Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

A Fibred Tableau Calculus for Modal Logics of Agents

In previous works we showed how to combine propositional multimodal logics using Gabbay's \emph{fibring} methodology. In this paper we extend the above mentioned works by providing a tableau-based proof technique for the combined/fibred logics. To achieve this end we first make a comparison between two types of tableau proof systems, (\emph{graph} $\&$ \emph{path}), with the help of a scenario (The Friend's Puzzle). Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system \KEM. We conclude with a discussion on \KEM's features.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Fixed bed reactors with catalyst poisoning - first order kinetics.

The long performance of an isothermal fixed bed reactor undergoing catalyst poisoning is theoretically analyzed using the dispersion model. First order reaction with dth order deactivation is assumed and the model equations are solved by matched asymptotic expansions for large Peclet number. Simple closed-form solutions, uniformly valid in time, are obtained.

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2\1) which depends on a continuous free parameter. This symmetry algebra contains the eta pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

New integrable model of correlated electrons with off-diagonal long-range order from so(5) symmetry

We present a new integrable model for correlated electrons which is based on so(5) symmetry. By using an eta-pairing realization we construct eigenstates of the Hamiltonian with off-diagonal long-range order. It is also shown that these states lie in the ground state sector. We exactly solve the model on a one-dimensional lattice by the Bethe ansatz.

Minimum-order stable recursive filter design via the genetic algorithm approach

In this paper, the minimum-order stable recursive filter design problem is proposed and investigated. This problem is playing an important role in pipeline implementation sin signal processing. Here, the existence of a high-order stable recursive filter is proved theoretically, in which the upper bound for the highest order of stable filters is given. Then the minimum-order stable linear predictor is obtained via solving an optimization problem. In this paper, the popular genetic algorithm approach is adopted since it is a heuristic probabilistic optimization technique and has been widely used in engineering designs. Finally, an illustrative example is sued to show the effectiveness of the proposed algorithm.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

Evaluating the efficiency of fractional integration parameter estimators

This article deals with the efficiency of fractional integration parameter estimators. This study was based on Monte Carlo experiments involving simulated stochastic processes with integration orders in the range]-1,1[. The evaluated estimation methods were classified into two groups: heuristics and semiparametric/maximum likelihood (ML). The study revealed that the comparative efficiency of the estimators, measured by the lesser mean squared error, depends on the stationary/non-stationary and persistency/anti-persistency conditions of the series. The ML estimator was shown to be superior for stationary persistent processes; the wavelet spectrum-based estimators were better for non-stationary mean reversible and invertible anti-persistent processes; the weighted periodogram-based estimator was shown to be superior for non-invertible anti-persistent processes.

The early sperm gets the good egg: mating order effects in free spawners

Mating order can have important consequences for the fertilization success of males whose ejaculates compete to fertilize a clutch of eggs. Despite an excellent body of literature on mating-order effects in many animals, they have rarely been considered in marine free-spawning invertebrates, where both sexes release gametes into the water column. In this study, we show that in such organisms, mating order can have profound repercussions for male reproductive success. Using in vitro fertilization for two species of sea urchin we found that the 'fertilization history' of a clutch of eggs strongly influenced the size distribution of unfertilized eggs, and consequently the likelihood that they will be fertilized. Males that had first access to a batch of eggs enjoyed elevated fertilization success because they had privileged access to the largest and therefore most readily fertilizable eggs within a clutch. By contrast, when a male's sperm were exposed to a batch of unfertilized eggs left over from a previous mating event, fertilization rates were reduced, owing to smaller eggs remaining in egg clutches previously exposed to sperm. Because of this size-dependent fertilization, the fertilization history of eggs also strongly influenced the size distribution of offspring, with first-spawning males producing larger, and therefore fitter, offspring. These findings suggest that when there is variation in egg size, mating order will influence not only the quantity but also the quality of offspring sired by competing males.