arXiv subjects
Publications and source records attributed to Ming-Sheng Liu.
In this paper, we establish five new sharp versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing Schwarz function in place of the initial coefficients in the power series representations of the functions involved and thereby, we generalize several related results of earlier authors.
In this paper, we investigate the Bohr radius for $K$-quasiregular sense-preserving harmonic mappings $f=h+\overline{g}$ in the unit disk $\mathbb{D}$ such that the translated analytic part $h(z)-h(0)$ is quasi-subordinate to some analytic function. The main aim of this article is to extend and to establish sharp versions of four recent theorems by Liu and Ponnusamy \cite{LP2019} and, in particular, we settle affirmatively the two conjectures proposed by them. Furthermore, we establish two refined versions of Bohr's inequalities and determine the Bohr radius for the derivatives of analytic functions associated with quasi-subordination.
Inspired by the newly observed $Ω_b$ states by the LHCb Collaboration, we investigate the two-body strong decays of the low-lying $λ$-mode $Ω_b$ baryons up to $N=2$ shell using the chiral quark model within the $j$-$j$ coupling scheme. Our results indicate that: (i) the newly observed states $Ω_b(6316)^-$ and $Ω_b(6330)^-$ are good candidates of the light spin $j=1$ states, while the spin-parity $J^P=1/2^-$ and $J^P=3/2^-$ cannot be distinguished. The other two states, $Ω_b(6340)$ and $Ω_b(6350)$ mostly correspond to the light spin $j=2$ states, while the spin-parity $J^P=3/2^-$ and $J^P=5/2^-$ cannot be distinguished as well.(ii) The $2S$ states with spin-parity $J^P=1/2^+$ and $J^P=3/2^+$, respectively, might be narrow states with a width of $Γ<2$ MeV. (iii) The $1D$ states are not broad and the total decay widths vary from several to dozens of MeV, which have a good potential to be observed in future experiments.
In this work we study the mass spectra of the fully-heavy tetraquark systems, i.e. $cc\bar{c}\bar{c}$, $bb\bar{b}\bar{b}$, $bb\bar{c}\bar{c}/cc\bar{b}\bar{b}$, $bc\bar{c}\bar{c}/cc\bar{b}\bar{c}$, $bc\bar{b}\bar{b}/bb\bar{b}\bar{c}$, and $bc\bar{b}\bar{c}$, within a potential model by including the linear confining potential, Coulomb potential, and spin-spin interactions. It shows that the linear confining potential has important contributions to the masses and is crucial for our understanding of the mass spectra of the fully-heavy tetraquark systems. For the fully-heavy tetraquarks $Q_1Q_2\bar{Q}_3\bar{Q}_4$ our explicit calculations suggest that no bound states can be formed below the thresholds of any meson pairs $(Q_1\bar{Q}_3)$-$(Q_2\bar{Q}_4)$ or $(Q_1\bar{Q}_4)$-$(Q_2\bar{Q}_3)$. Thus, we do not expect narrow fully-heavy tetraquark states to be existing in experiments.
In this work, we study the mass spectrum of the $Ω_{ccc}$ and $Ω_{bbb}$ baryons up to the $N=2$ shell within a nonrelativistic constituent quark model (NRCQM). The model parameters are adopted from the determinations by fitting the charmonium and bottomonium spectra in our previous works. The masses of the $Ω_{ccc}$ and $Ω_{bbb}$ baryon states predicted in present work reasonably agree with the results obtained with the Lattice QCD calculations. Furthermore, to provide more knowledge of the $Ω_{ccc}$ and $Ω_{bbb}$ states, we evaluate their radiative decays with the available masses and wave functions from the potential model.
Combining the recent developments of the observations of $Ω$ sates we calculate the $Ω$ spectrum up to the $N=2$ shell within a nonrelativistic constituent quark potential model. Furthermore, the strong and radiative decay properties for the $Ω$ resonances within the $N=2$ shell are evaluated by using the masses and wave functions obtained from the potential model. It is found that the newly observed $Ω(2012)$ resonance is most likely to be the spin-parity $J^P=3/2^-$ $1P$-wave state $Ω(1^{2}P_{3/2^{-}})$, it also has a large potential to be observed in the $Ω(1672)γ$ channel. Our calculation shows that the 1$P$-, 1$D$-, and 2$S$-wave $Ω$ baryons have a relatively narrow decay width of less than 50 MeV. Based on the obtained decay properties and mass spectrum, we further suggest optimum channels and mass regions to find the missing $Ω$ resonances via the strong and/or radiative decay processes.
Inspired by the new resonance $Y(10750)$, we calculate the masses and two-body OZI-allowed strong decays of the higher vector bottomonium sates within both screened and linear potential models. We discuss the possibilities of $Υ(10860)$ and $Y(10750)$ as mixed states via the $S-D$ mixing. Our results suggest that $Y(10750)$ and $Υ(10860)$ might be explained as mixed states between $5S$- and $4D$-wave vector $b\bar{b}$ states. The $Y(10750)$ and $Υ(10860)$ resonances may correspond to the mixed states dominated by the $4D$- and $5S$-wave components, respectively. The mass and the strong decay behaviors of the $Υ(11020)$ resonance are consistent with the assignment of the $Υ(6S)$ state in the potential models.
Using the newly measured masses of $B_c(1S)$ and $B_c(2S)$ from the CMS Collaboration and the $1S$ hyperfine splitting determined from the lattice QCD as constrains, we calculate the $B_c$ mass spectrum up to the $6S$ multiplet with a nonrelativistic linear potential model. Furthermore, using the wave functions from this model we calculate the radiative transitions between the $B_c$ states within a constituent quark model. For the higher mass $B_c$ states lying above $DB$ threshold, we also evaluate the Okubo-Zweig-Iizuka (OZI) allowed two-body strong decays with the $^{3}P_{0}$ model. Our study indicates that besides there are large potentials for the observations of the low-lying $B_c$ states below the $DB$ threshold via their radiative transitions, some higher mass $B_c$ states, such as $B_c(2^3P_2)$, $B_c(2^3D_1)$, $B_c(3^3D_1)$, $B_c(4^3P_0)$, and the $1F$-wave $B_c$ states, might be first observed in their dominant strong decay channels $DB$, $DB^*$ or $D^*B$ at the LHC for their relatively narrow widths.
In this paper, we first establish several general sufficient conditions for the biholomorphic convex mappings on the bounded convex balanced domain $D_{p}^n(p_{j}\geq 2,j=1,\cdots,n)$ in $C^{n}$, which extend some related results of earlier authors. From these, some concrete examples of biholomorphic convex mappings on $D_{p}^n$ are also provided.
In this paper, we first obtain several sharp inequalities of homogeneous expansion for both the subclass of all normalized biholomorphic quasi-convex mappings of type B and order alpha and the subclass of all normalized biholomorphic almost starlike mappings of order alpha defined on the unit ball $B$ of a complex Banach space X. Then, with these sharp inequalities, we derive the sharp estimates of the third and fourth homogeneous expansions for the above mappings defined on the unit polydisk $D^n$ in C(n).
Let $f(z)=h(z)+\overline{g(z)}$ be a harmonic mapping of the unit disk $U$. In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic mappings with $|h(z)|+|g(z)|\leq M$ are also provided. As their applications, Landau's theorems for certain biharmonic mappings are provided, which improve and refine the related results of earlier authors.
In this paper, we first introduce the concept of biholomorphic convex mapping of order alpha on the unit ball B in a complex Hilbert space X. Next we provide some sufficient conditions that a locally biholomorphic mapping f is a biholomorphic convex mapping of order alpha and give an Alexander's theorem between the subclass of convex mappings and the subclass of starlike mappings on B in Hilbert space. We also obtain the order of starlikeness of biholomorphic convex mappings of order alpha on B in Hilbert spaces. Finally, we construct some concrete examples of biholomorphic convex mappings of order alpha on B in Hilbert spaces by means of a linear operator.