Let （M, g） be an n-dimensional Riemannian manifold and T＊M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki ...Let （M, g） be an n-dimensional Riemannian manifold and T＊M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki type metric by using some compati-ble paracomplex structures on T＊M. Second, we construct locally decomposable Golden Riemannian structures on T＊M . Finally we investigate curvature properties of T＊M .展开更多
A neutrosophic multi-valued set(NMVS)is a crucial representation for true,false,and indeterminate multivalued information.Then,a consistent single-valued neutrosophic set(CSVNS)can effectively reflect the mean and con...A neutrosophic multi-valued set(NMVS)is a crucial representation for true,false,and indeterminate multivalued information.Then,a consistent single-valued neutrosophic set(CSVNS)can effectively reflect the mean and consistency degree of true,false,and indeterminate multi-valued sequences and solve the operational issues between different multi-valued sequence lengths in NMVS.However,there has been no research on consistent single-valued neutrosophic similarity measures in the existing literature.This paper proposes cotangent similarity measures and weighted cotangent similarity measures between CSVNSs based on cotangent function in the neutrosophic multi-valued setting.The cosine similarity measures showthe cosine of the angle between two vectors projected into amultidimensional space,rather than their distance.The cotangent similaritymeasures in this study can alleviate several shortcomings of cosine similarity measures in vector space to a certain extent.Then,a decisionmaking approach is presented in viewof the established cotangent similarity measures in the case of NMVSs.Finally,the developed decision-making approach is applied to selection problems of potential cars.The proposed approach has obtained two different results,which have the same sort sequence as the compared literature.The decision results prove its validity and effectiveness.Meantime,it also provides a new manner for neutrosophic multi-valued decision-making issues.展开更多
Let(M,J,g)be an anti-Kähler manifold of dimension n=2k with an almost complex structure J and a pseudo-Riemannian metric g and let T*M be its cotangent bundle with modifiedRiemannian extension metric g■,G.The mo...Let(M,J,g)be an anti-Kähler manifold of dimension n=2k with an almost complex structure J and a pseudo-Riemannian metric g and let T*M be its cotangent bundle with modifiedRiemannian extension metric g■,G.The modified Riemannian extension metric g,g is obtained by deformation in the horizontal part of the Riemannian extension known in the literature by means of the twin Norden metric G.The paper aims first to examine the curvature properties of the cotangent bundle T*M with modified Riemannian extension metric g,G and second to study some geometric solitons on the cotangent bundle T*M according to the modifiedRiemannian extension metric g■,G.展开更多
Let k be an algebraically closed field of characteristic p 〉 0, X a smooth projective variety over k with a fixed ample divisor H, FX：X → X the absolute Frobenius morphism on X. Let E be a rational GLn（k）-bundle ...Let k be an algebraically closed field of characteristic p 〉 0, X a smooth projective variety over k with a fixed ample divisor H, FX：X → X the absolute Frobenius morphism on X. Let E be a rational GLn（k）-bundle on X, and ρ：GLn（k） → GLm（k） a rational GLn（k）-representation of degree at most d such that ρ maps the radical R（GLn（k）） of GLn（k） into the radical R（GLm（k）） of GLm（k）. We show that if FXN＊（E） is semistable for some integer N ≥ max0 〈 r 〈 m （rm） · logp（dr）, then the induced rational GLm（k）-bundle E（GLm（k）） is semistable. As an application, if dim X=n, we get a sufficient condition for the semistability of Frobenius direct image FX＊（ρ＊（ΩX1））, where ρ＊（ΩX1） is the vector bundle obtained from ΩX1 via the rational representation ρ.展开更多
In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
In this paper,the modern geometrical structure of analytical mechanics,the exterior differential forms and the geometrical meaning of dynamic equations are briefly discussed.
The ends of the velocity vectors of the decay particles of resonance represent material points-velocities in the hyperbolic Lobachevsky velocity space of negative curvature k=−1/C2(C=1 is the speed of light,the rest m...The ends of the velocity vectors of the decay particles of resonance represent material points-velocities in the hyperbolic Lobachevsky velocity space of negative curvature k=−1/C2(C=1 is the speed of light,the rest masses of the decay particles are assigned to the points-velocities).Two points-velocities of the decay particles can be connected by a line segment and an arc of a line of constant curvature 0,called the oricycle.Archimedes’leverage laws define a 3rd point on the arc of the oricycle to which an additive mass(sum of rest masses of particles)is assigned.Connecting 3 points-velocities by line segments,we obtain isosceles triangles of decays of resonances in the Beltrami model of the Lobachevsky velocity space.In the decay triangles of resonances,the golden section is found and the Stewart,Brettschneider theorems on oricyclic arcs are satisfied.Near the decay triangles of scalar,strange mesons andΔ,N baryons,isosceles triangles-satellites with integer values of their characteristics were found.On the satellite triangles,the Lorentz invariant function—the product of the length of the arc of the oricycle subtending the base and the cotangent of half the angle at the vertex opposite the base—takes integer values.The function is called the oricyclic cotangent of a triangle(OCT).In addition to the integer values of OCT,these satellite triangles also have the sum of the hyperbolic cosines of the lengths of the lateral sides and the hyperbolic cosines of the base lengths equal to integers.These satellite triangles are called Heron triangles.On Heron triangles,the generalized cosines of the angles between the tangent to the oricycle at the point-velocity of the additive mass and the tan-gent at the point-velocity of the base of the triangle take multiples of 1/2 values.展开更多
In [2-4], symplectic schemes of arbitrary order are constructed by generating functions. However the construction of generating functions is dependent on the chosen coordinates. One would like to know that under what ...In [2-4], symplectic schemes of arbitrary order are constructed by generating functions. However the construction of generating functions is dependent on the chosen coordinates. One would like to know that under what circumstance the construction of generating functions will be independent of the coordinates. The generating functions are deeply associated with the conservation laws, so it is important to study their properties and computations. This paper will begin with the study of Darboux transformation, then in section 2, a normalization Darboux transformation will be defined naturally. Every symplectic scheme which is constructed from Darboux transformation and compatible with the Hamiltonian equation will satisfy this normalization condition. In section 3, we will study transformation properties of generator maps and generating functions. Section 4 will be devoted to the study of the relationship between the invariance of generating functions and the generator maps. In section 5, formal symplectic erengy of symplectic schemes are presented.展开更多
Using the complete lift on tangent bundles, the authors construct the complete lift on cotangent bundles of tensor fields with the aid of a musical isomorphism. In this new framework, the authors have a new intrepreta...Using the complete lift on tangent bundles, the authors construct the complete lift on cotangent bundles of tensor fields with the aid of a musical isomorphism. In this new framework, the authors have a new intrepretation of the complete lift of tensor fields on cotangent bundles.展开更多
The author shows the non-differentiability of the Teichmuller cometric for infinite-dimensional Teichmuller spaces. Let Y be a Riemann surface, the Teichm uller space of Y denoted by T(Y). For[X, f]∈T(Y), where [X. f...The author shows the non-differentiability of the Teichmuller cometric for infinite-dimensional Teichmuller spaces. Let Y be a Riemann surface, the Teichm uller space of Y denoted by T(Y). For[X, f]∈T(Y), where [X. f] is an equivalent class of marked Riemann surfaces (X. f),展开更多
Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that...Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ω~b-related.As consequence of analyze of connections between the complete lift ~cω_(T M )of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle,the authors proved that dp is a pullback o f^cω_(TM)by ω~?.Also,the authors investigate the complete lift ~cφ_T~*_M )of almost complex structure φ to cotangent bundle and prove that it is a transform by ω~?of complete lift^cφ_(T M )to tangent bundle if the triple(M,ω,φ)is an almost holomorphic A-manifold.The transform of complete lifts of vector-valued 2-form is also studied.展开更多
The main purpose of this paper is to study the deformed Riemannian extension▽g +VG··in the cotangent bundle, where G is a twin Norden metric on the base manifold.
文摘Let （M, g） be an n-dimensional Riemannian manifold and T＊M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki type metric by using some compati-ble paracomplex structures on T＊M. Second, we construct locally decomposable Golden Riemannian structures on T＊M . Finally we investigate curvature properties of T＊M .
文摘A neutrosophic multi-valued set(NMVS)is a crucial representation for true,false,and indeterminate multivalued information.Then,a consistent single-valued neutrosophic set(CSVNS)can effectively reflect the mean and consistency degree of true,false,and indeterminate multi-valued sequences and solve the operational issues between different multi-valued sequence lengths in NMVS.However,there has been no research on consistent single-valued neutrosophic similarity measures in the existing literature.This paper proposes cotangent similarity measures and weighted cotangent similarity measures between CSVNSs based on cotangent function in the neutrosophic multi-valued setting.The cosine similarity measures showthe cosine of the angle between two vectors projected into amultidimensional space,rather than their distance.The cotangent similaritymeasures in this study can alleviate several shortcomings of cosine similarity measures in vector space to a certain extent.Then,a decisionmaking approach is presented in viewof the established cotangent similarity measures in the case of NMVSs.Finally,the developed decision-making approach is applied to selection problems of potential cars.The proposed approach has obtained two different results,which have the same sort sequence as the compared literature.The decision results prove its validity and effectiveness.Meantime,it also provides a new manner for neutrosophic multi-valued decision-making issues.
文摘Let(M,J,g)be an anti-Kähler manifold of dimension n=2k with an almost complex structure J and a pseudo-Riemannian metric g and let T*M be its cotangent bundle with modifiedRiemannian extension metric g■,G.The modified Riemannian extension metric g,g is obtained by deformation in the horizontal part of the Riemannian extension known in the literature by means of the twin Norden metric G.The paper aims first to examine the curvature properties of the cotangent bundle T*M with modified Riemannian extension metric g,G and second to study some geometric solitons on the cotangent bundle T*M according to the modifiedRiemannian extension metric g■,G.
基金Supported by National Natural Science Foundation of China(Grant No.11501418)Shanghai Sailing Program(Grant No.15YF1412500)
文摘Let k be an algebraically closed field of characteristic p 〉 0, X a smooth projective variety over k with a fixed ample divisor H, FX：X → X the absolute Frobenius morphism on X. Let E be a rational GLn（k）-bundle on X, and ρ：GLn（k） → GLm（k） a rational GLn（k）-representation of degree at most d such that ρ maps the radical R（GLn（k）） of GLn（k） into the radical R（GLm（k）） of GLm（k）. We show that if FXN＊（E） is semistable for some integer N ≥ max0 〈 r 〈 m （rm） · logp（dr）, then the induced rational GLm（k）-bundle E（GLm（k）） is semistable. As an application, if dim X=n, we get a sufficient condition for the semistability of Frobenius direct image FX＊（ρ＊（ΩX1））, where ρ＊（ΩX1） is the vector bundle obtained from ΩX1 via the rational representation ρ.
文摘In this paper.we discuss Lagrangian vector field on Kahler manifold and use it to describe and solve some problem in Newtonican and Lagrangian Mechanics on Kahler Manifold.
基金Work supported by NSF of Henan Education Commission
文摘In this paper,the modern geometrical structure of analytical mechanics,the exterior differential forms and the geometrical meaning of dynamic equations are briefly discussed.
基金financed by the LLP“Industry 4.0”,Almaty,Kazakhstan.
文摘The ends of the velocity vectors of the decay particles of resonance represent material points-velocities in the hyperbolic Lobachevsky velocity space of negative curvature k=−1/C2(C=1 is the speed of light,the rest masses of the decay particles are assigned to the points-velocities).Two points-velocities of the decay particles can be connected by a line segment and an arc of a line of constant curvature 0,called the oricycle.Archimedes’leverage laws define a 3rd point on the arc of the oricycle to which an additive mass(sum of rest masses of particles)is assigned.Connecting 3 points-velocities by line segments,we obtain isosceles triangles of decays of resonances in the Beltrami model of the Lobachevsky velocity space.In the decay triangles of resonances,the golden section is found and the Stewart,Brettschneider theorems on oricyclic arcs are satisfied.Near the decay triangles of scalar,strange mesons andΔ,N baryons,isosceles triangles-satellites with integer values of their characteristics were found.On the satellite triangles,the Lorentz invariant function—the product of the length of the arc of the oricycle subtending the base and the cotangent of half the angle at the vertex opposite the base—takes integer values.The function is called the oricyclic cotangent of a triangle(OCT).In addition to the integer values of OCT,these satellite triangles also have the sum of the hyperbolic cosines of the lengths of the lateral sides and the hyperbolic cosines of the base lengths equal to integers.These satellite triangles are called Heron triangles.On Heron triangles,the generalized cosines of the angles between the tangent to the oricycle at the point-velocity of the additive mass and the tan-gent at the point-velocity of the base of the triangle take multiples of 1/2 values.
文摘In [2-4], symplectic schemes of arbitrary order are constructed by generating functions. However the construction of generating functions is dependent on the chosen coordinates. One would like to know that under what circumstance the construction of generating functions will be independent of the coordinates. The generating functions are deeply associated with the conservation laws, so it is important to study their properties and computations. This paper will begin with the study of Darboux transformation, then in section 2, a normalization Darboux transformation will be defined naturally. Every symplectic scheme which is constructed from Darboux transformation and compatible with the Hamiltonian equation will satisfy this normalization condition. In section 3, we will study transformation properties of generator maps and generating functions. Section 4 will be devoted to the study of the relationship between the invariance of generating functions and the generator maps. In section 5, formal symplectic erengy of symplectic schemes are presented.
基金supported by the Scientific and Technological Research Council of Turkey(No.112T111)
文摘Using the complete lift on tangent bundles, the authors construct the complete lift on cotangent bundles of tensor fields with the aid of a musical isomorphism. In this new framework, the authors have a new intrepretation of the complete lift of tensor fields on cotangent bundles.
文摘The author shows the non-differentiability of the Teichmuller cometric for infinite-dimensional Teichmuller spaces. Let Y be a Riemann surface, the Teichm uller space of Y denoted by T(Y). For[X, f]∈T(Y), where [X. f] is an equivalent class of marked Riemann surfaces (X. f),
文摘Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ω~b-related.As consequence of analyze of connections between the complete lift ~cω_(T M )of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle,the authors proved that dp is a pullback o f^cω_(TM)by ω~?.Also,the authors investigate the complete lift ~cφ_T~*_M )of almost complex structure φ to cotangent bundle and prove that it is a transform by ω~?of complete lift^cφ_(T M )to tangent bundle if the triple(M,ω,φ)is an almost holomorphic A-manifold.The transform of complete lifts of vector-valued 2-form is also studied.
基金supported by the Scientific and Technological Research Council of Turkey(MFAG-1001,No.112T111)
文摘The main purpose of this paper is to study the deformed Riemannian extension▽g +VG··in the cotangent bundle, where G is a twin Norden metric on the base manifold.
