We introduce a new class of simple Lie algebras W (n, m) (see Definition 1) that generalize the Witt algebra by using " exponential " functions, and also a subalgebra W * (n, m) thereof; and we show each derivation of W * (1, 0) can be written as a sum of an inner derivation and a scalar derivation (Theorem. 2) [10]. The Lie algebra W (n, m) is Z-graded and is infinite growth [4].

Extracytoplasmic function (ECF) sigma factors constitute a diverse family of proteins, within the class of the sigma 70 subunit of RNA polymerase. Most members of the family studied to date are known to regulate gene expression in response to stress conditions. The Bacillus subtilis genome encodes at least 17 distinct sigma factors, seven of which are members of the ECF subfamily. Among these, ...

Let A1 = K〈X,Y | [Y,X] = 1〉 be the (first) Weyl algebra over a field K of characteristic zero. It is known that the set of eigenvalues of the inner derivation ad(Y X) of A1 is Z. Let A1 → A1, X 7→ x, Y 7→ y, be a K-algebra homomorphism, i.e. [y, x] = 1. It is proved that the set of eigenvalues of the inner derivation ad(yx) of theWeyl algebra A1 is Z and the eigenvector algebra of ad(yx) is K〈x...

The sleep electroencephalogram (EEG) was recorded from anterior (Fz/Cz) and posterior (Pz/Oz) bipolar derivations in two developmental groups: 20 pre- or early pubertal (Tanner 1/2, mean age 11.4 +/- 1.1 years, 11 boys) and 20 late pubertal or mature adolescents (Tanner 4/5, 14.1 +/- 1.3 years, 8 boys). A sleep-state independent reduction of EEG power over almost the entire frequency range was ...

The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to Tduality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backg...

In this paper we study the Lie algebras of derivations two-step nilpotent algebras. We obtain a class with trivial center and abelian ideal inner derivations. Among these, relations between complex real case indecomposable Heisenberg Leibniz are thoroughly described. Finally show that every almost derivation algebra one-dimensional commutator ideal, three exceptions, is an derivation.

This article concerns the blow up behavior for Henon type parabolic equation withexponential nonlinearity, $$ u_t=\Delta u+|x|^{\sigma}e^u\quad \text{in } B_R\times \mathbb{R}_+, where \(\sigma\geq 0\) and \(B_R=\{x\in\mathbb{R}^N: |x|<R\}\).We consider all cases in which blowup of solutions occurs, i.e. \(N\geq 10+4\sigma\).Grow rates are established by a certain matching different asymptot...

In this note we propose a definition of inner derivation for nonassociative algebras. This definition coincides with the usual one for Lie algebras, and for associative algebras with no absolute right (left) divisor of zero. I t is well known that all derivations of semi-simple associative or Lie algebras over a field of characteristic zero are inner. Recent correspondence with N. Jacobson has ...

For primes p>3 we produce a new derivation of the universal p-adic sigma function and Weierstrass zeta functions Mazur Tate for elliptic curves with good ordinary or multiplicative reduction by method that highlights congruences among coefficients in Laurent expansions functions, works simultaneously generalized defined equations.