In the present paper some Newton-like iteration methods are developed to enclose solutions of nonlinear operator equations
of the kindF(x)=0. HereF maps a certain subset of a partially ordered vector space into another partially ordered vector space. The obtained results
are proved without any special properties of the orderings by taking use of a new kind of a generalized divided difference
operator, so that they even hold for nonconvex operators. Furthermore a method for constructing including starting points
is presented and two examples are given.
A combination alpha and conversion electron spectrometer was developed to quantify 239Pu/240Pu and 238Pu/241Am isotopic ratios of plated sources. The spectrometer was constructed with a commercially available low noise passivated ion-implanted planar silicon (PIPS) detector that was cooled to 77 K with liquid nitrogen. The combination spectrometer was used to quantify alpha-particles, conversion electrons, gamma-rays and X-rays associated with the decay of various plutonium isotopes and 241Am. Two amplifiers operated in parallel with different gains allowed for simultaneous acquisition of the lower energy region (21-60 keV) for internal conversion electrons, gamma-rays and X-rays, and the higher energy region (5050 keV-5550 keV) for alpha-particles. Energy resolutions of 2.2 keV FWHM (full-width at half maximum) for the 38.7 keV M conversion electrons and 11.2 keV for the 5499.2 keV alpha-particles from 238Pu were measured. The energy resolution combined with a spectral deconvolution method was sufficient to be able to quantify the radioactivity using the alpha-spectra as well as the electron spectra; however, quantification of the radioactivity using the internal conversion electron spectra was more problematic because of the presence of X-rays, gamma-rays, Compton scatter electrons and the number of electron peaks present. Deconvolution of the alpha-spectra yielded 239Pu and 240Pu activities (as % of total Pu activity), which differed from expected values by -3.0% to 5.4%. Deconvolution of an internal conversion electron spectrum of a high 239Pu and low 241Am activity sample yielded 239Pu and 240Pu activities, which differed by -17.1 and -35.5% relative to the alpha-measurements, respectively. Determination of the Pu activity using the electron spectra was more problematic in samples where the 241Am activity dominated. Determination of 238Pu and 241Am activity by the electron spectroscopy data was also obtained and compared with the alpha-spectroscopy results. Theoretical investigation of the removal of 241Am or use of a 400 eV electron spectrometer indicated that the internal conversion electron spectra could be used to determine the 238Pu, 239Pu, 240Pu/241Am (when present) activity with and without spectral deconvolution, respectively.