共查询到20条相似文献,搜索用时 140 毫秒
1.
2.
In this paper, a new method for geometrically continuous interpolation in spheres is proposed. The method is entirely based on the spherical B′ezier curves defined by the generalized de Casteljau algorithm. Firstly we compute the tangent directions and curvature vectors at the endpoints of a spherical B′ezier curve. Then, based on the above results, we design a piecewise spherical B′ezier curve with G 1 and G 2 continuity. In order to get the optimal piecewise curve according to two different criteria, we also give a constructive method to determine the shape parameters of the curve. According to the method, any given spherical points can be directly interpolated in the sphere. Experimental results also demonstrate that the method performs well both in uniform speed and magnitude of covariant acceleration. 相似文献
3.
张建康 《数学物理学报(B辑英文版)》1984,(2)
This paper makes a painstaking discussion for the generalized birth and death processes, describes some properties of processes in fixed quantity: Such as the uniqueness criterion of processes and the distributions of runs and passage times of the generalized birth 相似文献
4.
李志深 《数学物理学报(B辑英文版)》1985,(4)
In this paper the asymptotic solutions of the reduced wave equation (1) in the vicinity of a higher caustic have been found out by means of asymptotic expansions of the generalized Airy function, and the order (or the singularity inder) and the phase's increment of solutions on the higher caustic have been obtained, too. 相似文献
5.
METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE*** 总被引:13,自引:0,他引:13
The Moore-Penrose metric generalized inverse T of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T will be given, and some properties of T will be investigated in this paper. 相似文献
6.
SOME COMPARISONS BETWEEN GENERALIZED ORDER STATISTICS 总被引:1,自引:0,他引:1
Qiu Guoxin Wang Jinshan 《高校应用数学学报(英文版)》2007,22(3):325-333
Some stochastic comparisons of generalized order statistics under the right spread order,the location independent riskier order and the total time transform order are investigated in this paper.The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics. 相似文献
7.
张建康 《数学物理学报(A辑)》1984,(2)
This paper makes a painstaking discussion for the generalized birth and death processes, describes some properties of processes in fixed quantity: Such as the uniqueness criterion of processes and the distributions of runs and passage times of the generalized birth and death processes which non—recurrent in (I); and stay time, 相似文献
8.
Wenhua SUN~* Wancheng SHENG~ 《数学年刊B辑(英文版)》2007,28(6):701-708
The non-selfsimilar Riemann problem for two-dimensional zero-pressure flow in gas dynamics with two constant states separated by a convex curve is considered.By means of the generalized Rankine-Hugoniot relation and the generalized characteristic analysis method,the global solution involving delta shock wave and vacuum is constructed.The explicit solution for a special case is also given. 相似文献
9.
10.
《数学研究与评论》1990,(2)
Ⅰ. Introduction In paper, the embedding theorem and the compact theorem of Rellich and Kondrachev for the Sobolev spaces are generalized to finite element spaces with certain properties. By means of them, the convergence of finite element methods for a class of nonlinear problems are proved in papers.In this paper, the trace embedding and compact theorems for Sobolev spaces will be generalized 相似文献
11.
Bao-huai Sheng 《应用数学学报(英文版)》2005,21(4):529-536
Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f(x)∈L^p(S^q-1),f(x)≥0,f absohutely unegual to 0,1≤p≤+∞,Then,it is proved in the present paper that there is a spherical harmonics PN(x) of order≤N and a constant C〉0 such that where ω(f,δ)L^p=sup 0〈t≤δ‖St(f)-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω(f,N^-1)L^p,St(f,μ)=1/|S^q-2|Sin^2λt ∫-μμ’=t f(μ')dμ' is a translation operator. 相似文献
12.
Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrices 总被引:1,自引:0,他引:1
Li Xia YE Zhi Xiang WU Xue Feng MEI 《数学学报(英文版)》2007,23(10):1729-1744
Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d(y), which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d(y) and weak A-forms of wUq^d(y). 相似文献
13.
A. L. Smirnov 《Journal of Mathematical Sciences》2008,151(3):3052-3068
14.
Zhao Hui HUO Bo Ling GUO 《数学学报(英文版)》2005,21(5):1191-1196
The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local well- posedness is obtained for data in H^s(R)(s 〉 -3/4). For k = 2, local result for data in H^S(R)(s 〉1/4) is obtained. For k = 3, local result for data in H^S(R)(s 〉 -1/6) is obtained. Moreover, the solutions of generalized Korteweg-de Vries-Benjamin-Ono equation converge to the solutions of KdV equation if the term of Benjamin-Ono equation tends to zero. 相似文献
15.
F. Brackx H. De Schepper N. De Schepper F. Sommen 《Advances in Applied Clifford Algebras》2007,17(3):311-330
Orthogonal Clifford analysis in flat m–dimensional Euclidean space focusses on monogenic functions, i.e. null solutions of the rotation invariant vector valued
Dirac operator
, where (
) forms an orthogonal basis for the quadratic space
underlying the construction of the Clifford algebra
. When allowing for complex constants and taking the dimension to be even: m = 2n, the same set of generators produces the complex Clifford algebra
, which we equip with a Hermitean Clifford conjugation and a Hermitean inner product. Hermitean Clifford analysis then focusses
on the simultaneous null solutions of two mutually conjugate Hermitean Dirac operators, naturally arising in the present context
and being invariant under the action of a realization of the unitary group U (n). In this so–called Hermitean setting Clifford–Hermite polynomials are constructed, starting from a Rodrigues formula involving
both Dirac operators mentioned. Due to the specific features of the Hermitean setting, four different types of polynomials
are obtained, two types of even degree and two types of odd degree. We investigate their properties: recurrence relations,
structure, explicit form and orthogonality w.r.t. a deliberately chosen weight function. They also give rise to the definition
of the Hermitean Clifford–Hermite functions, and may be used to develop a Hermitean continuous wavelet transform, see [4]. 相似文献
16.
Some Limit Theorems for a Particle System of Single Point Catalytic Branching Random Walks 总被引:2,自引:0,他引:2
Vladimir VATUTIN Jie XIONG 《数学学报(英文版)》2007,23(6):997-1012
We study the scaling limit for a catalytic branching particle system whose particles perform random walks on Z and can branch at 0 only. Varying the initial (finite) number of particles, we get for this system different limiting distributions. To be more specific, suppose that initially there are n^β particles and consider the scaled process Zt^n(·) = Znt(√n·), where Zt is the measure-valued process 1 and to a representing the original particle system. We prove that Ztn converges to 0 when β 〈1/4 and to a nondegenerate discrete distribution when β=1/4.In addition,if 1/4〈β〈1/2 then n-^(2β-1/2)Zt^n converges to a random limit,while if β 〉21then n^-βZtn converges to a deterministic limit. 相似文献
17.
We study the null solutions of iterated applications of the spherical (Atiyah-Singer) Dirac operator on locally defined polynomial forms on the unit sphere of ; functions valued in the universal Clifford algebra , here called spherical k-regular functions. We construct the kernel functions, get the integral representation formula and Cauchy integral formula
of spherical k-regular functions, and as applications, the weak solutions of higher order inhomogeneous spherical (Atiyah-Singer) Dirac
equations . We obtain, in particular, the weak solution of an inhomogeneous spherical Poisson equation Δ
s
g = f.
This work was partially supported by NNSF of China (No.10471107) and RFDP of Higher Education (No.20060486001). 相似文献
18.
Let
be a unit sphere of the d–dimensional Euclidean space ℝ
d
and let
(0 < p ≤ 1) denote the real Hardy space on
For 0 < p ≤ 1 and
let
E
j
(f,H
p
) (j = 0, 1, ...) be the best approximation of f by spherical polynomials of degree less than or
equal to j, in the space
Given a distribution f on
its Cesàro mean of order δ > –1 is
denoted by
For 0 < p ≤ 1, it is known that
is the critical index for the uniform
summability of
in the metric H
p
. In this paper, the following result is proved:
Theorem
Let
0<p<1 and
Then for
where
A
N
(f)≈B
N
(f) means that there’s a positive constant C, independent of N and f, such that
In the case
d = 2, this result was proved by Belinskii in 1996.
The authors are partially supported by NNSF of China under the grant # 10071007 相似文献
19.
Herz-type Triebel-Lizorkin Spaces, Ⅰ 总被引:1,自引:0,他引:1
Jing Shi XU Da Chun YANG 《数学学报(英文版)》2005,21(3):643-654
Let s ∈R,0〈β≤∞, 0〈 q, p〈 ∞ and-n/q〈α. In this paper the authors introduce the Herz-type Triebel-Lizorkin spaces,Kq^α,pFβ^s(R^n)andKq^α,pFβ^s(R^n)which are the generalizations of the well-known Herz-type spaces and the inhomogeneous Triebel-Lizorkin spaces, Some properties on these Herz-type Triebel Lizorkin spaces are also given. 相似文献
20.
Lowest Landau level approach in superconductivity for the Abrikosov lattice close to
$$H_{{c}_{2}}$$
We study the Ginzburg–Landau energy for a superconductor submitted to a magnetic field just below the “second critical field” . When the Ginzburg–Landau parameter ε is small, we show that the mean energy per unit volume can be approximated by a reduced
energy on a torus. Moreover, we expand this reduced energy in terms of : when this quantity gets small, the problem amounts to a minimization problem on a finite-dimensional space, equivalent to
the “lowest Landau level” in other approaches. The functions in this finite-dimensional space can themselves be expressed
via the Jacobi Theta function of a lattice. This connects the Ginzburg–Landau energy to the “Abrikosov problem” of locating
vortices optimally on a lattice.
相似文献