8 citations · 11 across the 5 of their papers we have counts for
5 papers
A Borsuk-Ulam Type Generalization of the Leray-Schauder Fixed Point Theorem
Anatoliy K. Prykarpatsky
A generalization of the classical Leray-Schauder fixed point theorem, based on the in finite- dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely differ…
Introductive Backgrounds of Modern Quantum Mathematics with Application to Nonlinear Dynamical Systems
Anatoliy K. Prykarpatsky, Nikolai N. Bogolubov, Jolanta Golenia +1
Introductive backgrounds of a new mathematical physics discipline - Quantum Mathematics - are discussed and analyzed both from historical and analytical points of view. The magic p…
A Symplectic Generalization of the Peradzynski Helicity Theorem and Some Applications
Anatoliy K. Prykarpatsky, Nikolai N. Bogoliubov, Jolanta Golenia
Symplectic and symmetry analysis for studying MHD superfluid flows is devised, a new version of the Z. Peradzynski helicity theorem based on differential - geometric and group-theo…
Analytical Properties of an Ostrovsky-Whitham Type Dynamical System for a Relaxing Medium with Spatial Memory and its Integrable Regularization
Nikolai Bogolubov, Anatoliy Prykarpatsky, Ilona Gucwa +1
Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-hol…
De Rham-Hodge-Skrypnik theory. A survey of the spectral and differential geometric aspects of the De Rham-Hodge-Skrypnik theory related with Delsarte transmutation operators in multidimension and its applications to spectral and soliton problems. Part 1
Y. A. Prykarpatsky, A. M. Samoilenko, A. K. Prykarpatsky
A review on spectral and differential-geometric properties of Delsarte transmutation operators in multidimension is given. Their differential geometrical and topological structure…