This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics.
The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas.
V. Abramov, Weil algebra, 3-Lie algebra and B.R.S. algebra.- V. Abramov, R. Kerner, and O. Liivapuu, Algebras with ternary composition law combining Z2 and Z3 gradings.- V. Abramov and P. Lätt, Ternary Lie Superalgebras and Nambu-Hamilton Equation in Superspace.- A. Ben Abdeljelil, M. Elhamdadi, I. Kaygorodov, and A. Makhlouf, Generalized Derivations of n-BiHom-Lie algebras.- A. Kitouni, A. Makhlouf and S. Silvestrov, On n-ary generalization of BiHom-Lie algebras and BiHomassociative algebras.- A. Kitouni, A. Makhlouf and S. Silvestrov, On solvability and nilpotency for (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras.- I. Bakayoko and S. Silvestrov, Multiplicative n-Hom-Lie color algebras.- A. Makhlouf and M. Mehidi, On classification of Filiform Hom-Lie algebras.- E. Ongong'a, Johan Richter, and S. Silvestrov, Classification of low-dimensional Hom-Lie algebras.- A. Armakan and S. Silvestrov, Enveloping algebras of certain types of color hom-Lie algebras.- S. K. Mishra and S. Silvestrov, A Review on Hom-Gerstenhaber algebras and Hom-Lie algebroids.- L. Hellström, Strong Hom-associativity.- Tianshui Ma, S. Silvestrov, and H. Zheng, On Hom-Yetter-Drinfeld category.- I. R. Churchill, M. Elhamdadi and N. Van Kempen, On the classification of f - quandles.- P. Nystedt, Noncommutatively graded algebras.- A. Dimakis and F. Müller-Hoissen, Differential Calculi on Associative Algebras and Integrable Systems.- V. V. Bavula, The Jacobian Conjecture2 n implies the Dixmier Problem n.- A. B. Tumwesigye, J. Richter, S. Silvestrov, Commutants in crossed product algebras for piecewise constant functions on the real line.- A. B. Tumwesigye, J. Richter, S. Silvestrov, Ore extensions of functional algebras.- A. B. Tumwesigye, J. Richter, S. Silvestrov, Centralizers in PBW Extensions.- J. Musonda, S. Kaijser, and S. Silvestrov, Reordering, centralizers and centers in an algebra with three generators and Lie type relations.- J. Musonda, J. Richter, and S. Silvestrov, Reordering in noncommutative algebras associated with iterated function systems.- J. Musonda, J. Richter, and S. Silvestrov, Twisted difference operator representations of deformed Lie type commutation relations.- R. R. Cantuba and S. Silvestrov, Torsion-type q-deformed Heisenberg algebra and its Lie polynomials.- R. R. Cantuba, S. Silvestrov, Lie polynomial characterization problems.- S. Silvestrov, P. M. Rajkovic, S. D. Marinkovic, and M. S. Stankovic.- Relations Between the Fractional Operators in q-Calculus.- T. Ernst, On the exponential and trigonometric q;w-special functions.- M. Mitrovic and S. Silvestrov, Isomorphism theorems for basic constructive algebraic structures with special emphasize on constructive semigroups with apartness -an overview.- M. Mitrovic and S. Silvestrov, Semilatice decompositions of semigroups. Hereditariness and periodicity - an overview.- T. Nazir and S. Silvestrov, Common Fixed Point for Integral Type Contractive Mappings in Multiplicative Metric Spaces.- T. Nazir and S. Silvestrov, Cyclic Contractions and Common Fixed Point Results of Integral Type Contractions in Multiplicative Metric Spaces.- K. Lundengård, J. Österberg, S. Silvestrov, Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinant.- A. K. Muhumuza, K. Lundengård, J. Österberg, S. Silvestrov, J. M. Mango and G. Kakuba, Extreme Points of the Vandermonde Determinant on Surfaces Implicitly Determined by a Univariate Polynomial.- A. K. Muhumuza, K. Lundengård, J. Österberg, S. Silvestrov, J. M. Mango, and G. Kakuba, Optimization of the Wishart joint eigenvalue probability density distribution based on the Vandermonde determinant.- A. Malyarenko, H. Nohrouzian, and S. Silvestrov, An algebraic method for pricing financial instruments on post-crisis market.- B. Canhanga, A. Malyarenko, J.-P. Murara, Y. Ni and S. Silvestrov, Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities.- C. Nhangumbe, E. Fredericks and B. Canhanga, Lie Symmetry Analysis on Pricing Weather Derivatives by Partial Differential Equations.- D. Silvestrov, S. Silvestrov, B. Abola, P. S. Biganda, C. Engström, J. M. Mango and G. Kakuba, Perturbation analysis for stationary distributions of Markov chains with damping component.- M. Dogan, Uniqueness of p-adic Gibbs measures for p-adic l-Ising model on Cayley Tree of arbitrary order.- I. Chandarki and B. Singh, On Pade Approximants Series Solutions of MHD Flow Equations with Heat and Mass Transfer Due to a Point Sink.- Index.