In this paper difference methods to solve "fuzzy partial differential equations" (FPDE) such as fuzzy hyperbolic and fuzzy parabolic equations are considered. The existence of the solution and stability of the method are examined in detail. Finally examples are presented to show that the Hausdorff  distance between the exact solution and approximate solution tends to zero.

It is well known that Martin-Löf randomness can be characterized by a number of equivalent test concepts, based either on effective nullsets (Martin-Löf and Solovay tests) or on prefix-free Kolmogorov complexity (lower and upper entropy). These equivalences are not preserved as regards the partial randomness notions induced by effective Hausdorff measures or partial incompressibility. Tadaki [2...

In a previous paper [11], the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS and studied some applications in one dimension. The key idea, which has been known in varying degrees of generality for many years, is to associate to the IFS a parametrized family of positive, linear, Perron-Frobenius operators ...

The domain-theoretic model of computational geometry provides us with continuous and computable predicates and binary operations. It can also be used to generalise the theory of computability for real numbers and real functions into geometric objects and geometric operations. A geometric object is computable if it is the effective limit of a sequence of finitary partial objects of the same type...

We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces X, the corresponding partial dcpo’s of continuous real valued functions on X are continuous partial dcpos; (iii) if a space X is Hausdorff compact, the latt...

The concept of ‘topological right transversal’ is introduced to study right transversals in topological groups. Given any right quasigroup S with a Tychonoff topology T , it is proved that there exists a Hausdorff topological group in which S can be embedded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological rig...

The sample paths of Lévy processes generate various random fractals and many of their properties have been studied since 1960’s [see the survey papers of Fristedt (1974), Taylor (1986) and Xiao (2004)]. The lectures will cover the following topics: Hausdorff dimension and exact Hausdorff measure functions for random fractals determined by Lévy processes; Hausdorff dimension computation using po...