Evaluation of the probability of bankruptcy for a model of insurance company

We study the problem of evaluation of the probability of ruin of an insurance company for infinitely many steps in the case where the company can invest its capital to bank deposits at any time. As a distribution of the amounts of claims to the insurance company, we use the gamma-distribution with the parameters n and α. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 447–457, April, 2007.     

A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over

In this paper, the multi-item, single-level, capacitated, dynamic lot sizing problem with set-up carry-over and backlogging, abbreviated to CLSP⁺, is considered. The problem is formulated as a mixed integer programming problem. A heuristic method consisting of four elements: (1) a demand shifting rule, (2) lot size determination rules, (3) checking feasibility conditions and (4) set-up carry-over determination, provides us with an initial feasible solution. The resulting feasible solution is improved by adopting the corresponding set-up and set-up carry-over schedule and re-optimizing it by solving a minimum-cost network flow problem. Then the improved solution is used as a starting solution for a tabu search procedure, with the value of moves assessed using the same minimum-cost network problem. Computational results on randomly generated problems show that the algorithm, which is coded in C++, is able to provide optimal solutions or solutions extremely close to optimal. The computational efficiency makes it possible to solve reasonably large problem instances routinely on a personal computer.     

Copolymers of acrylic acid with urea

Composition and rheological characteristics of aqueous solutions of acrylic acid/urea copolymers were studied, including the composition dependences of the equivalent conductivity and viscosity.     

Magnetic properties of HITPERM-type alloys at high temperature

(Fe,Co)–Zr,Hf)–Cu–B (HITPERM-type) alloys with variable Hf, Zr and Co content were isothermally crystallised at 500–650 °C for 1 h, and the optimum nanocrystallisation temperature was selected on the basis of the minimum coercive field at room temperature. The quasistatic hysteresis loops were measured at temperature from 20 to 650 °C. Subsequently, the optimally annealed alloys were subjected to long-term annealing at 500, 550 and 600 °C. Working temperature of 600°C is too high for the investigated alloys to maintain stable magnetic properties. Temperature of 550 or 500 °C permits the material to be magnetically stable for a long period. The magnetic hysteresis loops recorded for the nanocrystalline alloys, where Fe:Co ratio is close to 1 and refractory metals content is 7 at.%, prove that coercive field increases slightly with temperature, but remains in the range of 20–40 A/m (depending on the alloy composition) from 20 to 550 °C. This proves that the investigated alloys, after optimisation of chemical composition, may be suitable for high temperature use.     

Quantitative methods for nanopowders characterization

The size, shape and surface topology have a strong influence on powders properties, such as: mechanical, optical, catalytic, etc. In addition, when particles have a nanometer size, the dispersion of these features plays an important role.There are a number of techniques, which could be used in order to characterize powders in terms of particle size and shape. However, due to the scale of analysis, well beyond the wavelength of visible light, most of them cannot be applied for investigations of nanopowders.In this paper, transmission electron microscopy (TEM) image analysis and X-ray methods are presented as promising and complementary techniques. An example of their application to ZrO₂ nanopowder is shown. The advantages and limitations of each method are described.     

Infrared reflection absorption study of carbon monoxide adsorption on Pd/Cu(1 1 1)

Pd-Cu bimetallic surfaces formed through a vacuum-deposition of Pd on Cu(1 1 1) have been discussed on the basis of carbon monoxide (CO) adsorption: CO is used as a surface probe and infrared reflection absorption (IRRAS) spectra are recorded for the CO-adsorbed surfaces. Low energy electron diffraction (LEED) patterns for the bimetallic surfaces reveal six-fold symmetry even after the deposition of 0.6 nm. The lattice spacings estimated by the separations of reflection high-energy electron diffraction (RHEED) streaks increase with increasing Pd thickness. Room-temperature CO exposures to the bimetallic surfaces formed by the Pd depositions less than 0.3 nm thickness generate the IRRAS bands due to the three-fold-hollow-, bridge- and linear-bonded CO to Pd atoms. In particular, on the 0.1 nm-thick Pd surface, the linear-bonded CO band becomes apparent at an earlier stage of the exposure. In contrast, the bridge-bonded CO band dominates the IRRAS spectra for CO adsorption on the 0.6 nm-thick Pd surface, at which the lattice spacing corresponds to that of Pd(1 1 1). A 90 K-CO exposure to the 0.1 nm-thick Pd surface leads to the IRRAS bands caused not only by CO-Pd but also by CO-Cu, while the Cu-related band is almost absent from the spectra for the 0.3 nm-thick Pd surface. The results clearly reveal that local atomic structures of the outermost bimetallic surface can be discussed by the IRRAS spectra for the probe molecule.     

Study of the order–disorder transition and martensitic transformation in a Cu–Al–Be alloy by EELS

Changes in 3d states occupancy associated with order–disorder transition and martensitic transformation in a Cu–Al–Be alloy was investigated by electron energy loss spectroscopy (EELS) in both high energy and low energy loss regions. From the high energy loss region, the Cu L_2,3 white-line intensities, which reflect the unoccupied density of states in 3d bands, was measured for three states of the alloy: disordered austenite, ordered austenite and martensite. It was found that the white-line intensity remains the same during order–disorder transition but appears slightly smaller in martensite, indicating that some electrons left Cu 3d bands or some hybridization took place during phase transformation. From the low energy loss region, the optical joint density of states (OJDS) was obtained by Kramers–Kronig analysis. As maxima observed in the OJDS spectra are assigned to interband transitions, these spectra can be used to probe changes in the electronic band structure. The analysis shows that during the martensitic transformation, the peaks positions and relative intensities in the OJDS spectra undergoes noticeable changes, which are associated with interband transitions.     

Codes Over the p-adic Integers

We study codes over the p-adic integers and correct errors in the existing literature. We show that MDS codes exist over the p-adics for all lengths, ranks and p. We show that self-dual codes exist over the 2-adics if and only if the length is a multiple of 8 and that self-dual codes exist over the p-adics with p odd if and only if the length is 0 (mod 4) for p ≡ 3 (mod 4) and 0 (mod 2) for p ≡ 1 (mod 4).