Lp-dual Quermassintegral sums

In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral sums.Moreover,by using Lutwak's width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion bodies.As applications,we prove some interrelated results.     

Suzuki cross-coupling reactions using reverse-phase glass beads in aqueous media

Reverse-phase glass beads have been employed in Suzuki reactions to provide, in aqueous media, a route to diverse polar substrates in good yield and with low levels of palladium leaching.     

Sobolev空间中的几个不等式的推广

本文将Sobolev空间中的Clarkson不等式的几个引理作了适当的推广,并给出了证明.     

Number of lattice points in the hyperbolic cross

An asymptotic formula for the number of points of an arbitrary lattice in the hyperbolic cross is obtained. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 363–369, March, 1998. The authors wish to thank Professors N. M. Korobov and V. I. Nechaev for their attention and useful discussions.     

Partial Ovoids in Classical Finite Polar Spaces

Ovoids in finite polar spaces are related to many other objects in finite geometries. In this article, we prove some new upper bounds for the size of partial ovoids in Q ^–(2n+1,q) and W(2n+ 1,q). Further, we give a combinatorial proof for the non-existence of ovoids of H(2n +1,q ²) for n>q ³.     

Generalized Polar Decompositions on Lie Groups with Involutive Automorphisms

The polar decomposition, a well-known algorithm for decomposing real matrices as the product of a positive semidefinite matrix and an orthogonal matrix, is intimately related to involutive automorphisms of Lie groups and the subspace decomposition they induce. Such generalized polar decompositions, depending on the choice of the involutive automorphism σ , always exist near the identity although frequently they can be extended to larger portions of the underlying group. In this paper, first of all we provide an alternative proof to the local existence and uniqueness result of the generalized polar decomposition. What is new in our approach is that we derive differential equations obeyed by the two factors and solve them analytically, thereby providing explicit Lie-algebra recurrence relations for the coefficients of the series expansion. Second, we discuss additional properties of the two factors. In particular, when σ is a Cartan involution, we prove that the subgroup factor obeys similar optimality properties to the orthogonal polar factor in the classical matrix setting both locally and globally, under suitable assumptions on the Lie group G . September 12, 2000. Final version received: April 16, 2001.     

Highly Isospecific Polymerization of Silyl‐Protected ω‐Alkenols Using an [OSSO]‐Type Bis(phenolato) Dichloro Zirconium(IV) Precatalyst

The coordination polymerization of silyl‐protected ω‐alkenols such as ω‐alken‐α‐oxytriisopropylsilanes 1 provides poly(ω‐alkenyl‐α‐oxytriisopropylsilalne)s with a highly isospecific microstructure ([mmmm] > 95%) when a combination of [OSSO]‐type bis(phenolato) dichloro zirconium(IV) complex 2 and dried methylaluminoxane is used as the precatalyst and activator, respectively. The resulting siloxy‐substituted polymers could be efficiently transformed into the corresponding functionalized polyolefins, which contained up to 90% acetyl groups and ≈7% hydroxy groups in the terminal side chains.

     

A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces

Here we give a new approach to the Paley–Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of polar‐analytic function in the Mellin setting and Mellin–Bernstein spaces. A notion of Hardy spaces in the Mellin setting is also given along with applications to exponential sampling formulas of optical physics.     

A REVIEW OF POLAR STRATOSPHERIC CLOUD FORMATION

Liquid and solid particles in polar stratospheric clouds （PSCs） have been known to play a crucial role in the chemical loss of stratospheric ozone over the Antarctic and Arctic regions in late winter and early spring. The stratospheric aerosol and cloud particles provide the sites where fast heterogeneous chemical reactions convert inactive halogen reservoir species into potential ozone destroying radicals. The sedimentation of nitric acid-containing PSC particles irreversibly removes HNO3 gas （denitrification） from the lower stratosphere, which slows the return of chlorine to its inactive forms, resulting in more severe stratospheric ozone destruction. Although these clouds have been investigated extensively during the past decade using in situ field observation, laboratory experiment and modeling studies, the detailed microphysics processes under cold stratospheric conditions are still uncertain. This paper reviews the recent advances in our understanding of PSCs.