Abstract Let $E/\mathbb {Q}$ be an elliptic curve. For a prime p of good reduction, let $r(E,p)$ the smallest non-negative integer that gives x -coordinate point maximal order in group $E(\mathbb {F}_p)$ . We prove unconditionally $r(E,p)> 0.72\log \log p$ for infinitely many , and 0.36 under assumption Generalized Riemann Hypothesis. These can viewed as curve analogues classical lower bound...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

We propose the interaction of two quantum memristors via capacitive and inductive coupling in feasible superconducting circuit architectures. In this composed system input gets correlated time, which changes dynamic response each memristor terms its pinched hysteresis curve nontrivial entanglement. sense, concurrence memristive dynamics follow an inverse behavior, showing maximal values entangl...

In this paper we exhibit some examples of non-Gorenstein Hecke algebras, and hence some modular forms for which mod 2 multiplicity one does not hold. Define S2(Γ0(N)) to be the space of classical cuspidal modular forms of weight 2, level N , and trivial character. The Hecke algebra TN is defined to be the subring of End(S2(Γ0(N)) generated by the Hecke operators {Tp : p 6 |N} and {Uq : q|N}. Le...

Pulmonary function was investigated in 31 consecutive patients with relatively severe Parkinson's disease. Clinical disability was assessed by Hoehn and Yahr scale, Northwestern University Disability Scale and Websterscore. All patients were on levodopa substitution therapy and used anticholinergics. Pulmonary function was investigated by spirography, determination of a maximal inspiratory and ...

In normal subjects in vivo the dose-response curve to inhaled nonsensitizing stimuli reaches a plateau at mild degrees of airway narrowing. We investigated whether the limitation of the response is due to non-optimal smooth muscle activation, by administering high doses of histamine and methacholine together. In fifteen normal subjects a complete dose-response curve to methacholine was recorded...

Ciprofloxacin has a four-fold greater in-vitro activity than levofloxacin against Pseudomonas aeruginosa, but levofloxacin has a four-fold higher area under the serum concentration-time curve (AUC) for an equivalent dose. It has been proposed that the AUC/MIC ratio is a general predictor of antibacterial efficacy for quinolones. Using an in-vitro kill curve technique, performed in quadruplicate...