
Katsurada,Hidenori; Kawamura,Hisaaki

Izumiya,S.; Marar,W.L.
We give a relation between Euler characteristics of a generic closed Legendrian surface and its wavefront.

Kubo,Masahiro; Yamazaki,Noriaki
We study periodic solutions of quasilinear ellipticparabolic variational inequalities with timedependent constraints. Assuming that the constraint changes periodically in time, we prove existence of periodic solutions. Moreover, applications of the general results are given.

Shibukawa,Youichi
In this work, we propose and investigate dynamical YangBaxter maps, some of which produce solutions to the (quantum) dynamical YangBaxter equation. Suppose that L is a loop and a group. If their unit elements coincide, then L gives birth to a bijective dynamical YangBaxter map from L x L to L x L whose dynamical parameter belongs to L. The above group L is abelian if and only if the corresponding dynamical YangBaxter map satisfies the unitary condition.

Kubo,Masahiro; Yamazaki,Noriaki
We study variational inequalities with timedependent constraints for quasilinear parabolic PDE of divergence form. Introducing a general condition on the constrains, we prove existence, uniqueness and order property of solution. Some applications are given.

Kubo,Masahiro; Yamazaki,Noriaki
We study variational inequalities for ellipticparabolic eqnations with timedependent constraints. Introducing a general condition for the timedependence of convex sets defining the constraints, we establish theorems concerning existence, uniqueness as well as order property of solution. Some applications of the general results are given.

Giga,MiHo; Giga,Yoshikazu; Pozar,Norbert
We introduce a new notion of viscosity solutions for a class of very singular nonlinear parabolic problems of nondivergence form in a periodic domain of arbitrary dimension, whose di usion on flat parts with zero slope is so strong that it becomes a nonlocal quantity. The problems include the classical total variation flow and a motion of a surface by a crystalline mean curvature. We establish a comparison principle, the stability under approximation by regularized parabolic problems, and an existence theorem for general continuous initial data.

Katsurada,Hidenori
We give an explicit formula for the twisted KoecherMaa? series of the DukeImamogluIkeda lift. As an application we prove a certain algebraicity result for the values of twisted RankinSelberg series at integers of halfintegral weight modular forms.

Yamada,Michio; Yoneda,Tsuyoshi
An incompressible twodimensional flow on a β plane is considered. The β plane is a tangent plane of a sphere to approximately describe fluid motion on a rotating sphere assuming that the Coriolis parameter is a linear function of the latitude. Rossby waves are expected to dominate the β plane dynamics, and here in this paper, a mathematical support for the crucial role of the resonant pairs of the Rossby waves is given.

Yamaguchi,K.

Inoue,A
We prove a representation of the partial autocorrelation function α(・) of a stationary process { Xn : n ∈ Z}, in terms of the AR(∞) and MA(∞) coefficients. We apply it to show what α(n) looks like for large n, especially, when {Xn} is a longmemory process. For example, if {Xn} is a fractional ARIMA(p. d. q) process, then we have a(n)～d/n as n → ∞.

Lehmann,D; Suwa,T

Matsuda,Kouichi
The author chose not to have the body of the paper
published at this time.

Nishimori,Toshiyuki

YAMAGUCHI, KEIZO

Giga, Yoshikazu; Hamamuki, Nao
We consider the initial value problem for a fullynonlinear degenerate parabolic equation with a dynamic boundary condition in a half space. Our setting includes geometric equations with singularity such as the levelset mean curvature ﬂow equation. We establish a comparison principle for a viscosity sub and supersolution. We also prove existence of solutions and Lipschitz regularity of the unique solution. Moreover, relation to other types of boundary conditions is investigated by studying the asymptotic behavior of the solution with respect to a coefficient of the dynamic boundary condition.

maekawa,yasunori
This paper studies the large time asymptotic behavior of derivatives of the vorticity solving the twodimensional vorticity equations equivalent to the NavierStokes equations. It is wellknown by now that the vorticity behaves asymptotically as the Oseen vortex provided that the initial vorticity is integrable. This paper shows that each derivative of the vorticity also behave asymptotically as that of the Oseen vortex. For the proof new spatial decay estimates for derivatives are established. These estimates control behavior at the space infinity. The convergence result follows from a rescaling and compactness argument.

Sawada,Okihiro; Usui,Toshiomi
The locallyintime solvability of the Cauchy problem of the incompressible NavierStokes equations is established with nitial velocity U0 of the form U0(x) := u0(x)  Mx, where M is a realvalued matrix and u0 is a bounded function. It is also hown that in 2dimensional case the NavierStokes equations admit unique globallyintime smooth solution, due to the uniform bound for vorticity. Although the semigroup is not analytic, our mild solution satisfies the NavierStokes equations in the classical sense, provided the pressure term is suitably chosen. The form of the pressure is uniquely determined, provided the disturbance of velocity is bounded...

Ibrahim,Slim; Yoneda,Tsuyoshi
Existence of localintime unique solution and loss of smoothness of full MagnetHydroDynamics system (MHD) is considered for periodic initial data. The result is proven using FujitaKato's method in l^1 based (for the Fourier coeffcients) functional spaces enabling us to easily estimate nonlinear terms in the system as well as solutions to Maxwells's equations. A loss of smoothness result is shown for the velocity and magnetic field. It comes from the dampedwave operator which does not have any smoothing effect.

Fukunaga,Tomonori; Takahashi,Masatomo
A framed surface is a smooth surface in the Euclidean space with a moving frame. The framed surfaces may have singularities. We treat smooth surfaces with singular points, that is, singular surfaces more directly. By using the moving frame, the basic invariants and curvatures of the framed surface are introduced. Then we show that the existence and uniqueness for the basic invariants of the framed surfaces. We give properties of framed surfaces and typical examples. Moreover, we construct framed surfaces as oneparameter families of Legendre curves along framed curves. We give a criteria for singularities of framed surfaces by using...