A Primitive Non-symmetric 3-Class Association Scheme on 36 Elements with p11 = 0 Exists and is Unique

In this paper we construct a primitive, non-symmetric 3-class association scheme with parameters v = 36, v₁ = 7, p¹₁₁ = 0 and p²₁₁ = 4 and show that such a scheme is determined by its parameters.     

Optical Tunnelling from One-Dimensional Square-Well Potentials

The authors study a one-dimensional model for optical tunnellingwith a refractive index in the shape of a square well. The relevanceof the model and its limiting cases are discussed. The mainresult is the leading behaviour of the exponentially small imaginarypart of the eigenvalue which determines the radiation loss.The leading behaviour of the imaginary part is calculated usingBerry's formula which controls the asymptotic expansion of theAiry function Bi(z) to better-than-exponential accuracy.     

Expression of theSU(2) rotation matrices D( j ) in terms of normalized irreducible tensorial matrices

TheSU(2) rotation matricesD ^(j), specified in terms of axis and angle of rotation, are expressed as linear combination of normalized irreducible tensorial matricces (NITM) of rankl = 0 to 2j rotated to the polar angles of the axis. The rotated NITM are constructed from spherical harmonics of the same rank. Since this formulation requires no matrix products, it may be computationally more efficient than Euler angle formulas, particularly for largej. Rotated NITM and formulas for theD ^(j) withj = 1/2 andj = 1 are written out explicitly. A formula for the structure constants of the products of conformable NITM is also given in terms of 3-j and 6-j symbols.     

Silver nitrate-acetonitrile and iodine-benzene complexes as studied by NMR in thermotropic liquid crystals

Silver nitrate-acetonitrile and π iodine-benzene complexes in thermotropic liquid crystals have been studied by ¹H, ²H, and ¹³C NMR spectroscopy and by optical microscopy. Evidence for at least two silver complexes in each liquid crystal is presented.     

Numerical method for a model of inhomogeneous muscle fibers

The numerical solution of a nonlinear and nonlocal system of integro-differential equations that models the contraction of a single heterogeneous muscle fiber is studied. The method proposed is a form of the finite difference method of characteristics. Optimal error bounds are established for the resulting approximation. © 1993 John Wiley & Sons, Inc.     

On finite element approximation and stabilization methods for compressible viscous flows

This work is devoted to the numerical solution of the Navier–Stokes equations for compressible viscous fluids. Finite element approximations and stabilization techniques are addressed. We present methods to implement discontinuous approximations for the pressure and the density. An upwinding methodology is being investigated which combines the ideas behind the stream line Petrov–Galerkin method and the flux limiter methods aiming to introduce numerical diffusion only where it is necessary.     

Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields

A representation in the form of a functional integral is obtained for the partition function of the inhomogeneous 2D Ising model on a triangular lattice where the coupling parameters are arbitrary functions of coordinates. The method for transforming the partition function into an integral uses an auxiliary six-component Grassmann field in which the Grassmann fields corresponding to one of the components commute with the others. Thus, one pair of components realizes a representation of the q-deformed group SL_q(2, R) with q=–1 and the other two pairs correspond to the usual Grassmann spinors (q=1). An explicit expression in terms of the modified Pfaffian is found for the Gaussian integral over these fields and its relation to the ordinary Grassmann functional integral is established.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 441–463, December, 1996.     

The star chromatic number of a graph

We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. © 1993 John Wiley & Sons, Inc.