let $g$ be a finite $p$-soluble group‎, ‎and $p$ a sylow $p$-sub-group of $g$‎. ‎it is proved‎ ‎that if all elements of $p$ of order $p$ (or of order ${}leq 4$ for $p=2$) are‎ ‎contained in the $k$-th term of the upper central series of $p$‎, ‎then the $p$-length of‎ ‎$g$ is at most $2m+1$‎, ‎where $m$ is the greatest integer such that‎ $p^m-p^{m-1}leq k$‎, ‎and the exponent of the image of $p$...

Let K be a totally real number field and consider Fermat-type equation A p + B b q = C c r $Aa^p+Bb^q=Cc^r$ over K. We call the triple of exponents ( , ) $(p,q,r)$ signature equation. prove various results concerning solutions to Fermat with 2 $(p,p,2)$ 3 $(p,p,3)$ using method involving modularity, level lowering image inertia comparison. These generalize extend recent work I?ik, Kara Özman. F...

In radiotherapy, only a few immobilization systems, such as open-face mask and head mold with a bite plate, are available for claustrophobic patients with a certain degree of discomfort. The purpose of this study was to develop a remote-controlled and self-contained audiovisual (AV)-aided interactive system with the iPad mini with Retina display for intrafractional motion management in brain/H&...

Since the pioneering work of Fatt and Katz at the neuromuscular junction (NMJ), spontaneous synaptic release (minis), that is, the quantal discharge of neurotransmitter molecules which occurs in the absence of action potentials, has been unanimously considered a memoryless random Poisson process where each quantum is discharged with a very low release probability independently from other quanta...

In this paper, we establish a lower bound on the number of inducing simple n-gons in grid-like arrangements of lines. We also show that the complexity associated with counting the number of inducing n-gons in an arrangement of collinear segments is #P-complete.

We investigate the power of non-deterministic circuits over restricted sets of base gates. We note that the power of non-deterministic circuits exhibit a dichotomy, in the following sense: For weak enough bases, non-deterministic circuits are no more powerful than deterministic circuits, and for the remaining bases, non-deterministic circuits are super polynomial more efficient than determinist...

In this paper we consider three restricted variants of P systems with active membranes: (1) P systems using out communication rules only, (2) P systems using elementary membrane division and dissolution rules only, and (3) polarizationless P systems using dissolution and restricted evolution rules only. We show that every problem in P can be solved with uniform families of any of these variants...

a $p$-group $g$ is $p$-central if $g^{p}le z(g)$‎, ‎and $g$ is‎ ‎$p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,yin‎ ‎g$‎. ‎we prove that for $g$ a finite $p^{2}$-abelian $p$-central‎ ‎$p$-group‎, ‎excluding certain cases‎, ‎the order of $g$ divides the‎ ‎order of $text{aut}(g)$‎.