in this paper, we consider the finitely 2-generated groups k(s,l) and g_m as follows:k(s,l) = ;g_m = and find the explicit formulas for the probability of having nth-roots for them. also weinvestigate integers n for which, these groups are n-central.

We analyze Neuberger’s double pass algorithm for the matrix-vector multiplication R(H) · Y (where R(H) is (n − 1, n)-th degree rational polynomial of positive definite operator H), and show that the number of floating point operations is independent of the degree n, provided that the number of sites is much larger than the number of iterations in the conjugate gradient. This implies that the ma...

In this paper, first we introduce the notions of k-nilpotent (solvable) ideals and BCK-algebras. Specially, show that every commutative ideal is 1-nilpotent (solvable). Second, state an equivalent condition to k-nilpotency (solvablity) BCK-algebra. Finally, study n-fold 2-nilpotent BCK-algebras as a generalization BCK-algebras, relation between these two concepts. Basically, compare solvable (B...

Xavier Gourdon and Pascal Sebah February 12, 2003 Is it possible to compute directly the n-th digit of π without computing all its first n digits ? At first sight, the problem seems of the same complexity. Recently [1], a formula which permits to find directly the n-th bit of π with very little memory and in quasi-linear time was exhibited. In other words, the question has a positive answer in ...

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...

In 2004, Csörgő constructed a loop of nilpotency class three with abelian group of inner mappings. As of now, no other examples are known. We construct many such loops from groups of nilpotency class two by replacing the product xy with xyh in certain positions, where h is a central involution. The location of the replacements is ultimately governed by a symmetric trilinear alternating form. c ...

OBJECTIVE To investigate the factors affecting rehabilitation outcomes in children with congenital muscular torticollis (CMT). METHODS We retrospectively reviewed the medical records of 347 patients who were clinically suspected as having CMT and performed neck ultrasonography to measure sternocleidomastoid (SCM) muscle thickness. Fifty-four patients met the inclusion criteria. Included were ...

Let Fq be the finite field with q elements and let ! be a primitive n-th root of unity in an extension eld Fqd of Fq. Given a polynomial P 2 Fq[x] of degree less than n, we will show that its discrete Fourier transform (P (1); P (!); :::; P (!n¡1)) 2Fqd n can be computed essentially d times faster than the discrete Fourier transform of a polynomial Q 2 Fqd[x] of degree less than n, in many case...

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...