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On vector‐valued Hardy martingales and a generalized Jensen′s inequality

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 9, Page 527-532, 2003., 2003
We establish a generalized Jensen′s inequality for analytic vector‐valued functions on 𝕋N using a monotonicity property of vector‐valued Hardy martingales. We then discuss how this result extends to functions on a compact abelian group G, which are analytic with respect to an order on the dual group.
Annela R. Kelly, Brian P. Kelly
wiley +1 more source

A note on Hammersley′s inequality for estimating the normal integer mean

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 34, Page 2147-2156, 2003., 2003
Let X1, X2, …, Xn be a random sample from a normal N(θ, σ2) distribution with an unknown mean θ = 0, ±1, ±2, …. Hammersley (1950) proposed the maximum likelihood estimator (MLE) d=[X¯n], nearest integer to the sample mean, as an unbiased estimator of θ and extended the Cramér‐Rao inequality.
Rasul A. Khan
wiley +1 more source

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 52, Page 3299-3313, 2003., 2003
Self‐similar random fractal measures were studied by Hutchinson and Rüschendorf. Working with probability metric in complete metric spaces, they need the first moment condition for the existence and uniqueness of these measures. In this paper, we use contraction method in probabilistic metric spaces to prove the existence and uniqueness of self‐similar
József Kolumbán, Anna Soós, Ibolya Varga +2 more
wiley +1 more source

A Comparison of Modern Hyperbolic Methods for Semiconductor Device Simulation: NTK Central Scheme Vs. CLAWPACK

VLSI Design, Volume 15, Issue 4, Page 721-728, 2002., 2002
Two modern hyperbolic methods—a second‐order Godunov method in the software package CLAWPACK and the second‐order Nessyahu–Tadmor–Kurganov (NTK) central scheme—are compared for simulating an electron shock wave in the classical hydrodynamic model for semiconductor devices.
Carl L. Gardner, Anne Gelb, Justin Hernandez +2 more
wiley +1 more source

On the projections of Laplacians under Riemannian submersions

International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 1, Page 33-42, 2001., 2001
We give a condition on Riemannian submersions from a Riemannian manifold M to a Riemannian manifold N which will ensure that it induces a differential operator on N from the Laplace‐Beltrami operator on M. Equivalently, this condition ensures that a Riemannian submersion maps Brownian motion to a diffusion.
Huiling Le
wiley +1 more source

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ÐŸÐžÐ”Ð“ÐžÐ¢ÐžÐ’ÐšÐ Ð¡Ð¢Ð£Ð”Ð•ÐÐ¢ÐžÐ’ Ðš ÐŸÐ ÐžÐ¤Ð•Ð¡Ð¡Ð˜ÐžÐÐÐ›Ð¬ÐÐžÐ™ Ð˜ÐÐÐžÐ’ÐÐ¦Ð˜ÐžÐÐÐžÐ™ Ð”Ð•Ð¯Ð¢Ð•Ð›Ð¬ÐÐžÐ¡Ð¢Ð˜ Ð’ Ð ÐÐœÐšÐÐ¥ Ð¡ÐŸÐ•Ð¦Ð˜ÐÐ›Ð¬ÐÐžÐ“Ðž Ð£Ð§Ð•Ð‘ÐÐžÐ“Ðž ÐšÐ£Ð Ð¡Ð

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