共查询到20条相似文献,搜索用时 15 毫秒
1.
On the geometry of the nets in the n-dimensional space of Weyl 总被引:1,自引:0,他引:1
Chebyshev and geodesic curvatures of the lines of an arbitrary net belonging to the n-dimensional space of Weyl Wn are introduced. Characteristics of the following special nets in Wn are found: strongly parallel, b-net, c-net and orthogonal (theorems 1.2, 1.3, 1.5, 1.6). Some properties of the Chebyshev nets, orthogonal b-nets and orthogonal c-nets, of the Chebyshev vectors of the second kind, of the orthogonal nets and nets containing Chebyshev subnets are established (theorems 1.1, 1.7, 1.8, 1.4). The fundamental formulae in the case of an orthogonal coordinate net are obtained. The spaces Wn containing one of the following special orthogonal nets — strongly parallel of the first kind, Chebyshev net of the second kind and b-net are defined. 相似文献
2.
Asymptotic approximations are developed for zeros of the solutions Gi(z) and Hi(z) of the inhomogeneous Airy differential equation
. The solutions are also called Scorer functions. Tables are given with numerical values of the zeros. 相似文献
3.
Y. Fujikoshi 《Journal of multivariate analysis》1977,7(3):386-396
Asymptotic expansions are given for the density function of the normalized latent roots of S1S2?1 for large n under the assumption of , where S1 and S2 are independent noncentral and central Wishart matrices having the and Wp(n, Σ) distributions, respectively. The expansions are obtained by using a perturbation method. Asymptotic expansions are also obtained for the density function of the normalized canonical correlations when some of the population canonical correlations are zero. 相似文献
4.
Michael Stewart 《Linear algebra and its applications》2006,419(1):53-77
This paper gives SVD perturbation bounds and expansions that are of use when an m × n, m ? n matrix A has small singular values. The first part of the paper gives subspace bounds that are closely related to those of Wedin but are stated so as to isolate the effect of any small singular values to the left singular subspace. In the second part first and second order approximations are given for perturbed singular values. The subspace bounds are used to show that all approximations retain accuracy when applied to small singular values. The paper concludes by deriving a subspace bound for multiplicative perturbations and using that bound to give a simple approximation to a singular value perturbed by a multiplicative perturbation. 相似文献
5.
Ya. D. Pyanylo 《Journal of Mathematical Sciences》2001,107(1):3655-3658
Integral representations of the Fourier–Jacobi coefficients are constructed in the form of Riemann–Mellin integrals, and on this basis asymptotic formulas for calculating coefficients for large-order numbers are derived. 相似文献
6.
We consider parabolic subgroups of a general linear group over an algebraically closed field k whose Levi part has exactly t factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup P has an open dense P-orbit. In the complement to this dense orbit, there are infinitely many orbits as soon as the number t of factors in the Levi part is ≥6. In this paper, we describe the irreducible components of the complement. In particular, we show that there are at most t ? 1 irreducible components. We are also able to determine their codimensions. 相似文献
7.
S. L. Skorokhodov D. V. Khristoforov 《Computational Mathematics and Mathematical Physics》2007,47(11):1802-1818
A method for computing the eigenvalues λ mn (b, c) and the eigenfunctions of the Coulomb spheroidal wave equation is proposed in the case of complex parameters b and c. The solution is represented as a combination of power series expansions that are then matched at a single point. An extensive numerical analysis shows that certain b s and c s are second-order branch points for λ mn (b, c) with different indices n 1 and n 2, so that the eigenvalues at these points are double. Padé approximants, quadratic Hermite-Padé approximants, the finite element method, and the generalized Newton method are used to compute the branch points b s and c s and the double eigenvalues to high accuracy. A large number of these singular points are calculated. 相似文献
8.
Sui Yuefei 《数学学报(英文版)》1993,9(3):225-230
One new notation, called theA-prompt permitting, is defined in the Turing reducibility, and its basic properties are given, by which we shall show that
two r.e. setsA andB are one minimal pairs if and only ifB is notA-prompt permitting. It is proved that there are no maximal minimal pairs.
Research partially supported by NSF grand JJ890406 of China.
The same results were proved by Harrington and Soare [ta] in 1988, which were reported at the recursion theory meeting at
Oberwolfach in Mar. 1989 and at the set theory meeting at Berkeley in Oct. 1990, respectively. 相似文献
9.
Real three-phase solutions of the sine-Laplace equation are constructed. All smooth and singular real doubly periodic solutions
are found. The corresponding three-dimensional theta functions are reduced to the elliptic Jacobi functions. Some classes
of solutions with symmetries giving possibilities for physical applications are determined. Bibliography: 18 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 235, 1996, pp. 199–216. 相似文献
10.
Herbert H.H. Homeier 《Numerical Algorithms》1998,17(3-4):223-239
The stability of a large class of nonlinear sequence transformations is analyzed. Considered are variants of the J transformation [17]. Suitable variants of this transformation belong to the most successful extrapolation algorithms that
are known [20]. Similar to recent results of Sidi, it is proved that the
p
{J} transformations, the Weniger S transformation, the Levin transformation and a special case of the generalized Richardson extrapolation process of Sidi are
S-stable. An efficient algorithm for the calculation of stability indices is presented. A numerical example demonstrates the
validity of the approach.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
11.
Abstract. Identifying codes in the square lattice are considered. The motivation for these codes is the following: if a multiprocessor
system is modelled by the square lattice, then we can locate faulty processors in the system with the aid of identifying codes.
Constructions, some of which are optimal, are given. 相似文献
12.
A(R) is the lattice-ordered group (l-group) of all order-automorphisms of the real lineR, with the usual pointwise order and “of course” with composition as the group operation. In fact, what other choices are there for a group operation having the same identity that would give anl-group? Composition in the reverse order would work. But there are no other choices — the group operation can be recognized in the lattice. Several classes of abelianl-groups having a unique group operation have been found by Conrad and Darnel, but this is the first non-abelian example having the minimum of two group operations. “Conversely”, Holland has shown that for the groupA(R) under composition, the only lattice orderings yielding anl-group are the pointwise order and its dual. These results also hold for the rational lineQ. 相似文献
13.
Mohamed A. Ramadan Mokhtar A. Abdel Naby Ahmed M.E. Bayoumi 《Mathematical and Computer Modelling》2009,50(9-10):1400-1408
In this paper, we consider the explicit solutions of two matrix equations, namely, the Yakubovich matrix equation V−AVF=BW and Sylvester matrix equations AV−EVF=BW,AV+BW=EVF and AV−VF=BW. For this purpose, we make use of Kronecker map and Sylvester sum as well as the concept of coefficients of characteristic polynomial of the matrix A. Some lemmas and theorems are stated and proved where explicit and parametric solutions are obtained. The proposed methods are illustrated by numerical examples. The results obtained show that the methods are very neat and efficient. 相似文献
14.
G. R. Burton 《Israel Journal of Mathematics》1977,28(4):339-349
We show that a convex bodyK of dimensiond≧3 is an ellipsoid if it has any of the following properties: (1) the “grazes” of all points close toK are flat, (2) all sections of small diameter are centrally symmetric, (3) parallel (d−1)-sections close to the boundary are width-equivalent, (4)K is strictly convex and all (d−1)-sections close to the boundary are centrally symmetric; the last two results are deduced from their 3-dimensional cases
which were proved by Aitchison. 相似文献
15.
Takao Nishizeki 《Discrete Mathematics》1979,25(2):149-156
Lower bounds on the cardinality of the maximum matchings of graphs are established in terms of a linear polynomial of p, p(1), p(2) and γ whose coefficients are functions of κ, where p is the number of the vertices of a graph, p(i) the number of the vertices of degree i (i = 1,2), γ the genus and κ the connectivity. 相似文献
16.
In this paper we give two topological conditions on the graphs of two linear relations E and F on a Hilbert space ${\mathcal H}$ , one of which is sufficient to ensure the closure of the product EF, the other being sufficient to ensure the closure of the sum E?+?F. Note that these conditions are not necessary and in particular do not include the cases when E and F are continuous everywhere defined operators. Other related results are established. 相似文献
17.
Angelo Miele 《Journal of Optimization Theory and Applications》1967,1(1):70-82
This paper considers the minimization of the product of the powers ofn integrals, each of which depends on a functiony(x) and its derivative
. The necessary conditions for the extremum are derived within the frame of the Mayer-Bolza formulation of the calculus of variations, and it is shown that the extremal arc is governed by a second-order differential equation involvingn undetermined multipliers related to the unknown values of the integrals. After the general solution is combined with the definitions of the multipliers and the end conditions, a system ofn+2 algebraic equations is obtained; it involvesn+2 unknowns, that is, then undetermined multipliers and two integration constants.The procedure discussed here can be employed in the study of shapes which are aerodynamically optimum at supersonic, hypersonic, and free-molecular flow velocities, that is, wings and fuselages having the maximum lift-to-drag ratio or the minimum drag. The problem of a slender body of revolution having the minimum pressure drag in Newtonian hypersonic flow is developed as an example. First, a general solution is derived for any pair of conditions imposed on the length, the thickness, the wetted area, and the volume. Then, a particular case is treated, that in which the thickness and the wetted area are given, while the length and the volume are free; the shape minimizing the pressure drag is a cone.This research, supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-828-67, is a condensed version of the investigation described in Ref. 1. The author is indebted to Messrs. H. Y. Huang, J. C. Heideman, and J. N. Damoulakis for analytical and numerical assistance. 相似文献
18.
Properties of coefficients of the Slevinsky-Safouhi formula are derived. These properties are: matrix and orthogonality properties; the characterization of a zero array; generating functions; asymptotics; and, recurrence relations for computing a sum as efficiently as possible. These properties are useful in a numerical or computational setting. 相似文献
19.
Mahmoud Benkhalifa 《Journal of Pure and Applied Algebra》2007,210(2):343-362
The present paper is devoted to the classification problem of the quasi-isomorphism classes of free differential graded algebras (dgas) over a (P.I.D) R. We introduce the notion of coherent homomorphisms, perfect and quasi-perfect dgas (the Adams-Hilton model of simply connected CW-complex such that H∗(X,R) is free is a such a dga) and our first main result asserts that two perfect (quasi-perfect) dgas are quasi-isomorphic if and only if their Whitehead exact sequences are coherently isomorphic. Moreover we define the notion of a strong isomorphism between the Whitehead exact sequences and we show that two free R-dgas, of which their Whitehead exact sequences are strongly isomorphic, are quasi-isomorphic. 相似文献
20.
The global and local topological zeta functions are singularityinvariants associated to a polynomial f and its germ at 0, respectively.By definition, these zeta functions are rational functions inone variable, and their poles are negative rational numbers.In this paper we study their poles of maximal possible order.When f is non-degenerate with respect to its Newton polyhedron,we prove that its local topological zeta function has at mostone such pole, in which case it is also the largest pole; wegive a similar result concerning the global zeta function. Moreover,for any f we show that poles of maximal possible order are alwaysof the form 1/N with N a positive integer. 1991 MathematicsSubject Classification 14B05, 14E15, 32S50. 相似文献