The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type enclosing n-ary Nambu algebras, n-ary Nambu-Lie algebras, n-ary Lie algebras, and n-ary algebras of associative type enclosing n-ary totally associative and n-ary partially associative algebras. Also, we provide a way to construct examples starting… (More)
A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α, β : A → A such that α(a)(bc) = (ab)β(c), for all a, b, c ∈ A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and… (More)
Applying the averaging theory of first and second order to a class of generalized polynomial Liénard differential equations, we improve the known lower bounds for the maximum number of limit cycles that this class can exhibit.
In this paper some fixed point principle is applied to prove, in a separable Banach space, the existence of solutions for delayed second order differential inclusions with three-point boundary conditions of the form ¨ u(t) ∈ F (t, u(t), u(h(t)), ˙ u(t)) + H(t, u(t), u(h(t)), ˙ u(t)) a.e. t ∈ [0, 1], where F is a convex valued multifunction upper semi… (More)
Let B ⊆ A be an H-Galois extension. If M is a Hopf bimodule then HH * (A, M), the Hochschild homology of A with coefficients in M , is a right comodule over the coalgebra C H = H/[H, H]. Given an injective left C H-comodule V , our aim is to investigate the relationship between HH * (A, M) CH V and HH * (B, M CH V). The roots of this problem can be found in… (More)