On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums

The paper develops a method for the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums.     

Electrothermal AAS studies of Sm, Eu, Dy, and Er separated from uranium

Summary Studies were conducted on the assay of Sm, Eu, Dy and Er separated from uranium using aqueous standards by electrothermal AAS with Massmann type graphite furnace. The working curves were found to be linear in the ranges Sm (1–10 g/ml), Eu (0.05–0.6 g/ml), Dy (0.1–0.8 g/ml) and Er (0.1–1.0 g/ml). The values obtained for synthetic samples agreed favourably with those obtained by emission spectrographic method. Experiments using pyrolytic carbon coated tubes with and without pretreatment by La, Ta and Y have shown an enhancement with treatment upto a maximum of 15% and improve the memory effect marginally. The effect of Ta treatment was found to be singularly useful in improving the general behaviour of Sm. The interference effects of lanthanides, other than the analyte, were found to be negligible. However, the presence of uranium was found to affect the absorbance. The absorbance of Eu was found to be nearly independent of uranium after an initial increase. On the other hand, the absorbance of other elements studied was found to drastically decrease after an initial enhancement. Detailed investigations of temperature dependence of absorbance were carried out using Eu, Dy and Er. The differences in the behaviour of these elements is attributed to probable differences in the modes of their atomization.

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Untersuchung von aus Uran abgetrenntem Samarium, Europium, Dysprosium und Erbium durch elektrothermische Atomabsorptions-Spektralphotometrie

Zusammenfassung Die Untersuchungen wurden mit Hilfe des Graphitrohrofens nach Maßmann durchgeführt. In folgenden Bereichen ergaben sich lineare Eichkurven: Sm 1–10 g/ml, Eu 0,05–0,6 g/ml, Dy 0,1–0,8 g/ml, Er 0,1-1,0 g/ml. Die aus synthetischen Proben erhaltenen Ergebnisse stimmten gut mit den durch Emissionsspektrographie erhaltenen überein. Versuche wurden mit Röhren mit pyrolytischen Kohlenstoffüberzug mit und ohne Vorbehandlung durch La, Ta und Y durchgeführt und ergaben eine bis 15%ige Steigerung durch die Behandlung sowie eine mäßige Besserung des Memoryeffektes. Eine Behandlung mit Ta war besonders für Sm vorteilhaft. Störungen durch andere Lanthanide waren vernachlässigbar. Uran beeinflußte jedoch die Absorption. Im Falle von Eu zeigte sich nach anfänglicher Zunahme fast eine Unabhängigkeit, während bei den anderen untersuchten Elementen nach anfänglicher Zunahme eine beträchtliche Abnahme auftrat. Mit Eu, Dy und Er wurde ebenfalls die Temperaturabhängigkeit der Absorption untersucht. Festgestellte Unterschiede im Verhalten werden auf unterschiedliche Atomisierung zurückgeführt.

     

The distribution of special subsets of the Farey sequence

We will examine the subset of Farey fractions of order Q consisting of those fractions whose denominators are not divisible by a fixed prime p. In particular, we will provide an asymptotic result on the distribution of H-tuples of consecutive fractions in , as Q→∞.     

Integers with dense divisors 2

Let 1=d₁(n)<d₂(n)<?<d_τ(n)=n be the sequence of all positive divisors of the integer n in increasing order. We say that the divisors of n are t-dense iff max_1?i<τ(n)d_i+1(n)/d_i(n)?t. Let D(x,t) be the number of positive integers not exceeding x whose divisors are t-dense. We show that for x?3, and , we have , where , and d(w) is a continuous function which satisfies d(w)?1/w for w?1. We also consider other counting functions closely related to D(x,t).     

Monte Carlo simulations of electron dynamics in N2/CO2 mixtures

Motivated by experimental investigations of electrical discharges in N₂/CO₂/H₂O, Monte Carlo (MC) electron dynamics simulations in atmospheric N₂/CO₂ mixtures were performed. The goal was to obtain electron energy distribution functions (EEDFs), mean free path, drift velocity, collision frequency and mean energy of electrons, rate coefficients of electron-impact reactions, ionisation and attachment coefficients, as functions of the reduced electric field strength (E/N) and of the concentration of individual gas components. The results obtained by MC simulations were fitted with polynomials of up to the 3rd order with reasonable accuracy for E/N above 80 Td. The studied parameters below 80 Td were strongly non-linear as functions of E/N. This is mostly due to the influence of elastic collisions of electrons with CO₂ molecules prevailing in CO₂-dominant mixtures for E/N < 40 Td, and vibrational excitation collisions of N₂ species prevailing in N₂-dominant mixtures for E/N from 40 to 80 Td. The effect of these electron-impact processes was specific for each of the studied parameters.     

22 dB all-fiber green amplifier using Er-doped fluoride fiber

We demonstrate a 22 dB all-fiber amplifier at 546 nm using Er³⁺-doped fluoride fiber by forward upconversion pumping of a 974 nm laser diode. The gain saturation effects and the power conversion efficiency of this amplifier are investigated in detail based on gain characteristics and numerical simulations.     

Phase and velocity distributions in vertically upward high-viscosity two-phase flow

The two-phase pressure drop in vertical industrial pipes is mainly determined by gravitation and acceleration of the fluid, which means that the void fraction is key an important parameter in any model to predict pressure drops. Typically, these models are applied in industry to size pumps and, e.g., emergency relief systems. There is a shortage of void fraction data in the literature for liquids with a dynamic viscosity above 1000 mPa s. Adiabatic experiments have been performed of mixtures of nitrogen and solutions of polyvinylpyrrolidone (Luviskol^®) in water with dynamic viscosities in the range 900–7000 mPa s. Inner tube diameter was 54.5 mm. Mass flux and quality were varied in a wide range: 8–3500 kg/m²/s and 0–82%, respectively. The corresponding superficial velocities were 0.005–3.4 m/s for the liquid and 0–30 m/s for the nitrogen. For comparison, reference measurements were taken of mixtures of nitrogen with water (1 mPa s). Care has been taken to measure only well-developed flows.     

Isometries of the space of distribution functions with respect to the Kolmogorov-Smirnov metric

In this paper we describe the general forms of surjective isometries of the space of all probability distribution functions on R with respect to the Kolmogorov-Smirnov metric.     

A memetic algorithm with dynamic population management for an integrated production–distribution problem

This paper studies an NP-hard multi-period production–distribution problem to minimize the sum of three costs: production setups, inventories and distribution. This problem is solved by a very recent form of metaheuristic called memetic algorithm with population management (MA∣PM). Contrary to classical two-phase methods (production planning, then distribution planning), the algorithm simultaneously tackles production and distribution decisions. Several versions with different population management strategies are evaluated and compared with a two-phase heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP), on 90 randomly generated instances with 20 periods and 50, 100 or 200 customers. The significant savings obtained compared to the two other methods confirm both the interest of integrating production and distribution decisions and of using the MA∣PM template.     

A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge

This paper considers a two-stage distribution problem of a supply chain that is associated with a fixed charge. Two kinds of cost are involved in this problem: a continuous cost that linearly increases with the amount transported between a source and a destination, and secondly, a fixed charge, that incurs whenever there exists a transportation of a non-zero quantity between a source and a destination. The objective criterion is the minimisation of the total cost of distribution. A genetic algorithm (GA) that belongs to evolutionary search heuristics is proposed and illustrated. The proposed methodology is evaluated for its solution quality by comparing it with the approximate and lower bound solutions. Thus, the comparison reveals that the GA generates better solution than the approximation method and is capable of providing solution either equal or closer to the lower bound solution of the problem.