Rearrangements of Conditionally Integrable Functions

ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

Towards classification of conditionally integrable evolution systems in (1 + 1) dimensions by A. Sergyeyev TOWARDS CLASSIFICATION OF CONDITIONALLY INTEGRABLE EVOLUTION SYSTEMS IN (1 + 1) DIMENSIONS

We generalize earlier results of Fokas and Liu and find all locally analytic (1+1)-dimensional evolution equations of order n that admit an N -shock type solution with N ≤ n+ 1. To this end, we develop a refinement of the technique from our earlier work (A. Sergyeyev, J. Phys. A: Math. Gen, 35 (2002), 7653–7660), where we completely characterized all (1+1)-dimensional evolution systems ut = F (...

On rearrangements of conditionally convergent series

Results of the Chebyshev type inequality for Pseudo-integral

In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results  to the case of comonotone functions.

Towards classification of conditionally integrable evolution systems

Given a generalized (Lie–Bäcklund) vector field, we classify (under certain nondegeneracy assumptions) all (1+1)-dimensional evolution systems which admit this vector field as a conditional symmetry. The connection with the theory of symmetries of systems of ODEs and with the theory of invariant modules is discussed.