The first paper in this series initiated a study of Sylow theory for quasigroups and Latin squares, based on orbits of the left multiplication group. The current paper is based on socalled pseudo-orbits, which are formed by the images of a subset under the set of left translations. The two approaches agree for groups, but differ in the general case. Subsets are described as sectional if the pse...

Kosaraju in “Computation of squares in a string” briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w |)-time the minimal kth power, with period of length larger than s, starting at each position in a word w for arbitrar...

This article studies the least-squares finite element method for the linearized, stationary Navier–Stokes equation based on the stress-velocity-pressure formulation in d dimensions (d = 2 or 3). The least-squares functional is simply defined as the sum of the squares of the L2 norm of the residuals. It is shown that the homogeneous least-squares functional is elliptic and continuous in the H(di...

Least squares kinetic upwind mesh-free (LSKUM) method has been the subject of research over twenty years in our research group. LSKUM method requires a cloud (W) of points or nodes and connectivity N(P 0 ) for every 0 P Î W . The connectivity of P0 is a set of neighbours 0 ( ) i P N P Î of P0. The cloud can be a simple cloud, Cartesian cloud or chimera cloud or can be obtained rapidly using adv...

X. Cui Department of Informatics, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies (Sokendai), 2-1-2, Hitotsubashi, Chiyoda-ku, Tokyo, Japan, 101-8430 K. Hayami Principles of Informatics Research Division, National Institute of Informatics, 2-1-2, Hitotsubashi, Chiyodaku, Tokyo, Japan, 101-8430 J. Yin Department of Mathematics, Tongji University, Shanghai, P.R....

where L = (Lij)m×n is a block m×n matrix differential operator of at most first order, B = (Bij)l×n is a block l × n matrix operator, U = (Ui)n×1 is unknown, F = (Fi)m×1 is a given block vector-valued function defined in Ω, G = (Gi)l×1 is a given block vector-valued function defined on ∂Ω. Assume that first-order system (1.1) has a unique solution U . Boundary conditions in a least-squares form...

vii List of Figures x List of Tables xi I Direct Minimization of the Equation Residuals 1