It is well known, and was first proved by Sylow (1872), that every group of prime-power order p has a presentation of the form {a1, . . . , an | api = vii, 1 ≤ i ≤ n, [ak, aj ] = vjk, 1 ≤ j < k ≤ n}, where vjk is a word in the elements ak+1, . . . , an for 1 ≤ j ≤ k ≤ n . A presentation of this form is now called a power-commutator presentation for the group and written briefly {A | R} . As was...

input frequency is one of the important variables in design and performance analysis of single-sided linear induction motors (slims). changing the frequency changes both the dimension of the slim in design process and the performance of the designed motor. the frequency influences the induced eddy currents in the secondary sheet as well as saturation level of the secondary back-iron. in this pa...

The conversion or photo conversion of asphaltenes to polycyclic aromatic hydrocarbons (PAH’s) promoted by a laser source is analyzed using both experimental and theoretical methods. We propose that during measurements performed at an intermediate laser power, fragmentation to afford PAH’s and ring fusion to yield fused PAH’s (FPAH’s) may occur either within molecular clusters (resin case) or wi...

LetN be a normal subgroup of a groupG and let p be a prime. We prove that if the p-part of jx j is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.

Let {Xn, n ≥ 1} be independent and identically distributed random variables with each Xn following skew normal distribution. Let Mn = max{Xk, 1 ≤ k ≤ n} denote the partial maximum of {Xn, n ≥ 1}. Liao et al. (2014) considered the convergence rate of the distribution of the maxima for random variables obeying the skew normal distribution under linear normalization. In this paper, we obtain the a...

It was proved in [1] that lower and upper powerdomain constructions commute on all domains. In that proof, domains were represented as information systems. In [2] a rather complicated algebraic proof was given which relied on universality properties of powerdomains proved in the previous works of the author of [2]. Here we give an elementary algebraic proof that upper and lower powerdomain cons...