On Fleck quotients

Let $p$ be a prime, and let $n>0$ and $r$ be integers. In this paper we study Fleck's quotient $$F_p(n,r)=(-p)^{-\lfloor(n-1)/(p-1)\rfloor} \sum_{k=r(mod p)}\binom {n}{k}(-1)^k\in Z.$$ We determine $F_p(n,r)$ mod $p$ completely by certain number-theoretic and combinatorial methods; consequently, if $2\le n\le p$ then $$\sum_{k=1}^n(-1)^{pk-1}\binom{pn-1}{pk-1} \equiv(n-1)!B_{p-n}p^n (mod p^{n+1}),$$ where $B_0,B_1,...$ are Bernoulli numbers. We also establish the Kummer-type congruence $F_p(n+p^a(p-1),r)\equiv F_p(n,r) (mod p^a)$ for $a=1,2,3,...$, and reveal some connections between Fleck's quotients and class numbers of the quadratic fields \Q(\sqrt{\pm p}) and the $p$-th cyclotomic field \Q(\zeta_p). In addition, generalized Fleck quotients are also studied in this paper.Comment: 28 page

Unitarity Quadrangles of Four Neutrino Mixing

We present a classification of the unitarity quadrangles in the four-neutrino mixing scheme. We find that there are totally thirty-six distinct topologies among twelve different unitarity quadrangles. Concise relations are established between the areas of those unitarity quadrangles and the rephasing invariants of CP and $T$ violation.Comment: RevTex 10 pages. Minor changes made. Accepted for publication in Phys. Rev.

Technical Progress and the Share of Labor Income

Changes in the labor share of national income affect inequality (Piketty 2014). This paper aims at investigating the relationship between the labor share and technical progress, based on provincial data of the People’s Republic of China (PRC) from 1978 to 2012. Our main empirical results show that technical progress in the PRC had been mostly capital biased, contributing to the fast rises in income inequality in the PRC. However, the employment proportion of state-owned enterprises seems to have played a role in offsetting this negative effect, helping contain inequality. In recent years, both effects have become more significant and larger in absolute terms

Radiative Neutrino Mass with Z3Z_3 Dark matter: From Relic Density to LHC Signatures

In this work we give a comprehensive analysis on the phenomenology of a specific $\mathbb{Z}_3$ dark matter (DM) model in which neutrino mass is induced at two loops by interactions with a DM particle that can be a complex scalar or a Dirac fermion. Both the DM properties in relic density and direct detection and the LHC signatures are examined in great detail, and indirect detection for gamma-ray excess from the Galactic Center is also discussed briefly. On the DM side, both semi-annihilation and co-annihilation processes play a crucial role in alleviating the tension of parameter space between relic density and direct detection. On the collider side, new decay channels resulting from $\mathbb{Z}_3$ particles lead to distinct signals at LHC. Currently the trilepton signal is expected to give the most stringent bound for both scalar and fermion DM candidates, and the signatures of fermion DM are very similar to those of electroweakinos in simplified supersymmetric models.Comment: 40 pages, 24 figure

Analysis of the X(1576) as a tetraquark state with the QCD sum rules

In this letter, we take the point of view that the X(1576) be tetraquark state which consists of a scalar-diquark and an anti-scalar-diquark in relative $P$-wave, and calculate its mass in the framework of the QCD sum rules approach. The numerical value of the mass $m_X=(1.66\pm 0.14) GeV$ is consistent with the experimental data, there may be some tetraquark component in the vector meson X(1576).Comment: 6 pages, 1 figure, second version, typos correcte

The rare semi-leptonic BcB_c decays involving orbitally excited final mesons

The rare processes $B_c\to D_{(s)J} ^{(*)}\mu\bar{\mu}$, where $D_{(s)J}^{(*)}$ stands for the final meson $D_{s0}^*(2317)$, $D_{s1}(2460,2536)$,~$D_{s2}^*(2573)$, $D_0^*(2400)$, $D_{1}(2420,2430)$ or~$D_{2}^*(2460)$, are studied within the Standard Model. The hadronic matrix elements are evaluated in the Bethe-Salpeter approach and furthermore a discussion on the gauge-invariant condition of the annihilation hadronic currents is presented. Considering the penguin, box, annihilation, color-favored cascade and color-suppressed cascade contributions, the observables $\text{d}Br/\text{d}Q^2$, $A_{LPL}$, $A_{FB}$ and $P_L$ are calculated

Maximum norm error estimates of the Crank–Nicolson scheme for solving a linear moving boundary problem

AbstractThe Crank–Nicolson scheme is considered for solving a linear convection–diffusion equation with moving boundaries. The original problem is transformed into an equivalent system defined on a rectangular region by a linear transformation. Using energy techniques we show that the numerical solutions of the Crank–Nicolson scheme are unconditionally stable and convergent in the maximum norm. Numerical experiments are presented to support our theoretical results