In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total vari...In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.展开更多
The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were...The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were derived. Furthermore, whether these curves lie on a curvature line or not was investigated and some applications were given.展开更多
In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obt...In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obtain the relativity-corrected geometric potential V_(g)’,and a novel effective potential V(g) related to both the Gaussian curvature and the geodesic curvature of the rotating surface.The Coriolis effect and the centrifugal potential also appear in the equation.Subsequently,we apply the surface Schrodinger equation to a rotating cylinder,sphere and toms surfaces,in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.展开更多
Necessary and sufficient conditions for the existence of the group inverse of the block matrix in Minkowski Space are studied, where are both square and . The representation of this group inverse and some related addi...Necessary and sufficient conditions for the existence of the group inverse of the block matrix in Minkowski Space are studied, where are both square and . The representation of this group inverse and some related additive results are also given.展开更多
In this paper,a new generalized m-CMP inverse is introduced into the Minkowski space,and its related properties are discussed.Secondly,three different expressions of m-CMP inverse are listed,namely Hartwig-Spindel-boc...In this paper,a new generalized m-CMP inverse is introduced into the Minkowski space,and its related properties are discussed.Secondly,three different expressions of m-CMP inverse are listed,namely Hartwig-Spindel-bock decomposition,full-rank decomposition and integral expression.Finally,the application of the inverse m-CMP equation in solving linear equations is given.展开更多
Studying the geometric flow plays a powerful role in mathematics and physics. In this paper, we introduce the mean curvature flow on Finsler manifolds and give a number of examples of the mean curvature flow. For Mink...Studying the geometric flow plays a powerful role in mathematics and physics. In this paper, we introduce the mean curvature flow on Finsler manifolds and give a number of examples of the mean curvature flow. For Minkowski spaces, a special case of Finsler manifolds, we prove the short time existence and uniqueness for solutions of the mean curvature flow and prove that the flow preserves the convexity and mean convexity.We also derive some comparison principles for the mean curvature flow.展开更多
Many complete extremal surfaces of mixed type are constructed with explicit expressions. Itis proved that there exist complete extremal surfaces of mixed type which have a given numberof time-like spans and a given nu...Many complete extremal surfaces of mixed type are constructed with explicit expressions. Itis proved that there exist complete extremal surfaces of mixed type which have a given numberof time-like spans and a given number of annular ends.展开更多
In this paper we study translation surfaces of some new types in 3-Minkowski space E13 and give some classifications of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.
A class of curvature estimates of spacelike admissible hypersurfaces related to translating solitons of the higher order mean curvature flow in the Minkowski space is ob- tained, which may offer an idea to study an op...A class of curvature estimates of spacelike admissible hypersurfaces related to translating solitons of the higher order mean curvature flow in the Minkowski space is ob- tained, which may offer an idea to study an open question of the existence of hypersurfaces with the prescribed higher mean curvature in the Minkowski space.展开更多
1 .Introduotion Theudy of ojnal surfaee,in Euolidean,Paoe(or other Rleman"iananifold。)has a long history.There were plen of very deop and very beautifulsults obtained byveral generations of rnathe
The distinctions between locality and non-locality as well as causality and excess correlation may be related to coupling between increments of space-time or to the total space-time within the universe as a unit. The ...The distinctions between locality and non-locality as well as causality and excess correlation may be related to coupling between increments of space-time or to the total space-time within the universe as a unit. The most likely candidates for the latter are the proton and the electron when related by Minkowski’s space-time. When two velocities: light in a vacuum for locality and the “entanglement” velocity based upon parameters that define the universe for non-locality, are considered the two times required to produce identities for the -v<sup>2</sup>t<sup>2</sup> components are frequencies whose energies approximate the neutral hydrogen line (primarily associated with shifts in electron spin direction) and the mass equivalence of a proton. The values for the additional three spatial dimensions required to produce a solution whose square root is not imaginary and greater than zero are within the domains of the surface areas of the human cerebrum. Detailed calculations converge to show that the proportions of energy that represent the electron’s Compton energy and the proton’s mass equivalent may be central to the condition of excess correlation within the cerebral volume. Proton channels within the neuronal cell plasma membranes whose pH-dependent specific currents produce the required magnetic field strengths could be the physical substrates by which excess correlations between brain activities of human subjects separated by non-local distances might occur. If protons are considered as the basic Eddington (number) units of the universe then Mach’s principle that any component of the universe is determined by all of its components may be testable empirically.展开更多
Let the coordinatex=(x 0,x 1,x 2,x 3) of the Minkowski spaceM 4 be arranged into a matrix $$H_x = \left( {\begin{array}{*{20}c} {x^0 + x^1 x^2 + ix^3 } \\ {x^2 - ix^3 x^0 - x^1 } \\ \end{array} } \right).$$ Then the M...Let the coordinatex=(x 0,x 1,x 2,x 3) of the Minkowski spaceM 4 be arranged into a matrix $$H_x = \left( {\begin{array}{*{20}c} {x^0 + x^1 x^2 + ix^3 } \\ {x^2 - ix^3 x^0 - x^1 } \\ \end{array} } \right).$$ Then the Minkowski metric can be written as $$ds^2 = \eta _{jk} dx^j dx^k = det dH_x $$ . Imbed the space of 2 × 2 Hermitian matrices into the complex Grassmann manifoldF(2,2), the space of complex 4-planes passing through the origin ofC 2×4. The closure $\bar M^4 $ ofM 4 inF(2,2) is the compactification ofM 4. It is known that the conformal group acts on $\bar M^4 $ . It has already been proved that onF(2,2) there is anSu(2)-connection $$B(Z, dZ) = \Gamma (Z, dZ) - \Gamma (Z, dZ)^ + - \frac{{tr[\Gamma (Z, dZ) - \Gamma (Z, dZ^ + ]}}{2}I.$$ whereZ is a 2 × 2 complex matrix andZ ?the complex conjugate and transposed matrix ofZ. Restrict this connection to $\bar M^4 $ $$C(H_x ,dH_x ) = [B(Z, dZ)]_{z = H_x } = C_j (x)dx^j ,$$ which is anSu(2)-connection on $\bar M^4 $ . It is proved that its curvature form $$F: = dC + C \Lambda C = \frac{1}{2}\left[ {\frac{{\partial C_k }}{{\partial x^j }} - \frac{{\partial C_j }}{{\partial x^k }} + C_j C_k - C_k C_j } \right]dx^j \Lambda dx^k = :F_{jk} dx^j \Lambda dx^k $$ satisfies the Yang-Mills equation $$\eta ^\mu \left[ {\frac{{\partial F_{jk} }}{{\partial x^l }} + C_l F_{jk} - F_{jk} C_l } \right] = 0.$$ .展开更多
We reexamined the elastic collision problems in the special relativity for both one and two dimensions from a different point of view. In order to obtain the final states in the laboratory system of the collision prob...We reexamined the elastic collision problems in the special relativity for both one and two dimensions from a different point of view. In order to obtain the final states in the laboratory system of the collision problems, almost all textbooks in the special relativity calculated the simultaneous equations. In contrast to this, we make a detour through the center-of-mass system. The two frames of references are connected by the Lorentz transformation with the velocity of the center-of-mass. This route for obtaining the final states is easy for students to understand the collision problems. For one dimensional case, we also give an example for illustrating the states of the particles in the Minkowski momentum space, which shows the whole story of the collision.展开更多
We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkow...We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkowski space will be characterized by using some aspects of differential geometry. Types of the deformation retracts of some curves in Minkowski 3-space are obtained. The relations between the foldings and the deformation retracts of some curves are deduced. The connections between some transformations and time like, space like, light like of some curves in Minkowski 3-space are also presented.展开更多
基金Supported in part by NSFC(No.11971005)the Fundamental Research Funds for the Central Universities(Nos.GK202101008,GK202102012)。
文摘In this paper,we use the solution of the even functional Minkowski problem to show that there is a minimizing affine Minkowski total variation of the function of bounded variation.Moreover,for the Minkowski total variation,we use the method of convexation to establish the same conclusion as the convex body space.
文摘The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were derived. Furthermore, whether these curves lie on a curvature line or not was investigated and some applications were given.
基金jointly supported by the National Nature Science Foundation of China(Grants No.11774157,No.11934008,No.12075117,No.51721001,No.11890702,No.11625418,No.11535005,No.11690030)funded by the Natural Science Foundation of Shandong Province of China(Grant No.ZR2020MA091)。
文摘In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obtain the relativity-corrected geometric potential V_(g)’,and a novel effective potential V(g) related to both the Gaussian curvature and the geodesic curvature of the rotating surface.The Coriolis effect and the centrifugal potential also appear in the equation.Subsequently,we apply the surface Schrodinger equation to a rotating cylinder,sphere and toms surfaces,in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.
文摘Necessary and sufficient conditions for the existence of the group inverse of the block matrix in Minkowski Space are studied, where are both square and . The representation of this group inverse and some related additive results are also given.
文摘In this paper,a new generalized m-CMP inverse is introduced into the Minkowski space,and its related properties are discussed.Secondly,three different expressions of m-CMP inverse are listed,namely Hartwig-Spindel-bock decomposition,full-rank decomposition and integral expression.Finally,the application of the inverse m-CMP equation in solving linear equations is given.
基金supported by National Natural Science Foundation of China(Grant No.11471246)
文摘Studying the geometric flow plays a powerful role in mathematics and physics. In this paper, we introduce the mean curvature flow on Finsler manifolds and give a number of examples of the mean curvature flow. For Minkowski spaces, a special case of Finsler manifolds, we prove the short time existence and uniqueness for solutions of the mean curvature flow and prove that the flow preserves the convexity and mean convexity.We also derive some comparison principles for the mean curvature flow.
文摘Many complete extremal surfaces of mixed type are constructed with explicit expressions. Itis proved that there exist complete extremal surfaces of mixed type which have a given numberof time-like spans and a given number of annular ends.
基金Supported by the Joint Research of National Nature Science Foundation of ChinaNational Research Foundation (Grant No.11071032)Chern Institute of Mathematics and Northeastern University
文摘In this paper we study translation surfaces of some new types in 3-Minkowski space E13 and give some classifications of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.
基金the National Natural Science Foundation of China(No.11001261)
文摘A class of curvature estimates of spacelike admissible hypersurfaces related to translating solitons of the higher order mean curvature flow in the Minkowski space is ob- tained, which may offer an idea to study an open question of the existence of hypersurfaces with the prescribed higher mean curvature in the Minkowski space.
文摘1 .Introduotion Theudy of ojnal surfaee,in Euolidean,Paoe(or other Rleman"iananifold。)has a long history.There were plen of very deop and very beautifulsults obtained byveral generations of rnathe
文摘The distinctions between locality and non-locality as well as causality and excess correlation may be related to coupling between increments of space-time or to the total space-time within the universe as a unit. The most likely candidates for the latter are the proton and the electron when related by Minkowski’s space-time. When two velocities: light in a vacuum for locality and the “entanglement” velocity based upon parameters that define the universe for non-locality, are considered the two times required to produce identities for the -v<sup>2</sup>t<sup>2</sup> components are frequencies whose energies approximate the neutral hydrogen line (primarily associated with shifts in electron spin direction) and the mass equivalence of a proton. The values for the additional three spatial dimensions required to produce a solution whose square root is not imaginary and greater than zero are within the domains of the surface areas of the human cerebrum. Detailed calculations converge to show that the proportions of energy that represent the electron’s Compton energy and the proton’s mass equivalent may be central to the condition of excess correlation within the cerebral volume. Proton channels within the neuronal cell plasma membranes whose pH-dependent specific currents produce the required magnetic field strengths could be the physical substrates by which excess correlations between brain activities of human subjects separated by non-local distances might occur. If protons are considered as the basic Eddington (number) units of the universe then Mach’s principle that any component of the universe is determined by all of its components may be testable empirically.
文摘Let the coordinatex=(x 0,x 1,x 2,x 3) of the Minkowski spaceM 4 be arranged into a matrix $$H_x = \left( {\begin{array}{*{20}c} {x^0 + x^1 x^2 + ix^3 } \\ {x^2 - ix^3 x^0 - x^1 } \\ \end{array} } \right).$$ Then the Minkowski metric can be written as $$ds^2 = \eta _{jk} dx^j dx^k = det dH_x $$ . Imbed the space of 2 × 2 Hermitian matrices into the complex Grassmann manifoldF(2,2), the space of complex 4-planes passing through the origin ofC 2×4. The closure $\bar M^4 $ ofM 4 inF(2,2) is the compactification ofM 4. It is known that the conformal group acts on $\bar M^4 $ . It has already been proved that onF(2,2) there is anSu(2)-connection $$B(Z, dZ) = \Gamma (Z, dZ) - \Gamma (Z, dZ)^ + - \frac{{tr[\Gamma (Z, dZ) - \Gamma (Z, dZ^ + ]}}{2}I.$$ whereZ is a 2 × 2 complex matrix andZ ?the complex conjugate and transposed matrix ofZ. Restrict this connection to $\bar M^4 $ $$C(H_x ,dH_x ) = [B(Z, dZ)]_{z = H_x } = C_j (x)dx^j ,$$ which is anSu(2)-connection on $\bar M^4 $ . It is proved that its curvature form $$F: = dC + C \Lambda C = \frac{1}{2}\left[ {\frac{{\partial C_k }}{{\partial x^j }} - \frac{{\partial C_j }}{{\partial x^k }} + C_j C_k - C_k C_j } \right]dx^j \Lambda dx^k = :F_{jk} dx^j \Lambda dx^k $$ satisfies the Yang-Mills equation $$\eta ^\mu \left[ {\frac{{\partial F_{jk} }}{{\partial x^l }} + C_l F_{jk} - F_{jk} C_l } \right] = 0.$$ .
文摘We reexamined the elastic collision problems in the special relativity for both one and two dimensions from a different point of view. In order to obtain the final states in the laboratory system of the collision problems, almost all textbooks in the special relativity calculated the simultaneous equations. In contrast to this, we make a detour through the center-of-mass system. The two frames of references are connected by the Lorentz transformation with the velocity of the center-of-mass. This route for obtaining the final states is easy for students to understand the collision problems. For one dimensional case, we also give an example for illustrating the states of the particles in the Minkowski momentum space, which shows the whole story of the collision.
文摘We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkowski space will be characterized by using some aspects of differential geometry. Types of the deformation retracts of some curves in Minkowski 3-space are obtained. The relations between the foldings and the deformation retracts of some curves are deduced. The connections between some transformations and time like, space like, light like of some curves in Minkowski 3-space are also presented.
