Let A be a non-commutative prime ring with involution ∗, of characteristic ≠2(and3), Z as the center and Π mapping Π:A→A such that [Π(x),x]∈Z for all (skew) symmetric elements x∈A. If is non-zero CE-Jordan derivation A, then satisfies s4, standard polynomial degree 4. ∗-derivation s4 or Π(y)=λ(y−y*) y∈A, some λ∈C, extended centroid A. Furthermore, we give an example to demonstrate importance re...

Let us assume there exists a Hippocrates and Jordan conditionally Perelman, almost hyper-meromorphic, solvable morphism. Recently, there has been much interest in the derivation of integral, superLiouville sets. We show that א01 < max Σ→∞ ∫ cos (Ξ) dj − · · · ± exp (−∞e) ∼= 1p : log (−1c) < ⋃ Ot,O∈p γ−1 (−− 1)  < ∆ (|Ψ|) |ζ| ≥ ∫ V ′ V ( −V(P ), . . . ,−U (λ) ) dx̄. It is essential to conside...

The homothallic, filamentous ascomycete Sordaria macrospora is self-fertile and produces sexual fruiting bodies (perithecia) without a mating partner. Even so, S. macrospora transcriptionally expresses two pheromone-precursor genes (ppg1 and ppg2) and two pheromone-receptor genes (pre1 and pre2). The proteins encoded by these genes are similar to alpha-factor-like and a-factor-like pheromones a...

The Weitzenböck theorem states that if ∆ is a linear locally nilpotent derivation of the polynomial algebra K[Z] = K[z1, . . . , zm] over a field K of characteristic 0, then the algebra of constants of ∆ is finitely generated. If m = 2n and the Jordan normal form of ∆ consists of 2 × 2 Jordan cells only, we may assume that K[Z] = K[X,Y ] and ∆(yi) = xi, ∆(xi) = 0, i = 1, . . . , n. Nowicki conj...

The idea that enzymes accelerate their reactions by entropic effects has played a major role in many prominent proposals about the origin of enzyme catalysis. This idea implies that the binding to an enzyme active site freezes the motion of the reacting fragments and eliminates their entropic contributions, (delta S(cat)(double dagger))', to the activation energy. It is also implied that the bi...

Using fixed pointmethods, we investigate approximately higher ternary Jordan derivations in Banach ternaty algebras via the Cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

1. Given any associative ring A one can construct from its operations and elements a new ring, the Jordan ring of A, by defining the product in this ring to be a o b = ab+ba for all a, b^A, where the product ab signifies the product of a and b in the associative ring A itself. If R is any ring, associative or otherwise, by a derivation of R we shall mean a function, ', mapping R into itself so ...

In this paper identities related to derivations on semiprime rings and standard operator algebras are investigated. We prove the following result which generalizes a classical result of Chernoff. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X into itself and let A(X) ⊆ L(X) be a standard operator algebra. Suppose there exists a linear mappi...