A process of evolving random graphs is considered where vertices are added to the graph one by one, and edges connecting the
new vertex to the old ones are drawn independently, each with probability depending linearly on the degree of the endpoint.
In the paper the asymptotic degree distribution and the order of the maxdegree are determined.
For everyk≥1 consider the waiting time until each pattern of lengthk over a fixed alphabet of sizen appears at least once in an infinite sequence of independent, uniformly distributed random letters. Lettingn→∞ we determine the limiting finite dimensional joint distributions of these waiting times after suitable normalization and
provide an estimate for the rate of convergence. It will turn out that these waiting times are getting independent.
In a one-parameter model for evolution of random trees strong law of large numbers and central limit theorem are proved for the number of vertices with low degree. The proof is based on elementary martingale theory.
Sufficient conditions of covariance type are presented for weighted averages of random variables with arbitrary dependence
structure to converge to 0, both for logarithmic and general weighting. As an application, an a.s. local limit theorem of
Csáki, Földes and Révész is revisited and slightly improved.
In a string ofn independent coin tosses we consider the difference between the lengths of the longest blocks of consecutive heads resp. tails. A complete characterization of the a.s. limit properties of this quantity is proved.
When an opportunistic predator is looking for a given type of prey and encounters another one from different species, it tries to utilize this random opportunity. We characterize the optimal levels of this opportunism in the framework of stochastic models for the two prey-one predator case. We consider the spatial dispersal of preys and the optimal diet choice of predator as well. We show that when both preys have no handling time, the total opportunism provides maximal gain of energy for the predator. When handling times differ with prey, we find a conditional optimal behavior: for small density of both prey species the predator prefers the more valuable one and is entirely opportunistic. However, when the density of the more valuable prey is higher than that of the other species, then the predator prefers the first one and intentionally neglects the other. Furthermore, when the density of the less valuable prey is high and that of the other one is small, then predator will look for the less valuable prey and is therefore totally opportunistic. We demonstrate that prey preference is remunerative whenever the advantage of a proper prey preference is larger than the average cost of missed prey preference. We also propose a dynamics which explicitly contains two sides of shared predation: apparent mutualism and apparent competition, and we give conditions when the rare prey goes extinct.
The volatilization losses of mercury before, during and after neutron irradiation were studied. To minimize the losses, respectively,
were added to the standards, thiourea, L-cysteine, thioacetamide and ammonium sulfide. It was possible to minimize the losses
by preserving the standard at −20°C after irradiation. No loss was seen in the biological materials after irradiation.
This study reports the effect of a nonionic perfluorinated surfactant, N-polyoxyethylene-N-propyl perfluorooctane sulfonamide (PFOSA), as additive of background electrolyte on capillary electrophoresis (CE) of common inorganic cations. The association constants (Kass) for PFOSA estimated from the electrophoretic mobility of analyte cations were the order of Mg2+ > Ca2+ > Sr2+ > K+ ≈ NH4+ > Na+ ≈ Li+. The Kass values were larger than those for zwitterionic and nonionic surfactants with hydrocarbon moiety. Use of PFOSA made another essential contribution to the determination of inorganic cations in a protein-containing sample. This was considered because high solubility of PFOSA for proteins functioned as suppressor for protein adsorption to the capillary wall. Four inorganic cations, Na+, K+, Mg2+, and Ca2+, in human saliva sample were successfully determined by sample injection without any pretreatments except for filtration and dilution.