A positive integer n is called a square-free number if it is not divisible by a perfect square except 1. Let p be an odd prime. For n with (n, p) = 1, the smallest positive integer f such that n^{f} ≡ 1 (mod p) is called the exponent of n modulo p. If the exponent of n modulo p is p − 1, then n is called a primitive root mod p. Let A(n) be the characteristic function of the square-free primitive roots modulo p. In this paper we study the distribution \sum\limits_{n \leqslant x} {A(n)A(n + 1)} and give an asymptotic formula by using properties of character sums., Huaning Liu, Hui Dong., and Obsahuje seznam literatury
Příspěvek navrhuje varianty transkripce výslovnosti českých slov pro rodilé mluvčí angličtiny. Tento okrajový problém nabývá na důležitosti s rostoucím počtem anglicko-českých konverzačních příruček a učebnic a jeví se jako kompromis mezi anglickým pravopisem pro češtinu použitelných nebo modifikovaných sekvencí anglických fonémů, speciálními symboly a praktičností transkripce.
We prove that the one-parameter group of holomorphic automorphisms induced on a strictly geometrically bounded domain by a biholomorphism with a model domain is parabolic. This result is related to the Greene-Krantz conjecture and more generally to the classification of domains having a non compact automorphisms group. The proof relies on elementary estimates on the Kobayashi pseudo-metric., François Berteloot, Ninh Van Thu., and Obsahuje seznam literatury
For any positive integer $D$ which is not a square, let $(u_1,v_1)$ be the least positive integer solution of the Pell equation $u^2-Dv^2=1,$ and let $h(4D)$ denote the class number of binary quadratic primitive forms of discriminant $4D$. If $D$ satisfies $2\nmid D$ and $v_1h(4D)\equiv0 \pmod D$, then $D$ is called a singular number. In this paper, we prove that if $(x,y,z)$ is a positive integer solution of the equation $x^y+y^x=z^z$ with $2\mid z$, then maximum $\max\{x,y,z\}<480000$ and both $x$, $y$ are singular numbers. Thus, one can possibly prove that the equation has no positive integer solutions $(x,y,z)$., Xiaoying Du., and Obsahuje bibliografické odkazy
We are concerned with the problem of differentiability of the derivatives of order m + 1 of solutions to the “nonlinear basic systems” of the type {\left( { - 1} \right)^m}\sum\limits_{\left| \alpha \right| = m} {{D^\alpha }{A^\alpha }\left( {{D^{\left( m \right)}}u} \right)} + \frac{{\partial u}}{{\partial t}} = 0\;in\;Q. We are able to show that {D^\alpha }u \in {L^2}\left( { - a,0,{H^\partial }\left( {B\left( \sigma \right),{\mathbb{R}^N}} \right)} \right),\;\left| \alpha \right| = m + 1, for \partial\in \left ( 0,1/2 \right )and this result suggests that more regularity is not expectable., Roberto Amato., and Obsahuje seznam literatury
For a finite group $G$, the intersection graph of $G$ which is denoted by $\Gamma(G)$ is an undirected graph such that its vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H\cap K\neq1$. In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of
${\rm Aut}(\Gamma(G))$., Hossein Shahsavari, Behrooz Khosravi., and Obsahuje bibliografii
For any positive integer k ≥ 3, it is easy to prove that the k-polygonal numbers are an(k) = (2n+n(n−1)(k−2))/2. The main purpose of this paper is, using the properties of Gauss sums and Dedekind sums, the mean square value theorem of Dirichlet L-functions and the analytic methods, to study the computational problem of one kind mean value of Dedekind sums S(an(k)ām(k), p) for k-polygonal numbers with 1 ≤ m, n ≤ p − 1, and give an interesting computational formula for it., Jing Guo, Xiaoxue Li., and Obsahuje seznam literatury
The study of the bulla from 18 lemaeopodid copepod species collected on 15 marine fish species and one freshwater fish species taken mainly from the Gulf of Lions in the Mediterranean Sea reveals a great morphological and structural variability. It is however possible to bring forth three general remarks: - the bulla of Lernaeopodidae parasites of Selachii have a remarkably constant structure probably due to the tegument nature of the attachment substratum; - the bulla of Lernaeopodidae parasites of Teleostei has a morphology influenced by the nature of the attachment tissue; - when species of a same genus (i.e. Clavellotis) are attached on a same organ, the shape of the bulla can constitute a taxonomic characteristic.
We prove and discuss some new (Hp,Lp)-type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients {q_{k}:k\geqslant 0}. These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of general Nörlund means tn with non-increasing coefficients analogous results can be obtained for Fejér and Cesàro means by choosing the generating sequence {q_{k}:k\geqslant 0} in an appropriate way., István Blahota, Lars-Erik Persson, Giorgi Tephnadze., and Obsahuje seznam literatury
The effect of three therapeutically used drugs and five polyphenolic compounds on the mechanism of oxidative burst was compared in whole blood and isolated neutrophils at cellular and molecular level. In 10 μM concentration, the compounds investigated decreased the oxidative burst of whole blood in the rank order of potency: N-feruloylserotonin (N-f-5HT) > curcumin (CUR) > quercetin (QUER) > arbutin (ARB) > resveratrol (RES) > dithiaden (DIT) > carvedilol (CARV) > brompheniramine (BPA). The ratio between the percentage inhibition of extracellular versus intracellular chemiluminescence (CL) followed the rank order QUER > N-f-5HT > RES > CUR > DIT and is indicative of the positive effect of the compounds tested against oxidative burst of neutrophils, demonstrating suppression of reactive oxygen species extracellularly with minimal alteration of intracellular reactive oxygen species (ROS). Activation of protein kinase C was significantly decreased by DIT, CUR, QUER and N-f-5HT. CARV, DIT, QUER and ARB reduced activated neutrophil myeloperoxidase release more significantly compared with the effect on superoxide anion generation. All compounds tested increased the activity of caspase-3 in cell-free system. It is suggested that other regulatory mechanisms than protein kinase C might participate in the inhibition of neutrophil activation with the compounds tested. Different mechanisms are concerned in controlling the assembly of NADPH oxidase and the regulatory role of calcium ions is suggested. Compounds decreasing the amount of extracellular ROS generation, yet affecting but minimally intracellular ROS generation, are promising for further investigation in vivo., R. Nosáľ, K. Drábiková, V. Jančinová, T. Mačičková, J. Pečivová, T. Perečko, J. Harmatha, J. Šmidrkal., and Obsahuje bibliografii