Denis Blackmore

Blackmore, Denis, & Byszewski, Ludwik, & Balinsky, Alexander, & Prykarpatski, Anatolij, & Lustyk, M. (2020). Solvability, completeness and computational analysis of a perturbed control system with delays. Mathematics and Statistics , 8, 187-200.

Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2020). Non-associative structure of commutative algebras related with quadratic Poisson brackets. European Journal of Mathematics, 6, 21 pages.

Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prkarpatski, Anatolij (2019). Theory of multidimensional Delsarte--Lions transmutation operators. II. Ukranian Mathematics Journal, 71, 921-955.

Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2019). Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics. SIGMA, 15, 20.

Blackmore, Denis, & Addabbo, Raymond (2019). A Dynamical Systems-Based Hierarchy for Shannon, Metric and Topological Entropy. Entropy, 21, 14 pages.

Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2019). Theory of multidimensional Delsarte--Lions transmutation operators. I. Ukrainian Mathematical Journal, 70, 1913-1952.

Blackmore, Denis, & Hentosh, Oksana, & Kyshakevych, Bohdan, & Prykarpatski, Anatolij (2019). New Fractional Nonlinear Integrable Hamiltonian Systems. Applied Mathematics Letters, 88, 41-49.

Blackmore, Denis, & Artemovych, Orest, & Balinsky, Alexander, & Prykarpatski, Anatolij (2018). Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky--Novikov Type Symmetry Algebras and Related Hamiltonian Operators. Symmetry, 10, 28 pages.

Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2018). A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy. Miskolc Math. Notes, 27,

Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2018). Generalized Lie-algebraic structures related to integrable dispersionless dynamical systems and their application. Journal of Mathematical Science and Modelling, 1, 105-130..

Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2018). Examples of Lie and Balinsky--Novikov algebras related to Hamiltonian operators. Topological Algebra and Its Applications/de Gruyter, 6, 43-52.

Blackmore, Denis, & Rahman, Aminur, & Jordan, Ian (2018). Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops. Proceeding of the Royal Society A, 474, 18 pages.

Blackmore, Denis, & Rahman, Aminur, & Joshi, Yogesh (2017). Sigma Map Dynamics and Bifurcations. Regular & Chaotic Dynamics, 22, 740-749.

Blackmore, Denis, & Prykarpatski, Anatolij, & Vovk, M., & Pukach, P., & Prykarpatsky, Yarema (2017). The Pfeiffer-Lax-Sato vector field equations and related integrable versal deformations. Matematychni Studii, 48(2), 124-133.

Singh, Pushpendra, & Benouaguef, I. , & Musunuri, N., & Amah, E., & Blackmore, Denis, & Fischer, Ian (2017). Flow induced on a salt waterbody due to the impingement of a freshwater drop or a water source. Mechanics Research Communications, 85, 89–95.

Blackmore, Denis, & Rahman, Aminur (2017). Threshold voltage dynamics of chaotic RS flip-flops. Chaos, Solitons & Fractals , 103, 555-566.

Blackmore, Denis, & Windows-Yule, C.R.K., & Rosato, Anthony (2017). Energy decay in a tapped granular column: Can a one-dimensional toy model provide insight into fully three-dimensional systems?. Phys. Rev. E, 96, 11.

Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2017). Lie-algebraic structure of Lax—Sato integrable heavenly equations and the Lagrange—d’Alembert principle. J. Geometry & Phys. , 120, 208-227.

Blackmore, Denis, & Soltanov, Kamal, & Prykarpatski, Anatolij (2017). Long-time behavior of solutions and chaos in reaction-diffusion equations . Chaos, Solitons & Fractals, 99, 91-100.

Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2017). Hamiltonian operators and related integrable differential-algebraic Novikov—Leibniz type structures . Asian Journal of Mathematical and Computational Research, 17, 184-203.

Blackmore, Denis, & Rosato, Anthony, & Sen, Surajit, & Wu, Hao (2017). Simulation, modeling and dynamical analysis of multibody flows. International Journal of Modern Physics B, 31, 14 pages.

Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2017). Poisson brackets, Novikov—Leibniz structures and integrable Riemann hydrodynamic systems. Journal of Nonlinear Mathematical Physics , 24, 41-72.

Blackmore, Denis, & Hentosh, Oksana, & Prykarpatski, Anatolij (2017). The novel Lie-algebraic approach to studying integrable heavenly type equations. Journal of Generalized Lie Theory and Applications , 11(3), 19 pages.

Blackmore, Denis, & Rahman, Aminur (2016). Neimark—Sacker bifurcations and evidence of chaos in a discrete dynamical system model of walkers. Chaos, Solitons & Fractals, 91, 339-349.

Rosato, Anthony, & Zuo, Luo, & Blackmore, Denis, & Wu, Hao, & Horntrop, David, & Parker, David, & Windows-Yule, Christopher (2016). Tapped granular column dynamics: simulations, experiments and modeling. Computational Particle Mechanics, 3(3), 333-348.

Blackmore, Denis, & Bogolubov Jr., Nikolai, & Prykarpatsky, Anatoliy (2016). The Lagrangian and Hamiltonian aspects of the electromagnetic vacuum-field theory models. Boson J. Modern Phys. , 2, 92 pages.

Blackmore, Denis, & Rohn, Eli (2015). The augmented unified localizable crisis scale . Technological Forecasting and Social Change , 100, 186-197.

Blackmore, Denis, & Prykarpatsky, Anatoliy, & Özçag, E. , & Soltanov, Kamal (2015). Integrability analysis of a two-component Burgers type hierarchy. Ukr. Math. J., 67, 167- 185.

Blackmore, Denis, & Bogolubov Jr., Nikolai, & Prykarpatsky, Anatoliy (2015). Maxwell--Lorentz electrodynamics models revisited via the Lagrangian formalism and the Feynman proper time paradigm. Mathematics, 3, 190-257.

Blackmore, Denis, & Joshi, Yogesh (2014). Strange attractors for asymptotically zero maps. Chaos, Solitons & Fractals, 68, 123-138.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2014). Dark equations and their light integrability. Journal of Nonlinear Mathematical Physics, 21 , 407-428..

Blackmore, Denis, & Prykarpatsky, Yarema, & Bogolubov (Jr.), Nikolai, & Prykarpatsky, Anatoliy (2014). Integrability of and differential-algebraic structures for spatially 1D hydrodynamics systems of Riemann type. Chaos, Solitons & Fractals, 59, 59-81.

Blackmore, Denis, & Rosato, Anthony, & Tricoche, Xavier, & Urban, Kevin, & Zuo, Luo (2014). Analysis, Simulation, Visualizaiton of 1D Tapping via Reduced Dynamical Systems Models. Physica D, 273-74, 14-27.

Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). Hidden symmetry analysis of Lax integrable nonlinear systems. Applied Mathematics, 4, 96-116.

Blackmore, Denis, & Prykarpatsky, Anatoliy, & Bogolubov (Jr.), Nikolai, & Slawianowski, Jan (2013). Mathematical foundations of the classical Maxwell-Lorentz electrodynamic model via canonical Lagrangian and Hamiltonian. Universal Journal of Physics and Applications, 1(2), 160-178.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2013). New vortex invariants in magneto-hydrodynamics and a related helicity theorem. Chaotic Modeling and Simulation , 2, 239-245.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2013). A new exactly solvable spatially one-dimensional quantum superradiance Fermi-medium model and its quantum solitonic states. Condensed Matter Physics, 16, 1-9.

Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole type transformations. Ukrainian Mathematics Journal, 65(1), 44-57.

Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). A vertex operator representation of solutions to a Gurevich--Zybin hydrodynamical system. Opuscula Mathematica, 33(1), 139-149 .

Blackmore, Denis, & Ratnaswamy, Vish, & Rosato, Anthony, & Tricoche, Xavier, & Ching, Nathaniel, & Zuo, Luo (2012). Evolution of solids fraction surfaces in tapping: Simulation and dynamical systems analysis. Granular Matter, 14, 169-174.

Blackmore, Denis, & Joshi, Yogesh (2012). Exponentially decaying discrete dynamical systems. Recent Patents on Space Tech, 2(1), 37-48.

Ratnaswamy, Vishagan, & Rosato, Anthony, & Blackmore, Denis, & Tricoche, Xavier, & Ching, Nathaniel, & Zuo, Luo (2012). Evolution of Solids Fraction Surfaces in Tapping: Simulation and Dynamic Systems Analysis. Granular Matter, 14, 163-168.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2012). The AKNS hierarchy revisited: A vertex operator approach and its Lie-algebraic structure. J. Nonlinear Math. Phys., 19, 15 pages.

Blackmore, Denis, & Prykarpatsky, Anatoliy, & Prykarpatsky, Yarema (2012). Isospectral integrability analysis of dynamical systems on discrete manifolds. Opuscula Math. , 32(1), 41-66.

Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2011). The AKNS hierarchy and the Gurevich--Zybin dynamical system integrability revisited. Math. Bull. Shevchenko Scientific Soc, 8, 258-282.

Blackmore, Denis, & Rosato, Anthony, & Tricoche, Xavier, & Urban, Kevin, & Ratnaswamy, Vishagan (2011). Tapping dynamics for a column of particles and beyond. J. Mech. Materials & Structures, 6, 71-86 .

Blackmore, Denis, & Urban, Kevin, & Rosato, Anthony (2010). Integrability analysis of regular and fractional Blackmore-Samulyak-Rosato fields. Condensed Matter Physics, 13, 43403: 1-7.

Blackmore, Denis, & Joshi, Yogesh (2010). Bifurcation and chaos in higher dimensional pioneer-climax systems. Int’l. Electronic J. Pure and Appl. Math., 1(3), 303-337.

Blackmore, Denis, & Zhou, J., & Vas, A. (2010). Fractal geometry surface modeling and measurement for musical cymbal surface texture design and rapid manufacturing. Periodical of Key Engineering Materials, 437, 145-149.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2009). A solution set analysis of a nonlinear operator equation using a. Topology, 48, 182-185.

Blackmore, Denis, & Rohn, Eli (2009). A unified localizable emergency events scale. Int. J. Information Sys. for Crisis Response & Management (IJISCRAM), 1(1), 1-14.

Blackmore, Denis, & Wang, Xiaxia, & Wang, Chengwen (2009). The ω-limit sets of a flow and periodic orbits. Chaos, Solitons and Fractals, 41, 2690-2696.

Blackmore, Denis, & Wang, Chengwen, & Wang, Xiaoxia (2009). Upper and lower solutions method for a superlinear Duffing equation. Communications in Applied Nonlinear Analysis, 16, 19-29.

Blackmore, Denis, & Gafiychuk, V., & Datsko, B., & Meleshko, V. (2009). Analysis of the solutions of coupled nonlinear fractional reaction-diffusion equations. Chaos, Solitons and Fractals/Elsevier, 41, 1095-1104.

Blackmore, Denis, & Rahman, A., & Shah, J. (2009). Discrete dynamical modeling and analysis of the R-S flip-flop circuit. Chaos, Solitons and Fractals/Elsevier, 42, 951-963.

Blackmore, Denis, & Brons, Morten, & Goullet, Arnaud (2008). A coaxial vortex ring model for vortex breakdown. Physica D/Elsevier, 237, 2817-2844.

Rosato, Anthony, & Blackmore, Denis, & Buckley, Liam, & Oshman, Christopher, & Johnson, Mark (2004). Experimental, Simulation and Nonlinear Dynamics Analysis of Galton’s Board. International Journal of Nonlinear Sciences and Numerical Simulation , 5(4), 289-312.

Rosato, Anthony, & Blackmore, Denis, & Zhang, Ninghua, & Lan, Yidan (2002). A Perspective of Vibration-Induced Size Segregation of Granular Materials. Chemical Engineering Science, 57(2), 265-275.

Blackmore, Denis, & Samulyak, Roman, & Rosato, Anthony (2001). Chaos in Vibrating Granular Flows. Dynamic Systems and Applications, 3, 77-84.

Blackmore, Denis, & Samulyak, Roman, & Rosato, Anthony New Mathematical Models for Particle Flow Dynamics. Journal of Nonlinear Mathematical Physics, 6(2), 198-221.

Dynamical Systems-Simulation-Visualization Approach to Tapping and Other Granular Flow Phenomena: First Steps
Proc. NSF CMMI Grantees Conference, Jan. 4-7, 2011, January (1st Quarter/Winter) 2011

Analysis of a nonlinear operator equation using a Leray-Schauder type theorem point approach
Proc. Workshop on Infinite Dimensional Functional Analysis and Topology (IDAT), Yaremczha City, Ukraine, Sept., 2009, October (4th Quarter/Autumn) 2009

Two-vortex models for vortex breakdown
ASME Conference Journal/ASME/DSCC, June 2009

Dynamics of planar vortex clusters with binaries
PAMM/GAMM/ICIAM'07, December 2008

Invariant tori in perturbed three vortex motion
PAMM/GAMM/ICIAM'07, December 2008