On geometry of fronts in wave propagations

We give a geometric description of (wave) fronts in wave propagation processes. The concrete form of the defining function of a wave front issuing from the initial algebraic variety is obtained with the aid of the Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagation on the plane, we get restrictions on the types of possible cusps that can appear on the wave front

Hyperbolic Cauchy problem and Leray's residue formula

We give an algebraic description of wave fronts that appear in strictly hyperbolic Cauchy problem. Concrete form of definig function of wave front issued from initial algebraic variety is obtained by the aid of the Gauss-Manin systems satisfied by Gel'fand -Leray integrals.Comment: 14 pages, Talk at the International Banach Mathematical Centre, Warsaw, March 199

Invariant of the hypergeometric group associated to the quantum cohomology of the projective space

We present a simple method to calculate the Stokes matrix for the quantum cohomology of the projective spaces ${CP}^{k-1}$ in terms of certain hypergeometric group. We present also an algebraic variety whose fibre integrals are solutions to the given hypergeometric equation.Comment: 12 pages, 13 reference

On monodromy representation of period integrals associated to an algebraic curve with bi-degree (2,2)

We study a problem related to Kontsevich's homological mirror symmetry conjecture for the case of a generic curve $\cal Y$ with bi-degree (2,2) in a product of projective lines ${\Bbb P}^{1} \times {\Bbb P}^{1}$. We calculate two differenent monodromy representations of period integrals for the affine variety ${\cal X}^{(2,2)}$ obtained by the dual polyhedron mirror variety construction from $\cal Y$. The first method that gives a full representation of the fundamental group of the complement to singular loci relies on the generalised Picard-Lefschetz theorem. The second method uses the analytic continuation of the Mellin-Barnes integrals that gives us a proper subgroup of the monodromy group. It turns out both representations admit a Hermitian quadratic invariant form that is given by a Gram matrix of a split generator of the derived category of coherent sheaves on on $\cal Y$ with respect to the Euler form

ISO observations of the planetary nebula Lindsay 305 in the Small Magellanic Cloud

We present ISO (Infrared Space Observatory) observations of the planetary nebula Lindsay 305 (L 305) in the Small Magellanic Cloud. L 305 is very prominent in the ISOCAM frames at 6.75 and 11.5 $\mu$m, although it is under the detection limit at 4.5 $\mu$m. The obtained spectral energy distribution shows a strong mid-IR excess, which, depending on the amount of energy radiated at wavelengths longer than 11.5 $\mu$m, may be as large as $\sim 1500 L_{\odot}$. However, since an accurate estimate of the total nebular luminosity is not available up to date, the evolutionary status of L 305 can not yet be constrained precisely.Comment: 4 pages, 2 figures, to appear in the Publications of the Astronomical Society of Japa