Abstract:
Several reports have described magnetic resonance (MR) findings in canine and feline lysosomal storage diseases such as gangliosidoses and neuronal ceroid lipofuscinosis. Although most of those studies described the signal intensities of white matter in the cerebrum, findings of the corpus callosum were not described in detail. A retrospective study was conducted on MR findings of the corpus callosum as well as the rostral commissure and the fornix in 18 cases of canine and feline lysosomal storage diseases. This included 6 Shiba Inu dogs and 2 domestic shorthair cats with GM1 gangliosidosis; 2 domestic shorthair cats, 2 familial toy poodles, and a golden retriever with GM2 gangliosidosis; and 2 border collies and 3 chihuahuas with neuronal ceroid lipofuscinoses, to determine whether changes of the corpus callosum is an imaging indicator of those diseases. The corpus callosum and the rostral commissure were difficult to recognize in all cases of juvenile-onset gangliosidoses (GM1 gangliosidosis in Shiba Inu dogs and domestic shorthair cats and GM2 gangliosidosis in domestic shorthair cats) and GM2 gangliosidosis in toy poodles with late juvenile-onset. In contrast, the corpus callosum and the rostral commissure were confirmed in cases of GM2 gangliosidosis in a golden retriever and canine neuronal ceroid lipofuscinoses with late juvenile- to early adult-onset, but were extremely thin. Abnormal findings of the corpus callosum on midline sagittal images may be a useful imaging indicator for suspecting lysosomal storage diseases, especially hypoplasia (underdevelopment) of the corpus callosum in juvenile-onset gangliosidoses.

Indemanding for repair items or standard products, customers sometimes require multiple common items. In this study, the waiting time of demand which requires multiple items under base stock policy is analyzed theoretically and numerically. It is assumed that the production time has an exponential distribution andthe demand is satisfied under a FCFS rule. Each demand waits until all of its requirements are satisfied. An arriving process of demand is assumed to follow a Poisson process and the numbers of required items are independent and generally distributed. A method for deriving waiting time distribution of demandis shown by using methods for computing M^{X}/M/1 waiting time distribution and for deriving the distribution on the order corresponding to the last item the current customer requires. By using the analytical results, properties of waiting time distribution of demand and optimal numbers of base stocks are discussed through numerical experiments.

Abstract:
Operating just once the naive Foldy-Wouthuysen-Tani transformation on the Schr\"odinger equation for $Q\bar q$ bound states described by a hamiltonian, we systematically develop a perturbation theory in $1/m_Q$ which enables one to solve the Schr\"odinger equation to obtain masses and wave functions of the bound states in any order of $1/m_Q$. It is shown that positive energy projection with respect to the heavy quark sector of a wave function is, at each order of perturbation, proportional to the 0-th order solution. There appear also negative components of the wave function except for the 0-th order, which contribute also to higher order corrections to masses.

Abstract:
This is a note on toroidalization, formulated as the problem of resolution of singularities of morphisms in the logarithmic category. It is submitted to the proceedings of the Barrett conference held at the University of Tennessee at Knoxville in April 2002.

Abstract:
Let G be the split special orthogonal group of degree 2n+1 over a field F of char F \ne 2. Then we describe G-orbits on the triple flag varieties G/P\times G/P\times G/P and G/P\times G/P\times G/B with respect to the diagonal action of G where P is a maximal parabolic subgroup of G of the shape (n,1,n) and B is a Borel subgroup. As by-products, we also describe GL_n-orbits on G/B, Q_{2n}-orbits on the full flag variety of GL_{2n} where Q_{2n} is the fixed-point subgroup in Sp_{2n} of a nonzero vector in F^{2n} and 1\times Sp_{2n}-orbits on the full flag variety of GL_{2n+1}. In the same way, we can also solve the same problem for SO_{2n} where the maximal parabolic subgroup P is of the shape (n,n).

Abstract:
This is an expanded version of the notes for the lectures given by the author at RIMS in the summer of 1999 to give a detailed account of the proof for the (weak) factorization theorem of birational maps by Abramovich-Karu-Matsuki-W{\l}odarczyk.

Abstract:
It was proved by Huckleberry that the Akhiezer-Gindikin domain is included in the ``Iwasawa domain'' using complex analysis. But we can see that we need no complex analysis to prove it. In this paper, we generalize the notions of the Akhiezer-Gindikin domain and the Iwasawa domain for two associated symmetric subgroups in real Lie groups and prove the inclusion. Moreover, by the symmetry of two associated symmetric subgroups, we also give a direct proof of the known fact that the Akhiezer-Gindikin domain is included in all cycle spaces.

Abstract:
This is a correction to the afore-mentioned paper in Duke Math. J. vol. 75 (1994), 99-119 by S. Keel, K. Matsuki, and J. McKernan. We completely rewrite Chapter 6 according to the original manuscript of the second author, in order to fix some crucial mistakes pointed out by Dr. Qihong Xie.

Abstract:
In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_C/P and conjectured that the connected component C(S)_0 of the identity would be equal to the Akhiezer-Gindikin domain D if S is of nonholomorphic type. This conjecture was proved for closed S in [WZ2,WZ3,FH,M4] and for open S in [M4]. It was proved for the other orbits in [M5] when G_R is of non-Hermitian type. In this paper, we prove the conjecture for an arbitrary non-closed K_C-orbit when G_R is of Hermitian type. Thus the conjecture is completely solved affirmatively.

Abstract:
In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_C/P and conjectured that the connected component C(S)_0 of the identity will be equal to the Akhiezer-Gindikin domain D if S is of nonholomorphic type. This conjecture was proved for closed S in [WZ1,WZ2,FH,M6] and for open S in [M6]. In this paper, we prove the conjecture for all the other orbits when G_R is of non-Hermitian type.