THE 97-TH PROBLEM OF F. SMARANDACHE

The main purpose of this paper is using the analytic method to study the n-ary sieve sequence, and solved one conjecture about this sequence

On character sums over flat numbers

Let $q\geqslant2$ be an integer, $\chi$ be any non-principal character mod $q$, and $H=H(q)\leqslant q.$ In this paper the authors prove some estimates for character sums of the form $$\mathcal{W}(\chi,H;q)=\sum_{n\in\mathscr{F}(H)}\chi(n),$$ where \mathscr{F}(H)=\left\{n\in\mathbb{Z}|(n,q)=1,1\leqslant n,\bar{n}\leqslant q, |n-\bar{n}|\leqslant H\}, $\bar{n}$ is defined by $n\bar{n}\equiv1\pmod q.$Comment: 9 pages, with a complete proof of Theorem 3, Section 5. Accepted by J. Number Theor

ON A PROBLEM OF F. SMARANDACHE

The main purpose of this paper is to give two exact ca:lculating formulas for A1 (x) and A2 (x)

A Refined Holographic QCD Model and QCD Phase Structure

We consider the Einstein-Maxwell-dilaton system with an arbitrary kinetic gauge function and a dilaton potential. A family of analytic solutions is obtained by the potential reconstruction method. We then study its holographic dual QCD model. The kinetic gauge function can be fixed by requesting the linear Regge spectrum of mesons. We calculate the free energy to obtain the phase diagram of the holographic QCD model.Comment: 21 pages, 17 figures. arXiv admin note: substantial text overlap with arXiv:1301.038

Confinement-Deconfinment Phase Transition for Heavy Quarks

We study confinement-deconfinement phase transition for heavy quarks in a bottom-up holographic QCD model. We consider a black hole background in an Einstein-Maxwell-scalar system and add probe open strings to the background. Combining the various configurations of the open strings and the phase structure of the black hole background itself, we obtain the confinement-deconfinement phase diagram for heavy quarks in the holographic QCD model.Comment: 23 pages, 14 figures, published in JHEP. arXiv admin note: text overlap with arXiv:1301.038