共查询到20条相似文献,搜索用时 46 毫秒
1.
We propose a fast summation algorithm for slowly convergent power series of the form
j=j
0
z
j
j
j
i=1
s
(j+
i
)–
i
, where R,
i
0 and
i
C, 1is, are known parameters, and
j
=(j), being a given real or complex function, analytic at infinity. Such series embody many cases treated by specific methods in the recent literature on acceleration. Our approach rests on explicit asymptotic summation, started from the efficient numerical computation of the Laurent coefficients of . The effectiveness of the resulting method, termed ASM (Asymptotic Summation Method), is shown by several numerical tests. 相似文献
2.
In this paper we solve the problem of unique factorization of products ofn-variate nonsingular normal distributions with covariance matrices of the form ,
ij
=p
i
j
forij, =
i
2
,j=j,p0. 相似文献
3.
We construct -framed Kripke models of i1 and i1 non of whose worlds satisfies xy(x=2yx=2y+1) and x,yzExp(x, y, z) respectively. This will enable us to show that i1 does not prove ¬¬xy(x=2yx=2y+1) and i1 does not prove ¬¬x, yzExp(x, y, z). Therefore, i1¬¬lop and i1¬¬i1. We also prove that HAl1 and present some remarks about i2.
Mathematics Subject Classification (2000):03F30, 03F55, 03H15. 相似文献
4.
Mark S. MacLean 《Journal of Algebraic Combinatorics》2003,17(2):125-147
Let denote a bipartite distance-regular graph with diameter D 4, valency k 3, and distinct eigenvalues 0 > 1 > ··· > D. Let M denote the Bose-Mesner algebra of . For 0 i D, let E
i denote the primitive idempotent of M associated with
i
. We refer to E
0 and E
D as the trivial idempotents of M. Let E, F denote primitive idempotents of M. We say the pair E, F is taut whenever (i) E, F are nontrivial, and (ii) the entry-wise product E F is a linear combination of two distinct primitive idempotents of M. We show the pair E, F is taut if and only if there exist real scalars , such that
i + 1
i + 1 –
i – 1
i – 1 =
i
(
i + 1 –
i – 1) +
i
(
i + 1 –
i – 1) + (1 i D – 1)where 0, 1, ...,
D
and 0, 1, ...,
D
denote the cosine sequences of E, F, respectively. We define to be taut whenever has at least one taut pair of primitive idempotents but is not 2-homogeneous in the sense of Nomura and Curtin. Assume is taut and D is odd, and assume the pair E, F is taut. We show
for 1 i D – 1, where = 1, = 1. Using these equations, we recursively obtain 0, 1, ..., D and 0, 1, ...,
D
in terms of the four real scalars , , , . From this we obtain all intersection numbers of in terms of , , , . We showed in an earlier paper that the pair E
1, E
d is taut, where d = (D – 1)/2. Applying our results to this pair, we obtain the intersection numbers of in terms of k, , 1, d, where denotes the intersection number c
2. We show that if is taut and D is odd, then is an antipodal 2-cover. 相似文献
5.
The unit sphere of Hilbert space, 2, is shown to contain a remarkable sequence of nearly orthogonal sets. Precisely, there exist a sequence of sets of norm one elements of 2, (C
i
)
i=1
, and reals
i
0 so that a) each setC
i
has nonempty intersection with every infinite dimensional closed subspace of 2 and b) forij,xC, andyC
j
, |x, y|<min(i, j)
E. Odell was partially supported by NSF and TARP. Th. Schlumprecht was partially supported by NSF and LEQSF. 相似文献
6.
G. M. Feldman 《Journal of Theoretical Probability》2004,17(4):929-941
It is well-known Heyde's characterization theorem for the Gaussian distribution on the real line: if
j
are independent random variables,
j
,
j
are nonzero constants such that
i
±
j
–1
j
0 for all i j and the conditional distribution of L
2=1 1 + ··· +
n
n
given L
1=1 1 + ··· +
n
n
is symmetric, then all random variables
j
are Gaussian. We prove some analogs of this theorem, assuming that independent random variables take on values in a finite Abelian group X and the coefficients
j
,
j
are automorphisms of X. 相似文献
7.
G. V. Kuz'mina 《Journal of Mathematical Sciences》1978,10(2):241-256
We obtain a complete solution of the problem of the maximum of the fourth diameter in the family of continua with capacity 1. Let E(o, ei, e–i). 0<2, be a continuum of minimum capacity containing the points o, ei, e–i; H(=cap E(o, ei, e–i). Let C() be the common point of three analytic arcs which form E(o, ei, e–i). One shows that the indicated maximum is realized by the continuum ={z:H(0)z
2E(o, ei, e–i)} where
0, o<02, is a solution of the equation. Any other extremal continuum of the gives problem is an image of under the mappingz ei
z+C ( is a real and C is a complex constant). One finds the value of the required maximum. The paper contains a brief exposition of the proof of this result.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 59, pp. 60–79, 1976. 相似文献
8.
Let bea distance-regular graph with diameter d. For vertices x and y of at distancei, 1 i d, we define the setsC
i(x,y) = i–1(x) (y), A
i
(x,y) =
i
(x) (y) and B
i
(x,y) =
i+1(x) (y).Then we say has the CABj property,if the partition CAB
i
(x,y) = {C
i
(x,y),A
i
(x,y),B
i
(x,y)}of the local graph of y is equitable for each pairof vertices x and y of at distance i j. We show that in with the CABj property then the parameters ofthe equitable partitions CAB
i(x,y) do not dependon the choice of vertices x and y atdistance i for all i j. The graph has the CAB property if it has the CAB
d
property. We show the equivalence of the CAB property and the1-homogeneous property in a distance-regular graph with a
1 0. Finally, we classify the 1-homogeneous Terwilligergraphs with c
2 2. 相似文献
9.
Martin Krüskemper 《manuscripta mathematica》1989,65(2):225-243
In this paper we examine for which Witt classes ,..., n over a number field or a function fieldF there exist a finite extensionL/F and 2,..., n L* such thatT
L/F
()=1 andTr
L/F
(i)=i fori=2,...n. 相似文献
10.
Akos Seress 《Designs, Codes and Cryptography》2001,22(1):5-17
A-design is a family B
1,B
2,...,B
v
of subsets of X={1, 2,..., v} such that B
i
B
j
= for all i jand not all B
i
are of the same size. Ryser's andWoodall's -design conjecture states thateach -design can be obtained from a symmetricblock design by a certain complementation procedure. Our mainresult is that the conjecture is true when is twice a prime number. 相似文献
11.
Andriy Panasyuk 《Annals of Global Analysis and Geometry》1997,15(4):313-324
Given a complex manifold Mi, structures of Poisson algebras on (Mi)=C(Mi,C) which are associated with a nondegenerate -closed (2,0)-form i on Mi are considered. It is shown that every isomorphism of Poisson structures (M1) (M2) is generated by a biholomorphic map :M2 M1 such that 2 = *1 相似文献
12.
We construct an infinite family{
n}n=5 of finite connected graphs
n that are multiple extensions of the well-known extended grid discovered in [1] (which is isomorphic to
5). The graphs
n are locally
n–1 forn > 5, and have the following property: the automorphism groupG(n) of
n permutes transitively the maximal cliques of
n (which aren-cliques) and the stabilizer of somen-clique of
n inG(n) induces
n on the vertices of. Furthermore we show that the clique complexes of the graphs
n are simply connected. 相似文献
13.
M. Katchalski 《Aequationes Mathematicae》1978,17(1):249-254
Denoting by dimA the dimension of the affine hull of the setA, we prove that if {K
i:i T} and {K
i
j
:i T} are two finite families of convex sets inR
n
and if dim {K
i
:i S} = dim {K
i
j
:i S}for eachS T such that|S| n + 1 then dim {K
i
:i T} = dim {K
i
: {i T}}. 相似文献
14.
Toshio Honda 《Annals of the Institute of Statistical Mathematics》2000,52(3):459-470
Let (Xi,Y
i) be a set of observations form a stationary -mixing process and (x) be the conditional -th quantile of Y given X = x. Several authors considered nonparametric estimation of (x) in the i.i.d. setting. Assuming the smoothness of FF(x), we estimate it by local polynomial fitting and prove the asymptotic normality and the uniform convergence. 相似文献
15.
One investigates the scattering theory for the positive self-adjoint operatorH=–· acting in
with = × and a bounded open set in
n–1,n2. The real-valued function belongs toL
(), is bounded from below byc>0 and there exist real-valued functions
1 and
2 inL
() such that –
j
,j=1,2 is a short range perturbation of
j
when (–1)
j
x
n
+. One assumes
j
=
(j)
1R,j=1,2, with
(j)
L
bounded from below byc>0. One proves the existence and completeness of the generalized wave operators
j
±
=s –
j
e
–itHj
,j=1,2, withH
j
=–·
j
and
j
: equal to 1 if (–1)
j
x
n
>0 and to 0 if (–1)
j
x
n
<0. The ranges ofW
j
±
:=(
j
±
)* are characterized so that
W
1
±
=Ran and
. The scattering operator can then be defined. 相似文献
16.
M. Menéndez D. Morales L. Pardo I. Vajda 《Annals of the Institute of Statistical Mathematics》2001,53(2):277-288
The paper considers statistical models with real-valued observations i.i.d. by F(x, 0) from a family of distribution functions (F(x, ); ), R
s
, s 1. For random quantizations defined by sample quantiles (F
n
–1 (1),, F
n
–1 (
m–1)) of arbitrary fixed orders 0 < 1 < m-1 < 1, there are studied estimators ,n
of 0 which minimize -divergences of the theoretical and empirical probabilities. Under an appropriate regularity, all these estimators are shown to be as efficient (first order, in the sense of Rao) as the MLE in the model quantified nonrandomly by (F
–1 (1,0),, F
–1 (
m–1, 0)). Moreover, the Fisher information matrix I
m
(0, ) of the latter model with the equidistant orders = (
j
= j/m : 1 j m – 1) arbitrarily closely approximates the Fisher information J(0) of the original model when m is appropriately large. Thus the random binning by a large number of quantiles of equidistant orders leads to appropriate estimates of the above considered type. 相似文献
17.
Ben Green 《Combinatorica》2005,25(3):307-326
Given a set A
/N we may form a Cayley sum graph G
A
on vertex set /N by joining i to j if and only if i+j A. We investigate the extent to which performing this construction with a random set A simulates the generation of a random graph, proving that the clique number of G
A
is almost surely O(logN). This shows that Cayley sum graphs can furnish good examples of Ramsey graphs. To prove this result we must study the specific structure of set addition on /N. Indeed, we also show that the clique number of a random Cayley sum graph on =(/2)
n
is almost surely not
O(log ||).* Supported by a grant from the Engineering and Physical Sciences Research Council of the UK and a Fellowship of Trinity College Cambridge. 相似文献
18.
A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations 总被引:22,自引:0,他引:22
K. J. In 't Hout 《BIT Numerical Mathematics》1992,32(4):634-649
This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU(t)=U(t)+U(t–) with , C, Re()<–||, and >0. Ifc
i
denotes theith abscissa of a given Runge-Kutta method, then in thenth stept
n–1t
n
:=t
n–1+h of the numerical process our interpolation procedure computes an approximation toU(t
n–1+c
i
h–) from approximations that have already been generated by the process at pointst
j–1+c
i
h(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem. 相似文献
19.
We consider the approximation by piecewise-constant functions for classes of functions of many variables defined by moduli of continuity of the form (1, ...,
n
) = 1(1) + ... +
n
(
n
), where
i
(
i
) are ordinary moduli of continuity that depend on one variable. In the case where
i
(
i
) are convex upward, we obtain exact error estimates in the following cases: (i) in the integral metric L
2 for (1, ...,
n
) = 1(1) + ... +
n
(
n
); (ii) in the integral metric L
p (p 1) for (1, ...,
n
) = c
11 + ... + c
n
n
; (iii) in the integral metric L
(2, ..., 2, 2r) (r = 2, 3, ...) for (1, ...,
n
) = 1(1) + ... +
n – 1(
n – 1) + c
n
n
. 相似文献
20.
Since the genus of the modular curve X_1 (8) = _1 (8)
* is zero, we find a field generator j
1,8(z) = 3(2z)/3(4z) (3(z) :=
n
ein
2z
) such that the function field over X
1(8) is (j
1,8). We apply this modular function j
1,8 to the construction of some class fields over an imaginary quadratic field K, and compute the minimal polynomial of the singular value of the Hauptmodul N(j
1,8) of (j
1,8). 相似文献