Regular polynomials with quaternionic coefficients admit only isolated zeroes and spherical zeroes. In this paper we prove
a factorization theorem for such polynomials. Specifically, we show that every regular polynomial can be written as a product
of degree one binomials and special second degree polynomials with real coefficients. The degree one binomials are determined
(but not uniquely) by the knowledge of the isolated zeroes of the original polynomial, while the second degree factors are
uniquely determined by the spherical zeroes. We also show that the number of zeroes of a polynomial, counted with their multiplicity
as defined in this paper, equals the degree of the polynomial. While some of these results are known in the general setting
of an arbitrary division ring, our proofs are based on the theory of regular functions of a quaternionic variable, and as
such they are elementary in nature and offer explicit constructions in the quaternionic setting.
Partially supported by G.N.S.A.G.A.of the I.N.D.A.M. and by M.I.U.R..
Lecture held by G. Gentili in the Seminario Matematico e Fisico on February 12, 2007.
Received: August 2008 相似文献
The paper represents new computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives. The main contents of the paper are: (i) application of a predesigned parabolic function of transmission errors for reduction of noise, (ii) computerized simulation of noise caused by transmission errors, (iii) modification of the basic algorithm of tooth contact analysis, and (iv) application of approaches developed for enhanced design and simulation of meshing of the following gear drives: (a) spiral bevel gear drives, (b) face-gear drives (including an approach for grinding), and (c) modified helical gear drives. The developed theory is illustrated with numerical examples. 相似文献
Anode-supported solid oxide fuel cells (SOFCs) based on thin BaZr0.8Y0.2O3 ? δ (BZY) electrolyte films were fabricated by pulsed laser deposition (PLD) on sintered NiO–BZY composite anodes. After insitu reduction of NiO to Ni, the anode substrates became porous, while retaining good adhesion with the electrolyte. A slurry-coated composite cathode made of La0.6Sr0.4Co0.2Fe0.8O3?δ (LSCF) and BaCe0.9Yb0.1O3?δ (BCYb), specifically developed for proton conducting electrolytes, was used to assemble fuel cell prototypes. Depositing by PLD 100 nm thick LSCF porous films onto the BZY thin films was essential to improve the cathode/electrolyte adhesion. A power density output of 110 mW/cm2 at 600 °C, the largest reported value for an anode-supported fuel cell based on BZY at this temperature, was achieved. Electrochemical impedance spectroscopy (EIS) measurements were used to investigate the different contributions to the total polarization losses. 相似文献
The phonon modes of crystalline benzoic acid have been investigated using terahertz time-domain spectroscopy, rigid molecule atom-atom model potential and plane-wave density functional theory lattice dynamics calculations. The simulation results show good agreement with the measured terahertz spectra and an assignment of the terahertz absorption features of benzoic acid is made with the help of both computational methods. Focussing on the strongest interactions in the crystal, we describe each vibration in terms of distortions of the benzoic acid hydrogen bonded dimers that are present in the crystal structure. The terahertz spectrum is also shown to be highly sensitive to the location of the carboxylic acid hydrogen atoms in the cyclic hydrogen-bonded dimers and we have systematically explored the influence of the observed disorder in the hydrogen atom positions on the lattice dynamics. 相似文献
The quinoidal versus biradicaloid character of the ground state of a series of thiophene‐based heterophenoquinones is investigated with quantum‐chemical calculations. The role of the ground‐state electronic character on molecular structure and vibrational properties is emphasized. The vibrational activities are experimentally determined and their analysis is performed by taking advantage of the definition of a collective vibrational coordinate (the