Here we prove that a compact Stein manifoldW 2n+2 of dimension 2n+2 > 4 admits a Lefschetz fibration over the disk D with Stein fibers, such that the monodromy of the fibration is a symplectomorphism induced by compositions of “generalized Dehn twists” along imbedded n-spheres on the generic fiber. Also, the open book on the boundary ∂W , which is determined by the fibration, is compatible with...

This result has been extended to open sets in Stein manifolds. But nothing is known about this if (Dj)j≥1 is a family of a Stein complex space X, even when X has isolated singularities. The main new result of this article concerns a generalization of this theorem for families of q-complete open sets in Stein spaces. By using a description of q-convex functions in terms of linear sets, introduce...

This paper applies the bootstrap methods proposed by Efron (1979) to the Stein variance estimator proposed by Stein (1964). It is shown by Monte Carlo experiments that the parametric bootstrap yields the considerable accurate estimates of mean, standard error and confidence limits of the Stein variance estimator.

It is well-known that the associated analytic space of an affine variety defined over complex number field is Stein but the converse is not true, that is, an algebraic Stein variety is not necessarily affine. In this talk, we will give sufficient and necessary conditions for an algebraic Stein variety to be affine. One of our results is that a quasi-projective variety Y defined over complex num...

We prove that a pseudoholomorphic diffeomorphism between two almost complex manifolds with boundaries satisfying some pseudoconvexity type conditions cannot map a pseudoholomorphic disc in the boundary to a single point. This can be viewed as an almost complex analogue of a well known theorem of J.E.Fornaess.

The Reverse Stein Effect is identified and illustrated: A statistician who shrinks his/her data toward a point chosen without reliable knowledge about the underlying value of the parameter to be estimated but based instead upon the observed data will not be protected by the minimax property of shrinkage estimators such a" that of James and Stein, but instead will likely incur a greater error th...

We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f . We show, for instance, that if an X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurfac...

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model. We find explicit formulas for leading terms in asymptotic expansions of the...

We continued the study of the contact homology of subcritical Stein manifolds initiated by Mei-Lin Yau. With the technical assumption that the first Chern class of the Stein domain vanishes, we determined the full contact homology of the boundary of a subcritical Stein domain. Moreover we calculated the genus 0 correlators and descendants of one marked point for the Stein domain. As an applicat...