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1.
Francesca?PelosiEmail author Rida?T.?Farouki Carla?Manni Alessandra?Sestini 《Advances in Computational Mathematics》2005,22(4):325-352
It is shown that, depending upon the orientation of the end tangents t0,t1 relative to the end point displacement vector p=p1–p0, the problem of G1 Hermite interpolation by PH cubic segments may admit zero, one, or two distinct solutions. For cases where two interpolants exist, the bending energy may be used to select among them. In cases where no solution exists, we determine the minimal adjustment of one end tangent that permits a spatial PH cubic Hermite interpolant. The problem of assigning tangents to a sequence of points p0,...,pn in R3, compatible with a G1 piecewise-PH-cubic spline interpolating those points, is also briefly addressed. The performance of these methods, in terms of overall smoothness and shape-preservation properties of the resulting curves, is illustrated by a selection of computed examples. 相似文献
2.
We investigated the propagation and transformation of laser beams and the formation of caustics in particular directions,
including optical axes of crystals. We found a direct connection between the particular directions and the curvature of wave
surfaces that is determined by the symmetry and optical properties of the crystals. We demonstrated that caustics in particular
directions are characterized by a degree of the curvature degeneracy and are described by particular solutions of the corresponding
nonlinear equations.
__________
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 4, pp. 491–498, July–August, 2007. 相似文献
3.
本文叙述Kustaanheimo–Stiefel变量及其从四元数发展形成的过程,以及Kustaanheimo–Stiefel变换在二体问题正规化中的应用。
相似文献4.
zcan Bekta 《Mathematical Methods in the Applied Sciences》2019,42(16):5215-5232
The split and hyperbolic (countercomplex) octonions are eight‐dimensional nonassociative algebras over the real numbers, which are in the form , where em's have different properties for them. The main purpose of this paper is to define the split‐type octonion and its matrix whose inputs are split‐type octonions and give some properties for them by using the real quaternions, split, and hyperbolic (countercomplex) octonions. On the other hand, to make some definitions, we present some operations on the split‐type octonions. Also, we show that every split‐type octonions can be represented by 2 × 2 real quaternion matrix and 4 × 4 complex number matrix. The information about the determinants of these matrix representations is also given. Besides, the main features of split‐type octonion matrix concept are given by using properties of real quaternion matrices. Then, 8n × 8nreal matrix representations of split‐type octonion matrices are shown, and some algebraic structures are examined. Additionally, we introduce real quaternion adjoint matrices of split‐type octonion matrices. Moreover, necessary and sufficient conditions and definitions are given for split‐type octonion matrices to be special split‐type octonion matrices. We describe some special split‐type octonion matrices. Finally, oct‐determinant of split‐type octonion matrices is defined. Definitive and understandable examples of all definitions, theorems, and conclusions were given for a better understanding of all these concepts. 相似文献
5.
Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane). 相似文献
6.
传递对准是舰载武器惯导系统初始对准的一种有效办法,为满足舰载武器要反应快的要求,必须在短时间内对初始不对准角进行估计并加以补偿。文中建立了采用四元数的传递对准的,线性模型,在此基础上进行卡尔曼滤波,解决了舰载垂直发射导弹的初始对准问题,同时又克服了一般四元数对准模型非线性滤波计算量大,对准时间长的缺点,使导弹能在短时间内完成对准,提高其反应速度,增加其命中率。仿真结果表明,该文提出的快速对准方法具有对准速度快、精度高的优点。 相似文献
7.
《Mathematische Nachrichten》2017,290(14-15):2259-2279
In this paper we continue the study of important Banach spaces of slice hyperholomorphic functions on the quaternionic unit ball by investigating the BMO‐ and VMO‐spaces of slice hyperholomorphic functions. We discuss in particular conformal invariance and a refined characterization of these spaces in terms of Carleson measures. Finally we show the relations with the Bloch and Dirichlet space and the duality relation with the Hardy space . The importance of these spaces in the classical theory is well known. It is therefore worthwhile to study their slice hyperholomorphic counterparts, in particular because slice hyperholomorphic functions were found to have several applications in operator theory and Schur analysis. 相似文献
8.
四元数广义正则函数的斜微商边值问题 总被引:5,自引:0,他引:5
乔玉英 《数学物理学报(A辑)》1997,17(4):447-451
该文前半部分研究四元数广义正则函数的斜微商边值问题解的存在唯一性,后半部分在闻国格教授工作[2]的基础上,研究会有四个自变数一队退化椭圆组的斜微商边值问题解的存在性. 相似文献
9.
In this paper, we discuss the generalized quaternion matrix equation AXB+CX⋆D=E, where X⋆ is one of X, X*, the η-conjugate or the η-conjugate transpose of X with η∈{i,j,k}. Two new real representations of a generalized quaternion matrix are proposed. By using this method, the criteria for the existence and uniqueness of solutions to the mentioned matrix equation as well as the existence of X=± X⋆ solutions to the generalized quaternion matrix equation AXB+CXD=E are derived in a unified way. 相似文献
10.
Gromoll and Meyer have represented a certain exotic 7-sphere as a biquotient of the Lie group . We show for a 2-parameter family of left invariant metrics on that the induced metric on has strictly positive sectional curvature at all points outside four subvarieties of codimension which we describe explicitly.