In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall Q−functions. More precisely, a simple probabilistic method is firstly given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum Q−function and its deformations is established with respect to each of the three parameters. Sinc...

There is a natural action of SL(2,R) on the moduli space of translation surfaces, and this yields an action of the unipotent subgroup U = {( 1 ∗ 0 1 )} . We classify the U -invariant ergodic measures on certain special submanifolds of the moduli space. (Each submanifold is the SL(2,R)-orbit of the set of branched covers of a fixed Veech surface.) For the U -action on these submanifolds, this is...

ILLIAM NUTTALL, an English stutterer, writing in the journal Psyche, in 1937, said, in effect, that whoever finds a cure for stuttering will have found a cure for all the ills of society .. We should not permit his possible exaggeration to distract us from the peculiarly fundamental wisdom which he expressed . In a sense, what he said of stuttering might also be said of such other perplexing fo...

This research forum pertains to the topic of subject selection in augmentative and alternative communication (AAC) research. The following two papers present opposing views on the use of nondisabled persons in AAC research. Specifically, Higginbotham (1995) offers an argument in favor of the use of nondisabled persons as subjects, while Bedrosian (1995) addresses current limitations in using th...

In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall -functions. More precisely, a simple probabilistic method is first given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum -function and its deformations is established with respect to each of the three parameters. Since th...

1. Nuttall FQ. Body mass index: Obesity, BMI, and health: A critical review. Nutrition Today. 2015;50(3):117–128. CrossRef Google Scholar

The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal employed in various fields, such as filter design, processing, communication theory. However, it falls short representing signals generalized domains. To address this limitation, we propose novel integral transform, coined quadratic-phase transform. preliminary study encomp...

Two earlier trips, one to Delaware, where Nuttall contracted malaria, and one to Niagara Falls and Ontario paved the way for the travels recounted in this diary. Nuttall's 1810 expedition, the first months of which are described in the diary, was unquestionably undertaken for Barton at his expense. The route, objectives, and full terms of agreement were set down in detail by Barton. Nuttall, co...