Mass spectral fragmentations of 6-aryl-5,6,7,8-tetrahydro-4H-1,3,2,6-dioxathiazocine 2-Oxides

The mass spectral fragmentation of 4-, 5-, and 4,8-disubstituted derivatives of 6-aryl-5,6,7,8-tetrahydro-4H-1,3,2,6-dioxathiazocine 2-oxides is reported.     

On first passage time structure of random walks

For continuous time birth-death processes on {0,1,2,…}, the first passage time T⁺_n from n to n + 1 is always a mixture of (n + 1) independent exponential random variables. Furthermore, the first passage time T_0,n+1 from 0 to (n + 1) is always a sum of (n + 1) independent exponential random variables. The discrete time analogue, however, does not necessarily hold in spite of structural similarities. In this paper, some necessary and sufficient conditions are established under which T⁺_n and T_0,n+1 for discrete time birth-death chains become a mixture and a sum, respectively, of (n + 1) independent geometric random variables on {1,2,…};. The results are further extended to conditional first passage times.     

On p-class groups of relative cyclic p-extensions

Archiv der Mathematik - We prove a general stability theorem for p-class groups of number fields along relative cyclic extensions of degree $$p^2$$ , which is a generalization of a finite-extension...     

Temperature sensitivity of Ge-B-SiO(2) waveguide Bragg gratings on a crystallized glass substrate

Waveguide Bragg gratings were fabricated by plasma-enhanced chemical-vapor deposition followed by irradiation with KrF excimer laser light through a phase mask. The period of the Bragg grating was 0.53 mum, and the Bragg wavelength was ~1.53 mum . The temperature dependence of the Bragg wavelength was 11 pm/ degrees C for a 10GeO(2) -90SiO(2)(mol.%) core waveguide on a Si substrate, and the Bragg wavelength shift was successfully reduced to 5.0pm/ degrees C by use of a 14GeO(2)-12B(2)O(3)-74SiO(2) (mol.%) core and a crystallized glass substrate with a thermal-expansion coefficient of -2.0x10(-6)(/ degrees C) .     

Optimal Control Problem Associated with Jump Processes

An optimal portfolio/control problem is considered for a two-dimen\-sional model in finance. A pair consisting of the wealth process and cumulutative consumption process driven by a geometric Lévy process is controlled by adapted processes. The value function appears and turns out to be a viscosity solution to some integro-differential equation, by using the Bellman principle.     

Computation of multiple eigenvalues of infinite tridiagonal matrices

In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of ; (B) the zeros of ; (C) the EVP of the Mathieu differential equation; and (D) the EVP of the spheroidal wave equation. The results of experiments are shown for the three cases (A)-(C) for the computation of their ``double pairs'.

     

Canceling branch points and cusps on projections of knotted surfaces in -space

For a knotted surface in -space, its generic projection into -space has branch points as its singularities, and its successive projection into -space has fold points and cusps as its singularities. In this paper, we show that for non-orientable knotted surfaces, the numbers of branch points and cusps can be minimized by isotopy.

     

Symmetrization of Nonsymmetric Macdonald Polynomials and Macdonald's Inner Product Identities

We study the Macdonald polynomials that give eigenstates of some quantum many-body system with long-range interactions. Scalar products of the nonsymmetric Macdonald polynomials are algebraically evaluated through their Rodrigues-type formulas. We present a new proof of Macdonald's inner product identities without recourse to the shift operators; that is, we calculate square norms of the Macdonald polynomials through Weyl-symmetrization of those of the nonsymmetric Macdonald polynomials.     

The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations

We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda. As an application of those inequalities, the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations in and the gradient flow to the harmonic map to the sphere are discussed. Namely the Serrin-Ohyama type regularity criteria are improved in the terms of the Besov spaces. Received: 21 September 2000; in final form: 16 Feburary 2001 / Published online: 18 January 2002