Splitting scheme is applied to numerically solve the time dependent Ginzburg-Landau and Maxwell equations which describe superconducting state in materials. First and second order splitting schemes are constructed with spacial differece method by using the link variables. We perform various numerical experiments and compare numerical stability by changing order of the schemes.

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In this paper we develop a simple model of travel distance/time distribution in a rectangular or a rectangular parallelepiped city with rectilinear distance. Sometimes we bypass on arterial transportation axes such as a freeway or a rapid train, so that we can save time. Starting from two typical travel distance distribution on a line segment, we derive travel distance/time distributions in two- or three-dimensional urban space, which could describe such a behavior as detour on transportation axes, in a mathematically explicit form. We show that higher dimension of urban space becomes, larger proportion of travel distance around mean is brought, and that travel distance distribution with a typical configuration of transportation axes can be obtained by convoluting lower dimensional travel distance distributions which correspond to each axis of urban space. As an implication in urban context, we find out that each of transportation network configuration has its superiority or inferiority with respect to urban density, that optimal form of a compact city is influenced by transportation network, and that there is a limitation in reducing mean travel time by installation of rapid transportation networks. Results of the present paper enable us to systematize effects of designing transportation network on travel distance/time in urban snare.

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A widely used strategy to decrease the execution time of robust geometric algorithms using multiprecision integer arithmetic is the hybrid use of integer and floating-point arithmetic. In this strategy, multiprecision integer arithmetic is avoided if the sign decision in floating-point arithmetic used in advance is regarded as sufficiently reliable. It is important for this strategy to estimate the upper bound of the error calculated in floating-point arithmetic. However, the method of the estimation is not unique. The more tightly the error is estimated, the more frequently multiprecision integer arithmetic is avoided. However, a tight upper bound requires high computational cost. This paper investigates how the suitable estimation varies as the type and the scale of inputs vary. Experimental consideration is done using the incremental method for constructing the Voronoi diagram as an example of the geometric algorithm.

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We construct a model for valuing Fading Out Swaps and characterize these claims. Fading Out Swaps are swap contracts whose payments of cashflows after default by either counterparty of swap contracts will be cancelled. Note that Fading Out Swaps are different from claims subject to default by both contracting parties proposed from Duffie and Huang or Jarrow and Turnbull. In Fading Out Currency Swaps, the fraction of market value paid to the non-defaulting party is zero when the swap has negative net market value for defaulting party, and also there is no compensate for defaulting party when the swap has positive net market value for defaulting party. While the valuation model applies to both Fading Out Interest Rate Swaps and Fading Out Currency Swaps, we focus on Fading Out Currency Swaps with an exchange of principal, implying an increase in counterparty risk.

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