The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of projections in the proper perspective of noncommutative geometry. keyword: Index problem, crossed product, Fredholm module, pair of projections. MSC 46L87.

We report empirical studies on the personal income distribution, and clarify that the distribution pattern of the lognormal with power law tail is the universal structure. We analyze the temporal change of Pareto index and Gibrat index to investigate the change of the inequality of the income distribution. In addition some mathematical models which are proposed to explain the power law distribu...

A universal decoding procedure is proposed for memoryless Gaussian channels with deterministic interfering signals from a certain class. The universality of the proposed decoder is in the sense of W i g independent of the channel parameters and the unknown interfering signal, and at the same time attaining the same random coding e m r exponent as the optimal maximum likelihood (ML) decoder, whi...

We propose a universal channel coding when each output distribution forms an exponential family even in a continuous output system. We propose two types of universal codes; One has the exponentially decreasing error with explicit a lower bound for the error exponent. The other attains the ǫ-capacity up to the second order. Our encoder is the same as the previous paper [CMP 289, 1087]. For our d...

We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function , the persistence probability distributions describe dynamic correlations non-local in time. Universal and non-universal behaviors of the German DAX and Shanghai Index are analyzed, and numerical simulations of some microscopic models are also...