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1.
On a finite segment [0, l], we consider the differential equation
with a parameter C. In the case where a(x), (x) L
[0, l],
j
(x) L
1[0, l], j = 1, 2, a(x) m
0 > 0 and (x) m
1 > 0 almost everywhere, and a(x)(x) is a function absolutely continuous on the segment [0, l], we obtain exponential-type asymptotic formulas as
for a fundamental system of solutions of this equation. 相似文献
2.
A. A. Saakyan 《Mathematical Notes》2003,74(1-2):255-265
In this paper, we prove that for any compact set
there exists a homeomorphism of the closed interval
such that for an arbitrary function f the Fourier series of the function F(x,y) = f((x),(y)) converges uniformly on
simultaneously over rectangles, over spheres, and over triangles. 相似文献
3.
Dipl.-Ing. Dr. techn. R. Hafner 《Probability Theory and Related Fields》1972,21(2):96-108
Zusammenfassung Ist U eine symmetrische Menge des R
m
(i. e. -U=U R
m
), so heien zwei Punkte x
1, x
2 R
m
U-koinzident falls x
1–x2U gilt. Dieser Koinzidenzbegriff wurde in [1] eingeführt. In dieser Arbeit wurde folgendes allgemeine Resultat bewiesen:Sind x
1,...,x
n
ER
m gegebene Punkte, ist AR
m beliebig und U=–UR
m
, so bezeichne K(x1,h.,xn; U, A) die Anzahl der U-koinzidenten Paare unter denjenigen der Punkte x
1,...,x
n, die in A fallen. Ist
eine Folge von unabhÄngigen, m-dimensionalen Zufallsvariablen, mit der allen gemeinsamen, quadratisch integrierbaren Dichte f, so ordne man jeder Folge
von symmetrischen Borelmengen des R
m
die Folge der stochastischen Prozesse
zu. Weiters bezeichne
den durch das Ma
induzierten Poissonproze.Dann wurde in [1] gezeigt, da unter geeigneten Voraussetzungen über die Folge
und für beliebige
die Folge der gemeinsamen Verteilungen von (K(x
1,h.,xn; U
n
, A
j
): j=1(1)r) gegen die gemeinsame Verteilung von (K(A
j
): j=1(1) r) strebt.In der vorliegenden Arbeit wird der Begriff der k-fachen U-Koinzidenz eingeführt und ein analoges Resultat für die asymptotische Verteilung der Anzahlen von k-fachen Koinzidenzen hergeleitet. 相似文献
4.
In this paper we shall consider the critical elliptic
equation
where
and a(x)
is a real continuous, non
negative function, not identically zero. By using a local Pohozaev
identity, we show that problem (0.1) does not admit a
family of solutions
which blows-up and concentrates as
at some zero point x0 of a(x)
if the order of flatness of the function a(x) at x0 is
相似文献
5.
Let
be a random walk with independent identically distributed increments
. We study the ratios of the probabilities P(S
n
>x) / P(1 > x) for all n and x. For some subclasses of subexponential distributions we find upper estimates uniform in x for the ratios which improve the available estimates for the whole class of subexponential distributions. We give some conditions sufficient for the asymptotic equivalence P(S
> x) E P(1 > x) as x . Here is a positive integer-valued random variable independent of
. The estimates obtained are also used to find the asymptotics of the tail distribution of the maximum of a random walk modulated by a regenerative process. 相似文献
6.
T. I. Seidman 《Journal of Optimization Theory and Applications》1980,30(4):535-547
One standard approach to solvingf(x)=b is the minimization of f(x)–b2 overx in
, where
corresponds to a parametric representation providing sufficiently good approximation to the true solutionx*. Call the minimizerx=A(
). Take
=
N
for a sequence {
N
} of subspaces becoming dense, and so determine an approximating sequences {x
N
A (
N
)}. It is shown, withf linear and one-to-one, that one need not havex
Nx* iff
–1 is not continuous.This work was supported by the US Army Research Office under Grant No. DAAG-29-77-G-0061. The author is indebted to the late W. C. Chewning for suggesting the topic in connection with computing optimal boundary controls for the heat equation (Ref. 2). 相似文献
7.
R. A. Doney 《Probability Theory and Related Fields》1989,81(2):239-246
Summary Let
x
denote the time at which a random walk with finite positive mean first passes into (x, ), wherex0. This paper establishes the asymptotic behaviour of Pr {
x
>n} asn for fixedx in two cases. In the first case the left hand tail of the step-distribution is regularly varying, and in the second the step-distribution satisfies a one-sided Cramér type condition. As a corollary, it follows that in the first case
Pr {
x
>n}/Pr{
0
>n} coincides with the limit of the same quantity for recurrent random walk satisfying Spitzer's condition, but in the second case the limit is more complicated. 相似文献
8.
Najim Christopher A. Russo Ralph P. 《Methodology and Computing in Applied Probability》2003,5(1):23-33
Let U
1, U
2,... be a sequence of i.i.d. random elements in Rd. For x>0, a graph G
n
(x) may be formed by connecting with an edge each pair of points in
that are separated by a distance no greater than x. The points of G
n
(x) could represent the stations in a telecommunications network and the edge set the lines of communication that exist among them. Let
be a collection of graphs on mn points having a specified form or structure, and let
denote the number of subgraphs embedded in G
n
(x) and contained in
. It is shown that a SLLN, CLT and LIL for
follow easily from the theory of U-statistics. In addition, a uniform (in x) SLLN is proved for collections
that satisfy a certain monotonicity condition. Some applications are mentioned and the results of some simulations presented. The scaling constants appearing in the CLT are usually hard to obtain. These are worked out for some special cases. 相似文献
9.
V. M. Badkov 《Mathematical Notes》1973,13(5):453-459
For the polynomials {pn(t)}
0
, orthonormalized on [–1, 1] with weightp(t) = (1–t) (1+t)
v=1
m
, we obtain necessary and sufficient conditions for boundedness of the sequences of norms: 1)
2)
and 3)
with the conditions that
on [–1, 1] and (H,)–1 L2(0, 2), where(H,) is the modulus of continuity in C(–1, 1) of function H.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 759–770, May, 1973. 相似文献
10.
Summary Let (W, H, ) be an abstract Wiener space and letR(w) be a strongly measurable random variable with values in the set of isometries onH. Suppose that Rh is smooth in the Sobolev sense and that it is a quasi-nilpotent operator onH for everyhH. It is shown that (R(w)h) is again a Gaussian (0, |h|
H
2
)-random variable. Consequently, if (e
i
,i)W
* is a complete, orthonormal basis ofH, then
defines a measure preserving transformation, a rotation, onW. It is also shown that if for some strongly measurable, operator valued (onH) random variableR, (R(w+k)h) is (0, |h|
H
2
)-Gaussian for allk, hH, thenR is an isometry and Rh is quasi-nilpotent for allHH. The relation between the stochastic calculi for these Wiener pathsw and
, as well as the conditions of the inverbibility of the map
are discussed and the problem of the absolute continuity of the image of the Wiener measure under Euclidean motion on the Wiener space (i.e.
composed with a shift) is studied.The research of the second author was supported by the Fund for the Promotion of Research at the TechnionDedicated to the memory of Albert Badrikian 相似文献
11.
Mitsuhiro Miyazaki 《manuscripta mathematica》1989,63(2):245-254
Letk be a field and an abstract simplicial complex with vertex set
. In this article we study the structure of the Ext modules Ext
a
i
(A/m
(l
,k[]) of the Stanley-Reisner ringk[] whereA=k[x
1,...,x
n
] andm
l
=(x
l
1
,...,x
l
n
). Using this structure theorem we give a characterization of Buchsbaumness ofk[] by means of the length of the modules Ext
A
i
(A/m
l
,k[]). That isk[] is Buchsbaum if and only if for allik[], the length of the modules Ext
A
i
(A/m
l
,k[]) is independent ofl. 相似文献
12.
Jelena V. Manojlović 《Czechoslovak Mathematical Journal》2005,55(1):41-60
New oscillation criteria are given for the second order sublinear differential equation
where a C
1 ([t
0, )) is a nonnegative function, , f C() with (x) 0, xf(x) / (x) > 0 for x 0, , f have continuous derivative on \ {0} with [f(x) / #x03C8;(x)] 0 for x 0 and q C([t
0, )) has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients q and a and extend known oscillation criteria for the equation x (t) + q(t)x(t) = 0. 相似文献
13.
A note on smoothed estimating functions 总被引:1,自引:0,他引:1
A. Thavaneswaran Jagbir Singh 《Annals of the Institute of Statistical Mathematics》1993,45(4):721-729
The kernel estimate of regression function in likelihood based models has been studied in Staniswalis (1989,J. Amer. Statist. Assoc.,84, 276–283). The notion of optimal estimation for the nonparametric kernel estimation of semimartingale intensity (t) is proposed. The goal is to arrive at a nonparametric estimate
of 0=(t
0) for a fixed pointt
0 [0, 1]. We consider the estimator that is a solution of the smoothed optimal estimating equation
is the optimal estimating function as in Thavaneswaran and Thompson (1986,J. Appl. Probab.,23, 409–417). 相似文献
14.
Summary The local limit problem is investigated for sequences (p
n
) of probability densities with stable limit densitiesq
having characteristic exponent (0, 2).It is shown that certain continuity-properties (Hölder-continuity) are necessary and - under appropriate additional conditions-sufficient for
asn. In this sence the speed of convergence is also studied. 相似文献
15.
Commutativity of Rings with Constraints Involving a Subset 总被引:1,自引:0,他引:1
Moharram A. Khan 《Czechoslovak Mathematical Journal》2003,53(3):545-559
Suppose that R is an associative ring with identity 1, J(R) the Jacobson radical of R, and N(R) the set of nilpotent elements of R. Let m 1 be a fixed positive integer and R an m-torsion-free ring with identity 1. The main result of the present paper asserts that R is commutative if R satisfies both the conditions(i) [x
m, y
m] = 0 for all
and(ii) [(xy)
m
+ y
m
x
m, x] = 0 = [(yx)
m
+ x
m
y
m, x], for all
This result is also valid if (i) and (ii) are replaced by (i) [x
m, y
m] = 0 for all
and (ii) [(xy)
m
+ y
m
x
m, x] = 0 = [(yx)
m
+ x
m
y
m, x] for all
Other similar commutativity theorems are also discussed. 相似文献
16.
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
17.
W. Hazod 《Probability Theory and Related Fields》1971,20(4):259-270
Ohne ZusammenfassungBezeichnungen und Symbole
G
lokalkompakte topologische Gruppe
-
M(G)/R(G)/P(G)/
regulÄre komplexe/reelle/positive Ma\e/
-
Q(G)/W(G)
Ma\e mit · l/Wahrscheinlichkeitsma\e
-
x
Punktma\:
x(f)=f(x)
-
v
Faltung,
— Bekanntlich bildet M(G) bezüglich der Faltung eine Banachalgebra;
-
Involution in M(G),
, wobei — die Komplexkonjugierte bezeichnet
- ×
diskreter Anteil eines Ma\es,
-
T
gm
Faltungsoperator auf L
2 (G) (bezüglich des linken Haarschen Ma\es),
f.ü.
-
p(·)/q(·)/u(·)
- exp(·.)
Exponentialfunktion, exp
- normal/unitÄr/symmetrisch/positiv definit
bezeichnet man ein Ma\ , wenn der Faltungsoperator T
diese Eigenschaft besitzt
- invertierbar
hei\t
M(G), wenn ein vM(G) existiert, so da\ v = v=
e
-
1/n
n-te Wurzel von
1
hei\t wenn(
1/n)n=
1
-
1 hei\t unendlich teilbar
wenn zu jedem natürlichen n eine n-te Wurzel
1/n von existiert
-
N
Menge der natürlichen Zahlen 相似文献
18.
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
19.
Cindy de Volder 《Geometriae Dedicata》2001,85(1-3):237-251
We consider the blowing-up Y
k
of the projective plane along k general points P
1,...,P
k
. Let
k
: Y
k
2 be the projection map and E
i
the exceptional divisor corresponding to P
i
for 1ik. For m2 and km(m+3)/2–4 let
k
be the invertible sheaf
k
*(
2(m))
Y
k
(–E
1–···–E
k
) on Y
k
, and let k: Y
k
N
be the morphism corresponding to
k
. As
k
is a local embedding, the Gauss map
k
corresponding to
k
is defined on Y
k
by
k
(x)=(d
x
k
)(T
x
(Y
k
)) for all xY
k
. We prove that this Gauss map
k
is injective. 相似文献
20.
Winfried Just 《Algebra Universalis》1985,20(2):135-142
In this paper we show that the following is relatively consistent withZFC +CH: There is no superatomic Boolean algebra of height 2+1 and width, and there is no superatomic Boolean algebraA with
for 0<<1 and
Presented by J. Mycielski. 相似文献