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1.
Rolf Riesinger 《Journal of Geometry》1997,60(1-2):127-145
Throughout this paper, the underlying projective space is 3-dimensional and Pappian. A spreadL admits aregulization , if is a collection of reguli contained inL and if each element ofL, except at most two lines, is contained either in exactly one regulus of or in all reguli of . Replacement of each regulus of by its complementary regulus (exceptional lines remain unchanged) produces thecomplementry congruence
L
c
of
L
with respect to . IfL
c
is an elliptic linear congruence of lines, then we call anelliptic regulization. Applying a method due to Thas and Walker we construct topological spreads of PG(3,) which admit one elliptic and no further regulization. For each of these spreads we determine the group of automorphic collineations. Among others we obtain also spreads which are the complete intersection of a general linear complex of lines and of a cubic complex of lines.In conclusion, I would like to thank H. H{upavlicek} (Vienna) for valuable suggestions in the preparation of this article. 相似文献
2.
Rabanovich V. I. Samoilenko Yu. S. Strelets A. V. 《Ukrainian Mathematical Journal》2001,53(10):1673-1687
We investigate the presence of polynomial identities in the algebras Q
n, generated by n idempotents with the sum e (
and e is the identity of an algebra). We prove that Q
4,2 is an algebra with the standard polynomial identity F
4, whereas the algebras Q
4,, 2, and Q
n,, n 5, do not have polynomial identities. 相似文献
3.
M. B. Nathanson 《Acta Mathematica Hungarica》2000,87(3):179-195
Let A be a set of positive integers with gcd (A) = 1, and let p
A
(n) be the partition function of A. Let c
0 = 2/3. If A has lower asymptotic density and upper asymptotic density , then lim inf log p
A
(n)/c
0 n and lim sup log p
A
(n)/c
0 n . In particular, if A has asymptotic density > 0, then log p
A
(n) c0n. Conversely, if > 0 and log p
A
(n) c
0 n, then the set A has asymptotic density . 相似文献
4.
Z. A. Chanturiya 《Mathematical Notes》1978,23(2):123-127
Let (n) be a system, close to the orthonormal complete system (x
n). An estimate is obtained for the deviation of the system {fn}, obtained from {n} by Schmidt's method, from the system {xn}. This estimate is used to show that, in any LP(–1,1), withp (1,4/3] [4,), and for any >e¦4 = i,13..., there exists an orthogonal algebraic system (P
n
(x))
n=0
, forming a basis in LP and such that n = degP
n
(x) n for n>no(p,).Translated from Matematicheskie Zametki, Vol. 23, No. 2, pp. 223–230, February, 1978. 相似文献
5.
Tianze Wang 《数学学报(英文版)》1995,11(2):156-167
Denote byE(X) the number of integersn X which are not a sum of a prime and a square. Set = 1 – 0.994428b, whereb min(0.9365/c
3, 0.02578/c
4),c
3,c
4 being given in Lemma 8. The resultE(x) x
is proved in this paper.Project Supported by the National Natural Science Foundation of China. 相似文献
6.
Let X, X
1, X
2,... be a sequence of independent and identically distributed random variables with common distribution function F. Denote by F
n
the distribution function of centered and normed sum S
n
. Let F belong to the domain of attraction of the standard normal law , that is, lim F
n
(x)= (x), as n , uniformly in x . We obtain extended asymptotic expansions for the particular case where the distribution function F has the density p(x) = cx
––1 ln(x), x > r, where 2, , c > 0, and r > 1. We write the classical asymptotic expansion (in powers of n
–1/2) and then add new terms of orders n
–/2 ln
n, n
–/2 ln-1
n, etc., where 0. 相似文献
7.
Jean Bertoin 《Journal of Theoretical Probability》1994,7(3):551-563
One says thatt>0 is an increase time for a real-valued path if stays above the level (t) immediately after timet, and below (t) immediately before timet. Dvoretzkyet al.,(10) proved that Brownian motion has no increase times a.s. This result is extended here to (strictly) stable processes. Specifically, the probability that a stable processX possesses increase times is 0 if and only ifP(X
10)1/2. 相似文献
8.
A. Boyarsky 《Journal of Optimization Theory and Applications》1977,22(3):429-445
Letx
t
u
() be a stochastic control system on the probability space (, ,P) intoR
n. We say that the pointxR
n is (, ) attainable at timet if there exists an admissible controlu such thatP
xo{x
t
u
()S
(x)}, wherex
0()=x
0, 0, 10, andS
(x) is the closed Euclidean -ball inR
n centered atx. We define the attainable setA
(t) to be the set of all pointsxR
n which are (, ) attainable at timet. For a large class of stochastic control systems, it is shown thatA
(t) is compact for eacht and continuous as a function oft in an appropriate metric. From this, the existence of stochastic time-optional controls is established for a large class of nonlinear stochastic differential equations.This research was supported by the National Research Council of Canada, Grant No. A-9072. 相似文献
9.
S. V. Lapin 《Mathematical Notes》1977,21(5):346-352
For a given -function (u), a condition on a -function (u) is found such that it is necessary and sufficient for the following to hold: if fn(x) f(x) and f
n
(x)M (n=1, 2, ...) where M>0 is an absolute constant, then f
n
(x)–f(x)0(n). An analogous condition for convergence in Orlicz spaces is obtained as a corollary.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 615–626, May, 1977.The author thanks V. A. Skvortsov for his constant attention and guidance on this paper. 相似文献
10.
We address the problem of monitoring a linear functional (c, x)Eof an unknown vectorx of a Hilbert spaceE, the available data being the observationz, in a Hilbert spaceF, of a vectorAx depending linearly onx through some known operatorA(E; F). WhenE=E
1×E
2,c=(c
1 0), andA is injective and defined through the solution of a partial differential equation, Lions ([6]–[8]) introduced sentinelssF such that (s, Ax)Fis sensitive to x1 E
1 but insensitive to x2 E2. In this paper we prove the existence, in the general case, of (i) a generalized sentinel (s, ) ×E, where F withF dense in 80, such that for anya priori guess x0 ofx, we have s, Ax + (, x0)E=(c, x)E, where x is the least-squares estimate ofx closest tox
0, and (ii) a family of regularized sentinels (s
n
,
n
) F×E which converge to (s, ). Generalized sentinels unify the least-squares approach (by construction !) and the sentinel approach (whenA is injective), and provide a general framework for the construction of sentinels with special sensitivity in the sense of Lions [8]). 相似文献
11.
Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory 总被引:2,自引:0,他引:2
Let {X
k
, 1 k n} be n independent and real-valued random variables with common subexponential distribution function, and let {k, 1 k n} be other n random variables independent of {X
k
, 1 k n} and satisfying a
k
b for some 0 < a b < for all 1 k n. This paper proves that the asymptotic relations P (max1 m n
k=1
m
k
X
k
> x) P (sum
k=1
n
k
X
k
> x) sum
k=1
n
P (
k
X
k
> x) hold as x . In doing so, no any assumption is made on the dependence structure of the sequence {
k
, 1 k n}. An application to ruin theory is proposed. 相似文献
12.
Ali Fardoun 《manuscripta mathematica》2005,116(1):57-69
We consider weakly p-harmonic maps (p2) from a compact connected Riemannian manifold Mm(m2) to the the standard sphere Sn with values in the closed hemisphere Sn+ = {x Sn : xn+1 0 } (n 2). We first prove that if u=(u1,...,un+1):MSn is a weakly p-harmonic map satisfying un+1(x)>0 a.e. on M, then it is a minimizing p-harmonic map. Next, we give a necessary and sufficient condition for the boundary data : M Sn+ to achieve uniqueness; and when this condition fails, we are able to describe the set of all minimizers. When M is without boundary, we obtain a Liouville type Theorem for weakly p-harmonic maps.Mathematics Subject Classification (2000): 58E20; 35J70 相似文献
13.
Summary It is proved that the operatorP: L
1 (0, ) L
1(0, ), given byPg(z) =
z/c
[g(x)/cx]dx, is completely mixing, i.e.,P
n
g
1 0 forg L
1(0, ) with g dx = 0. This implies that, forc (0, 1), each continuous and bounded solution of the equationf(x)=
0
cx
f(t)dt/(cx) (x (0, 1]) is constant. 相似文献
14.
A. T. Semenov 《Mathematical Notes》1974,15(4):362-366
Let 1, 2, ... be a sequence of independent identically distributed random variables with zero means. We consider the functional
n
=
k=o
n
(S
k
) where S1=0, Sk=
i=1
k
i (k1) and(x)=1 for x0,(x) = 0 for x<0. It is readily seen that n is the time spent by the random walk Sn, n0, on the positive semi-axis after n steps. For the simplest walk the asymptotics of the distribution P (n = k) for n and k, as well as for k = O(n) and k/n<1, was studied in [1]. In this paper we obtain the asymptotic expansions in powers of n–1 of the probabilities P(hn = nx) and P(nx1 n nx2) for 0<1, x = k/n 2<1, 0<1x122<1.Translated from Matematicheskie Zametki, Vol. 15, No. 4, pp. 613–620, April, 1974.The author wishes to thank B. A. Rogozin for valuable discussions in the course of his work. 相似文献
15.
H. Queffelec 《Monatshefte für Mathematik》1992,114(2):135-138
Let (c
n)
nZ
be a double-sided sequence of complex numbers; if, for quasi-all (i.e. in the Baire sense) choices of signs (
n)
nZ
, (
n
c
n)
nZ
is a Fourier-Stieltjes sequence, then we prove that (c
n)
nZ
l
2 (Z); this extends a result of Littlewood and at the same time provides a very simple proof of this result. 相似文献
16.
Let (x) stand for the number of primes not exceedingx. In the present work it is shown that if 23/421,yx
andx>x() then (x)–(x–y)>y/(100 logx). This implies for the difference between consecutive primes the inequalityp
n+1–p
n
p
n
23/42
. 相似文献
17.
Peter Hellekalek 《Monatshefte für Mathematik》1992,114(3-4):199-208
Leta be irrational and letf:[0,1] be Riemann-integrable with integral zero. Letf
n
(x) denote the Weyl sumf
n
(x):=
k=0
n–1
f({x
k>}),x/[0,1[,n. We prove criteria for the boundedness of the sequence (f
n
)
n1 and discuss the relation of this question to irregularities of the distribution of sequences. 相似文献
18.
Geoffrey Grimmett 《Journal of Theoretical Probability》1992,5(4):767-773
Denote byc
j
(F) thejth cumulant (or semi-invariant) of the distribution functionF. We say thatF is specified by its higher-order cumulants if it is the unique distribution functionG having the following property: there exists a positive integerJ such thatc
j
(G)=c
j
(F) forj=1,2 andjJ. Let (F
n
n1) be a sequence of distribution functions, and suppose that there existsJ such thatc
j
(F
n
)c
j
(F) asn, forj=1,2 andjJ. It is proved thatF
n
F so long asF is specified by its higher-order cumulants. It is an open problem to characterize the family of distributions which are specified by their higher-order cumulants. 相似文献
19.
John Dye 《Integral Equations and Operator Theory》1989,12(1):12-22
Let {T1, ..., TN} be a finite set of linear contraction mappings of a Hilbert space H into itself, and let r be a mapping from the natural numbers N to {1, ..., N}. One can form Sn=Tr(n)...Tr(1) which could be described as a random product of the Ti's. Roughly, the Sn converge strongly in the mean, but additional side conditions are necessary to ensure uniform, strong or weak convergence. We examine contractions with three such conditions. (W): xn1, Txn1 implies (I-T)xn0 weakly, (S): xn1, Txn1 implies (I-T)xn0 strongly, and (K): there exists a constant K>0 such that for all x, (I-T)x2K(x2–Tx2).We have three main results in the event that the Ti's are compact contractions. First, if r assumes each value infinitely often, then Sn converges uniformly to the projection Q on the subspace i=
1
N
[x|Tix=x]. Secondly we prove that for such compact contractions, the three conditions (W), (S), and (K) are equivalent. Finally if S=S(T1, ..., TN) denotes the algebraic semigroup generated by the Ti's, then there exists a fixed positive constant K such that each element in S satisfies (K) with that K. 相似文献
20.
LetZ be a compact set of the real space with at leastn + 2 points;f,h1,h2:Z continuous functions,h1,h2 strictly positive andP(x,z),x(x
0,...,x
n
)
n+1,z , a polynomial of degree at mostn. Consider a feasible setM {x
n+1z Z, –h
2(z) P(x, z)–f(z)h
1(z)}. Here it is proved the null vector 0 of
n+1 belongs to the compact convex hull of the gradients ± (1,z,...,z
n
), wherez Z are the index points in which the constraint functions are active for a givenx* M, if and only ifM is a singleton.This work was partially supported by CONACYT-MEXICO. 相似文献