This workbook is essentially a collection of computer experiments and complementary theoretical synopses that are designed to support or amplify the usual topics in standard elementary differentialâ€¦ (More)

To the memory of Auberon Waugh (1939â€“2001), a light in the darkness. Abstract Observing the Universe, astronomers have concluded that the motion of stars can not be accounted for unless one assumesâ€¦ (More)

where P+ is a differential operator whose coefficients are differential polynomials in u, that is, polynomials in u and its x-derivatives u (s~. (The subscript + may be ignored at this point: weâ€¦ (More)

X iv :m at h/ 00 04 18 7v 1 [ m at h. H O ] 1 A pr 2 00 0 Journal of Nonlinear Mathematical Physics 2000, V.7, N 2, 244â€“262. (Re)-Examining the Past q-Newton Binomial: From Euler To Gauss Boris A.â€¦ (More)

The multiplication in a quasiassociative algebra R satisfies the property a âˆ— (b âˆ— c) âˆ’ (a âˆ— b) âˆ— c = b âˆ— (a âˆ— c) âˆ’ (b âˆ— a) âˆ— c, a, b, c âˆˆ R. (âˆ—âˆ—) This property is necessary and sufficient for theâ€¦ (More)

Abstract The sequence of period 6 starting with 1, 1, 0,âˆ’1,âˆ’1, 0 appears in many different disguises in mathematics. Various q-versions of this sequence are found, and their relations with Eulerâ€™sâ€¦ (More)

Various Hamiltonian actions of loop groups G and of the algebra diff 1 of first order differential operators in one variable are defined on the cotangent bundle T * G. The moment maps generating theâ€¦ (More)

q-analogs of classical formulae go back to Euler, q-binomial coefficients were defined by Gauss, and q-hypergeometric series were found by E. Heine in 1846. The q-analysis was developed by F. Jacksonâ€¦ (More)

Abstract A large class of two-dimensional free-surface hydrodynamical systems is determined that can be selfconsistently reduced by the condition that the velocity profile has a constant shear. Theâ€¦ (More)