this paper,we study Liouville theorem for 3D steady Q-tensor system of liquid crystal in mixed Lorentz spaces.We obtain u=0,Q=0 on the conditions that μ∈L^(p,∞x_(1)L^(q,∞x_(2)L^(r,∞x_(3)(R^(4)∩H^(1)(R^(3),Q∈H^(...this paper,we study Liouville theorem for 3D steady Q-tensor system of liquid crystal in mixed Lorentz spaces.We obtain u=0,Q=0 on the conditions that μ∈L^(p,∞x_(1)L^(q,∞x_(2)L^(r,∞x_(3)(R^(4)∩H^(1)(R^(3),Q∈H^(2)(R^(3),p,q,r∈(3,∞],and 1/p+1/q+1/r≥2/3, which extends some known results.展开更多
Topological insulators represent a new phase of matter,characterized by conductive surfaces,while their bulk remains insulating.When the dimension of the system exceeds that of the topological state by at least two,th...Topological insulators represent a new phase of matter,characterized by conductive surfaces,while their bulk remains insulating.When the dimension of the system exceeds that of the topological state by at least two,the insulators are classified as higher-order topological insulators(HOTI).The appearance of higher-order topological states,such as corner states,can be explained by the filling anomaly,which leads to the fractional spectral charges in the unit cell.Previously reported fractional charges have been quite limited in number and size.In this work,based on the two-dimensional(2D)Su-Schrieffer-Heeger model lattice,we demonstrated a new class of HOTIs with adjustable fractional charges that can take any value ranging from 0 to 1,achieved by utilizing the Lorentz transformation.Furthermore,this transformation generates novel bound-state-in-continuum-like corner states,even when the lattice is in a topological trivial phase,offering a new approach to light beam localization.This work paves the way for fabricating HOTIs with diverse corner states that offer promising applicative potential.展开更多
In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piece...In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.展开更多
The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and ide...The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and identify the cause of the incorrect implementation of the method. The cause is related to the incorrect proof of the equality φ(v)=1for the unknown function φ(v)arising in the process of derivation of the Lorentz transformations. We develop proof of the equality φ(v)=1and eliminate the cause of the incorrect implementation of the method of derivation of the Lorentz transformations used by Einstein.展开更多
基金Supported by the National Natural Science Foundation of China(11871305)。
文摘this paper,we study Liouville theorem for 3D steady Q-tensor system of liquid crystal in mixed Lorentz spaces.We obtain u=0,Q=0 on the conditions that μ∈L^(p,∞x_(1)L^(q,∞x_(2)L^(r,∞x_(3)(R^(4)∩H^(1)(R^(3),Q∈H^(2)(R^(3),p,q,r∈(3,∞],and 1/p+1/q+1/r≥2/3, which extends some known results.
基金supported by the Natural Science Basic Research Program of Shaanxi Province(No.2024JC-JCQN-06)the National Natural Science Foundation of China(Nos.12474337,12304370)Fundamental Research Funds for the Central Universities(No.xzy012024135).
文摘Topological insulators represent a new phase of matter,characterized by conductive surfaces,while their bulk remains insulating.When the dimension of the system exceeds that of the topological state by at least two,the insulators are classified as higher-order topological insulators(HOTI).The appearance of higher-order topological states,such as corner states,can be explained by the filling anomaly,which leads to the fractional spectral charges in the unit cell.Previously reported fractional charges have been quite limited in number and size.In this work,based on the two-dimensional(2D)Su-Schrieffer-Heeger model lattice,we demonstrated a new class of HOTIs with adjustable fractional charges that can take any value ranging from 0 to 1,achieved by utilizing the Lorentz transformation.Furthermore,this transformation generates novel bound-state-in-continuum-like corner states,even when the lattice is in a topological trivial phase,offering a new approach to light beam localization.This work paves the way for fabricating HOTIs with diverse corner states that offer promising applicative potential.
基金supported in part by the NSFC(11801496,11926352)the Fok Ying-Tung Education Foundation(China)the Hubei Key Laboratory of Applied Mathematics(Hubei University).
文摘In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.
文摘The Lorentz transformations are the mathematical basis of Einstein’s theory of special relativity. We conduct a thorough examination of the method of derivation of the Lorentz transformations used by Einstein and identify the cause of the incorrect implementation of the method. The cause is related to the incorrect proof of the equality φ(v)=1for the unknown function φ(v)arising in the process of derivation of the Lorentz transformations. We develop proof of the equality φ(v)=1and eliminate the cause of the incorrect implementation of the method of derivation of the Lorentz transformations used by Einstein.
