On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.     

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.     

Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

A highly sensitive and rapid assay for protein determination in human urine and penicillin using a Rayleigh light-scattering technique with benzeneazo-8-acetylamino-1-naphthol-3,6-disulfonic acid sodium salt.

A simple and sensitive method was conducted for the determination of trace amounts of proteins with benzeneazo-8-acetylamino-1-naphthol-3,6-disulfonic acid sodium salt (azophloxine, AP) using a Rayleigh light-scattering (RLS) technique. At pH 2.60 and in the presence of an emulsifier OP microemulsion, the RLS of AP can be greatly enhanced by proteins, owing to the interaction between AP and protein. The enhanced intensity is proportional to the concentration of proteins. Four proteins, including bovine serum albumin (BSA), human serum albumin (HSA), lysozyme (Lys) and gamma globulin (gamma-G) have been tested. For example, the linear range of BSA was 0 - 0.06 microg mL(-1) with detection limits of 2.38 ng mL(-1). The method was applied to the analysis of protein in human urine and penicillin samples with satisfactory results. The relative standard deviation was in all instances less than 4.0%, and the recovery was in the range of 97.5 - 104%.     

The newton filtration and d-determination of bifurcation problems related to C 0 contact equivalence

In this paper, from the Newton filtration’s point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C ⁰ contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

Bull-free Berge graphs are perfect

Abull is the (self-complementary) graph with verticesa, b, c, d, e and edgesab, ac, bc, bd, ce; a graphG is calledBerge if neitherG not its complement contains a chordless cycle whose length is odd and at least five. We prove that bull-free Berge graphs are perfect; a part of our argument relies on a new property of minimal imperfect graphs.This work was done while both authors were at the School of Computer Science, McGill University; support by NSERC is gratefully acknowledged.     

Modelling of composting of food waste in a column reactor

The composting of organic solid waste, the mixture of fruit and vegetable leftovers enriched with night soil, was investigated in a closed thermally insulated reactor. It was found that 80.9 % of the original substrate biodegraded after 14 days. A mathematical model of the column reactor was proposed where the biodegradation rate of the organic solid waste was described using simple n-thorder kinetics. A good prediction of process performance was obtained using the proposed kinetics and experimentally obtained reaction heat. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Composition formulae for some integro-differential operators and their applications

Institute of Mathematics and Informatics. Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys. Vol. 36, No. 1, pp. 27–38, January–March,. 1996.     

Dimensional reduction for Helmholtz's equation on a bounded domain

Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results. Received April 2, 1996 / Revised version received July 30, 1990     

Entropy of Bogoliubov automorphisms of the canonical anticommutation relations

We compute the entropyh _A ( _U ) in the sense of Connes, Narnhofer and Thirring of Bogoliubov automorphisms _U of the CAR-algebra with respect to invariant quasifree states _A with 0A1 having pure point spectrum.Supported in part by a grant from the National Science Foundation