After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...

A perfect algebraic immune function is a Boolean function with perfect immunity against algebraic and fast algebraic attacks. The main results are that for a perfect algebraic immune balanced function the number of input variables is one more than a power of two; for a perfect algebraic immune unbalanced function the number of input variables is a power of two. Also the Carlet-Feng functions on...

If X is a Minkowski space, i.e. a finite dimensional real normed space, then S ⊂ X is an equilateral set if all pairs of points of S determine the same distance with respect to the norm. Kusner conjectured that e(`p) = d +1 for 1 < p < ∞ and e(`1) = 2d [6]. Using a technique combining linear algebra and approximation theory, we prove that for all 1 < p < ∞, there exists a constant Cp > 0 such t...

Let X be an algebraic variety over a finite field Fq, homogeneous under a linear algebraic group. We show that there exists an integer N such that for any positive integer n in a fixed residue class mod N , the number of rational points of X over Fqn is a polynomial function of q with integer coefficients. Moreover, the shifted polynomials, where q is formally replaced with q +1, have non-negat...

We outline three principles that should guide us in the construction of a theory of canonical quantum gravity: 1) di eomorphism invariance, 2) implementing the proper dynamics and related constraint algebra, 3) local Lorentz invariance. We illustrate each of them with its role in model calculations in loop quantum gravity. ∗ Corresponding author. Email: [email protected]. Tel/Fax: +1 225 578 0464.

The algebra of O(3, 3) is contracted to that of E(2)-like groups in the infinite-momentum limit. It is shown through this process that there are 18 different possibilities for the representations of E(2)-like algebra if they are to be expressed in terms of Dirac γmatrices. It is also pointed out that the generators of this algebra are independent of the particular representation of the γ-matric...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

A new “non-standard” quantization of the universal enveloping algebra of the split (natural) real form so(2, 2) of D2 is presented. Some (classical) graded contractions of so(2, 2) associated to a Z2 × Z2 grading are studied, and the automorphisms defining this grading are generalized to the quantum case, thus providing quantum contractions of this algebra. This produces a new family of “non-st...

We consider fragments of first-order logic and as models we allow finite and infinite words simultaneously. The only binary relations apart from equality are order comparison < and the successor predicate +1. We give characterizations of the fragments Σ2 = Σ2[<,+1] and FO2 = FO2[<,+1] in terms of algebraic and topological properties. To this end we introduce the factor topology over infinite wo...