We present a new expression of the polynomial Hamiltonian of the Garnier system in two variables. 1. Main results The Garnier system in two variables is equivalent to the rational Hamiltonian system given by (see [18], cf. [3]) dq1 = ∂H1 ∂p1 dt + ∂H2 ∂p1 ds, dp1 = − ∂H1 ∂q1 dt− ∂H2 ∂q1 ds, dq2 = ∂H1 ∂p2 dt + ∂H2 ∂p2 ds, dp2 = − ∂H1 ∂q2 dt− ∂H2 ∂q2 ds, H1 = − q1(q1 − 1)(q1 − t)(q1 − s)(q2 − t) (...

Abstract: Objectives: Cancer is among four major Non-Communicable Diseases (NCD). Based on the World Health Organization (WHO), it biggest cause of mortality globally, claiming about 10 million lives in recent years. Tankyrases a poly polymerase (ADP-ribose) family enzyme, inhibiting its enzymatic processes plays crucial part cancer etiology. Materials and Methods: The Algorithm Kennard-Stone w...

Given q1, q2 ∈ C \ {0}, we construct a unital Banach algebra Bq1,q2 which contains a universal normalized solution to the (q1, q2)-deformed Heisenberg–Lie commutation relations in the following specific sense: (i) Bq1,q2 contains elements b1, b2, and b3 which satisfy the (q1, q2)-deformed Heisenberg–Lie commutation relations (that is, b1b2 − q1b2b1 = b3, q2b1b3 − b3b1 = 0, and b2b3 − q2b3b2 = 0...