We present a method for solving polynomial equations over idempotent ω-continuous semirings. The idea is to iterate over the semiring of functions rather than the semiring of interest, and only evaluate when needed. The key operation is substitution. In the initial step, we compute a linear completion of the system of equations that exhaustively inserts the equations into one another. With func...

Abstract Non-equilibrium Pd–Ru alloys were synthesized by leaching quasicrystal (icosahedral quasicrystal, IQC: Al 71 Pd 19 Ru 10 ) and approximants (3/2 approximant, P 40 : 72 16.4 11.6 , 1/1 C 1 70.4 14.7 14.9 of Al–Pd–Ru with 20 wt% NaOH aqueous solution. The Pd-Ru investigated using XRD HAADF-STEM, which showed that mixed formed a non-equilibrium state (atomic ratio: 0.9 < Pd/Ru 2). allo...

In this paper, univariate Pade approximation is applied to fractional power sries solutions of integro-differential equations with non-local boundary conditions. As it seen from comparisons, gives reliable and numerical results.

QSP-10 APPLICATION OF AN IN SILICO PHYSIOLOGICALLY BASED PHARMACOKINETIC MODEL TO SIMULATE ORAL DRUG BIOAVAILABILITY OF ATORVASTATIN ACID AND CYCLOSPORINE POST BARIATRIC SURGERY. A. S. Darwich,1 D. Pade,2 K. Rowland-Yeo,2 M. Jamei,2 A. Åsberg,3 H. Christensen,3 D. M. Ashcroft,1 A. Rostami-Hodjegan1; 1Centre for Applied Pharmacokinetic Research, University of Manchester, Manchester, United Kingd...

The error autocorrection effect means that in a calculation all the intermediate errors compensate each other, so the final result is much more accurate than the intermediate results. In this case standard interval estimates (in the framework of interval analysis including the so-called a posteriori interval analysis of Yu. Matijasevich) are too pessimistic. We shall discuss a very strong form ...

Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are incompatible with periodicity. Two dense phases of regular tetrahedra have been reported recently. The densest known tetrahedron packing is achieved in a crystal ...

Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of error autocorrection is considered. This effect occurs in efficient methods of rational approximation (e.g., Padé approximations, linear and nonlinear Padé–...

This paper is devoted to introduce analytic solutions by Differential Transform Method-Pade approximants with theoretical study for the problem of the hydromagnetic flow due to a permeable stretching surface embedded in a porous medium in the presence of transverse magnetic field. The governing momentum equation which is a nonlinear partial differential equation is reduced into a nonlinear ordi...

Given a finite point set P ⊂ R, we call a multiset A a one-sided weak ε-approximant for P (with respect to convex sets), if |P ∩ C|/|P | − |A ∩C|/|A| ≤ ε for every convex set C. We show that, in contrast with the usual (two-sided) weak ε-approximants, for every set P ⊂ R there exists a one-sided weak ε-approximant of size bounded by a function of ε and d.

A new beam propagation method (BPM) is developed based on a direct approximation to the propagator by its [(p-1)/p] Padé approximant. The approximant is simple to construct and has the desired damping effect for the evanescent modes. The method is applied to a tapered waveguide for TM-polarized waves, based on the energy-conserving improvement of the one-way Helmholtz equation. Numerical result...