An optimal repeat inspection plan with several classifications

Multicharacteristic critical components exist in many systems. Such components could be a part of an aircraft, space shuttle or a gas ignition system. A component is critical if it causes disaster or a very high cost upon failure. In this paper, a new inspection plan for critical multicharacteristic components is presented. A mathematical model that depicts the plan is developed. An algorithm is proposed for finding the optimal number of repeat inspections and the sequence of characteristics for inspection that minimizes expected total cost per accepted component. The expected cost consists of the cost of inspection and the cost of misclassifications. The inspection plan and the model developed generalize existing models in the literature and provide a more realistic formulation. An example is given to demonstrate the plan and the model.     

Sn-Sb and Sn-Bi alloys as anode materials for lithium-ion batteries

Sn/SnSb, Sn/Bi, and Sn/SnSb/Bi multi-phase materials were synthesised via reduction of cationic precursors with NaBH₄ and with Zn, and were tested for their suitability as anode materials for Li-ion batteries by galvanostatic cycling. The rapid reduction with NaBH₄ yielded the finer materials with the better cycling stabilities, whereas the reduction with Zn yielded the purer materials with the lower irreversible capacities in the first cycle. Reversible capacities of ∼ 600 mAh g⁻¹, ∼ 350 – 400 mAh g⁻¹, and ∼ 500 mAh g⁻¹ were obtained for Sn/SnSb, Sn/Bi, and Sn/SnSb/Bi, respectively. The cycling stability of the materials decreased in the order Sn/SnSb>Sn/SnSb/Bi>Sn/Bi, which is in part attributed to the presence / absence of intermetallic phases which undergo phase-separation during lithiation. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16–22, 2001.     

Use of interphase catalysis in the synthesis of 2-acyl-4-oxopyrazino[2,1-α]isoquinolines and 4-acyl-2-piperazinones

2-Acetyl-4-oxopyrazino[2,1-a]isoquinolines and 4-acyl-2-piperazinones have been synthesized, with interphase catalysis, by the intramolecular N-alkylation of the corresponding diamides.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1107–1109, August, 1991.     

Estimates of Petersson's inner squares of cusp forms and arithmetic applications

Uniform estimates are given for Petersson's inner squares of cusp forms in the case of increasing levels and weights. The considered cusp forms are newforms or cusp forms occurring in the theta series associated with positive definite quadratic forms. Arithmetic applications of the obtained estimates are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 168, pp. 158–179, 1988.     

A census of semisymmetric cubic graphs on up to 768 vertices

A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms, its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of the list are identified with these. The special case of those graphs having K_1,3 as a normal quotient is investigated in detail. Supported in part by N.Z. Marsden Fund (grant no. UOA 124) and N.Z. Centres of Research Excellence Fund (grant no. UOA 201) Supported in part by “Ministrstvo za šolstvo, znanost in šport Slovenije”, research program no. 101-506. Supported in part by research projects no. Z1-4186-0101 and no. Z1-3124-0101. The fourth author would like to thank the University of Auckland for hospitality during his visit there in 2003.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.