetiky. [I.]

Ludvík Kraus (1883)

Časopis pro pěstování mathematiky a fysiky

Zerlegungsähnlichkeit von Punktmengen.

Ch. Meier (1972)

Elemente der Mathematik

Zero-one laws for graphs with edge probabilities decaying with distance. Part II

Saharon Shelah (2005)

Fundamenta Mathematicae

Let Gₙ be the random graph on [n] = 1,...,n with the probability of i,j being an edge decaying as a power of the distance, specifically the probability being $p_{| i - j |} = 1 / {| i - j |}^{α}$ , where the constant α ∈ (0,1) is irrational. We analyze this theory using an appropriate weight function on a pair (A,B) of graphs and using an equivalence relation on B∖A. We then investigate the model theory of this theory, including a “finite compactness”. Lastly, as a consequence, we prove that the zero-one law (for first order logic)...

Zero-one laws for graphs with edge probabilities decaying with distance. Part I

Saharon Shelah (2002)

Fundamenta Mathematicae

Let Gₙ be the random graph on [n] = 1,...,n with the possible edge i,j having probability $p_{| i - j |} = 1 / {| i - j |}^{α}$ for j ≠ i, i+1, i-1 with α ∈ (0,1) irrational. We prove that the zero-one law (for first order logic) holds..

Zero-set property of o-minimal indefinitely Peano differentiable functions

Andreas Fischer (2008)

Annales Polonici Mathematici

Given an o-minimal expansion ℳ of a real closed field R which is not polynomially bounded. Let $^{\infty}$ denote the definable indefinitely Peano differentiable functions. If we further assume that ℳ admits $^{\infty}$ cell decomposition, each definable closed subset A of Rⁿ is the zero-set of a $^{\infty}$ function f:Rⁿ → R. This implies $^{\infty}$ approximation of definable continuous functions and gluing of $^{\infty}$ functions defined on closed definable sets.