共查询到20条相似文献,搜索用时 31 毫秒
1.
Swanhild Bernstein Helmut Schaeben 《Mathematical Methods in the Applied Sciences》2005,28(11):1269-1289
We consider a one‐dimensional Radon transform on the group SO (3), which is motivated by texture goniometry. In particular, we will derive several inversion formulae and compare them with the inversion of the one‐dimensional spherical Radon transform on ??3 for even functions. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
2.
We consider cubature formulae which are invariant with respect to a transformation group and prove sufficient conditions for such formulae to have positive weights. This is worked out for different symmetries: we consider central symmetric, symmetric and fully symmetric cubature formulae. The theoretical results are illustrated with examples. 相似文献
3.
This article is about spherical simplices in the unit sphere.One of the purposes is to give a relation of dihedral anglesof a spherical simplex and its polar, and the other is to givetwo simple formulae of volumes of spherical simplices and theirpolars. We can calculate the volume of a spherical simplex andthe sum of volumes of it and its polar from these formulae forthe unit sphere in the odd- and even-dimensional Euclidean spaces,respectively. 相似文献
4.
Wolfgang Weil 《Mathematische Nachrichten》2001,223(1):161-184
The iterated translative versions of classical kinematic integral formulae for intrinsic volumes and curvature measures have led to a series of mixed functionals and mixed measures of convex bodies. Here, we present a systematic study of the integral geometric relations which hold for these mixed measures and functionals. We give new formulae involving halfspaces, reduction formulae and some spherical representations and also generalize some earlier results. 相似文献
5.
Sam Elliott 《Journal of Functional Analysis》2009,256(12):4162-4186
Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known necessary condition for the boundedness of such operators, and use it to provide a complete classification of the bounded composition operators with rational symbol. We then consider some specific examples, comparing our formulae with each other, and with other easily deduced formulae for simple cases. 相似文献
6.
《Journal of Computational and Applied Mathematics》1997,81(1):83-99
We consider interpolatory quadrature formulae, relative to the Legendre weight function on [−1, 1], having as nodes the zeros of the nth-degree Chebyshev polynomial of the third or fourth kind. Szegö has shown that the weights of these formulae are all positive. We derive explicit formulae for the weights, and subsequently use them to establish the convergence of the quadrature formulae for functions having a monotonic singularity at one or both endpoints of [−1, 1]. Moreover, we generate two new quadrature formulae, by adding 1, −1 to the sets of nodes considered previously, and show that these new formulae have almost all weights positive, exceptions occurring only among the weights corresponding to 1, −1. Also, we determine the precise degree of exactness of all the quadrature formulae in consideration, we obtain asymptotically optimal error bounds for these formulae, and show that almost all of them are nondefinite, exceptions occurring only among the formulae with a small number of nodes. 相似文献
7.
In this paper we study weighted spherical semidesigns, i.e., systems of points on a sphere of a specific type. We propose a new proof of the necessary and sufficient condition for a system of points on a sphere to be a weighted spherical semidesign. This criterion gives new approaches to the construction of cubature formulae for calculating integrals over a sphere with the degree of accuracy of 5 and 9. 相似文献
8.
In applications, for instance in optics and astrophysics, thereis a need for high-accuracy integration formulae for functionson the sphere. To construct better formulae than previouslyused, almost equidistantly spaced nodes on the sphere and weightsbelonging to these nodes are required. This problem is closelyrelated to an optimal dispersion problem on the sphere and tothe theories of spherical designs and multivariate Gauss quadratureformulae. We propose a two-stage algorithm to compute optimal point locationson the unit sphere and an appropriate algorithm to calculatethe corresponding weights of the cubature formulae. Points aswell as weights are computed to high accuracy. These algorithmscan be extended to other integration problems. Numerical examplesshow that the constructed formulae yield impressively smallintegration errors of up to 10-12. 相似文献
9.
Hans E. Debrunner 《Geometriae Dedicata》1990,33(2):123-152
We exhibit a dissection, with one degree of freedom, of an arbitrary orthoscheme in Euclidean, spherical or hyperbolic d-space into d+1 orthoschemes (Section 2); this can be interpreted as a set of relations in the scissors congruence group or, weaker, as a set of functional equations for the volume. Besides special cases where the dissection is into mutually congruent parts, we obtain, in the spherical case and for a special value of the parameter, scissors congruence formulae similar to Schläfli's period formulae for the spherical orthoscheme volume (see Section 5). In Section 6 we use the dissection to explain the structure of the volume formula for asymptotic hyperbolic 3-orthoschemes due to Lobachevsky. Finally, in Section 7, by exploiting symmetries, we show that two systems of special volume relations of Schläfli (in spherical d-space) and Coxeter (for all three geometries in dimension 3) hold even on the level of dissection. In particular, it seems that all the presently known exact values for the volume of special spherical 3-simplexes hold, independently of Schläfli's differential formula, as consequences of scissors congruence relations. 相似文献
10.
Richard M. Slevinsky Hassan Safouhi 《Journal of Computational and Applied Mathematics》2009,233(2):405-419
We present new formulae (the Slevinsky–Safouhi formulae I and II) for the analytical development of higher order derivatives. These formulae, which are analytic and exact, represent the kth derivative as a discrete sum of only k+1 terms. Involved in the expression for the kth derivative are coefficients of the terms in the summation. These coefficients can be computed recursively and they are not subject to any computational instability. As examples of applications, we develop higher order derivatives of Legendre functions, Chebyshev polynomials of the first kind, Hermite functions and Bessel functions. We also show the general classes of functions to which our new formula is applicable and show how our formula can be applied to certain classes of differential equations. We also presented an application of the formulae of higher order derivatives combined with extrapolation methods in the numerical integration of spherical Bessel integral functions. 相似文献
11.
We consider a discrete-time risk model,in which insurance risks and financial risks jointly follow a multivariate Farlie-Gumbel-Morgenstern distribution,and the insurance risks are regularly varying tailed.Explicit asymptotic formulae are obtained for finite-time and infinite-time ruin probabilities.Some numerical results are also presented to illustrate the accuracy of our asymptotic formulae. 相似文献
12.
S. A. Sergeev 《Differential Equations》2011,47(5):746-757
We find necessary and sufficient conditions for the existence of a boundary control of vibrations of a string or a spherical
layer for critical and subcritical times. We completely analyze the existence of a boundary control of vibrations of a spherical
layer by a force on two spheres. We find necessary and sufficient existence conditions for the control. Along with the control
problem for vibrations of a spherical layer, we consider a similar control problem for string vibrations. 相似文献
13.
Gradimir V. Milovanović Aleksandar S. Cvetković Marija P. Stanić 《Numerische Mathematik》2009,112(3):425-448
In this paper we consider interpolatory quadrature formulae with multiple nodes, which have the maximal trigonometric degree
of exactness. Our approach is based on a procedure given by Ghizzeti and Ossicini (Quadrature formulae, Academie-Verlag, Berlin,
1970). We introduce and consider the so-called σ-orthogonal trigonometric polynomials of semi-integer degree and give a numerical method for their construction. Also, some numerical examples are included.
The authors were supported in part by the Serbian Ministry of Science and Technological Development (Project: Orthogonal Systems
and Applications, grant number #144004) and the Swiss National Science Foundation (SCOPES Joint Research Project No. IB7320-111079
“New Methods for Quadrature”). 相似文献
14.
David Borwein Jonathan M. Borwein David M. Bradley 《Journal of Mathematical Analysis and Applications》2006,316(1):328-338
We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these sums. 相似文献
15.
Sotirios E. Notaris 《Numerische Mathematik》1990,57(1):271-283
Summary We consider the Gaussian quadrature formulae for the Bernstein-Szegö weight functions consisting of any one of the four Chebyshev weights divided by an arbitrary quadratic polynomial that remains positive on [–1, 1]. Using the method in Akrivis (1985), we compute the norm of the error functional of these quadrature formulae. The quality of the bounds for the error functional, that can be obtained in this way, is demonstrated by two numerical examples. 相似文献
16.
Summary. We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its
Zakharov-Shabat formulation. We obtain explicit formulae for the Darboux transformed potentials in terms of Grammian type
determinants. We also study the n -th Gel'fand-Dickey hierarchy introducing spectral operators and obtaining similar results. We reduce the above-mentioned
results to the Kadomtsev-Petviashvili I and II real forms, obtaining corresponding vectorial Darboux transformations. In particular
for the Kadomtsev-Petviashvili I hierarchy, we get the line soliton, the lump solution, and the Johnson-Thompson lump, and
the corresponding determinant formulae for the nonlinear superposition of several of them. For Kadomtsev-Petviashvili II apart
from the line solitons, we get singular rational solutions with its singularity set describing the motion of strings in the
plane. We also consider the I and II real forms for the Gel'fand-Dickey hierarchies obtaining the vectorial Darboux transformation
in both cases.
Received June 4, 1997; final revision received March 6, 1998; accepted March 23, 1998 相似文献
17.
We consider a discrete-time queueing system in which the arriving customers decide with a certain probability to be served under a LCFS-PR discipline and with complementary probability to join the queue. The arrivals are assumed to be geometrical and the service times are arbitrarily distributed. The service times of the expelled customers are independent of their previous ones. We carry out an extensive analysis of the system developing recursive formulae and generating functions for the steady-state distribution of the number of customers in the system and obtaining also recursive formulae and generating functions for the stationary distribution of the busy period and sojourn time as well as some performance measures. 相似文献
18.
On Symmetric Invariants of Level Surfaces Near Regular Points 总被引:1,自引:0,他引:1
We consider the symmetric invariants of the level surfaces ofa smooth function away from its critical points, and prove forthem some formulae in divergence from. We then apply these formulaeto obtain an isoperimetric inequality for the surface area oflevel surfaces of p-capacity potentials. 相似文献
19.
We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing
spectral properties of Laplacians, we prove several versions of trace formulae, relating Laplace spectra to sums over periodic
orbits on the graph. This includes trace formulae with, respectively, absolutely and conditionally convergent periodic orbit
sums; the convergence depending on properties of the test functions used. We also prove a trace formula for the heat kernel
and provide small-t asymptotics for the trace of the heat kernel.
Submitted: May 20, 2008., Accepted: January 6, 2009. 相似文献
20.
球形涂层粒子增强复合材料的有效模量 总被引:2,自引:0,他引:2
本文通过四相球模型和复合材料的等效介质理论,研究了球形涂层粒子增强复合材料的有效模量性质,得到了这种增强复合材料的有效体积模量和有效剪切模量的理论预测公式。这些结果在特殊情况下,可退化到三相球模型确定的球形粒子增强复合材料的有效模量公式。 相似文献