In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary ...In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bézier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms： AH B-Spline surface and AH T-Spline surface.展开更多
The recurrence algorithm is given for the calculation of NUAH B-splines in the space Sn+1 = span{sinh t, cosh t,tn-3,...,t2.t, 1} (n≥3). The case of NUAH B-spline bases of low order with multiple knot sequences is st...The recurrence algorithm is given for the calculation of NUAH B-splines in the space Sn+1 = span{sinh t, cosh t,tn-3,...,t2.t, 1} (n≥3). The case of NUAH B-spline bases of low order with multiple knot sequences is studied. The limiting cases of UAH B-splines are recovered when shape parameters a's→0+and+∞. Then the corresponding NUAH B-spline curve is defined and its main properties such as shape-preserving properties are investigated.展开更多
Cubic algebraic hyperbolic （AH） Bezier curves and AH spline curves are defined with a positive parameter a in the space spanned by {1, t, sinht, cosht}. Modifying the value of a yields a family ofAH Bezier or spline...Cubic algebraic hyperbolic （AH） Bezier curves and AH spline curves are defined with a positive parameter a in the space spanned by {1, t, sinht, cosht}. Modifying the value of a yields a family ofAH Bezier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called ＂path of AH curve＂ （AH Bezier and AH spline curves） when a changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point.展开更多
Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable becaus...Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied展开更多
In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimens...In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n2 - 2 (where n is the dimension of domain).展开更多
Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The ...Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.展开更多
In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction ...In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and nonco- commutative Hopf algebras.展开更多
In this paper we give the definition of super hyperbolic type Kac-MoodyLie algebra and discuss its imaginary roots systems. Finally, we give the necessary andsufficient condition for Cartan matrices to be of super hyp...In this paper we give the definition of super hyperbolic type Kac-MoodyLie algebra and discuss its imaginary roots systems. Finally, we give the necessary andsufficient condition for Cartan matrices to be of super hyperbolic type.展开更多
WE use the geometric algebra in refs. [1, 2] to study hyperbolic geometry. The n-dimensional hyperbolic space H<sup>n</sup> is taken to be the unit sphere of G<sub>1</sub> (I<sub>-n,1<...WE use the geometric algebra in refs. [1, 2] to study hyperbolic geometry. The n-dimensional hyperbolic space H<sup>n</sup> is taken to be the unit sphere of G<sub>1</sub> (I<sub>-n,1</sub>) with antipodal points identified. We study typically H<sup>2</sup>: the dualities between generalized point and generalized line, between generalized triangle and imaginary triangle; convex generalized triangles; Lorentz transformations; generalized circles and double-cycles, etc. Below we list some of the results.展开更多
基金Projects supported by the National Natural Science Foundation of China (No. 10371110) and the National Basic Research Program (973) of China (No.G2002CB312101)
文摘In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bézier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms： AH B-Spline surface and AH T-Spline surface.
文摘The recurrence algorithm is given for the calculation of NUAH B-splines in the space Sn+1 = span{sinh t, cosh t,tn-3,...,t2.t, 1} (n≥3). The case of NUAH B-spline bases of low order with multiple knot sequences is studied. The limiting cases of UAH B-splines are recovered when shape parameters a's→0+and+∞. Then the corresponding NUAH B-spline curve is defined and its main properties such as shape-preserving properties are investigated.
基金the National Natural Science Foundation of China (No. 60773179)the National Basic Research Program (973) of China (No. G2004CB318000)the School Scientific Research Foundation of Hangzhou Dianzi University (No. KYS091507070), China
文摘Cubic algebraic hyperbolic （AH） Bezier curves and AH spline curves are defined with a positive parameter a in the space spanned by {1, t, sinht, cosht}. Modifying the value of a yields a family ofAH Bezier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called ＂path of AH curve＂ （AH Bezier and AH spline curves） when a changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point.
基金Project supported by the National Natural Science Foundation of China(Grant Nos10475055 and 90503006)the Science Research Fund of Zhejiang Provincial Education Department,China(Grant No20040969)
文摘Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied
基金Supported by the National Natural Science Foundation of China (10501036)the Natural Science Foundation of Fujian Province of China (Z0511003).
文摘In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n2 - 2 (where n is the dimension of domain).
文摘Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.
基金Supported by Zhejiang Provincial Natural Science Foundation of China(Y6100148,Y610027)Education Department of Zhejiang Province(201019063)National Natural Science Foundation of China(11171296)
文摘In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and nonco- commutative Hopf algebras.
文摘In this paper we give the definition of super hyperbolic type Kac-MoodyLie algebra and discuss its imaginary roots systems. Finally, we give the necessary andsufficient condition for Cartan matrices to be of super hyperbolic type.
文摘WE use the geometric algebra in refs. [1, 2] to study hyperbolic geometry. The n-dimensional hyperbolic space H<sup>n</sup> is taken to be the unit sphere of G<sub>1</sub> (I<sub>-n,1</sub>) with antipodal points identified. We study typically H<sup>2</sup>: the dualities between generalized point and generalized line, between generalized triangle and imaginary triangle; convex generalized triangles; Lorentz transformations; generalized circles and double-cycles, etc. Below we list some of the results.
