A note on weak convergence of random step processes

First, sufficient conditions are given for a triangular array of random vectors such that the sequence of related random step functions converges towards a (not necessarily time homogeneous) diffusion process. These conditions are weaker and easier to check than the existing ones in the literature, and they are derived from a very general semimartingale convergence theorem due to Jacod and Shiryaev, which is hard to use directly.     

Asymptotic Behavior of Critical Primitive Multi-Type Branching Processes with Immigration

Under natural assumptions a Feller-type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved that a sequence of appropriately scaled random step functions formed from a sequence of critical primitive multi-type branching processes with immigration converges weakly toward a squared Bessel process supported by a ray determined by the Perron vector of the offspring mean matrix.     

Nonlinear adsorption isotherm as a tool for understanding and characterizing molecularly imprinted polymers

Molecularly imprinted polymers (MIPs) have frequently been characterized by quantities which are easily determined from experiments but have no theoretical foundation. This makes it difficult to compare different MIP preparations or to transfer MIP based methods to different experimental conditions. Since the adsorption isotherms of MIPs are markedly nonlinear, one can build a better characterization strategy on isotherms as shown by examples in this paper.     

Laser soldering of flip-chips

A novel process for laser soldering of flip-chips on transparent printed circuit board assemblies is presented. The experiments were carried out on silver test patterns printed on glass wafers using a roller-type gravure offset printing method. The contact pads, where the bumps of the flip-chips are positioned, were covered with a thin layer of additional solder paste. The aligned samples (solder pad—solder paste—chip bump) were illuminated through the glass substrate using an Ar⁺ laser beam (, , at 1/e) to heat the printed pad and melt the solder paste, thus forming a joint between the printed pad and the chip bump. The heat-affected zone was modeled using computer-assisted finite element method. The solder joint cross-sections were analyzed using optical and electron microscopy as well as energy dispersive X-ray element analyses. The laser-soldered joints were of good mechanical and electrical quality and the process proved to be suitable for manufacturing customized circuit prototypes.     

Statistical maps and generalized random walks

We continue our study of statistical maps (equivalently, fuzzy random variables in the sense of Gudder and Bugajski). In the realm of fuzzy probability theory, statistical maps describe the transportation of probability measures on one measurable space into probability measures on another measurable space. We show that for discrete probability spaces each statistical map can be represented via a special matrix the rows of which are probability functions related to conditional probabilities and the columns are related to fuzzy n-partitions of the domain. Discrete statistical maps sending a probability measure p to a probability measure q can be represented via conditional distributions and correspond to joint probabilities on the product. The composition of statistical maps provide a tool to describe and to study generalized random walks and Markov chains.     

Estimation of the Mean of a Wiener Sheet

A shifted Wiener sheet is observed above a decreasing curve Γ. By the help of a direct discrete approach and under weaker assumptions than in the paper of Arató [Comput. Math. Appl. 33 (1997), 13–25], an explicit formula is derived for the maximum likelihood estimator of the shift parameter. This estimator is a weighted linear combination of the values at the endpoints of the curve Γ and weighted integrals of the observed process and its normal derivative along the curve Γ. This revised version was published online in June 2006 with corrections to the Cover Date.     

Limiting Connection between Discrete and Continuous Time Forward Interest Rate Curve Models

We study discrete time Heath–Jarrow–Morton (HJM) type of interest rate curve models, where the forward interest rates – in contrast to the classical HJM models – are driven by a random field. Our main aim is to investigate the relationship between the discrete time forward interest rate curve model and its continuous time counterpart. We derive a general result on the convergence of discrete time models and we give special focus on the nearly unit root spatial autoregression model.     

Preparative Synthesis of 4,4'-Bis[5-alkyl(aryl)benzoxazol-2-yl]biphenyls

An attempt was made to prepare 4,4'-bis[5-alkyl(aryl)benzoxazol-2-yl]biphenyls by reaction of dimethyl 4,4'-biphenyldicarboxylate with substituted o-aminophenols in a high-boiling solvent in the presence of boric acid.