In our recent paper we have established close relationships between state reduction of a fuzzy recognizer and resolution of a particular system of fuzzy relation equations. In that paper we have also studied reductions by means of those solutions which are fuzzy equivalences. In this paper we will see that in some cases better reductions can be obtained using the solutions of this system that a...

We study the problem of statistical inference of continuous-time diffusion processes, and develop methods for modeling threshold diffusion processes in particular. We derive the limiting properties of the quasi-likelihood estimator. We also propose a quasi-likelihood ratio test statistic for testing threshold diffusion process against linear alternative. We begin in Chapter 1 with an introducti...

We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and tha...

In several e-commerce applications, non-truthful auctions have been preferred over truthful weakly dominant strategy ones partly because of their simplicity and scalability. Although nontruthful auctions can have weaker incentive constraints than truthful ones, the question of how much more revenue they can generate than truthful auctions is not well understood. We study this question for natur...

We investigate the weakly non-linear evolution of cosmic gravitational clustering in phase space by looking at the Zel’dovich solution in the discrete wavelet transform (DWT) representation. We show that if the initial perturbations are Gaussian, the relation between the evolved DWT mode and the initial perturbations in the weakly non-linear regime is quasi-local. That is, the evolved density p...

This paper is a continuation of a series of papers in which (quasi-) hydrodynamic models for plasmas are rigorously derived by means of asymptotic analysis. Here, the quasi-neutral limit (zero-Debye-length limit) in the drift-diiusion equations is performed in the two cases: weakly ionized plasmas and not weakly ionized plasmas. The model consists of the continuity equations for the electrons a...

The notion of causal operators is extended to periodic boundary value problems with nonlinear boundary conditions in this paper. By utilizing the monotone iterative technique and the method of lower and upper solutions (resp. weakly coupled lower and upper solutions), we establish the existence of the extremal solutions (resp. weakly coupled extremal quasi-solutions) for nonlinear periodic boun...