In this paper, we consider the problem of approximate solutions of set-valued stochastic differential equations. We firstly prove an inequality of set-valued Itô integrals, which is related to classical Itô isometry, and an inequality of set-valued Lebesgue integrals. Both of the inequalities play an important role to discuss set-valued stochastic differential equations. Then we mainly state th...

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...

Probability theory is an important tool of modeling randomness in a practical problem. But besides randomness, in the real world, there exists other kind of uncertainties such as impreciseness or vagueness. Set-valued functions are employed to model the impreciseness in applied field such as in Economics, control theory (see for example [1]). Integrals of set-valued functions have been received...

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.