This paper proposes a novel recursive partitioning method based on constrained learning neural networks to find an arbitrary number (less than the order of the polynomial) of (real or complex) roots ...of arbitrary polynomials. Moreover, this paper also gives a BP network constrained learning algorithm (CLA) used in root-finders based on the constrained relations between the roots and the coefficients of polynomials. At the same time, an adaptive selection method for the parameter δP with the CLA is also given. The experimental results demonstrate that this method can more rapidly and effectively obtain the roots of arbitrary high order polynomials with higher precision than traditional root-finding approaches.
Under the hypotheses that the second-order and third-order derivative of function
f are bounded, an estimate of the radius of the convergence ball of Müller’s method is obtained, an error analysis is ...given which matches the convergence order of the method.
BackgroundAdverse reactions, such as anaphylactoid shock, have been reported to occur frequently with the use of polysulfone (PSf) membrane dialyzers. Polyvinylpyrrolidone (PVP) elution from the ...membrane may be a key factor in these reactions. In this paper, we discuss the problems in the evaluation of PVP elution from PSf membrane dialyzers sterilized by gamma-ray irradiation.Methods and ResultsPVP concentrations in the filling solutions in some wet-type PSf membrane dialyzers are measured by Müller’s method as a standard measurement method. The PVP concentrations in autoclave (AC)-sterilized dialyzers were one order of magnitude higher than those in the solutions in dialyzers sterilized by gamma-ray irradiation. Because it is difficult to determine the PVP concentrations in the filling solutions sterilized by gamma-ray irradiation by Müller’s method, single-fractionated-component PVP solutions with fractionated components of PVP (K90 or K30) were prepared and the PVP concentrations of the solutions before and after gamma-ray irradiation were determined. The results indicated that the PVP concentrations in the solutions could be determined by Müller’s method before irradiation, whereas PVP was undetectable in the solution after irradiation. For single-fractionated-component PVP solutions with K90 and K30, the changes in the structure of PVP before and after gamma-ray irradiation were analyzed by high-performance liquid chromatography (HPLC). The single-fractionated-component PVP solutions with K90 and K30 had a broad peak at retention times of 15 and 19 min, respectively, prior to the gamma-ray irradiation, whereas both solutions showed a similar sharp peak at a retention time of 23 min after the irradiation. Based on these results, it is surmised that PVP is degraded by irradiation to yield PVP degradation products of low molecular weight.Furthermore, nuclear magnetic resonance (NMR) spectroscopy for PVP K90 solution was performed to confirm the signals from the vinylpyrrolidone (VP) skeletal structures. Signals from the VP skeletal structures were detected before the gamma-ray irradiation but disappeared after the irradiation. Thus, it appears that the degradation products of PVP without VP skeletal structures cannot be detected by Müller’s method.ConclusionsThe measurement of PVP concentrations by Müller’s method is inappropriate for the evaluation of PVP elution from PSf membrane dialyzers sterilized by gamma-ray irradiation.
This paper presents a new algorithm called equal embedded algorithm is used to solve large scale economic load dispatch problem with prohibited zones and losses. The algorithm involves the selection ...of lambda values, then the output power expressions of generating unit are obtained in terms of the lambda by interpolation and finally the lambda is evaluated from the power balance equation by Muller method. The proposed algorithm was tested on a power system having 3, 6 and 20 generating units and the results were compared in terms of their solution quality, convergence characteristics and computation efficiency with the genetic algorithm, the two phase neural networks, the lambda iterative method and the particle swarm optimization method. Also the proposed algorithm was tested for large-scale system with 20 and 40 generating units. The proposed method gives minimum fuel cost with less computational time.
The nonlinear Schrodinger/Gross-Pitaevskii equation with a linear periodic potential and a nonlinearity coefficient ... with a discontinuity supports stationary localized solitary waves with ...frequencies inside spectral gaps, so-called surface gap solitons (SGSs). The authors compute families of one-dimensional SGSs using the arclength continuation method for a range of values of the jump in ... Using asymptotics, they show that when the frequency parameter converges to the bifurcation gap edge, the size of the allowed jump in ... converges to 0 for SGSs centered at any ... R. A numerically stable formulation is possible in the exterior algebra formulation and with the use of Grassmanian preserving ODE integrators. Eigenvalues with a positive real part larger than a small constant are then detected via the use of the complex argument principle and a contour parallel to the imaginary axis. The location of real eigenvalues is found via a straightforward evaluation of the Evans function along the real axis, and several complex eigenvalues are located using Muller's method. (ProQuest: ... denotes formulae/symbols omitted.)
The problem of solving the dispersion equation for waves guideway electrodynamic structures on the complex plane of one of the wave numbers is considered. Combined method based on the combination of ...positive properties Muller method and the method of phase variation, based on the principle of the argument is proposed. The procedure of the application of the method is described.
For finding a root of a function
f
, Müler’s method is a root-finding algorithm using three values of
f
in every step. The natural values available are values of
f
and values of its first number of ...derivatives, called standard information. Based on standard information, we construct an iteration method with maximal order of convergence. It is a natural generalization of Müller’s iteration method.
This paper proposes new modified constrained learning neural root finders (NRFs) of polynomial constructed by backpropagation network (BPN). The technique is based on the relationships between the ...roots and the coefficients of polynomial as well as between the root moments and the coefficients of the polynomial. We investigated different resulting constrained learning algorithms (CLAs) based on the variants of the error cost functions (ECFs) in the constrained BPN and derived a new modified CLA (MCLA), and found that the computational complexities of the CLA and the MCLA based on the root-moment method (RMM) are the order of polynomial, and that the MCLA is simpler than the CLA. Further, we also discussed the effects of the different parameters with the CLA and the MCLA on the NRFs. In particular, considering the coefficients of the polynomials involved in practice to possibly be perturbed by noisy sources, thus, we also evaluated and discussed the effects of noises on the two NRFs. Finally, to demonstrate the advantage of our neural approaches over the nonneural ones, a series of simulating experiments are conducted.
In recent papers a concept called vertical density representation was derived from the well-known Box-Muller method for generating normally distributed deviates. In this paper we show that this ...method may be regarded as one particular solution to a density composition equation. We then derive a second such solution. We also illustrate an extension of the method to certain normal-like densities.
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