We show a direct relation between the singular point analysis and the symmetry for ordinary differential equations. It is proved that a system with a meromorphic solution allows Laurent solutions depending on m arbitrary parameters if it has m independent symmetries, regardless of the existence of single-valued first integrals. Applying the result to Hamiltonian systems, we show a pairing prope...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

For [0,∞]-valued (monotone) measures and functions, universal integrals are introduced and investigated. For a fixed pseudomultiplication ⊗ on [0,∞] the smallest and the greatest universal integrals are given. Finally, a third construction method for obtaining universal integrals is introduced.