The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

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.     

Asymptotique de la norme $L^2$ d'un cycle géodésique dans les revêtements de congruence d'une variété hyperbolique arithmétique

Let M be an arithmetic hyperbolic manifold and be a codimension 1 geodesic cycle. In this paper, we study the asymptotic growth of the -norm of the lifts of F in the congruence tower above M. We obtain an explicit value for the growth rate of this norm. In particular, we provide a new proof of a celebrated result of Millson [Mi] on the homology of the arithmetic hyperbolic manifolds. The method is quite general and gives a new way of getting non zero homology classes in certain locally symmetric spaces. Received: 20 April 2001; in final form: 26 September 2001 / Published online: 28 February 2002     

Fine Dry Grinding of Zeolite in a Laboratory Ball Mill

This paper presents the importance and usage of natural zeolites, which was recently recognized in the industry. Therefore, the grinding properties of natural zeolite were studied with the emphasis on a kinetic study in a ball mill. The experimental mill employed was laboratory sized, 200 mm diameter, 191 mm length, providing a total mill volume of 6000 cm³, with a total mass of 5.62 kg of steel balls of 25 mm diameter with a charge of 20% of the mill volume and with a rotation speed of 76 rpm. The breakage parameters were determined by using single sized feed fractions of ?850+600 μm, ?600+425 μm, and ?425+300 μm for the zeolite samples. The S_i (specific rate of breakage) and B_{i, j} (primary breakage distribution) values were obtained for those feed size fractions in order to predict the product size distributions by simulation for comparison to the experimental data. From the experimental results, S_i values increased as the feed sizes became coarser, i.e., the highest S_i value was 0.85 min^?1 for ?850+600 μm, while the lowest S_i value was 0.65 min^?1 for ?425+300 μm feed ground in the mill. The B_{i, j} values obtained for the zeolite sample were γ=0.84, ?=0.61, and β=4.25. The breakage parameters obtained showed that the zeolite is broken faster than quartz and slower than calcite and barite in terms of the a_T values reported previously at the same experimental conditions. The simulations of the product size distributions of zeolite were in good agreement with the experimental data using a standard ball mill simulation program. The slowing‐down effect was also seen in the mill after 4 min. of grinding.     

Fabrication of Zeolite A Rods with Irregular Macropores by Self-assembly of Zeolite A Microcrystals Using Microwave-assisted Hydrothermal Synthesis

Zeolite A rods by self-assembly of zeolite A microcrystal were successfully synthesized by microwave-assisted hydrotherrnal synthesis. The average size of zeolite crystals consisting of self-assembling materials was about 300 nm and the length of zeolite rods was in the range of 15--30μm.     

Berezin transform on¶compact Hermitian symmetric spaces

Let X=G ^* be a compact Hermitian symmetric space. We study the Berezin transform on L ²(X) and calculate its spectrum under the decomposition of L ²(X) into the irreducible representations of G ^*. As applications we find the expansion of powers of the canonical polynomial (Bergman reproducing kernel for the canonical line bundle) in terms of the spherical polynomials on X, and we find the irreducible decomposition of tensor products of Bergman spaces on X. Received: 10 September 1996 / Revised version: 10 September 1997     

Intertwining differential operators and reducibility of generalized Verma modules

Supported in part by NSF Grant DMS-8610730     

Optimal convex hull algorithms on enhanced meshes

In this paper we propose time-optimal convex hull algorithms for two classes of enhanced meshes. Our first algorithm computes the convex hull of an arbitrary set ofn points in the plane inO (logn) time on a mesh with multiple broadcasting of sizen×n. The second algorithm shows that the same problem can be solved inO (1) time on a reconfigurable mesh of sizen×n. Both algorithms achieve time lower bounds for their respective model of computation.This work was supported by NASA under grant NCCI-99.Additional support by the National Science Foundation under grant CCR-8909996 is gratefully acknowledged.     

Countably compact topological group topologies on free Abelian groups from selective ultrafilters

Tkachenko showed in 1990 the existence of a countably compact group topology on the free Abelian group of size c using CH. Koszmider, Tomita and Watson showed in 2000 the existence of a countably compact group topology on the free Abelian group of size c² using a forcing model in which CH holds.Wallace's question from 1955, asks whether every both-sided cancellative countably compact semigroup is a topological group. A counterexample to Wallace's question has been called a Wallace semigroup. In 1996, Robbie and Svetlichny constructed a Wallace semigroup under CH. In the same year, Tomita constructed a Wallace semigroup from MAcountable.In this note, we show that the examples of Tkachenko, Robbie and Svetlichny, and Koszmider, Tomita and Watson can be obtained using a family of selective ultrafilters. As a corollary, the constructions presented here are compatible with the total failure of Martin's Axiom.     

Predicting automobile claims bodily injury severity with sequential ordered logit models

Despite the large cost of bodily injury (BI) claims in motor insurance, relatively little research has been done in this area. Many companies estimate (and therefore reserve) bodily injury compensation directly from initial medical reports. This practice may underestimate the final cost, because the severity is often assessed during the recovery period. Since the evaluation of this severity is often only qualitative, in this paper we apply an ordered multiple choice model at different moments in the life of a claim reported to an insurance company. We assume that the information available to the insurer does not flow continuously, because it is obtained at different stages. Using a real data set, we show that the application of sequential ordered logit models leads to a significant improvement in the prediction of the BI severity level, compared to the subjective classification that is used in practice. We also show that these results could improve the insurer’s reserves notably.