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1.
László Losonczi 《Aequationes Mathematicae》1997,53(1-2):141-154
Summary It is proved that, iff
ij:]0, 1[ C (i = 1, ,k;j = 1, ,l) are measurable, satisfy the equation (1) (with some functionsg
it, hjt:]0, 1[ C), then eachf
ij is in a linear space (called Euler space) spanned by the functionsx x
j(logx)
k
(x ]0, 1[;j = 1, ,M;k = 0, ,m
j – 1), where
1, , M are distinct complex numbers andm
1, , mM natural numbers. The dimension of this linear space is bounded by a linear function ofN. 相似文献
2.
Fang Jie 《数学学报(英文版)》1996,12(3):249-253
In this paper we introduce an algebraic concept of the product of Ockham algebras called the Braided product. We show that ifL
i
MS(i=1, 2, ,n) then the Braided product ofL
i(i=1, 2, ,n) exists if and only ifL
1, ,L
n have isomorphic skeletons. 相似文献
3.
H. S. P. Grässer 《Aequationes Mathematicae》1976,14(3):363-386
Notation Throughout this paper Greek indices, , , and Latin indicesi, j, h, k, assume the values 1, ,m, and 1, ,n respectively. The summation convention is operative in respect of both sets of indices.This work was supported by the South African Council for Scientific and Industrial Research.At time of writing Professor Grässer was Visiting Scholar at the University of Arizona, Tucson, Arizona. 相似文献
4.
H. Bresinsky 《manuscripta mathematica》1979,27(4):353-358
It is shown that if the prime ideal
,, x4], k an arbitrary field, has generic zero xi=tn
i, ni positive integers with g.c.d. equal l, l i 4, then P(S) is a set-theoretic complete intersection if the numerical semigroup S=1,, n4> is symmetric (i.e. if the extension of P(S) in k[[x1,, x4]] is a Gorenstein ideal). 相似文献
5.
Reinhardt Euler 《Mathematical Programming》1982,24(1):269-283
Let (E,I) be an independence system over the finite setE = {e
1, ,e
n
}, whose elements are orderede
1 e
n
. (E,I) is called regular, if the independence of {e
l
, ,e
l
k
},l
1 < <l
k
, implies that of {e
m
l
, ,e
m
k
}, wherem
l
< ··· <m
k
andl
1 m
1, ,l
k
m
k
. (E,I) is called a 2-system, if for anyI I,e E I the setI {e } contains at most 2 distinct circuitsC, C I and the number 2 is minimal with respect to this property. If, in addition, for any two independent setsI andJ the family (C J, C
C
(J, I)), whereC(J, I) denotes {C C:e J I C
{e}}, can be partitioned into 2 subfamilies each of which possesses a transversal, then (E,I) is called a (2, 2)-system. In this paper we characterize regular 2-systems and we show that the classes of regular 2-systems resp. regular (2, 2)-systems are identical. 相似文献
6.
Garth P. McCormick 《Mathematical Programming》1971,1(1):217-238
The relative merits of using sequential unconstrained methods for solving: minimizef(x) subject tog
i
(x) 0, i = 1, , m, h
j
(x) = 0, j = 1, , p versus methods which handle the constraints directly are explored. Nonlinearly constrained problems are emphasized. Both classes of methods are analyzed as to parameter selection requirements, convergence to first and second-order Kuhn-Tucker Points, rate of convergence, matrix conditioning problems and computations required.This paper was presented at the 7th Mathematical Programming Symposium 1970, The Hague, The Netherlands. 相似文献
7.
V. V. Makeev 《Journal of Mathematical Sciences》1990,52(1):2854-2860
A survey of known results and additional new ones on Knaster's problem: on the standard sphere Sn–1Rn find configurations of points A1, , Ak, such that for any continuous map fSn–1Rm one can find a rotation a of the sphere Sn–1 such that f(a(A1)==f(a(Ak)) and some problems closely connected with it. We study the connection of Knaster's problem with equivariant mappings, with Dvoretsky's theorem on the existence of an almost spherical section of a multidimensional convex body, and we also study the set {a S0(n)f(a(A1))==f(a(Ak))} of solutions of Knaster's problem for a fixed configuration of points A1, , AkSn–1 and a map fSn–1Rm in general position. Unsolved problems are posed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 167, pp. 169–178, 1987. 相似文献
8.
Jens Schwaiger 《Aequationes Mathematicae》1994,48(2-3):317-323
Summary We consider the functional equationf[x
1,x
2,, x
n
] =h(x
1 + +x
n
) (x
1,,x
n
K, x
j
x
k
forj k), (D) wheref[x
1,x
2,,x
n
] denotes the (n – 1)-st divided difference off and prove
Theorem. Let n be an integer, n 2, let K be a field, char(K) 2, with # K 8(n – 2) + 2. Let, furthermore, f, h: K K be functions. Then we have that f, h fulfil (D) if, and only if, there are constants aj K, 0 j n (a := an, b := an – 1) such thatf = ax
n
+bx
n – 1 + +a
0
and h = ax + b. 相似文献
9.
We consider the approximation of the function (x) and its derivative '(x) on [a, b] given that (x)C
2,N, i.e., belongs to the class of functions f(x) that satisfy the conditions f(x)L, f(xi)=yi, i=1,,N, where L and yi are given real numbers and xi are the nodes of an arbitrary grid, a=x1<x2<<XN=b. A solution algorithm on the class of functions C2,L,N is proposed which has optimal accuracy with a constant not exceeding 2. A bound on the approximation error of the function and its derivative is derived.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 57–61, 1985 相似文献
10.
Miriam Bareket 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1981,32(4):464-469
Let
1 (k)
2 (k) be the eigenvalues of an operator of a certain type depending on a real parameterk. The paper shows that under certain requirements on the operator and on the nature of its dependence onk, the sum
1 (k)++
N
(k) is a concave function ofk, for any positive integerN.
Zusammenfassung Seien 1 (k) 2 (k) die Eigenwerte eines von einem reellen Parameterk abhängigen Operators. Man zeigt, daß unter gewissen Voraussetzungen über den Operator und seine Abhängigkeit vonk die Summe 1 (k)++ N (k) für jedesN eine konkave Funktion vonk ist.相似文献
11.
B. A. Sevast'yanov 《Mathematical Notes》1968,3(4):247-251
Conditions are found which must be imposed on a function g(x) in order that M g(1+2+ + v < if M g(i) < and M g(v) < ,, 1, 2, , n, ... being non-negative and independent, being integral, and {i} being identically distributed. The result is applied to the theory of branching processes.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 387–394, April, 1968. 相似文献
12.
In this paper we are concerned with the summability of the geometric series
by matrix methods. We prove the following theorem: Suppose Mo:={z:|z|<1}, M1, M2, is a collection of countably many Lebesgue measureable, disjoint sets. For k=1,2, let fk be a prescribed function, analytic on
. Then there exists a triangular matrix
, such that the V-transform {n(z)} of the geometric series has the following properties: {n(z)} converges compactly to
on Mo; for k=1,2, there are sets Bk, such that
has Lebesgue-measure zero and n(z)fk(z) for zBk; if
there is a set B*, such that B*M* has Lebesgue-measure zero and {n(z)} diverges for zB*. 相似文献
13.
LetA be anM-matrix in standard lower block triangular form, with diagonal blocksA
ii irreducible. LetS be the set of indices such that the diagonal blockA
is singular. We define the singular graph ofA to be the setS with partial order defined by > if there exists a chain of non-zero blocksA
i, Aij, , Al.Let 1 be the set of maximal elements ofS, and define thep-th level
p
,p = 2, 3, , inductively as the set of maximal elements ofS
\(
1
p-1). Denote by
p
the number of elements in
p
. The Weyr characteristic (associated with 0) ofA is defined to be (A) = (
1, 2,,
h
), where
1 + +
p
= dim KerA
p
,p = 1, 2, , and
h > 0, h+1 = 0.Using a special type of basis, called anS-basis, for the generalized eigenspaceE(A) of 0 ofA, we associate a matrixD withA. We show that(A) = (
1, , h) if and only if certain submatricesD
p,p+1
,p = 1, , h – 1, ofD have full column rank. This condition is also necessary and sufficient forE(A) to have a basis consisting of non-negative vectors, which is a Jordan basis for –A.
We also consider a given finite partially ordered setS, and we find a necessary and sufficient condition that allM-matricesA with singular graphS have(A) = (
1, , h). This condition is satisfied ifS is a rooted forest.The work of the second-named author was partly supported by the National Science Foundation, under grant MPS-08618 A02. 相似文献
14.
P. E. Markov 《Journal of Mathematical Sciences》1994,72(4):3191-3200
For a Cr,-immersion z:X E, r 2, 0 < < 1, of an n-dimensional (n 1) simply-connected Cr+2,-manifold X into Euclidean space E, the metric I(z) induced by z has a neighborhood in Cr,-topology in which every metric from a given subbundle of metrics is Cr,-immersible into E. In particular, it is proved that metric ds
0
2
of the Riemannian product of p spheres of dimensions 1, , p 2 has a neighborhood in C2,-topology from which any conformally equivalent metric to ds
0
2
, is immersible into E with dimE = 1 + +
p
+ p. The proofs are based on the investigation of a varied system of Gauss—Codazzi—Ricci equations for an infinitely small deformation of surface z(X) in E with a prescribed variation of the metric.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 49–67, 1992. 相似文献
15.
Let Agl(n, C) and let p be a positive integer. The Hessenberg variety of degree p for A is the subvariety Hess(p, A) of the complete flag manifold consisting of those flags S
1
S
n–1
in n which satisfy the condition AS
i
S
i+p
,for all i. We show that if A has distinct eigenvalues, then Hess(p, A) is smooth and connected. The odd Betti numbers of Hess(p, A) vanish, while the even Betti numbers are given by a natural generalization of the Eulerian numbers. In the case where the eigenvalues of A have distinct moduli, |1|<<|1|, these results are applied to determine the dimension and topology of the submanifold of U(n) consisting of those unitary matrices P for which A
0=P
-1
AP is in Hessenberg form and for which the diagonal entries of the QR-iteration initialized at A
0 converge to a given permutation of 1,n.Research partially supported by the National Science Foundation under Grant ECS-8696108. 相似文献
16.
V. V. Ryzhkov 《Journal of Mathematical Sciences》1991,53(5):542-545
On an arc L of length h, of class Cn, and in Euclidean En, the set of n+1 points (the partition of the arc) P={0, 1 h, , n–1h, h}, 0<1<<n–1<1 determines a simplex Sh(P) inscribed in the arc. For its volume Vh(P) we evaluate lim
and prove that its greatest value is obtained for a unique choice of P=Pcr. The exact values for i from Pcr are found for n=2, 3, 4, 5, 6.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 114–120, 1990. 相似文献
17.
Chih-Wen Weng 《Graphs and Combinatorics》1995,11(2):201-207
LetY = (X, {R
i
}
oid) denote aP-polynomial association scheme. By a kite of lengthi (2 i d) inY, we mean a 4-tuplexyzu (x, y, z, u X) such that(x, y) R
1,(x, z) R
1,(y, z) R
1,(u, y) R
i–1,(u, z) R
i–1,(u, x) R
i. Our main result in this paper is the following. 相似文献
18.
A. L. Yampol'skii 《Journal of Mathematical Sciences》1994,69(1):916-920
Curves that are projections of geodesics of the Sasakian metric of the tangent and tangent sphere bundles of a complex projective space are considered. The main result is: THEOREM. If is a geodesic of TCPn (T1
CPn) then 0is a curve inCP
n for which curvatures k1, , k5 are constant and k6 = = k2n = 0.Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 121–126, 1991. 相似文献
19.
Shelly L. Wismath 《Aequationes Mathematicae》1995,49(1):205-213
Summary The medical varietyMV of semigroups is the variety defined by the medial identityxyzw = xzyw. This variety is known to satisfy the medial hyperidentitiesF(G(x
11
,, x
1n
),, G(x
n1
,, x
nn
)) = G(F(x
11
,, x
n1
),, F(x
1n
,, x
nn
)), forn 1. Taylor has observed in [2] thatMV also satisfies some other hyperidentities, which are not consequences of the medial ones. In [4] the author introduced a countably infinite family of binary hyperidentities called transposition hyperidentities, which are natural generalizations of then = 2 medial hyperidentity. It was shown that this family is irredundant, and that no finite basis is possible for theMV hyperidentities with one binary operation symbol.In this paper, we generalize the concept of a transposition hyperidentity, and extend it to cover arbitrary arityn 2. We show that theMV hyperidentities with onen-ary operation symbol have no finite basis, but do have a countably infinite basis consisting of these transposition hyperidentities.Research supported by NSERC of Canada. 相似文献
20.
Bang-Yen Chen 《Annals of Global Analysis and Geometry》1994,12(1):87-96
In the first part of this series, we prove that the tensor product immersionf
1
f
2k
of2k isometric spherical immersions of a Riemannian manifoldM in Euclidean space is of-type with k and classify tensor product immersionsf
1
f
2k
which are ofk-type. In this article we investigate the tensor product immersionsf
1
f
2k
which are of (k+1)-type. Several classification theorems are obtained. 相似文献