Often it is desired to test a composite null hypothesis against a composite alternative that is not in the same parametric family as the null hypothesis. For example, suppose we have independent, identically distributed (i.i.d.) observations U,, .., U, and we wish to test the hypothesis that these observations arise from a normal distribution against the alternative that they rise from a logist...

We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like inequalities. As part of the our methods, we give a different approach to a priori estimates of Foiaş, Guillopé and Temam.

We give a lower semicontinuous type regularity condition and a closedness type one which turn out to be necessary and sufficient for the fulfillment of two different formulae involving the εsubdifferential of a perturbation function, respectively. These regularity conditions prove to be sufficient also for having formulae for the classical subdifferential of a perturbation function. Some recent...

This paper considers a Kullback-Leibler distance (KLD) which is asymptotically equivalent to the KLD by Goutis and Robert [1] when the reference model (in comparison to a competing fitted model) is correctly specified and that certain regularity conditions hold true (ref. Akaike [2]). We derive the asymptotic property of this Goutis-Robert-Akaike KLD under certain regularity conditions. We also...

By using the Szemerédi Regularity Lemma [10], Alon and Sudakov [1] recently extended the classical Andrásfai-Erdős-Sós theorem [2] to cover general graphs. We prove, without using the Regularity Lemma, that the following stronger statement is true. Given any (r+1)-partite graph H whose smallest part has t vertices, there exists a constant C such that for any given ε > 0 and sufficiently large n...

Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on n vertices with o(n) copies of H can be made H-free by removing o(n) edges. We give a new proof which avoids Szemerédi’s regularity lemma and gives a better bound. This approach also works to give improved bounds for the directed and multicolored analogues of the graph removal lemma. This answers question...

The asymptotics of 2-colour Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs were recently determined [16, 17]. We address the same problem for Berge cycles and for 3 colours. Our main result is that the 3-colour Ramsey number of a 3-uniform Berge cycle of length n is asymptotic to 5n 4 . The result is proved with the Regularity Lemma via the existence of a monochromatic connec...

Regularity is a shared memory consistency condition that has received considerable attention. Lamport’s original definition of regularity assumed a single-writer model, however, and is not well defined when the shared register may have multiple writers. In this paper, we consider four possible definitions of multi-writer regularity. The definitions are motivated by variations on a quorum-based ...

Linearity-generating” processes offer a tractable procedure to model cash-flows and pricing kernels in a way that yields exact closed form expressions for bond and stock prices. Prices are simply affine (not exponential-affine) in the factors. The linearity-generating class operates in discrete and continuous time with an arbitrary number of factors. This paper presents novel and general regula...