Harmonic mappings of the Sierpinski gasket to the circle

Harmonic mappings from the Sierpinski gasket to the circle are described explicitly in terms of boundary values and topological data. In particular, all such mappings minimize energy within a given homotopy class. Explicit formulas are also given for the energy of the mapping and its normal derivatives at boundary points.

     

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     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

Likelihood Ratio Processes for Markovian Particle Systems with Killing and Jumps

We consider Markov processes built from pasting together pieces of strong Markov processes which are killed at a position dependent rate and connected via a transition kernel. We give necessary and sufficient conditions for local absolute continuity of probability laws for such processes on a suitable path space and derive an explicit formula for the corresponding likelihood ratio process. The main tool is the consideration of the process between successive jumps – what we call ‘elementary experiments’ – and criteria for absolute continuity of laws of the process there. We apply our results to systems of branching diffusions with interactions and immigrations. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Design for Automation of Pellet-Forming Process in HL-2A Pellet Fueling System

In the ever fusion experiments in SWIP, pellet forming process was carried out through adjusting relative devices by staff member in site, which will make every pellet-forming process slight distinction and will result in pellet difference in shape, size and intensity. In the intervals of HL-2A discharges, staff member have to go site to accomplish the pellet-forming process, this wastes human power and increase the potential danger. So it is necessary to develop a remote control system to perform the pellet-forming process. The control system needs have the features of real-time, reliability and be easy to operate and maintain.     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

稀疏过程在破产问题中的应用

本讨论一类人寿保险的风险过程，其中保单到达服从齐次Poisson过程。而描述退保及索赔发生的计数过程分别为这一过程的q-稀疏与p-稀疏．对此模型给出其破产概率的具体上界，并与其它一类风险模型进行比较．     

Synthesis of molecular imprinted organic-inorganic hybrid polymer binding caffeine

Random copolymers of poly{(methacrylamide)-co-(vinyl trimethoxysilane)} and poly{(methacrylic acid)-co-(vinyl trimethoxysilane)} were synthesized via a free radical polymerization reaction. Acid catalyzed sol-gel process of tetraethylorthosilicate (TEOS) with aforementioned polymers in the presence of methyl xanthine class of alkaloid like caffeine resulted in the formation of highly transparent monoliths. Solvent extraction of the template leaves behind the recognition sites intact with high selectivity towards the print molecule. The ionic and non-specific adsorptions, which are considered to be the main disadvantages of the molecularly imprinted polymers (MIP), are prevented to a considerable extent by the end capping of surface silanol groups. The template binding efficiencies of MIP were determined by HPLC analysis.     

Composite Silica Particles Using a Mixture of Organosilane Monomers

Composite silica particles were synthesized by a two-step (acid-base) process in an aqueous solution with a mixture of organoalkoxysilane monomers. The two-step process separates the hydrolysis and condensation procedures to easily control condensation rate. In this study, the silane monomers used were phenyltrimethoxysilane (PTMS), vinyltrimethoxysilane (VTMS), methyltrimethoxysilane (MTMS), and tetraethyl-orthosilicate (TEOS). The physical properties of the resultant composite particles were investigated with the change in the molar ratio of monomers. The size of the particles increased with increasing the molar ratio of R_aSi(OR)₃/R_bSi(OR)₃ or R_aSi(OR)₃/TEOS (R_a: phenyl; R_b: vinyl, methyl).     

Harnack inequality for some classes of Markov processes

In this paper we establish a Harnack inequality for nonnegative harmonic functions of some classes of Markov processes with jumps. Mathematics Subject Classification (2000): Primary 60J45, 60J75, Secondary 60J25.This work was completed while the authors were in the Research in Pairs program at the Mathematisches Forschungsinstitut Oberwolfach. We thank the Institute for the hospitality.The research of this author is supported in part by NSF Grant DMS-9803240.The research of this author is supported in part by MZT grant 0037107 of the Republic of Croatia.