We show that the image of a 2{dimensional set under d{dimensional, 2{ parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive (d=2){dimensional Bessel{Riesz capacity. Our methods solve a problem of J.-P. Kahane.

In this paper we extend an inequality of Littlewood concerning the higher variations of functions of bounded Fréchet variations of two variables (bimeasures) to a class of functions that are p-bimeasures, by using the machinery of vector measures. Using random estimates of Kahane-Salem-Zygmund, we show that the inequality is sharp.

We show that the image of a 2–dimensional set under d–dimensional, 2–parameter Brownian sheet can have positive Lebesgue measure if and only if the set in question has positive (d/2)–dimensional Bessel–Riesz capacity. Our methods solve a problem of J.-P. Kahane.

P h o to g ra p h s , u n le s s o th e rw is e n o te d , c o u rt e s y o f T h é rè s e M a ll ia v in . On June 3, 2010, Paul Malliavin died at the American Hospital in Paris. At the time of his death, he was four months short of his eighty-fifth birthday. Malliavin was a major mathematical figure throughout his career. He studied under Szolem Mandelbrojt, who had returned to France after W...

We extend the recent results of R. Lata la and O. Guédon about equivalence of Lq-norms of logconcave random variables (KahaneKhinchin’s inequality) to the quasi-convex case. We construct examples of quasi-convex bodies Kn ⊂ IRn which demonstrate that this equivalence fails for uniformly distributed vector on Kn (recall that the uniformly distributed vector on a convex body is logconcave). Our e...

In this paper, we present a formula for computing the Tutte polynomial of the signed graph formed from a labeled graph by edge replacements in terms of the chain polynomial of the labeled graph. Then we define a family of ‘ring of tangles’ links and consider zeros of their Jones polynomials. By applying the formula obtained, Beraha-Kahane-Weiss’s theorem and Sokal’s lemma, we prove that zeros o...

NHTSA has developed and conducted a vehicleto-vehicle crash test program to evaluate the statistical correlation between vehicle performance measures and the probability of driver fatality in a crash partner vehicle. The test program uncovered some concerns regarding NHTSA’s rigid barrier data collection and review methods. The vehicle-tovehicle tests did not provide clear insight into the mech...