arXiv subjects
Publications and source records attributed to Haidong Liu.
We prove that if the moduli $\mathbb Q$-b-divisor of a basic slc-trivial fibration is b-numerically trivial then it is $\mathbb Q$-b-linearly trivial. As a consequence, we prove that the moduli part of a basic slc-trivial fibration is semi-ample when the base space is a curve.
We show the boundedness of B-pluricanonical representations of lc log Calabi-Yau pairs in dimension $2$. As applications, we prove the boundedness of indices of slc log Calabi-Yau pairs up to dimension $3$ and that of non-klt lc log Calabi-Yau pairs in dimension $4$.
We prove that every quasi-log canonical pair has only Du Bois singularities. Note that our arguments are free from the minimal model program.
The log canonical ring of a projective plt pair with the Kodaira dimension two is finitely generated.
In this paper, we show that Fujita's basepoint-freeness conjecture for projective quasi-log canonical singularities holds true in dimension three. Immediately, we prove Fujita-type basepoint-freeness for projective semi-log canonical threefolds.
We prove Fujita-type basepoint-freeness for projective quasi-log canonical curves and surfaces.
This paper is concerned with the $p(x)$-Laplacian equation of the form \begin{equation}\label{eq0.1} \left\{\begin{array}{ll} -Δ_{p(x)} u=Q(x)|u|^{r(x)-2}u, &\mbox{in}\ Ω,\\ u=0, &\mbox{on}\ \partial Ω, \end{array}\right. \end{equation} where $Ω\subset\R^N$ is a smooth bounded domain, $1 p^+$ and $Q: \overlineΩ\to\R$ is a nonnegative continuous function. We prove that \eqref{eq0.1} has infinitely many small solutions and infinitely many large solutions by using the Clark's theorem and the symmetric mountain pass lemma.
The normalization of a quasi-log canonical pair is a quasi-log canonical pair.
Fujino and Tanaka established the minimal model theory for $\mathbb Q$-factorial log surfaces in characteristic $0$ and $p$, respectively. We prove that every intermediate surface has only log terminal singularities if we run the minimal model program starting with a pair consisting of a smooth surface and a boundary $\mathbb R$-divisor. We further show that such a property does not hold if the initial surface is singular.
This paper is concerned with the quasilinear Schrödinger equation \begin{equation*} -Δu+V(x)u- Δ(u^2)u =h(u), \ \ \mbox{in} \ \mathbb{R}^N, \end{equation*} where $N\geq 3$. Under appropriate assumptions on $V$ and $h$, we establish the existence of positive solutions. The main novelty is that, unlike most other papers on this problem, we do not assume $h$ is 4-superlinear at infinity.
We prove the Angehrn-Siu Type effective freeness and effective point separation for quasi-log canonical pairs. As a natural consequence, we obtain that these two results hold for semi-log canonical pairs. One of the main ingredients of our proof is the inversion of adjunction for quasi-log canonical pairs, which is established in this paper.
We present the analysis of $Υ\to e^{+}e^{-}$ production in d+Au collisions at $\sqrt{s_{NN}} = 200$ GeV from the STAR experiment. Using higher level dedicated $Υ$ triggers, STAR has sampled 32 nb$^{-1}$ of integrated luminosity in year 2008 d+Au run. The cross section is found as $BR\times{({{dσ}\over{dy}})}_{y=0}^{Υ(1S+2S+3S)}=35\pm4(stat.)\pm5(sys.)$ nb and it is consistent with NLO CEM prediction with anti-shadowing effects. In addition we calculated the nuclear modification factor $R_{dAu}=0.98\pm0.32(stat.)\pm0.28(sys.)$, which suggests the $Υ(1S+2S+3S)$ production follows $N_{bin}$ scaling.
We present the transverse momentum spectra at mid-rapidity for $d$, $\bar{d}$ ($1<p_{T}<4 GeV/c$) and $^{3}He$, $\bar{^{3}He}$ ($2<p_{T}<6 GeV/c$) measured by the STAR experiment at RHIC and extract the coalescence parameters $B_{2}$ and $B_{3}$ (respectively). We also present the $v_{2}$ measurement for $d(\bar{d})$ and $^{3}He(\bar{^{3}He})$. We find that the $d(\bar{d})$ and $p(\bar{p})$ $v_{2}$ follows the atomic mass number A scaling within errors and a negative $v_{2}$ has been observed for $\bar{d}$ at low $p_{T}$.
We compiled the systematical measurements of anti-nucleus production in ultra-relativistic heavy ion collisions as well as those in $pp$, $p\bar{p}$, $γp$ and $e^{+}e^{-}$ at various beam energies. The anti-baryon phase space density inferred from $\bar{d}/\bar{p}$ ratio in $A+A$, $p+A$, $pp(\bar{p})$ and $γp$ collisions is found to follow a universal distribution as a function of center of mass of beam energy and can be described in a statistical model. We demonstrated that anti-baryon density in all the collisions is the highest when the collisions are dominated by the processes of $g+g$ or $\bar{q}+g$. In $e^+e^-$ collisions at LEP, the cross section of $q\bar{q}g$ is suppressed by a factor of strong coupling constant $α_s$ relative to $q\bar{q}$. This can consistently explain the $\bar{d}$ suppression observed by ALEPH relative to that in $e^+e^-\to ggg$ by ARGUS. We discuss the implications to the baryon enhancement at high transverse momentum at RHIC when jet is quenched.
We propose a sensitive measurement of the charm total cross-section at RHIC through muon identification from charm semileptonic decay at low transverse momentum ($p_T$). This can test the binary-collision scaling ($N_{bin}$) properties of the charm total cross-section and be used to study whether heavy-flavor quarks, which are used as a probe, are produced exclusively at the initial impact in hadron-hadron collisions. The effect of the charm semileptonic decay form factor on extracting the total charm cross section and on the shape of the lepton spectra are also discussed in detail. We conclude that lepton spectra from charmed hadron decays at transverse momentum $p_T\simeq1.0$ GeV/$c$ are sensitive to the charmed hadron spectrum shape. Therefore, the interactions of heavy quarks with the medium created in relativistic heavy-ion collisions, especially the flow effects, can be extracted from the lepton spectra from charmed hadron decays at low $p_T$.