In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. We show that the splicing algebras are an n-ary envelope for algebras of DNA recombinati...

In this paper, we consider the finitely 2-generated groups $K(s,l)$ and $G_m$ as follows:$$K(s,l)=langle a,b|ab^s=b^la, ba^s=a^lbrangle,\G_m=langle a,b|a^m=b^m=1, {[a,b]}^a=[a,b], {[a,b]}^b=[a,b]rangle$$ and find the explicit formulas for the probability of having nth-roots for them. Also, we investigate integers n for which, these groups are n-central.

We pose the question of determining the lowest-degree polynomial with nonnegative coefficients divisible by the n-th cyclotomic polynomial Φn(x). We show this polynomial is 1+x+· · ·+x where p is the smallest prime dividing n whenever 2/p > 1/q1+· · ·+1/qk, where q1, . . . , qk are the other (distinct) primes besides p dividing n. Determining the lowestdegree polynomial with nonnegative coeffic...

The maximumof the degree of nonholonomy of the control system attached to a kinematic model for the car with n trailers is F n+3 where F n is the n th term of the Fibonacci's sequence (F 0 = 0; F 1 = 1; F n+2 = F n+1 + F n ; n 0). This value is obtained if and only if each trailer (except for the last one) is perpendicular to the previous one.

In this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $M$-hyponormal operator‎. ‎We show that every analytic extension of a $n$th roots of $M$-hyponormal operator is subscalar of order $2k+2n$‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator $T$ has a nonempty interior in $mathbb{C}$‎, ‎then $T$ has a nontrivial invariant subspace‎. ‎Finally‎, ‎w...

Non-commutative gauge theory with a non-constant non-commutativity parameter can be formulated as a decoupling limit of open strings ending on D3-branes wrapping a Melvin universe. We construct the action explicitly and discuss various physical features of this theory. The decoupled field theory is not supersymmetric. Nonetheless, the Coulomb branch appears to remain flat at least in the large ...