16 citations · 17 across the 2 of their papers we have counts for
3 papers
q-fin.MF2015★ 16 cited
Symmetry reduction and exact solutions of the non-linear Black--Scholes equation
Oleksii Patsiuk, Sergii Kovalenko
In this paper, we investigate the non-linear Black--Scholes equation: and show that the one can be reduced to the…
math.AP2014★ 1 cited
Lie group classification and invariant exact solutions of the generalized Kompaneets equations
Oleksii Patsiuk
In this paper, from the group-theoretic point of view it is investigated such class of the generalized Kompaneets equations (GKEs): $$u_t=\frac1{x^2}\cdot\left[x^4(u_x+f(u))\right]…
math.FA2011
On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl_2
Sergii Kuzhel, Oleksii Patsiuk
Let and be anti-commuting fundamental symmetries in a Hilbert space . The operators and can be interpreted as basis (generating) elements of the compl…