arXiv subjects

X. -J. Wang

Publications and source records attributed to X. -J. Wang.

9 recordsLinked to original sources

arXiv2024

Long time regularity of the $p$-Gauss curvature flow with flat side

In this paper, we prove the long time regularity of the interface in the $p$-Gauss curvature flow with flat side in all dimensions for $p>\frac1n$. Here the interface is the boundary of the flat part in the flow. In dimension $2$, this problem was solved in \cite{DL2004} for $p=1$ and in \cite{KimLeeRhee2013} for $p\in(1/2,1)$. We utilize the duality method to transform the Gauss curvature flow to a singular parabolic Monge-Ampère equation, and prove the regularity of the interface by studying the asymptotic cone of the parabolic Monge-Ampère equation in the polar coordinates.

math.AP↗

arXiv2021

Hadwiger conjecture for 8-coloring graph

Hadwiger Conjecture has been an open problem for over a half century1,6, which says that there is at most a complete graph Kt but no Kt+1 for every t-colorable graph. A few cases of Hadwiger Conjecture, such as 1, 2, 3, 4, 5, 6-colorable graphs have been completely proved to convince all1-5, but the proofs are tremendously difficult for over the 5-colorable graph6,7. Although the development of graph theory inspires scientists to understand graph coloring deeply, it is still an open problem for over 7-colorable graphs6,7. Therefore, we put forward a brand new chromatic graph configuration and show how to describe the graph coloring issues in chromatic space. Based on this idea, we define a chromatic plane and configure the chromatic coordinates in Euler space. Also, we find a method to prove Hadwiger Conjecture for every 8-coloring graph feasible.

math.CO↗

arXiv2021

A Study on Hand Proof for The Four-Color Theorem

For the four-color theorem that has been developed over one and half centuries, all people believe it right but without complete proof convincing all1-3. Former proofs are to find the basic four-colorable patterns on a planar graph to reduce a map coloring4-6, but the unavoidable set is almost limitless and required recoloring hardly implements by hand7-14. Another idea belongs to formal proof limited to logical operation15. However, recoloring or formal proof way may block people from discovering the inherent essence of a coloring graph. Defining creation and annihilation operations, we show that four colors are sufficient to color a map and how to color it. We find what trapped vertices and boundary-vertices are, and how they decide how many colors to be required in coloring arbitrary maps. We reveal that there is the fourth color for new adding vertex differing from any three coloring vertices in creation operation. To implement a coloring map, we also demonstrate how to color an arbitrary map by iteratively using creation and annihilation operations. We hope our hand proof is beneficial to understand the mechanisms of the four-color theorem.

math.GM↗

arXiv2001

Photoinjector design for the LCLS

The design of the Linac Coherent Light Source assumes that a low-emittance, 1-nC, 10-ps beam will be available for injection into the 15-GeV linac. The proposed rf photocathode injector that will provide a 150-MeV beam with rms normalized emittances of 1 mm in both the transverse and longitudinal dimensions is based on a 1.6-cell S-band rf gun that is equipped with an emittance compensating solenoid. The booster accelerator is positioned at the beam waist coinciding with the first emittance maximum and is provided with an accelerating gradient of ~25 MeV/m, i.e., the "new working point." The uv pulses required for cathode excitation will be generated by tripling the output of a Ti:sapphire laser system consisting of a highly stable cw mode-locked oscillator and two bow-tie amplifiers pumped by a pair of Q-switched Nd:YAG lasers. The large bandwidth of the Ti:sapphire system accommodates the desired temporal pulse shaping. Details of the design and the supporting simulations are presented.

physics.acc-ph↗

arXiv2000

Static Solution in Source-Free SU(2) Yang-Mills Theory

We show that a non-trivial topological effect breaks the conformal invariance of pure Yang-Mills theory. Thus it is possible that classic particle-like solutions exists in pure non-Abelian Yang-Mills theory. We find a static, non-singular solution in source-free SU(2) Yang-Mills theory in four-dimensional Minkowski space. This solution is a stable soliton characterized by non-trivial topology and imaginary $A_0^a$, i.e., $A_0^aA_0^a<0$. It yields hermitian Hamilton, and finite, positive energy.

hep-th↗

arXiv2000

Runing of Axial Coupling Constant

We illustrate that both of massless pseudoscalar meson fields and constitutent quark fields are dynamical field degrees of freedom in energy region between chiral symmetry spontaneously broken scale and quark confinement scale. This physical configuration yields a renormalization running axial coupling constant $g_{_A}(μ)$. The one-loop renormalization prediction $g_{_A}(μ=m_{_N})=0.75$ and $g_{_A}(μ=m_π)=0.96$ agree with $β$ decay of neutron and $π^0\toγγ$ respectively. We also calculate $ρ^\pm\toγπ$ and $ω\toγπ$ decays up to the next to leading order of $N_c^{-1}$ expansion and including all order effects of vector meson momentum expansion. The results strongly support prediction of renormalization running, $g_{_A}(μ=m_ρ)=0.77$.

hep-ph↗

arXiv2000

Light Quark Masses to All Orders of Chiral Expansion

We study light (current) quark masses in framework of chiral constitutent quark model. In our calculation the current quark masses are defined uniquely, and all order effects of the light quark masses are considered. The results at energy scale $μ=m_ρ$ are $m_s=(160\pm 15)$MeV, $m_s/m_d=20.2\pm 3.0$, $m_u/m_d=0.5\pm 0.09$.

hep-ph↗

arXiv2000

Isospin Breaking and $ω$->$ππ$ Decay

We study $ω\toπ^+π^-$ decay up to including all orders of the chiral expansion and one-loop level of mesons in formlism of chiral constituent quark model. This G-parity forbidden decay is caused by $m_u\neq m_d$ and electromagnetic interaction of mesons. We illustrate that in the formlism both nonresonant contact interaction and $ρ$ resonance exchange contribute to this process, and the contribution from $ρ$ resonance exchange is dominant. We obtain that transition matrix element is $<~ρ|H_{ρω}|ω>=[-(3956\pm 280)-(1697\pm 130)i]$MeV$^2$, and isospin breaking parameter is $m_d-m_u=3.9\pm 0.22$MeV at energy scale $μ\sim m_ω$.

hep-ph↗

arXiv2000

The Radiative Decay of Vector Mesons

In this paper, radiative decays $ρ^0 \to π^+π^-γ, π^0π^0γ$ ,$ϕ\to K^+K^-γ, K^0 \bar{K^0}γ$ are studied systematically in the U(3)$_L\timesU(3)_R$ chiral theory of mesons. The theoretical differential spectrum with respect to photon energy and branch ratio for $ρ^0 \to π^+π^-γ$ agree well with the experimental data. Differential spectrums and branch ratios for $ρ^0 \to π^0π^0γ, ϕ\to K^+ K^-γ,ϕ\to K^0\bar{K^0}γ$ are predicted. The process $ϕ\to K^0 \bar{K^0} γ$ is relevant to precision measurment of CP-violation parameters in the kaon systerm at a $ϕ$-factory. We give a complete estimate of the branch ratio for this decay process by including scalar resonance $f_0, a_0$ poles, nonresonant smooth amplitude and an abnormal parity process with $K^*$ pole which hasn't been considered before. We conclude that processes with intermediate $K^*$ do not pose a potential background problem for $ϕ\to K^0\bar{K}^0$ CP violation experiments.

hep-ph↗