Topological aspects in a two component Bose condensed system in neutron star

By making use of Duan-Ge's decomposition theory of gauge potential and the Duan's topological current theory proposed by Prof. Duan Yi-Shi, we study a two component superfluid Bose condensed system, which is supposed being realized in the interior of neutron stars in the form of a coexistent neutron superfluid and protonic superconductor. We propose that this system possesses vortex lines. The topological charge of the vortex lines are characterized by the Hopf indices and the Brower degrees of $\phi$-mapping.Comment: 9 pages, no figure

PoD-TPI: Probability-of-Decision Toxicity Probability Interval Design to Accelerate Phase I Trials

Cohort-based enrollment can slow down dose-finding trials since the outcomes of the previous cohort must be fully evaluated before the next cohort can be enrolled. This results in frequent suspension of patient enrollment. The issue is exacerbated in recent immune-oncology trials where toxicity outcomes can take a long time to observe. We propose a novel phase I design, the probability-of-decision toxicity probability interval (PoD-TPI) design, to accelerate phase I trials. PoD-TPI enables dose assignment in real-time in the presence of pending toxicity outcomes. With uncertain outcomes, the dose assignment decisions are treated as a random variable, and we calculate the posterior distribution of the decisions. The posterior distribution reflects the variability in the pending outcomes and allows a direct and intuitive evaluation of the confidence of all possible decisions. Optimal decisions are calculated based on 0-1 loss, and extra safety rules are constructed to enforce sufficient protection from exposing patients to risky doses. A new and useful feature of PoD-TPI is that it allows investigators and regulators to balance the trade-off between enrollment speed and making risky decisions by tuning a pair of intuitive design parameters. Through numerical studies, we evaluate the operating characteristics of PoD-TPI and demonstrate that PoD-TPI shortens trial duration and maintains trial safety and efficiency compared to existing time-to-event designs

First principles study of electronic transport through a Cu(111)|graphene junction

We report first principles investigations of the nonequilibrium transport properties of a Cu(111)|graphene interface. The Cu(111) electrode is found to induce a transmission minimum (TM) located -0.68eV below the Fermi level, a feature originating from the Cu-induced charge transfer resulting in n-type doped graphene with the Dirac point coinciding with the TM. An applied bias voltage shifts the n-graphene TM relative to the pure graphene TM and leads to a distinctive peak in the differential conductance indicating the doping level, a characteristic not observed in pure graphene.Comment: 3 pages, 3 figure

Proof of a congruence on sums of powers of qq-binomial coefficients

We prove that, if $m,n\geqslant 1$ and $a_1,\ldots,a_m$ are nonnegative integers, then \begin{align*} \frac{[a_1+\cdots+a_m+1]!}{[a_1]!\ldots[a_m]!}\sum^{n-1}_{h=0}q^h\prod_{i=1}^m{h\brack a_i} \equiv 0\pmod{[n]}, \end{align*} where $[n]=\frac{1-q^n}{1-q}$, $[n]!=[n][n-1]\cdots[1]$, and ${a\brack b}=\prod_{k=1}^b\frac{1-q^{a-k+1}}{1-q^k}$. The $a_1=\cdots=a_m$ case confirms a recent conjecture of Z.-W. Sun. We also show that, if $p>\max\{a,b\}$ is a prime, then \begin{align*} \frac{[a+b+1]!}{[a]![b]!}\sum_{h=0}^{p-1}q^h{h\brack a}{h\brack b} \equiv (-1)^{a-b} q^{ab-{a\choose 2}-{b\choose 2}}[p]\pmod{[p]^2}. \end{align*}Comment: 5 page

Molecular ordering of glycine on Cu(100): the p(2×42\times4) superstructure

Glycine molecules deposited on Cu(100) surface give rise to an anisotropic free-electron-like (FEL) electronic dispersion in its p(2$\times$4) superstructure, as reported in recent experiments [Phys. Rev. Lett. {\bf 99}, 216102 (2007); J. Am. Chem. Soc. {\bf 129}, 740 (2007)]. Using density functional theory and exhaustively calculating sixteen possible structures, we have determined the molecular arrangement that can give the experimentally observed FEL behavior. Eight configurations, among the sixteen, were not investigated before in the literature and one of them (denoted Str-3) is able to provide the FEL behavior in excellent agreement with the experiments. In addition, the particular configuration Str-3 satisfies other criteria of the observed p(2$\times$4) superstructure, e.g. chirality and cleavable orientation.Comment: 7 pages, 4 figures, 3 table

Proof of a conjecture of Z.-W. Sun on the divisibility of a triple sum

The numbers $R_n$ and $W_n$ are defined as \begin{align*} R_n=\sum_{k=0}^{n}{n+k\choose 2k}{2k\choose k}\frac{1}{2k-1},\ \text{and}\ W_n=\sum_{k=0}^{n}{n+k\choose 2k}{2k\choose k}\frac{3}{2k-3}. \end{align*} We prove that, for any positive integer $n$ and odd prime $p$, there hold \begin{align*} \sum_{k=0}^{n-1}(2k+1)R_k^2 &\equiv 0 \pmod{n}, \\ \sum_{k=0}^{p-1}(2k+1)R_k^2 &\equiv 4p(-1)^{\frac{p-1}{2}} -p^2 \pmod{p^3}, \\ 9\sum_{k=0}^{n-1}(2k+1)W_k^2 &\equiv 0 \pmod{n}, \\ \sum_{k=0}^{p-1}(2k+1)W_k^2 &\equiv 12p(-1)^{\frac{p-1}{2}}-17p^2 \pmod{p^3}, \quad\text{if $p>3$.} \end{align*} The first two congruences were originally conjectured by Z.-W. Sun. Our proof is based on the multi-variable Zeilberger algorithm and the following observation: $${2n\choose n}{n\choose k}{m\choose k}{k\choose m-n}\equiv 0\pmod{{2k\choose k}{2m-2k\choose m-k}},$$ where $0\leqslant k\leqslant n\leqslant m \leqslant 2n$.Comment: 18 page

qq-Analogues of two Ramanujan-type formulas for 1/π1/\pi

We give $q$-analogues of the following two Ramanujan-type formulas for $1/\pi$: \begin{align*} \sum_{k=0}^\infty (6k+1)\frac{(\frac{1}{2})_k^3}{k!^3 4^k} =\frac{4}{\pi} \quad\text{and}\quad \sum_{k=0}^\infty (-1)^k(6k+1)\frac{(\frac{1}{2})_k^3}{k!^3 8^k } =\frac{2\sqrt{2}}{\pi}. \end{align*} Our proof is based on two $q$-WZ pairs found by the first author in his earlier work.Comment: typos corrected, 5 page

Charged Higgs Pair Production at the LHC as a Probe of the Top-Seesaw Assisted Technicolor Models

The top-seesaw assisted technicolor (TC) model, which was proposed recently to explain the 126 GeV Higgs mass discovered by the Large Hadron Colliders (LHC), predicts light and heavy charged Higgs bosons in addition to the neutral Higgses. In this paper we will study the pair productions of the charged Higgs, proceeding through gluon-gluon fusion and quark-anti-quark annihilation, at the LHC in the frame of the top-seesaw assisted TC model. We find that in a large part of parameter space the production cross sections of the light charged Higgs pair at the LHC can be quite large compared with the low standard model backgrounds, while it is impossible for the pair production of the heavy ones to be detected with the strong final mass suppression. Therefore, at the LHC future experiments, the light charged Higgs pair production may be served as a probe of this new TC model.Comment: 24 pages, 6 figures; minor discussions adde

Large-momentum distribution of a polarized Fermi gas and p-wave contacts

We present a derivation of the adiabatic energy relations as well as the large momentum distribution of a polarized Fermi gas near p-wave Feshbach resonances. The leading asymptotic behavior ($k^{-2}$) and subleading behavior ($k^{-4}$) of the large momentum distribution have recently been predicted by Yu et al. [Phys. Rev. Lett. 115, 135304 (2015)] and by He et al. [Phys. Rev. Lett. 116, 045301 (2016)] using two different approaches. Here, we show that the subleading asymptotic behavior ($\sim k^{-4}$) can not fully be captured by the contact defined from the adiabatic energy relation related to the p-wave effective range, and there should be an extra term resulted from the center-of-mass motion of the pairs. The omission of this extra term is perhaps a reasonable approximation at zero temperature. However, it should be taken into account at finite temperature and should be of significant importance to understand the recently measured momentum distribution in a resonant p-wave Fermi gas of ultracold $^{40}$K atoms [Luciuk et al., Nature Phys. 12, 599 (2016)].Comment: 9 page

On the boundary Strichartz estimates for wave and Schr\"odinger equations

We consider the $L_t^2L_x^r$ estimates for the solutions to the wave and Schr\"odinger equations in high dimensions. For the homogeneous estimates, we show $L_t^2L_x^\infty$ estimates fail at the critical regularity in high dimensions by using stable L\'evy process in $\R^d$. Moreover, we show that some spherically averaged $L_t^2L_x^\infty$ estimate holds at the critical regularity. As a by-product we obtain Strichartz estimates with angular smoothing effect. For the inhomogeneous estimates, we prove double $L_t^2$-type estimates