Muon g-2 Anomaly confronted with the higgs global data in the Left-Right Twin Higgs Models

We will examine the Left-Right Twin Higgs(LRTH) Models as a solution of muon g-2 anomaly with the background of the Higgs global fit data. In the calculation, the joint constrains from the theory, the precision electroweak data, the 125 GeV Higgs data, the leptonic flavor changing decay \mu \to e\gamma decays, and the constraints m_{\nu_R}>m_T>m_{W_H} are all considered. And with the small mass of the \phi^0, the direct searches from the $h\to \phi^0\phi^0$ channels can impose stringent upper limits on Br(h\to \phi^0\phi^0) and can reduce the allowed region of m_{\phi^0} and f. It is concluded that the muon g-2 anomaly can be explained in the region of 200 GeV \leq M\leq 500 GeV, 700 GeV \leq f\leq 1100 GeV, 13 GeV \leq m_{\phi^0}\leq 55 GeV, 100 GeV \leq m_{\phi^\pm}\leq 900 GeV, and m_{\nu_R}\geq 15 TeV after imposing all the constraints mentioned above.Comment: 18 pages, 4 figures, some typos modifie

On Zudilin's q-question about Schmidt's problem

We propose an elemantary approach to Zudilin's q-question about Schmidt's problem [Electron. J. Combin. 11 (2004), #R22], which has been solved in a previous paper [Acta Arith. 127 (2007), 17--31]. The new approach is based on a q-analogue of our recent result in [J. Number Theory 132 (2012), 1731--1740] derived from q-Pfaff-Saalschutz identity.Comment: 5 page

A note on two identities arising from enumeration of convex polyominoes

Motivated by some binomial coefficients identities encountered in our approach to the enumeration of convex polyominoes, we prove some more general identities of the same type, one of which turns out to be related to a strange evaluation of ${}_3F_2$ of Gessel and Stanton.Comment: 10 pages, to appear in J. Comput. Appl. Math; minor grammatical change

Some q-analogues of supercongruences of Rodriguez-Villegas

We study different q-analogues and generalizations of the ex-conjectures of Rodriguez-Villegas. For example, for any odd prime p, we show that the known congruence \sum_{k=0}^{p-1}\frac{{2k\choose k}^2}{16^k} \equiv (-1)^{\frac{p-1}{2}}\pmod{p^2} has the following two nice q-analogues with [p]=1+q+...+q^{p-1}: \sum_{k=0}^{p-1}\frac{(q;q^2)_k^2}{(q^2;q^2)_k^2}q^{(1+\varepsilon)k} &\equiv (-1)^{\frac{p-1}{2}}q^{\frac{(p^2-1)\varepsilon}{4}}\pmod{[p]^2}, where (a;q)_0=1, (a;q)_n=(1-a)(1-aq)...(1-aq^{n-1}) for n=1,2,..., and \varepsilon=\pm1. Several related conjectures are also proposed.Comment: 14 pages, to appear in J. Number Theor