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1.
B. F. Skubenko 《Journal of Mathematical Sciences》1984,25(2):1089-1092
Let M be a complete module of a purely algebraic field of degree n3, let be the lattice of this module and let F(X) be its form. By we denote any lattice for which we have = , where is a nondiagonal matrix satisfying the condition ¦-I¦ , I being the identity matrix. The complete collection of such lattices will be denoted by {}. To each lattice we associate in a natural manner the decomposable form F(X). The complete collection of forms, corresponding to the set {}, will be denoted by {F} It is shown that for any given arbitrarily small interval (N–, N+), one can select an such that for each F(X) from {F} there exists an integral vector X0 such that N– < F(X0) < N+.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 167–171, 1981. 相似文献
2.
Joanna Janczewska 《Geometriae Dedicata》2002,91(1):7-21
The aim of this paper is to illustrate the use of topological degree for the study of bifurcation in von Kármán equations with two real positive parameters and for a thin elastic disk lying on the elastic base under the action of a compressing force, which may be written in the form of an operator equation F(x, , ) = 0 in some real Banach spaces X and Y. The bifurcation problem that we study is a mathematical model for a certain physical phenomenon and it is very important in the mechanics of elastic constructions. We reduce the bifurcation problem in the solution set of equation F(x, , ) = 0 at a point (0, 0, 0) X × IR
+
2 to the bifurcation problem in the solution set of a certain equation in IR
n
at a point (0, 0, 0) IR
n
× IR
+
2, where n = dim Ker F
x
(0, 0, 0) and F
x
(0, 0, 0): X Y is a Fréchet derivative of F with respect to x at (0, 0, 0). To solve the bifurcation problem obtained as a result of reduction, we apply homotopy and degree theory. 相似文献
3.
Summary Consider partial sumsS
n
of an i.i.d. sequenceX
1
X
2, ..., of centered random variables having a finite moment generating function in a neighborhood of zero. The asymptotic behaviour of
is investigated, where 1b
n
n denotes an integer sequence such thatb
n
/logn asn. In particular, ifb
n
=o(log
p
n) asn for somep>1, the exact convergence rate ofU
n
/b
n
n
=1 +0 (1) is determined, where
n
depends uponb
n
and the distribution ofX
1. In addition, a weak limit law forU
n
is derived. Finally, it is shown how strong invariance takes over if
b
n
(loglogn)2/log3
n=. 相似文献
4.
Karl -Heinz Küfer 《Mathematical Methods of Operations Research》1996,44(2):147-170
Leta
1 ...,a
m
be i.i.d. points uniformly on the unit sphere in
n
,m n 3, and letX:= {x
n
|a
i
T
x1} be the random polyhedron generated bya
1, ...,a
m
. Furthermore, for linearly independent vectorsu, in
n
, letS
u
, (X) be the number of shadow vertices ofX inspan(u,). The paper provides an asymptotic expansion of the expectation value¯S
n,m
:=
in4
1
E(S
u,
) for fixedn andm .¯S
n,m
equals the expected number of pivot steps that the shadow vertex algorithm — a parametric variant of the simplex algorithm — requires in order to solve linear programming problems of type max u
T
,xX, if the algorithm will be started with anX-vertex solving the problem max
T
,x X. Our analysis is closely related to Borgwardt's probabilistic analysis of the simplex algorithm. We obtain a refined asymptotic analysis of the expected number of pivot steps required by the shadow vertex algorithm for uniformly on the sphere distributed data. 相似文献
5.
Frédéric Bernardin 《Set-Valued Analysis》2003,11(4):393-415
In this paper we show the strong mean square convergence of a numerical scheme for a R
d
-multivalued stochastic differential equation: dX
t
+A(X
t
)dtb(t,X
t
)dt+(t,X
t
)dW
t
and obtain the rate of convergence O(( log(1/)1/2) when the diffusion coefficient is bounded. By introducing a discrete Skorokhod problem, we establish L
p
-estimates (p2) for the solutions and prove the convergence by using a deterministic result. Numerical experiments for the rate of convergence are presented. 相似文献
6.
Priscilla E. Greenwood Gerard Hooghiemstra 《Probability Theory and Related Fields》1991,89(2):201-210
Summary Between the operations which produce partial maxima and partial sums of a sequenceY
1,Y
2, ..., lies the inductive operation:X
n
=X
n-1(X
n-1+Y
n
),n1, for 0<<1. If theY
n
are independent random variables with common distributionF, we show that the limiting behavior of normed sequences formed from {X
n
,n1}, is, for 0<<1, parallel to the extreme value case =0. ForFD() we give a full proof of the convergence, whereas forFD()D(), we only succeeded in proving tightness of the involved sequence. The processX
n
is interesting for some applied probability models. 相似文献
7.
Robert Blackburn 《Journal of Theoretical Probability》2000,13(3):825-842
For X(t) a real-valued symmetric Lévy process, its characteristic function is E(e
iX(t))=exp(–t()). Assume that is regularly varying at infinity with index 1<2. Let L
x
t
denote the local time of X(t) and L*
t
=sup
xR
L
x
t
. Estimates are obtained for P(L
0
t
y) and P(L*
t
y) as y and t fixed. 相似文献
8.
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
9.
For a projective plane
n
of ordern, let(
n
) denote the minimum numberk, so that there is a coloring of the points of
n
ink colors such that no two distinct lines contain precisely the same number of points of each color. Answering a question of A. Rosa, we show that for all sufficiently largen, 5 (
n
) 8 for every projective plane
n
of ordern.
Research supported in part by Allon Fellowship and by a grant from the United States Israel Binational Science Foundation 相似文献
10.
V. N. Sudakov 《Mathematical Notes》1973,14(4):886-888
Let X and Y be locally compact-compact topological spaces, F X×Y is closed, and P(F) is the set of all Borel probability measures on F. For us to find, for the pair of probability measures (x, y P (X)×P(Y), a probability measure P(F) such that
X
=
X
–1
,
Y
=
Y
–1
it is necessary and sufficient that, for any pair of Borel sets A X, B Y for which (A× B) F=Ø, the condition
XA+
YB 1 holds.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 573–576, October, 1973. 相似文献
11.
Let (X
n
)
0 be a Markov chain with state space S=[0,1] generated by the iteration of i.i.d. random logistic maps, i.e., X
n+1=C
n+1
X
n
(1–X
n
),n0, where (C
n
)
1 are i.i.d. random variables with values in [0, 4] and independent of X
0. In the critical case, i.e., when E(log C
1)=0, Athreya and Dai(2) have shown that X
n
P
0. In this paper it is shown that if P(C
1=1)<1 and E(log C
1)=0 then(i) X
n
does not go to zero with probability one (w.p.1) and in fact, there exists a 0<<1 and a countable set (0,1) such that for all xA(0,1), P
x
(X
n
for infinitely many n1)=1, where P
x
stands for the probability distribution of (X
n
)
0 with X
0=x w.p.1. A is a closed set for (X
n
)
0.(ii) If is the supremum of the support of the distribution of C
1, then for all xA
(a)
for 12(b)
for 24(c)
for 24 under some additional smoothness condition on the distribution of C
1.(iii) The empirical distribution
converges weakly to
0, the delta measure at 0, w.p.1 for any initial distribution of X
0. 相似文献
12.
Jacques Simon 《Annali di Matematica Pura ed Applicata》1986,146(1):65-96
Summary A characterization of compact sets in Lp (0, T; B) is given, where 1P and B is a Banach space. For the existence of solutions in nonlinear boundary value problems by the compactness method, the point is to obtain compactness in a space Lp (0,T; B) from estimates with values in some spaces X, Y or B where XBY with compact imbedding XB. Using the present characterization for this kind of situations, sufficient conditions for compactness are given with optimal parameters. As an example, it is proved that if {fn} is bounded in Lq(0,T; B) and in L
loc
1
(0, T; X) and if {fn/t} is bounded in L
loc
1
(0, T; Y) then {fn} is relatively compact in Lp(0,T; B), p相似文献
13.
Pavle Mladenovic´ 《Extremes》1999,2(4):405-419
Let X
n1
*
, ... X
nn
*
be a sequence of n independent random variables which have a geometric distribution with the parameter p
n = 1/n, and M
n
*
= \max\{X
n1
*
, ... X
nn
*
}. Let Z
1, Z2, Z3, ... be a sequence of independent random variables with the uniform distribution over the set N
n = {1, 2, ... n}. For each j N
n let us denote X
nj = min{k : Zk = j}, M
n = max{Xn1, ... Xnn}, and let S
n be the 2nd largest among X
n1, Xn2, ... Xnn. Using the methodology of verifying D(un) and D'(un) mixing conditions we prove herein that the maximum M
n has the same type I limiting distribution as the maximum M
n
*
and estimate the rate of convergence. The limiting bivariate distribution of (Sn, Mn) is also obtained. Let
n, n Nn,
,
and T
n = min{M(An), M(Bn)}. We determine herein the limiting distribution of random variable T
n in the case
n ,
n/n > 0, as n . 相似文献
14.
M. Truszczyński 《Periodica Mathematica Hungarica》1988,19(4):273-286
A family of subtrees of a graphG whose edge sets form a partition of the edge set ofG is called atree decomposition ofG. The minimum number of trees in a tree decomposition ofG is called thetree number ofG and is denoted by(G). It is known that ifG is connected then(G) |G|/2. In this paper we show that ifG is connected and has girthg 5 then(G) |G|/g + 1. Surprisingly, the case wheng = 4 seems to be more difficult. We conjecture that in this case(G) |G|/4 + 1 and show a wide class of graphs that satisfy it. Also, some special graphs like complete bipartite graphs andn-dimensional cubes, for which we determine their tree numbers, satisfy it. In the general case we prove the weaker inequality(G) (|G| – 1)/3 + 1. 相似文献
15.
S. A. Telyakovskii 《Mathematical Notes》1970,8(5):817-819
It is proved that a quasiconvex sequence
v
of convergence factors transforms Fourier series of functions whose moduli of continuity do not exceed a given modulus of continuity(gd) into uniformly convergent series if and only if
n
(1/n) log n 0 for n . The sufficiency of this condition is already known.Translated from Matematicheskie Zametki, Vol. 8, No. 5,pp. 619–623, November, 1970. 相似文献
16.
Dr. J. Hüsler 《Monatshefte für Mathematik》1977,84(3):209-212
The strong law of large numbers for independent and identically distributed random variablesX
i
,i=1, 2, 3,... with finite expectationE|X
1| can be stated as, for any >0, the number of integersn such that
\varepsilon $$
" align="middle" border="0">
,N
is finite a. s. It is known thatEN
< iffEX
1
2
< and that 2 EN var X1 as 0, ifE X
1
2
<. Here we consider the asymptotic behaviour ofEN
(n) asn, whereN
(n) is the number of integerskn such that
\varepsilon $$
" align="middle" border="0">
andE N
1
2
=. 相似文献
17.
Hani Doss 《Probability Theory and Related Fields》1984,68(2):127-147
Summary Let X
i
=+
i for i=1, ..., n, where the
i's are i.i.d. F and F is symmetric about 0. F is assumed unknown or only partially known, and the problem is to estimate . Priors are put on the pair (F,). The priors on F are obtained from Doksum's neutral to the right priors, and include symmetrized Dirichlet priors. The marginal posterior distribution of given X
1, ..., X
nis computed and its general properties studied. It is found that for certain classes of distributions of the
i's, the posterior distribution of is for all large n a point mass at the true value of . If the distribution of the
i's is not exactly symmetric, the Bayes estimates can behave very poorly. 相似文献
18.
Let m= (1,..., m) denote an ordered field, where i+1>0 is infinitesimal relative to the elements of i, 0 < –i < m (by definition, 0= ). Given a system of inequalities f1 > 0, ..., fs > 0, fs+1 0, ..., fk 0, where fj m [X1,..., Xn] are polynomials such that, and the absolute value of any integer occurring in the coefficients of the fjs is at most 2M. An algorithm is constructed which tests the above system of inequalities for solvability over the real closure of m in polynomial time with respect to M, ((d)nd0)n+m. In the case m=, the algorithm explicitly constructs a family of real solutions of the system (provided the latter is consistent). Previously known algorithms for this problem had complexity of the order ofM(d d
0
m
2U(n)
.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Maternaticheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 174, pp. 3–36, 1988. 相似文献
19.
Jesüs M. Ruiz 《manuscripta mathematica》1984,46(1-3):193-214
Let XoR
n be an irreducible analytic germ and the order space of its field of meromorphicfunetion germs. A formal half-branch in Xo is a kind of C-map germ c[0,)Xo; an ordering is centered at c if it contains the functions which are positive on c. We obtain a partition 1,...,d, d=dim Xo, of the set * of central (i.e.: centered at some half-branch) orderings, according to the dimension of half-branches. Then we show that all e, e= 1,.,d, as well as the set \* of noncentral orderings, are dense in . Finally, we solve the 17th Hubert Problem for analytic germs. 相似文献
20.
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