The main purpose of this article is to offer some characterizations of $delta$-double derivations on rings and algebras. To reach this goal, we prove the following theorem:Let $n > 1$ be an integer and let $mathcal{R}$ be an $n!$-torsion free ring with the identity element $1$. Suppose that there exist two additive mappings $d,delta:Rto R$ such that $$d(x^n) =Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+Si...

In this paper, using Clarke’s generalized directional derivative and dI-invexity we introduce new concepts of nonsmooth K-α-dI-invex and generalized type I univex functions over cones for a nonsmooth vector optimization problem with cone constraints. We obtain some sufficient optimality conditions and Mond-Weir type duality results under the foresaid generalized invexity and type I cone-univexi...

The notion of a signed measure arises if a measure is allowed to take on both positive and negative values. A set that is both positive and negative with respect to a signed measure is termed as a null set. Some concepts in measure theory can be generalized by means of classes of null sets. An abstract formulation and proof of the Lebesgue decomposition theorem using the concept of null sets is...

Participants pressed computer keys to keep a moving dot stimulus within a rectangle, either alone or with a partner they could neither see nor hear. Pressing the A-key or L-key caused the dot to move right or left, respectively, for as long as the key was pressed. Switching between the A and L keys (i.e., turning) proved challenging: concurrently pressing both keys made the stimulus move upward...

Let g be a finite dimensional Lie algebra over a field k of characteristic zero. An element x of g is said to have an abstract Jordan-Chevalley decomposition if there exist unique s, n ∈ g such that x = s + n, [s, n] = 0 and given any finite dimensional representation π : g → gl(V ) the Jordan-Chevalley decomposition of π(x) in gl(V ) is π(x) = π(s) + π(n). In this paper we prove that x ∈ g has...

Curado and Rego-Monteiro introduced in [2] a new algebraic structure generalizing the Heisenberg algebra and containing also the q-deformed oscillator as a particular case. This algebra, called generalized Heisenberg algebra, depends on an analytical function f and the eigenvalues αn of the Hamiltonian are given by the one-step recurrence αn+1 = f(αn). This structure has been used in different ...