An ergodic study of Painlevé VI

An ergodic study of Painlevé VI is developed. The chaotic nature of its Poincaré return map is established for almost all loops. The exponential growth of the numbers of periodic solutions is also shown. Principal ingredients of the arguments are a moduli-theoretical formulation of Painlevé VI, a Riemann–Hilbert correspondence, the dynamical system of a birational map on a cubic surface, and the Lefschetz fixed point formula. Dedicated to Professor Masuo Hukuhara on his 100th birthday.     

Minimaxity of a preliminary test estimator for the mean of normal distribution

Summary The problem is to estimate the mean of the normal distribution under the situation where there is vague information that the mean might be equal to zero. A minimax property of the preliminary test estimator obtained by the use of AIC (Akaike information Criterion) procedure is proved under a loss function based on the Kullback-Leibler information measure.     

Vortex-lines motion for the Ginzburg-Landau equation with impurity

In this paper,we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity.We prove that,asymptotically,the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.     

高能核子-核子和核-核碰撞中电荷起伏的测量

利用强子-强子碰撞的模型PYTHIA以及核-核碰撞的模型RQMD比较了各种电荷起伏测量量的快度依赖性，结果发现，这些测量量对快度的依赖性依赖于模型. 但是，电荷关联能很好地测量整体电荷守恒以及短程快度关联性质. 因此，被认为是一个好的反应电荷起伏的测量量.     

A formula for the Mahler measure of axy+bx+cy+d

We introduce a formula for the Mahler measure of axy+bx+cy+d with complex coefficients a,b,c, and d and give examples which demonstrate a connection with L-functions. We then prove a generalization of Maillot's formula when the coefficients are real. Next, we discuss operations on the coefficients which fix the Mahler measure. Finally, we prove an alternate formulation of the main result in order to calculate the Mahler measure of a two-parameter family of polynomials in three variables.     

The volume measure for flat connections as limit of the Yang–Mills measure

We prove that integration over the moduli space of flat connections can be obtained as a limit of integration with respect to the Yang–Mills measure defined in terms of the heat-kernel for the gauge group. In doing this we also give a rigorous proof of Witten’s formula for the symplectic volume of the moduli space of flat connections. Our proof uses an elementary identity connecting determinants of matrices along with a careful accounting of certain dense subsets of full measure in the moduli space.     

Properties of stationary solutions of a generalized Tjon-Wu equation

A generalized version of the Tjon-Wu equation is considered. Solutions of this equation are functions with values in the space of probability measures on [0,∞). We prove that the stationary solution μ_∗ of the equation has the following property: Either μ_∗ is supported at one point or suppμ_∗=[0,∞). Moreover we show that in the second case the distribution function of μ_∗ is continuous. Some open questions are discussed.     

Noninjectivity of the Predual Bimodule of the Measure Algebra for Infinite Discrete Groups

In this paper, it is proved that the predual bimodule of the measure algebra of an infinite discrete group is not injective despite the fact that the measure algebra of an amenable group is amenable in the sense of Connes. Thus the well-known result of Khelemskii (claiming that, for a von Neumann algebra, Connes-amenability is equivalent to the condition that the predual bimodule is injective) cannot be extended to measure algebras. Moreover, for a discrete amenable group, we give a simple formula for a normal virtual diagonal of the measure algebra. It is shown that a certain canonical bimodule over the measure algebra is not normal.     

Automated Segmentation and Registration of Dermatological Images

During the last years, there has been a significant increase in the level of interest in image morphology, full-color image processing, image data compression, image recognition and knowledge based analysis systems for medical images. The present paper describes the implementation and tests the efficiency of algorithms dealing with the issues of segmentation and registration of digital images containing skin lesions. Those steps are considered of great importance in computer based characterization systems as they are responsible for the isolation of pathological findings and the matching of sequential images during follow-up studies in medical imaging. This revised version was published online in July 2006 with corrections to the Cover Date.