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[en] In this Letter we construct examples of discrete-continuous bispectral operators obtained by rational Darboux transformations applied to a regular pseudo-difference operator with constant coefficients. Moreover, we give an explicit procedure to write down the differential operators involved in the bispectral situation corresponding to the pseudo-difference operator obtained by the Darboux process.
[en] This letter presents 25 supernova candidates discovered from SDSS-DR7 by using our dedicated method, called Sample Decrease. Ten of them have been confirmed by other research groups, while the remaining 15, including 14 Type Ia and one Type II, are first discovered based on Supernova Identification analysis. The results demonstrate that our method is reliable. The description of the method and some detailed spectral analysis procedures are also presented. (letters)
[en] Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensemble. The first proof is based on a concept of the Fredholm Pfaffian; the second proof is purely linear algebraic. (fast track communication)
[en] An asymptotic formula, uniform in z and z', is obtained for the spectral function θ(z,z',λ) of the Laplace-Beltrami operator for cocompact discrete subgroups of SL2(R) with power-law lowering of the order of the remainder
[en] Long-period and quasicrystalline structures are represented as the limit sets of a multifractal corresponding to an arbitrary incommensurable structure. The investigation is based on a study of the simplest mappings representing the nodes of the lattice which arise upon superposition of incommensurable structures. We separately consider quasicrystalline structures and we investigate their fractal properties. We generalize to arbitrary incommensurable structures