There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplic...

We study the graded derivation-based noncommutative differential geometry of the Z2-graded algebra M(n|m) of complex (n+m)× (n+m)-matrices with the “usual block matrix grading” (for n 6= m). Beside the (infinite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated. In...

The N-point moving average (NPMA) is a mathematical low-pass filter that can smooth peaked noninvasively acquired radial pressure waveforms to estimate central aortic systolic pressure using a common denominator of N/4 (where N=the acquisition sampling frequency). The present study investigated whether the NPMA method can be applied to brachial pressure waveforms. In the derivation group, simul...

Usually, a parser for an LR(k)-grammar G is a deterministic pushdown transducer which produces backwards the unique rightmost derivation for a given input string x ∈ L(G). The best known upper bound for the size of such a parser is O(2|G||Σ| +k log |Σ|+log |G|) where |G| and |Σ| are the sizes of the grammar G and the terminal alphabet Σ, respectively. If we add to a parser the possibility to ma...

a unital $c^*$ -- algebra $mathcal a,$ endowed withthe lie product $[x,y]=xy- yx$ on $mathcal a,$ is called a lie$c^*$ -- algebra. let $mathcal a$ be a lie $c^*$ -- algebra and$g,h:mathcal a to mathcal a$ be $bbb c$ -- linear mappings. a$bbb c$ -- linear mapping $f:mathcal a to mathcal a$ is calleda lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

Let m,n, r be nonzero fixed positive integers, R a 2-torsion free prime ring, Q its right Martindale quotient ring, and L a non-central Lie ideal of R. Let D : R −→ R be a skew derivation of R and E(x) = D(xm+n+r)−D(xm)xn+r − xmD(xn)xr − xm+nD(xr). We prove that if E(x) = 0 for all x ∈ L, then D is a usual derivation of R or R satisfies s4(x1, . . . , x4), the standard identity of degree 4.

We prove that the automorphisms of the generalized Witt Lie algebras W(m , n) over arbitrary commutative rings of characteristic p > 3 all come from automorphisms of the algebras on which they are defined as derivations. By descent theory, this result then implies that if a Lie algebra over a field becomes isomorphic to W{m, n) over the algebraic closure, it is a derivation algebra of the type ...

We here give a first indication that there exists a Seiberg-Witten curve for SU(N) Seiberg-Witten theory with matter transforming in the totally antisymmetric rank three tensor representation. We present a derivation of the leading order hyperelliptic approximation of a curve for this case. Since we are only interested in the asymptotic free theory we are restricted to N = 6, 7, 8. The derivati...

We give a bijection between N/S/E/W walks and N/S walks that remain on one side of the origin and also a simple derivation of the enumeration of the former, based on Touchard’s identity.