Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type III. The Heun Case

The Heun equation can be rewritten as an eigenvalue equation for an ordinary differential operator of the form $-d^2/dx^2+V(g;x)$, where the potential is an elliptic function depending on a coupling vector $g\in{\mathbb R}^4$. Alternatively, this operator arises from the $BC_1$ specialization of the $BC_N$ elliptic nonrelativistic Calogero-Moser system (a.k.a. the Inozemtsev system). Under suitable restrictions on the elliptic periods and on $g$, we associate to this operator a self-adjoint operator $H(g)$ on the Hilbert space ${\mathcal H}=L^2([0,\omega_1],dx)$, where $2\omega_1$ is the real period of $V(g;x)$. For this association and a further analysis of $H(g)$, a certain Hilbert-Schmidt operator ${\mathcal I}(g)$ on ${\mathcal H}$ plays a critical role. In particular, using the intimate relation of $H(g)$ and ${\mathcal I}(g)$, we obtain a remarkable spectral invariance: In terms of a coupling vector $c\in{\mathbb R}^4$ that depends linearly on $g$, the spectrum of $H(g(c))$ is invariant under arbitrary permutations $\sigma(c)$, $\sigma\in S_4$

The Vertex-Face Correspondence and the Elliptic 6j-symbols

A new formula connecting the elliptic $6j$-symbols and the fusion of the vertex-face intertwining vectors is given. This is based on the identification of the $k$ fusion intertwining vectors with the change of base matrix elements from Sklyanin's standard base to Rosengren's natural base in the space of even theta functions of order $2k$. The new formula allows us to derive various properties of the elliptic $6j$-symbols, such as the addition formula, the biorthogonality property, the fusion formula and the Yang-Baxter relation. We also discuss a connection with the Sklyanin algebra based on the factorised formula for the $L$-operator.Comment: 23 page

A note on the Gauss decomposition of the elliptic Cauchy matrix

Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.Comment: 5 page

Stability of E' centers induced by 4.7eV laser radiation in SiO2

The kinetics of E' centers (silicon dangling bonds) induced by 4.7eV pulsed laser irradiation in dry fused silica was investigated by in situ optical absorption spectroscopy. The stability of the defects, conditioned by reaction with mobile hydrogen of radiolytic origin, is discussed and compared to results of similar experiments performed on wet fused silica. A portion of E' and hydrogen are most likely generated by laser-induced breaking of Si-H precursors, while an additional fraction of the paramagnetic centers arise from another formation mechanism. Both typologies of E' participate to the reaction with H_2 leading to the post-irradiation decay of the defects. This annealing process is slowed down on decreasing temperature and is frozen at T=200K, consistently with the diffusion properties of H_2 in silica.Comment: 12 pages, 3 figures, in press on J. Non cryst. solids (2007

Nd:YAG laser induced E' centers probed by in situ absorption measurements

We investigated various types of commercial silica irradiated with a pulsed Nd:YAG laser radiation (4.66 eV), with exposure time ranging up to 10000 s. Transient E' centers were probed in situ by measuring the amplitude of the optical absorption band at 5.8 eV (due to E' centers) both during and after irradiation. The laser-induced absorption is observed only in natural samples, whereas the synthetic materials exhibit high toughness to radiation effect. The reported results evidence that the kinetics of E' centers is influenced by their reaction with diffusing molecular hydrogen H2 made available by dimerization of radiolytic H0.Comment: Submitted to Journal of Non Crystalline Solid

Lattice sites of ion-implanted Li in diamond

Published in: Appl. Phys. Lett. 66 (1995) 2733-2735 citations recorded in [Science Citation Index] Abstract: Radioactive Li ions were implanted into natural IIa diamonds at temperatures between 100 K and 900 K. Emission channelling patterns of a-particles emitted in the nuclear decay of 8Li (t1/2 = 838 ms) were measured and, from a comparison with calculated emission channelling and blocking effects from Monte Carlo simulations, the lattice sites taken up by the Li ions were quantitatively determined. A fraction of 40(5)% of the implanted Li ions were found to be located on tetrahedral interstitial lattice sites, and 17(5)% on substitutional sites. The fractions of implanted Li on the two lattice sites showed no change with temperature, indicating that Li diffusion does not take place within the time window of our measurements.

CAT: A Critical-Area-Targeted Test Set Modification Scheme for Reducing Launch Switching Activity in At-Speed Scan Testing

Reducing excessive launch switching activity (LSA) is now mandatory in at-speed scan testing for avoiding test-induced yield loss, and test set modification is preferable for this purpose. However, previous low-LSA test set modification methods may be ineffective since they are not targeted at reducing launch switching activity in the areas around long sensitized paths, which are spatially and temporally critical for test-induced yield loss. This paper proposes a novel CAT (Critical-Area-Targeted) low-LSA test modification scheme, which uses long sensitized paths to guide launch-safety checking, test relaxation, and X-filling. As a result, launch switching activity is reduced in a pinpoint manner, which is more effective for avoiding test-induced yield loss. Experimental results on industrial circuits demonstrate the advantage of the CAT scheme for reducing launch switching activity in at-speed scan testing.2009 Asian Test Symposium, 23-26 November 2009, Taichung, Taiwa

UV-B radiation amplification factor determined based on the simultaneous observation of total ozone and global spectral irradiance

The Japan Meteorological Agency started the spectral observation of solar ultraviolet (UV) irradiance on 1 January 1990 at Tateno, Aerological Observatory in Tsukuba (35 deg N, 140 deg E). The observation has been carried out using the Brewer spectrophotometer for the wavelengths from 290 to 325 nm with a 0.5 nm interval every hour from 30 minutes before sunrise to 30 minutes after sunset throughout a year. Because of remarkable similarity within observed spectra, an observed spectrum can be expressed by a simple combination of a reference spectrum and two parameters expressing the deformation of the observed spectrum from the reference. By use of the relation between one of the deformation parameters and the total ozone simultaneously observed with the Dobson spectrophotometer, the possible increase of UV irradiance due to ozone depletion is estimated. For damaging UV, the irradiance possibly increases about 19 percent with the ozone depletion of 10 percent at noon throughout the year in the northern midlatitudes. DUV at noon on the summer solstice possibly increases about 5.6 percent with the ozone depletion of 10 m atm-cm for all latitudes in the Northern Hemisphere