(2) r n N I I P Ï 1/p r n N \\} E j ; ^ J >cp ExyTM>*J fr )l lli==1 II ; l l l i = 1 II ) Recalling that in general {E| f ^ } 1 ^ decreases to exp E log \f\ as p decreases to zero, one sees that (1) is a strictly stronger statement than (2); in fact (1) says simply that cp may be taken bounded away from zero in (2). Note that the inequality obtained from (1) by replacing ej with the jth Rademac...

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.

OBJECTIVES This study examined the rate of Gleason pattern 5 and the influence of tertiary Gleason pattern 5 on oncological outcomes. METHODS Four hundred sixty-six patients underwent a radical prostatectomy between 1993 and 2008. Each surgical specimen was reviewed and assessed for the tumor diameter, Gleason score (which was based on the 2005 International Society of Urological Pathology Co...

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...

background: presence of discordance between the gleason score on needle biopsy and the score of radical prostatectomy specimen is common and universal. in this study, we determined the accuracy of gleason grading of biopsies in predicting histological grading of radical prostatectomy specimens and the degree of overgrading and undergrading of prostatic adenocarcinoma in our center, which is one...

conclusions although the presence of pni in prostate biopsy is accompanied by higher surgical stages, pni is not an appropriate independent factor in risk stratification. patients and methods this cross-sectional study was conducted using a sample of 109 patients who attended a tertiary health care center from 2008 to 2013. the selection criteria were pni in prostate biopsy with gleason scores ...

Gleason has recently shown that the weight enumerators of binary and ternary self-dual codes are polynomials in two given polynomials. In this paper it is shown that classical invariant theory permits a straightforward and systematic proof of Gleason’s theorems and their generalizations. The joint weight enumerator of two codes (analogous to the joint density function of two random variables) i...