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تسجيل مستخدم جديدThe log(N)-log(S) and the Broadband Properties of the Sources in the HELLAS2XMM Survey
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We present the first results from an XMM-Newton serendipitous medium-deep survey, which covers nearly three square degrees. We show the log(N)-log(S) distributions for the 0.5-2, 2-10 and 5-10 keV bands, which are found to be in good agreement with previous determinations and with the predictions of XRB models. In the soft band we detect a break at fluxes around 5x10^-15 cgs. In the harder bands, we fill in the gap at intermediate fluxes between deeper Chandra and XMM-Newton observations and shallower BeppoSAX and ASCA surveys. Moreover, we present an analysis of the broad-band properties of the sources.
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We present the first results from an XMM-Newton serendipitous medium-deep survey, which covers nearly three square degrees. We detect a total of 1022, 495 and 100 sources, down to minimum fluxes of about 5.9 x 10^-16, 2.8 x 10^-15 and 6.2 x 10^-15 er
g cm^-2 s^-1, in the 0.5-2, 2-10 and 4.5-10 keV band, respectively. In the soft band this is one of the largest samples available to date and surely the largest in the 2-10 keV band at our limiting X-ray flux. The measured Log(N)-Log(S) are found to be in good agreement with previous determinations. In the 0.5-2 keV band we detect a break at fluxes around 5 x 10^-15 erg cm^-2 s^-1. In the harder bands, we fill in the gap at intermediate fluxes between deeper Chandra and XMM-Newton observations and shallower BeppoSAX and ASCA surveys.
Let $p(n)$ denote the partition function. Desalvo and Pak proved the log-concavity of $p(n)$ for $n>25$ and the inequality $frac{p(n-1)}{p(n)}left(1+frac{1}{n}right)>frac{p(n)}{p(n+1)}$ for $n>1$. Let $r(n)=sqrt[n]{p(n)/n}$ and $Delta$ be the differe
nce operator respect to $n$. Desalvo and Pak pointed out that their approach to proving the log-concavity of $p(n)$ may be employed to prove a conjecture of Sun on the log-convexity of ${r(n)}_{ngeq 61}$, as long as one finds an appropriate estimate of $Delta^2 log r(n-1)$. In this paper, we obtain a lower bound for $Delta^2log r(n-1)$, leading to a proof of this conjecture. From the log-convexity of ${r(n)}_{ngeq61}$ and ${sqrt[n]{n}}_{ngeq4}$, we are led to a proof of another conjecture of Sun on the log-convexity of ${sqrt[n]{p(n)}}_{ngeq27}$. Furthermore, we show that $limlimits_{n rightarrow +infty}n^{frac{5}{2}}Delta^2logsqrt[n]{p(n)}=3pi/sqrt{24}$. Finally, by finding an upper bound of $Delta^2 logsqrt[n-1]{p(n-1)}$, we prove an inequality on the ratio $frac{sqrt[n-1]{p(n-1)}}{sqrt[n]{p(n)}}$ analogous to the above inequality on the ratio $frac{p(n-1)}{p(n)}$.
Once first answers in any dimension to the Green-Griffiths and Kobayashi conjectures for generic algebraic hypersurfaces $mathbb{X}^{n-1} subset mathbb{P}^n(mathbb{C})$ have been reached, the principal goal is to decrease (to improve) the degree boun
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Context. We present a reanalysis of the distribution of galaxies in the $log(langle Irangle_e)-log(R_e)$ plane under a new theoretical perspective. Aims. Using the data of the WINGS database and those of the Illustris simulation we will demonstrate t
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Combining the ideas of Riesz $s$-energy and $log$-energy, we introduce the so-called $s,log^t$-energy. In this paper, we investigate the asymptotic behaviors for $N,t$ fixed and $s$ varying of minimal $N$-point $s,log^t$-energy constants and configur
ations of an infinite compact metric space of diameter less than $1$. In particular, we study certain continuity and differentiability properties of minimal $N$-point $s,log^t$-energy constants in the variable $s$ and we show that in the limits as $srightarrow infty$ and as $srightarrow s_0>0,$ minimal $N$-point $s,log^t$-energy configurations tend to an $N$-point best-packing configuration and a minimal $N$-point $s_0,log^t$-energy configuration, respectively. Furthermore, the optimality of $N$ distinct equally spaced points on circles in $mathbb{R}^2$ for some certain $s,log^t$ energy problems was proved.
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