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Dynamic Buffer Management in Massively Parallel Systems: The Power of Randomness. [PDF]

ACM Trans Parallel Comput
Pham M, Yuan Y, Li H, Mou C, Tu Y, Xu Z, Meng J.   +6 more
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Simultaneous diophantine approximation

Proceedings of the Indian Academy of Sciences - Section A, 1950
Summary of results. The principal result of this paper is as follows: given any set of real numbers z1, z2, & , zn and an integer t we can find an integer and a set of integers p1, p2 & , pn such that(0.11).Also, if n = 2, we can, given t, produce numbers z1 and z2 such that(0.12)This supersedes the results of Nils Pipping (Acta Aboensis, vol.
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ON THE SIMULTANEOUS DIOPHANTINE APPROXIMATION OF NEW PRODUCTS

Analysis (Germany), 2000
Let \(K\) denote \(\mathbb Q\) or \({\mathbb Q}(i)\) and let \(O_K\) be the ring of integers of \(K\). Let \(q\) be an element of \(O_K\) with \(|q|>1\) and let \(a\) and \(\alpha\) be non-zero elemts of \(K\) such that \(\pm\alpha, -a\alpha\neq q^j\) for any positive integer \(j\). Let \[ f(z)=\prod_{j=1}^\infty g(zq^{-j}) \] where \(g(z)=\left(1+az-z^
Keijo Väänänen, Peter Bundschuh
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Simultaneous Diophantine approximation on manifolds and Hausdorff dimension [PDF]

Journal of Number Theory, 2003
Let M be an m-dimensional, Ck manifold in Rn, for any k, m, n ? ?, and for any t> 0 let Lt(M)={x?M : ?qx?<q-t for infinitely many q??}, where, for x?R, ?x? min{ x - i :i?Z}, and for x=(x1,?,xn)???n, ?X? = max{?x1pr,?,?xn?}. In this paper it will be
Bryan Rynne
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Simultaneous Diophantine Approximation

Proceedings of the London Mathematical Society, 1952
Proof of the theorem: ``Let \(c > 46^{-1/4}\). Then, for every pair of real irrational numbers \(\alpha, \beta\), there exist infinitely many solutions \(p, q, r > 0\) of \(r(p-\alpha r)^2 < c\), \(r(q- \beta r)^2 < c\) in integers.'' This result slightly improves one by \textit{P. Mullender} [Ann. Math. (2) 52, 417-426 (1950; Zbl 0037.17102)].
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Simultaneous asymptotic Diophantine approximations

Mathematika, 1967
Let θ 1 , …, θ k be k real numbers. Suppose ψ( t ) is a positive decreasing function of the positive variable t . Define λ( N ), for all positive integers N , to be the number of solutions in integers p 1 …, p k , q of the inequalities ...
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