Let (X,H) be a pair of a smooth rational surface X and an ample divisor H on X . Assume that (KX , H) < 0. Let MH(r, c1, χ) be the moduli space of semi-stable sheaves E of rk(E) = r, c1(E) = c1 and χ(E) = χ. To consider relations between moduli spaces of different invariants is an interesting problem. If (c1, H) = 0 and χ ≤ 0, then Maruyama [Ma2], [Ma3] studied such relations and constructed a ...

‎in this paper lie symmetry analysis is applied in order to find new solutions for fokker plank equation of ornstein-uhlenbeck process‎. ‎this analysis classifies the solutions format of the fokker plank equation by using the lie algebra of the symmetries of our considered stochastic process‎.

We prove first existence of a classical solution to class parabolic problems with unbounded coefficients on metric star graphs subject Kirchhoff-type conditions. The result is applied the Ornstein–Uhlenbeck and harmonic oscillator operators graphs. We give an explicit formula for associated semigroup unique invariant measure. show that this inherits regularity prope...