In the eld of computational electrodynamics the discretization of Maxwell's equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extend...

The discrete Shannon entropy H was formulated only to measure indeterminacy effected through a set of probabilities, but the indeterminacy in a real-valued discrete variable depends on both the allowed outcomes x and the corresponding probabilities p. A fundamental measure that is sensitive to both x and p is derived here from the total differential entropy of a continuous real variable and its...

Let X be a locally compact Hausdorff space with n proper continuous self maps τ i : X → X for 1 ≤ i ≤ n. To this we associate various topological conjugacy algebras; and two emerge as the natural candidates for the universal algebra of the system, the tensor algebra A(X, τ) and the semicrossed product C 0 (X) × τ F + n. The C*-envelope of A(X, τ) is the Cuntz-Pimsner algebra C * (X, τ) as defin...

Let X be a locally compact Hausdorff space with n proper continuous self maps τ i : X → X for 1 ≤ i ≤ n. To this we associate various topological conjugacy algebras; and two emerge as the natural candidates for the universal algebra of the system, the tensor algebra A(X, τ) and the semicrossed product C 0 (X) × τ F + n. The C*-envelope of A(X, τ) is the Cuntz-Pimsner algebra C * (X, τ) as defin...

The invariance for the equation of fast diffusion in the 2D coordinate space has been proved, and its reduction to the 1D (with respect to the spatial variable) analog is demonstrated. On the basis of these results, new exact multi-dimensional solutions, which are dependent on arbitrary harmonic functions, are constructed. As a result, new exact solutions of the well-known Liouville equation – ...

to obtain detailed information of sowing density and defoliation intensity under more controlled conditions on herbage production and seed yield, paraggio medic was grown on raised-beds located outdoors at the waite agricultural research institute. a split split randomised block design was used. treatments comprised three sowing rates (densities): low (3 kg/ha), medium (15 kg/ha) and high (...

This paper proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems Bx = b with positive definite B for x. The goal is to replace the point estimates returned by existing methods with a Gaussian posterior belief over the elements of the inverse of B, which can be used to estimate errors. Recent probabilistic interpretations of the secant family of q...

In this paper‎, ‎two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS})‎ ‎conjugate gradient method are presented to solve unconstrained optimization problems‎. ‎A remarkable property of the proposed methods is that the search direction always satisfies‎ ‎the sufficient descent condition independent of line search method‎, ‎based on eigenvalue analysis‎. ‎The globa...