On the realization of Riemannian symmetric spaces in Lie groups

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G.     

Conditional independence models for seemingly unrelated regressions with incomplete data

We consider normal ≡ Gaussian seemingly unrelated regressions (SUR) with incomplete data (ID). Imposing a natural minimal set of conditional independence constraints, we find a restricted SUR/ID model whose likelihood function and parameter space factor into the product of the likelihood functions and the parameter spaces of standard complete data multivariate analysis of variance models. Hence, the restricted model has a unimodal likelihood and permits explicit likelihood inference. In the development of our methodology, we review and extend existing results for complete data SUR models and the multivariate ID problem.     

A nilpotent Roth theorem

Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L ²-norm for any u, v∈L ^∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T _-n A∩S ^{- n} A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L ²(X) for all u, v∈L ^∞(X) if and only if T×S is ergodic on X×X and the group generated by T ^-1 S, T ^-2 S ²,..., T ^-c S ^c acts ergodically on X. Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001     

On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002     

On the density of the space of continuous and uniformly continuous functions

For X a metrizable space and (Y,ρ) a metric space, with Y pathwise connected, we compute the density of (C(X,(Y,ρ)),σ)—the space of all continuous functions from X to (Y,ρ), endowed with the supremum metric σ. Also, for (X,d) a metric space and (Y,‖⋅‖) a normed space, we compute the density of (UC((X,d),(Y,ρ)),σ) (the space of all uniformly continuous functions from (X,d) to (Y,ρ), where ρ is the metric induced on Y by ‖⋅‖). We also prove that the latter result extends only partially to the case where (Y,ρ) is an arbitrary pathwise connected metric space.To carry such an investigation out, the notions of generalized compact and generalized totally bounded metric space, introduced by the author and A. Barbati in a former paper, turn out to play a crucial rôle. Moreover, we show that the first-mentioned concept provides a precise characterization of those metrizable spaces which attain their extent.     

Commutant Lifting Theorem for the Bergman Space

The central question of this paper is the one of finding the right analogue of the Commutant Lifting Theorem for the Bergman space L_a². We also analyze the analogous problem for weighted Bergman spaces L_a,α², − 1 < α < ∞.     

A novel and efficient synthesis of porphine

meso-Tetra(n-hexyloxycarbonyl)porphyrin was found to be converted into porphine, the mother compound of porphyrins, in a 77% yield when heated in aqueous sulfuric acid at 180 °C over 30 min under an inert atmosphere. The observation demonstrates that the substituted porphyrin serves as a novel and useful precursor for porphine.     

Inequalities for the Moments and Distribution of the Ladder Height of a Random Walk

We obtain upper bounds for the tail distribution of the first nonnegative sum of a random walk and for the moments of the overshoot over an arbitrary nonnegative level if the expectation of jumps is positive and close to zero. In addition, we find an estimate for the expectation of the first ladder epoch.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002