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Register a new userThe 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 erg 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 difference 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 bounds, knowing that the `celestial horizon lies near $d geqslant 2n$. For Green-Griffiths algebraic degeneracy of entire holomorphic curves, we obtain: [ d ,geqslant, big(sqrt{n},{sf log},nbig)^n, ] and for Kobayashi-hyperbolicity (constancy of entire curves), we obtain: [ d ,geqslant, big(n,{sf log},nbig)^n. ] The latter improves $d geqslant n^{2n}$ obtained by Merker in arxiv.org/1807/11309/. Admitting a certain technical conjecture $I_0 geqslant widetilde{I}_0$, the method employed (Diverio-Merker-Rousseau, Berczi, Darondeau) conducts to constant power $n$, namely to: [ d ,geqslant, 2^{5n} qquad text{and, respectively, to:} qquad d ,geqslant, 4^{5n}. ] In Spring 2019, a forthcoming prepublication based on intensive computer explorations will present several subconjectures supporting the belief that $I_0 geqslant widetilde{I}_0$, a conjecture which will be established up to dimension $n = 50$.
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 that the origin of the observed distribution in this parameter space can be understood only by accepting a new interpretation of the $log(L)$-$log(sigma)$ relation Methods. We simulate the distribution of galaxies in the $log(langle Irangle_e)-log(R_e)$ plane starting from the new $L=L_0sigma^beta$ relation proposed by DOnofrio et al. (2020) and we discuss the physical mechanisms that are hidden in this empirical law. Results. The artificial distribution obtained assuming that beta spans either positive and negative values and that $L_0$ changes with $beta$, is perfectly superposed to the observational data, once it is postulated that the Zone of Exclusion (ZoE) is the limit of virialized and quenched objects. Conclusions. We have demonstrated that the distribution of galaxies in the $log(langle Irangle_e)-log(R_e)$ plane is not linked to the peculiar light profiles of the galaxies of different luminosity, but originate from the mass assembly history of galaxies, made of merging, star formation events, star evolution and quenching of the stellar population.
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 configurations 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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