A formula for the determinant of a sum of matrices

We give a formula, involving circular words and symmetric functions of the eigenvalues, for the determinant of a sum of matrices. Theorem of Hamilton-Cayley is deduced from this formula.UQAM and LITPUniversité Paris 7 and LITP.     

Joint production of ϕ mesons andπ ±,π 0,p,\bar p,K s 0 andK ± in hadronic interactions

The joint production of ? mesons andπ ^±,π ⁰,p, \(\bar p\) ,K _s ⁰ andK ^± is investigated using a sample of 600,000 inclusive ? meson events obtained in hadron Be interactions with incidentπ ^±,p, \(\bar p\) andK ^± beams. Evidence is presented for the joint production of ? mesons and strange particles produced with non-strange incident beams. With incidentK ^± beam the number of additional strange particles is suppressed. The results are found to be in agreement with the qualitative predictions of a parton fusion model. The comparison with the Lund model for lowp _T processes is fair.     

Distribution and valence of the cations in the spinel system Fe3O4-Fe2VO4

The Mössbauer spectra of the solid solution Fe[Fe_xV_2–x]O₄ within 1.0×2.0 consist of two sets of sextets corresponding to A- and B-sites. From the superimposed sextets of the B-site pattern result typical values of isomer shift and internal magnetic field strength due to different environments of the B-site iron. It is shown that V ions both enhance the conduction electron density at the neighbouring Fe ions and diminish the strength of the magnetic interactions.     

Enhanced ionic conductivity at the interface between sapphire and solid lithium iodide

We have studied the enhanced ionic conductivity of thin films of LiI evaporated onto a planar sapphire surface carrying interdigital Au-electrodes. The interface conductivity parallel to the surface was measured in situ for increasing film thickness, up to 3,000 Å. The specific conductivity of LiI in the first 300 Å — adjacent to the sapphire — was found to exceed the bulk conductivity of LiI by nearly one order of magnitude. From our observations we conclude that the specific conductivity of LiI decreases exponentially with distance from the sapphire surface reaching the bulk LiI-value only at a distance of 3,000 Å. The conductivity of a 350 Å thick film varies with temperature (25°CT120°C) in accordance with an activation energy of 0.40±0.04 eV. This is in good agreement with the activation energy of bulk LiI in the extrinsic region.     

The magnetic hyperfine field of bromine in iron by NMR/ON

Nuclear magnetic resonance of⁸²Br oriented at low temperature in iron has been observed with a sample prepared by ion implantation atT<0.2 K. The asymmetric resonance signal can be decomposed in a broad background signal and a narrow line of FWHM=1.8 (4) MHz which can be attributed to⁸²Br in undisturbed substitutional sites of Fe. From the center frequency of this narrow line (B _ext=0)=201.86(13) MHz we derive the magnetic hyperfine field asB _hf(BrFe)=81.38(6) T. This value is considerably larger than the result of theoretical calculations.     

Two-photon four-level hologram recording in poly-(alkyl-α-cyanoacrylates)

We have investigated the suitability of poly-(alkyl--cyanoacrylates) (p-(alkyl-CAc)) for two-photon four-level holographic recording. It is shown that these materials follow indeed a two-photon four-level mechanism with the second absorption step in the near infrared. Light induces the polymerization of residual monomer in the matrix. The reaction is associated with positive density changes. The sensitivity ofp-(alkyl-CAc) depends strongly on composition and age of the sample. Maximum sensitivities achieved are comparable to the so far best-known two-photon four-level ir-sensitive systems.