Equivalence and Singularity of Gaussian Measures on the Conic Sigma-Field

The alternative: equivalence-singularity on the conic sigma-field is established for a pair of centered Gaussian distributions and a corresponding criterion is given. The behavior of the logarithmic variation is established for the Radon–Nikodym derivative on the conic sigma-subfield. Bibliography: 6 titles.     

Optimal pricing for a heterogeneous portfolio for a given risk factor and convex distance measure

Consider a portfolio containing heterogeneous risks. The premiums of the policyholders might not cover the amount of the payments which an insurance company pays the policyholders. When setting the premium, this risk has to be taken into consideration. On the other hand the premium that the insured pays has to be fair. This fairness is measured by a function of the difference between the risk and the premium paid—we call this function a distance function. For a given small probability of insolvency, we find the premium for each class, such that the distance function is minimized. Next we formulate and solve the dual problem, which is minimizing the insolvency probability under the constraint that the distance function does not exceed a given level. This paper generalizes a previous paper [Zaks, Y., Frostig, E., Levikson, B., 2006. Optimal pricing of a heterogeneous portfolio for a given risk level. Astin Bull. 36 (1), 161–185] where only a square distance function was considered.     

On modifications of random processes

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 194, pp. 150–169, 1992.     

Quantitative Impact of a Cognitive Modeling Intelligent Tutoring System on Student Performance in Balancing Chemical Equations

The need for improved interactive tutoring capabilities in educational software for chemistry problem solving is an important one clearly articulated by teachers and students. To deliver the next generation of individualized interactive capabilities users demand, it is necessary to go beyond the conventional computer-assisted instruction methodology. The focus of this paper is the assessment with first-semester general chemistry students of a recently developed artificial intelligence (AI) tutor for balancing chemical equations. This is the first such assessment of an AI-based learning tool in chemistry. Students in CHEM 121 in the Fall 2001 semester at Duquesne University (N = 273) participated in the study. Students were divided into a test group that used the AI tutor as part of their study activities and a control group that did not use the tutor. It was found that the tutor improved the performance of the test group students to a statistically significant degree, helping the weakest students the most. This study establishes the feasibility of an AI-based approach to creating advanced new tutoring software for chemistry problem solving. Access to a Web-based demonstration of the equation-balancing tutor may be obtained by emailing the corresponding author.     

A Ramsey‐type result for the hypercube

We prove that for every fixed k and ? ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Q_n with k colors contains a monochromatic cycle of length 2 ?. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k‐edge coloring of a sufficiently large Q_n contains a monochromatic copy of H. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 196–208, 2006     

Limit distribution “in the large” of linear functionals over a random process of the second order

An infinite-dimensional analogue of the theorem on the existence of an -typical distribution of linear functionals in a vector space of high dimension does not exist. There are given some additional conditions ensuring, nevertheless, the existence of a typical distribution of linear functionals in the infinite-dimensional case.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 199–202, 1980.The author is grateful to S. B. Makarov for pointing out and corresponding these errors.     

Photoionization dynamics of glycine adsorbed on a silicon cluster: "on-the-fly" simulations

Dynamics of glycine chemisorbed on the surface of a silicon cluster is studied for a process that involves single-photon ionization, followed by recombination with the electron after a selected time delay. The process is studied by "on-the-fly" molecular dynamics simulations, using the semiempirical parametric method number 3 (PM3) potential energy surface. The system is taken to be in the ground state prior to photoionization, and time delays from 5 to 50 fs before the recombination are considered. The time evolution is computed over 10 ps. The main findings are (1) the positive charge after ionization is initially mostly distributed on the silicon cluster. (2) After ionization the major structural changes are on the silicon cluster. These include Si-Si bond breaking and formation and hydrogen transfer between different silicon atoms. (3) The transient ionization event gives rise to dynamical behavior that depends sensitively on the ion state lifetime. Subsequent to 45 fs evolution in the charged state, the glycine molecule starts to rotate on the silicon cluster. Implications of the results to various processes that are induced by transient transition to a charged state are discussed. These include inelastic tunneling in molecular devices, photochemistry on conducting surfaces, and electron-molecule scattering.     

Oral malodor,assessed by closed-loop,gas chromatography,and ion-trap technology

A method is described for the analysis of volatile organic compounds in saliva and tongue coating samples. The techniue is based on an off-line preconcentration step by means of a closed-loop trapping system followed by gas chromatography-ion trap detection. With the closed-loop technique, the volatile organic compounds(VOCs) are released from the matrix and trapped on an adsorbent without interference of water. The VOCs are released from the adsorbent into the gas chromatograph by thermdesorption. After separation, identification of the compounds is performed by ion trap technology. By this technique 82 compounds could be demonstrated in saliva and tongue coating samples. The technique is also used to demonstrate the formation of volatile bacterial fermentation compounds when a protein substrate is added to tongue coating samples. It is considered a very promising tool in further research on oral malodor.     

Linear quadrupoles with added octopole fields

Two methods of adding relatively small octopole fields to the main quadrupole field of quadrupoles and linear ion traps with cylindrical rods are investigated. The first, 'stretching' the quadrupole by moving two rods out from the axis, produces a combination of higher order fields with similar magnitudes in which the octopole field is not necessarily the greatest. The quadrupole field strength is changed significantly and a large potential appears on the axis. The second method uses rod pairs of different diameters. It adds octopole components of up to several percent while all other higher order fields remain small. An axis potential is also added, but it is only a few percent of the radio-frequency (RF) voltage and approximately equal to the strength of the octopole field. The axis potential can be removed by moving the larger rod pair out from the axis or applying unbalanced RF to the electrodes.     

Syntheses and conformational analyses of some 3-amino-2,5-dioxo-2,3,4,5-tetrahydro-1H-1-benzazepine derivatives: X-ray crystal structure of 35–3-[[(1,1-dimethylethoxy)carbonyl]amino]-2,5-dioxo-2,3,4,5-tetrahydro-1H-1-benzazepine

The constrained dipeptide mimic 1 was synthesized from 2 in three steps with 65% overall yield. Analyses of the ¹H nmr data of a number of 3-amino-2,5-dioxo-2,3,4,5-tetrahydro-1H-1-benzazepine derivatives led to the conclusion that these compounds adopt a similar conformation and that this ring system is rigid. X-ray crystallography was used to define the structure of 3 , and computer-aided energy minimization of 6 gave a preferred conformation similar to that observed in the crystal of 3 .