Nonequivalence transformation of λ‐matrix eigenproblems and model embedding approach to model tuning

In this paper we present some theory for a non‐equivalence transformation of matrix eigenvalues for λ‐matrix polynomials. Application of this transformation to eigenvalue embedding for model tuning on a realistic industry problem is illustrated. The new approach has several advantages such as flexibility, efficiency, and structure‐preservation. A numerical experiment on a pseudosimulation data set from The Boeing Company is reported. Copyright © 2001 John Wiley & Sons, Ltd.     

Function Fields and Elementary Equivalence

Continuing work of Duret, we treat the relation between isomorphismand elementary equivalence of function fields over algebraicallyclosed fields. For function fields of curves, these are ‘usually’the same, but in characteristic zero, for elliptic curves withcomplex multiplication, a weak variant of elementary equivalenceof their function fields corresponds to isomorphism of the endomorphismrings of the curves, not to isomorphism of the curves themselves.1991 Mathematics Subject Classification 14H52, 11U09, 03C52.     

Spin polarized photoemission from La-doped EuO in the vacuum ultraviolet

The spin polarization of photoelectrons emitted form La doped EuO was measured as a function of light energy up to hv = 11 eV, together with the quantum yield. The spectrum of spin polarization can be understood in terms of the energy level diagram of bulk EuO.     

A small-scale multi-purpose reverberation room

A one-fourth scale model of the large (425 m³) National Bureau of Standards reverberation room is described. This facility was constructed to carry out acoustical research at relatively low cost in a frequency range two octaves higher than that used in the larger facility. Initial experimental measurements carried out in this facility concern sound power emitted by small sources. The pure tone qualification procedure specified in American National Standard S1.21-1972 ‘Metods for the Determination of Sound Power Levels of Small Sources in Reverberation Rooms’ was carried out using computer control of the experiment. This standard is of particular interest to the international acoustical community since it is technically equivalent to ISO Documents DIS 3741 and DIS 3742. The effect of increased low frequency absorption upon room qualification was tested in the model room. Future research plans to make use of the small-scale reverberation rooms are described.     

Two connected inverse spectral transforms

We establish a transformation which connects the potentials of the one-dimensional Dirac and Klein-Gordon operators. This transformation links the solutions of the nonlinear evolution equations solvable by means of the two inverse spectral transforms which use the Dirac and Klein-Gordon direct and inverse spectral problems.     

Synthesis of homoallylic amines by hydrozirconation-imine addition of allenes

Hydrozirconation of allenes followed by in situ transmetalation to dialkylzinc leads to the formation of an allylic zinc species that, upon addition of aldimines to the reaction mixture, provides homoallylic amines in 64-85% yield. [reaction: see text]     

Evaluation of energy efficiency fitting functions for HPGe detectors

Numerous and diverse mathematical methods have been used to model the full-energy photopeak (FEP) efficiency-to-energy relationship. All of the methods attempt to approximate this relationship using numerical analysis methods. Sophistication of the mathematics does not guarantee a meaningful and accurate determination of the physical relationships being modeled. This discrepancy stems from the fact that the data being modeled may suffer from spectral and nuclear effects which alter the counts in the full energy photopeak resulting from absorption and attenuation in the active volume of the diode, in the intervening materials between the detector diode and source, within the source itself, and in the shielding around the detector and source. Data must be free of these effects either as a result of acquiring the spectral data in geometries which minimize or eliminate these effects, or by pre-treatment of the net area counts to correct for these effects. If these corrections are not possible, then the choice of mathematical fitting method should be constrained to provide results which are consistent with physical-theoretical considerations of the energy-efficiency relationship being modeled. If possible, the method chosen should also provide a meaningful estimate of the uncertainty associated with the approximation of this function.     

X-ray photoelectron spectra of inorganic molecules XXlX. The characterization of mixed phosphido-phosphine and phosphido-phosphite complexes of transition metal carbonyl clusters using X-ray photoelectron spectroscopy

X-ray photoelectron spectroscopy has been found to provide a useful means of studying the electronic structure of the phosphorus atoms in PPh, PPh₂, PPh₃, PHPh and P(OMe)₃ ligands in a number of polynuclear cobalt and iron complexes.