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.

     

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'.

     

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.     

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...     

Complete Enumeration of Small Realizable Oriented Matroids

Enumeration of all combinatorial types of point configurations and polytopes is a fundamental problem in combinatorial geometry. Although many studies have been done, most of them are for 2-dimensional and non-degenerate cases. Finschi and Fukuda (Discrete Comput Geom 27:117–136, 2002) published the first database of oriented matroids including degenerate (i.e., non-uniform) ones and of higher ranks. In this paper, we investigate algorithmic ways to classify them in terms of realizability, although the underlying decision problem of realizability checking is NP-hard. As an application, we determine all possible combinatorial types (including degenerate ones) of 3-dimensional configurations of 8 points, 2-dimensional configurations of 9 points, and 5-dimensional configurations of 9 points. We also determine all possible combinatorial types of 5-polytopes with nine vertices.     

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.     

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) .     

Estimation of surface charges on dielectric materials for high power rf windows

The surface discharges observed at rf windows and vacuum circuit breakers (VCBs) are one of the difficulties faced when developing high-power rf windows or compact VCBs. The surface discharge is considered to take place due to the release of the surface charges. Despite the importance of the surface charging/discharging, these phenomena have not been well evaluated. In this paper, the surface charges are estimated using the multipulse method, where electron beam irradiates a sample up to the saturation condition of surface charges. The amount of surface charges on alumina and TiN coated alumina are compared and the charging mechanism is discussed.     

Influence of contamination layer on thickness evaluation by X-ray reflectometry

In this study, the effect of allowing for a contamination layer on a SiO₂ film/Si substrate system on thickness determination by X-ray reflectometry (XRR) was investigated. The calculated XRR profiles obtained using a calculation model that utilizes a contamination layer for analysis showed good agreement with measured profiles. Further, the obtained physical structures were promising and within acceptable limits. Where the existence of a contamination layer was ignored in the calculation process, a part of the thickness of the contamination layer was incorporated into the determined thickness of the SiO₂ layer. In that case, the evaluated thickness was proportional to the density ratio between the contaminated and SiO₂ layers. The results of investigation of the effect of X-ray energy on layer thickness determination indicated that the effects of contamination also depend on the X-ray energy used for XRR measurements. These effects increase in the case of experiments that employ X-ray energy with a high contrast for the contamination.     

Flexible host frameworks with diverse cavities in inclusion crystals of bile acids and their derivatives

We have systematically investigated structures and properties of inclusion crystals of bile acids and their derivatives. These steroidal compounds form diverse host frameworks having zero‐, one‐ and two‐dimensional cavities, causing various inclusion behaviors towards many organic compounds. The diverse host frameworks exhibit the following guest‐dependent flexibility. First, the frameworks mainly depend on the included guests in size and shape. The size‐dependence is quantitatively estimated by the parameter PCcavity, which is the volume ratio of a guest molecule to a host cavity. The resulting values of PCcavity lie in the range of 42–76%. Second, each of the host frameworks has its own range of the values. Some guests can employ two different frameworks with the boundary values, explaining formation of polymorphic crystals. Third, the host frameworks are selected by host–guest interactions through weak hydrogen bonds, such as NH/π and CH/O. The weak hydrogen bonds play an important role for various selective inclusion processes. Fourth, the host frameworks are dynamically exchangeable, resulting in intercalation and polymerization in the cavities. These static and dynamic structures of the frameworks demonstrate great potential of crystalline organic inclusion compounds as functional materials. © 2009 The Japan Chemical Journal Forum and Wiley Periodicals, Inc. Chem Rec 9: 124–135; 2009: Published online in Wiley InterScience ( www.interscience.wiley.com ) DOI 10.1002/tcr.20171