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 $\sigma(c)$, $\sigma\in S_4$

Application of different organic and mineral fertilizers on the growth, yield and nutrient accumulation of rice in a Japanese ordinary paddy field

A rice cultivation study was conducted at Kyushu University farm. Cow manure (CM), poultry manure (PM), rice straw + urea mix-application (SU), urea (UF) and M-coat, a slow released compound fertilizer (M-coat) were used as the N sources by comparing with no application (Control). Treatments were made with two levels application of each N source at 40 (level I) and 80 kg N ha-1(level II) excluding M-coat. In all urea treatments, three split applications were made. A study of soil incubation was conducted for 2 weeks to investigate the mineralized N of applied mineral and organic fertilizer. Plant growth characters, dry matter, yield and plant nutrient accumulations were higher in mineral fertilization than organic. Mineral fertilization was observed in correlation with the larger crop removal. PM-II as an organic matter provided comparatively higher nutrient accumulations which in turn enhanced the growth and yield of rice. CM and SU gave the lower plant growth, yield and nutrient accumulation. Mineralized N was higher in sole mineral N applications. Organic matter with high C/N ratio provided very low mineralized N and its net N mineralization percentage. Negative values of net N mineralization percentage were observed in SU due to N immobilization. Keywords: Cow Manure, Mineralized N, Paddy Soil, Poultry Manure, Rice (Oryza sativa L.), Rice Stra

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

On the Canonical Formalism for a Higher-Curvature Gravity

Following the method of Buchbinder and Lyahovich, we carry out a canonical formalism for a higher-curvature gravity in which the Lagrangian density ${\cal L}$ is given in terms of a function of the salar curvature $R$ as ${\cal L}=\sqrt{-\det g_{\mu\nu}}f(R)$. The local Hamiltonian is obtained by a canonical transformation which interchanges a pair of the generalized coordinate and its canonical momentum coming from the higher derivative of the metric.Comment: 11 pages, no figures, Latex fil

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