共查询到20条相似文献,搜索用时 62 毫秒
1.
Philippe Berthet 《Journal of Theoretical Probability》1997,10(3):557-579
We obtain outer rates of clustering in the functional laws of the iterated logarithm of Deheuvels and Mason(11) and Deheuvels,(7) which describe local oscillations of empirical processes. Considering increment sizes a
n 0 such that na
n and na
n(log n)–7/3 we show that the sets of properly rescaled increment functions cluster with probability one to the
n-enlarged Strassen ball in B(0, 1) endowed with the uniform topology, where
n 0 may be chosen so small as (log (1/a
n) + log log n)–2/3 for any sufficiently large . This speed of coverage is reduced for smaller a
n. 相似文献
2.
Péter Komjáth 《Analysis Mathematica》1984,10(4):283-293
. , A
0,A
1,— - lim supA
j
- H,
. , - - . , , ; , , . - . - . 相似文献
3.
For a non-decreasing integer sequence a=(a1,...,an) we define La to be the set of n-tuples of integers = (1,...,n) satisfying
. This generalizes the so-called lecture hall partitions corresponding to ai=i and previously studied by the authors and by Andrews. We find sequences a such that the weight generating function for these a-lecture hall partitions has the remarkable form
In the limit when n tends to infinity, we obtain a family of identities of the kind the number of partitions of an integer m such that the quotient between consecutive parts is greater than is equal to the number of partitions of m into parts belonging to the set P, for certain real numbers and integer sets P. We then underline the connection between lecture hall partitions and Ehrhart theory and discuss some reciprocity results. 相似文献
4.
In this article the topologically exact sequences
of locally convex spaces are characterized for which for every locally convex space F the map id : FE F Q is a homomorphism, or equivalently, the map id L : FK F E is a topological injection. This is motivated by the problem of lifting Q-valued functions with certain given properties to E-valued functions with the same or slightly weaker properties, which may also be considered as the investigation of parameter dependences of solutions of linear (differential) equations. Applications to partial differential equations and to Fredholm functions are given. 相似文献
5.
Let be a graph and G be a 2-arc transitive automorphism group of . For a vertex x let G(x)(x) denote the permutation group induced by the stabilizer G(x) of x in G on the set (x) of vertices adjacent to x in . Then is said to be a locally projective graph of type (n,q) if G(x)(x) contains PSLn(q) as a normal subgroup in its natural doubly transitive action. Suppose that is a locally projective graph of type (n,q), for some n 3, whose girth (that is, the length of a shortest cycle) is 5 and suppose that G(x) acts faithfully on (x). (The case of unfaithful action was completely settled earlier.) We show that under these conditions either n=4, q=2, has 506 vertices and
, and contains the Wells graph on 32 vertices as a subgraph. In the latter case if, for a given n, at least one graph satisfying the conditions exists then there is a universal graph W(n) of which all other graphs for this n are quotients. The graph W(3) satisfies the conditions and has 220 vertices. 相似文献
6.
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
7.
Dr. Krishna Balasundaram Athreya 《Probability Theory and Related Fields》1969,12(4):320-332
Summary Let X(t)=(X
1
(t), X
2
(t), , X
t
(t)) be a k-type (2k<) continuous time, supercritical, nonsingular, positively regular Markov branching process. Let M(t)=((m
ij
(t))) be the mean matrix where m
ij
(t)=E(X
j
(t)¦X
r
(0)=
ir
for r=1, 2, , k) and write M(t)=exp(At). Let be an eigenvector of A corresponding to an eigenvalue . Assuming second moments this paper studies the limit behavior as t of the stochastic process
. It is shown that i) if 2 Re >1, then · X(t)e{–t¦ converges a.s. and in mean square to a random variable. ii) if 2 Re 1 then [ · X(t)] f(v · X(t)) converges in law to a normal distribution where f(x)=(x)
–1
if 2 Re <1 and f(x)=(x log x)–1 if 2 Re =1, 1 the largest real eigenvalue of A and v the corresponding right eigenvector.Research supported in part under contracts N0014-67-A-0112-0015 and NIH USPHS 10452 at Stanford University. 相似文献
8.
Letf be analytic in a hyperbolic region . The Bloch constant
f
off is defined by
, where (z)|dz| is the Poincaré metric in . Suppose is hyperbolic and
where
. Then for allf withf() , we have
f
1/(). In this paper we study the extremal functions defined by
f
=1/() and the existence of those functions.Supported by the National Natural Science Foundation of China. 相似文献
9.
Sanming Zhou 《Czechoslovak Mathematical Journal》1998,48(1):45-53
Let G be a graph with order p, size q and component number . For each i between p – and q, let
be the family of spanning i-edge subgraphs of G with exactly components. For an integer-valued graphical invariant if H H
is an adjacent edge transformation (AET) implies |(H)-(H')|1 then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let M
j() and m
j() be the invariants defined by
. It is proved that both M
p–() and m
p–(;) interpolate over
, if is continuous with respect to AET, and that M
j() and m
j() interpolate over
, if is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized. 相似文献
10.
Let M
n =X1+...+Xn be a martingale with bounded differences Xm=Mm-Mm-1 such that {|Xm| m}=1 with some nonnegative m. Write 2=
1
2
+ ... +
n
2
. We prove the inequalities {M
nx}c(1-(x/)), {M
n x} 1- c(1- (-x/)) with a constant
. The result yields sharp inequalities in some models related to the measure concentration phenomena. 相似文献
11.
N. A. Davydov 《Mathematical Notes》1972,11(4):263-265
For a preassigned unbounded sequence {Sn} of complex numbers, and preassigned complex numbers z1 and z2z1 we construct: 1) regular matrices A=ank and B=bnk such that the same bounded sequences are summable by these matrices and that
, and
; 2) regular matrices A(1))=a
nk
(1)
and B(1)=b
nk
(1)
such that B(1) A(1),
and,
. Our results show that the well known theorem of MazurOrlicz on the bounded consistency of two regular matrices, one of which is boundedly stronger than the other, is exact.Translated from Matematicheskie Zametki, Vol. 11, No. 4, pp. 431–436, April, 1972. 相似文献
12.
V. V. Makeev 《Journal of Mathematical Sciences》2002,110(4):2774-2775
Let A1,...,An be points in
, let
be a fixed point, let p be a positive integer, and let 1,...,n be positive real numbers. If the
does not depend on the position of M on a sphere with center O, then one says that the point system {A1,...,An} has an invariant of degree p with weight system {,...,n}. It is proved that for arbitrary positive integers d and N there exists a finite point system
having invariants of degrees p=1,...,N with common positive weight system {1,...,n}. Bibliography: 2 titles. 相似文献
13.
A. Yu. Šadrin 《Analysis Mathematica》1986,12(3):175-184
. L
p
, 0<p<, . , f, {E
n
(f)
p
}
1
p>0 .
The author expresses his thanks to S. B. Stekin for the attention he has paid to this work. 相似文献
The author expresses his thanks to S. B. Stekin for the attention he has paid to this work. 相似文献
14.
Dr. Werner Rupp 《manuscripta mathematica》1977,22(2):137-150
Let (, i) be a probability space for i=1,2 with and : m a correspondence, i.e. () is a non-void subset of m for all . We give necessary and sufficient conditions under which it holds, that 2 extends 1. iff A d2 is equal to A d1 for all A, where A di is the set of all integrals A f di of functions f: m with f()() i.-a.e. 相似文献
15.
Let be the linear space of the Laurent polynomials and suppose that <, < is a positive-definite Hermitian inner product in with the additional property that
. Starting from the five-term recurrence relation for orthogonal Laurent polynomials with respect to <, <, we derive Laurent–Jacobi matrices
and
for the multiplication operator and its inverse in . These matrices are real and symmetric, and
generates a symmetric operator in the Hilbert space 2 with natural basis { e
n
}
n = 0
. We show that this operator has deficiency indices (0, 0) or (1, 1) and that every self-adjoint extension A in 2 has simple spectrum with generating vector e
0. Let E be the spectral measure of A. Then the measure
e
0 given by
e
0() =<E() e
0, e
0< for all Borel sets in
, satisfies
forf,g. In this way, we obtain a solution
e
0 of the Strong Hamburger Moment Problem (SHMP) for which is dense in L
2(
e
0). Some results concerning the relation between the deficiency indices andthe set of all solutions of the SHMP are established. Finally, we give an analogue of a theorem by M. H. Stone which tells us which self-adjoint operators are generatedby a Laurent–Jacobi matrix with deficiency indices (0, 0). 相似文献
16.
Clas-Olof Selenius 《Mathematische Annalen》1966,164(1):94-103
Zusammenfassung Periodische DIagonalkettenbrüche weisen — über die bekannte, in ihrer Definition begründete, Grundeigenschaft hinaus — bemerkenswerte Regelmäßigkeiten auf. IN dieser Arbeit ist aufgezeigt, daß der NäherungsbruchA
v–1
/B
v–1
der quadratischen Irrationalzahl
:Q
0 (normiert,Q
0>0 angenommen),dann und nur dann auch Näherungsbruch der Diagonal-kettenbruchentwicklung von 0 ist, wenn der NennerQ
v
in dem vollständigen Quotienten
:Q
v
von 0 kleiner ist als
(Satz 4), ausgenommen höchstens den Fall, daß der Vorperiode oder der 1. Periode der regelmäßigen Kettenbruchentwicklung von 0 angehört.Ist speziell
die Quadratwurzel aus einer natürlichen nichtquadratischen Zahl, so gilt die Regelmäßigkeit für alle 1 (Satz 1). In Satz 4 ist näher erläutert, von welchem an die Formel im allgemeinen Fall notwendig gilt.Das gegebene Kriterium erleichtert sowohl die Bestimmung der Diagonalkettenbruchentwicklung quadratischer Irrationalzahlen als auch die Lösung diophantischer Ungleichungen, wie es auch weitere, über den Rahmen dieser Arbeit hinausgehende, theoretische Schlußfolgerungen ermöglicht, auf die wir in anderem Zusammenhang eingehen werden.Herrn Prof.Nils Pipping, Helsingfors, zum 75. Geburtstag am 14. Mai 1965 gewidmet 相似文献
17.
Friedhelm Waldhausen 《Inventiones Mathematicae》1967,4(2):87-117
Ohne ZusammenfassungDies ist der zweite Teil einer aus technischen Gründen aufgeteilten Arbeit. Kenntnis des ersten Teils ([13]) ist notwendig für die Lektüre des zweiten Teils. Hinweise der Art (,), mit<=5, beziehen sich auf den ersten Teil. 相似文献
18.
Gikō Ikegami 《Inventiones Mathematicae》1989,95(2):215-246
Summary We define a constraint system
, [0,0), which is a kind of family of vector fields
on a manifold. This is a generalized version of the family of the equations
, [0,0),x
m
,y
n
. Finally, we prove a singular perturbation theorem for the system
, [0,0).Dedicated to Professor Kenichi Shiraiwa on his 60th birthday 相似文献
19.
Dr. Christoph Kopf 《Monatshefte für Mathematik》1976,81(2):119-129
Every elementary Markov process with a polish state space and with a discrete set of time parameter dense in +, whose finite dimensional distributions are derived from a semigroup (K
t) of Markov kernels continuous in 0 + and whose initial distribution satisfies K
t, can be imbedded in an elementary Markov process with the same state space and with parameter set + so that the corresponding finite dimensional distributions are equal. 相似文献
20.
Amitava Chakravorti 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1959,10(4):333-338
Zusammenfassung Die vorliegende Notiz behandelt das Problem der Auffindung des Biegungszentrums eines aus isotropem Material bestehenden Balkens, der einen durch eine parabolische und eine geradlinige Kante begrenzten Querschnitt besitzt. Die Last ist parallel zur geradlinigen Kante angenommen. Der Verfasser benützt zur Lösung der Aufgabe dasselbe Verfahren, dasSokolnikoff [1] für die Auffindung des Biegungszentrums eines halbkreisförmigen Balkens verwendete.
Nomenclature x, y, z rectangular co-ordinates - l, m, n direction cosines of outward drawn normal - x , y , z normal components of stress parallel tox, y, z axes - xy , yz , zx shearing stress components in rectangular co-ordinates - u, v, w components of displacement - T (x, y) stress function in rectangular coordinates - Poisson's ratio - shear modulus - yz , zx , xy shearing strain components in rectangular coordinates 相似文献
Nomenclature x, y, z rectangular co-ordinates - l, m, n direction cosines of outward drawn normal - x , y , z normal components of stress parallel tox, y, z axes - xy , yz , zx shearing stress components in rectangular co-ordinates - u, v, w components of displacement - T (x, y) stress function in rectangular coordinates - Poisson's ratio - shear modulus - yz , zx , xy shearing strain components in rectangular coordinates 相似文献