This paper presents a formal convergence proof for EIPFP, an algorithm that integrates low dimensional probabilistic constraints into a Bayesian network (BN) based on the mathematical procedure IPFP. It also extends E-IPFP to deal with constraints that are inconsistent with each other or with the BN structure. 12 1 CONVERGENCE OF E-IPFP Let ( , ) s P G G G  denote the given BN of n variables (...

an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

An amicable pair for an elliptic curve E/Q is a pair of primes (p, q) of good reduction for E satisfying #Ẽp(Fp) = q and #Ẽq(Fq) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j 6= 0) have no aliqout cycles of length greate...

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We show that E∗(P (n) ∗), the E-homology of the Ω-spectrum for P (n), is an E∗ free Hopf ring for E a complex oriented theory with In sent to 0. This covers the cases P (q)∗(P (n) ∗) and K(q)∗(P (n) ∗), q ≥ n. The generators of the Hopf ring are those necessary for the stable result. The motivation for this paper is to show that P (n) satisfies all of the conditions for the machinery of unstabl...

The equations of the restricted three-body problem describe the motion of a massless particle under the influence of two primaries of masses 1− μ and μ, 0 ≤ μ ≤ 1/2, that circle each other with period equal to 2π. When μ = 0, the problem admits orbits for the massless particle that are ellipses of eccentricity e with the primary of mass 1 located at one of the focii. If the period is a rational...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defi ned by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

Let G(V,E) be a graph with p vertices and q edges. A vertex labeling of G is an assignment f : V (G) → {1, 2, 3, . . . , p + q} be an injection. For a vertex labeling f, the induced Smarandachely edge m-labeling f S for an edge e = uv, an integer m ≥ 2 is defined by f ∗ S(e) = ⌈ f(u) + f(v) m ⌉ . Then f is called a Smarandachely super m-mean labeling if f(V (G))∪ {f(e) : e ∈ E(G)} = {1, 2, 3, ....

(1) i punti di W sono rappresentabili via l coordinate ~ A = (A1, . . . , Al) ∈ R, dette azioni, e l angoli ~ α = (α1, . . . , αl) ∈ [0, 2π] nel senso che i punti (~ p, ~q) ∈ W possono essere rappresentati, a mezzo di una trasformazione analitica di coordinate ~ p = ~ P ( ~ A, ~ α), ~q = ~ Q( ~ A, ~ α) con ( ~ A, ~ α) ∈ U × T l ove U ⊂ R è un dominio chiusura di un aperto connesso e limitato e ...