The aim of this work is to introduce and study the notions Hom-pre-Jordan algebra Hom-J-dendriform which generalize Hom-Jordan algebras. algebras are regarded as underlying algebraic structures behind Rota-Baxter operators O-operators introduced in paper. also analogues Hom-pre-Lie for anti-commutator a left multiplication operator gives representation algebra. On other hand, analogue Hom-dendr...

While the leftmost-innermost narrowing algorithm is incomplete, basic narrowing contains redundancies. We remove these redundancies by introducing a new narrowing procedure, called left-to-right basic narrowing algorithm. For each leftmost-innermost rewriting derivation from (s), there is an equivalent left-to-right basic rewriting derivation , which in turn can be projected on a left-to-right ...

In this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and Also investigate the Hyers-Ulam-Rassiasstability of n-jordan *-homomorphisms on C*-algebras.

We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let A be a Banach algebra and X a Banach A-module, f : X → X and g : A → A. The mappings Δ1 f,g , Δ2 f,g , Δ3 f,g , and Δ4 f,g are defined and it is proved that if ‖Δ1 f,g x, y, z,w ‖ resp., ‖Δ3 f,g x, y, z,w, α, β ‖ is dominated by φ x, y, z,w , then f is a generalized re...

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...

In 1909, Einstein derived a formula for the mean square energy fluctuation in blackbody radiation. This formula is the sum of a wave term and a particle term. In a key contribution to the 1926 Dreimännerarbeit with Born and Heisenberg, Jordan showed that one recovers both terms in a simple model of quantized waves. So the two terms do not require separate mechanisms but arise from a unified dyn...

The separating space of a derivation onA is a separating ideal [2, Chapter 5]; it also satisfies the same property for the left products. The following assertions are of the most famous conjectures about derivations on Banach algebras: (C1) every derivation on a Banach algebra has a nilpotent separating ideal; (C2) every derivation on a semiprime Banach algebra is continuous; (C3) every derivat...