Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations

Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$. The wave structure which contains four waves: the transonic(or degenerate) boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and 3-rarefaction wave to the inflow problem is described and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible Navier-Stokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the degeneracies of the transonic boundary layer solution and the wave interactions in the superposition wave.Comment: 27 page

Deformation of Schild String

We attempt to construct new superstring actions with a $D$-plet of Majorana fermions $\psi^{\cal B}_A$, where ${\cal B}$ is the $D$ dimensional space-time index and $A$ is the two dimensional spinor index, by deforming the Schild action. As a result, we propose three kinds of actions: the first is invariant under N=1 (the world-sheet) supersymmetry transformation and the area-preserving diffeomorphism. The second contains the Yukawa type interaction. The last possesses some non-locality because of bilinear terms of $\psi^{\cal B}_A$. The reasons why completing a Schild type superstring action with $\psi^{\cal B}_A$ is difficult are finally discussed.Comment: 12 pages, Latex, both title and abstract are changed, discussion of some relations among our results, Nambu-Goto string and super Yang-Mills theories, added. Results unchange

Passive Earth Pressure During Earthquakes

In order to investigate characteristics of the passive earth pressure during earthquakes against the front face of the part of sheet pile walls driven into the ground, dynamic earth pressure tests were performed by using a large scale oscillating soil bin. A movable wall from which inertial effects were eliminated was used in this study. The wall was moved toward sand filled in the bin during oscillation. The angle Φm deduced by inserting the observed peak wall load and wall friction angle at the maximum inertia force into the logarithmic spiral method was coincided with that of the static condition. The change in the wall friction angle induced by oscillation should not be neglected in an estimation of passive earth pressure during earthquake

On two theorems for flat, affine group schemes over a discrete valuation ring

We include short and elementary proofs of two theorems characterizing reductive group schemes over a discrete valuation ring, in a slightly more general context.Comment: 10 pages. To appear in C. E. J.

Kondo effect in CeXc_{c} (Xc_{c}=S, Se, Te) studied by electrical resistivity under high pressure

We have measured the electrical resistivity of cerium monochalcogenices, CeS, CeSe, and CeTe, under high pressures up to 8 GPa. Pressure dependences of the antiferromagnetic ordering temperature $T_{N}$, crystal field splitting, and the $\ln T$ anomaly of the Kondo effect have been studied to cover the whole region from the magnetic ordering regime at low pressure to the Fermi liquid regime at high pressure. $T_{N}$ initially increases with increasing pressure, and starts to decrease at high pressure as expected from the Doniach's diagram. Simultaneously, the $\ln T$ behavior in the resistivity is enhanced, indicating the enhancement of the Kondo effect by pressure. It is also characteristic in CeX$_{c}$ that the crystal field splitting rapidly decreases at a common rate of $-12.2$ K/GPa. This leads to the increase in the degeneracy of the $f$ state and further enhancement of the Kondo effect. It is shown that the pressure dependent degeneracy of the $f$ state is a key factor to understand the pressure dependence of $T_{N}$, Kondo effect, magnetoresistance, and the peak structure in the temperature dependence of resistivity.Comment: 9 pages, 5 figures, accepted for publication in J. Phys. Soc. Jp

Screening in Supersymmetric Gauge Theories in Two Dimensions

We show that the string tension in N=1 two-dimensional super Yang-Mills theory vanishes independently of the representation of the quark anti-quark external source. We argue that this result persists in SQCD_2 and in two-dimensional gauge theories with extended supersymmetry or in chiral invariant models with at least one massless dynamical fermion. We also compute the string tension for the massive Schwinger model, as a demonstration of the method of the calculation.Comment: 8 pages, Latex. Minor changes. Accepted to Phys.Lett.

Kodaira-Spencer formality of products of complex manifolds

We shall say that a complex manifold $X$ is emph{Kodaira-Spencer formal} if its Kodaira-Spencer differential graded Lie algebra $A^{0,*}_X(Theta_X)$ is formal; if this happen, then the deformation theory of $X$ is completely determined by the graded Lie algebra $H^*(X,Theta_X)$ and the base space of the semiuniversal deformation is a quadratic singularity.. Determine when a complex manifold is Kodaira-Spencer formal is generally difficult and we actually know only a limited class of cases where this happen. Among such examples we have Riemann surfaces, projective spaces, holomorphic Poisson manifolds with surjective anchor map $H^*(X,Omega^1_X) o H^*(X,Theta_X)$ and every compact K"{a}hler manifold with trivial or torsion canonical bundle. In this short note we investigate the behavior of this property under finite products. Let $X,Y$ be compact complex manifolds; we prove that whenever $X$ and $Y$ are K"{a}hler, then $X imes Y$ is Kodaira-Spencer formal if and only if the same holds for $X$ and $Y$. A revisit of a classical example by Douady shows that the above result fails if the K"{a}hler assumption is droppe