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1.
G. Ya. Beil'kin 《Journal of Mathematical Sciences》1983,21(3):251-254
The following inverse kinematic problem of seismology is considered. In the compact domain M of dimension ,2 with the metric, we consider the problem of constructing a new metricdu=nds according to the known formula where ,M and K, is the geodesic in the metric du, connecting the points , . One proves uniqueness and one obtains a stability estimate, where the refraction indices n1, n2 are the solutions of the inverse kinematic problem, constructed relative to the functions 1, 2, respectively, is the differential form on M×Mwhere =2–1,.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 84, pp. 3–6, 1979. 相似文献
2.
We give several internal characterizations for the metrizable absolute F
-spaces. The characterizing conditions involve the existence of compatible bicomplete quasi-metrics, of complete sequences of -discrete closed covers and of compact -discrete closed networks. 相似文献
3.
Unbounded pairs of self-adjoint operatorsA andB satisfying the algebraic relationF
1(A)B=BF
2(A) are studied. For these relations, various definitions of integrable pairs of operators are presented and the class of tame relations is indicated; for the tame relations, the irreducible pairs are described and a structure theorem is presented.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1253–1258, September, 1993. 相似文献
4.
P. Révész 《Probability Theory and Related Fields》1992,93(1):21-37
Summary We say that the discD()R
2, of radius , located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzD() there exists a 0tT such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those 's (0) is studied for which,D() isp-covered inT. 相似文献
5.
A. G. Pinus 《Mathematical Notes》1972,11(1):54-57
It is shown that if a linearly ordered set B does not contain as subsets sets of order type
and
*
then B can be embedded in 2
. We construct an example of a set satisfying the above conditions which cannot be embedded in any 2
if <
. Simultaneously we show that for any ordinal, 2
+1
cannot be embedded in 2
and that there exists at least
+1
distinct dense order types of cardinality 2
.Translated from Matematicheskie Zametki, Vol. 11, No. 1, pp. 83–88, January, 1972.In conclusion, I wish to take the opportunity to thank Yu. L. Ershov for kindness and assistance in this work. 相似文献
6.
R
n. , , , F R
n, F , R
n R
n .
p,q
(Rn), >0, 1, q, — ( ) Rn. ,
p,q
(Rn) F Rn. , q B
p,q
(F), = – (n–)/, >0, — « », ad — F, . , . : , F=R
d,F— « » F— R
n, « », F. .
This work has been supported in part by the Swedish Natural Science Research Council. 相似文献
This work has been supported in part by the Swedish Natural Science Research Council. 相似文献
7.
We fix a rich probability space (,F,P). Let (H,) be a separable Hilbert space and let be the canonical cylindrical Gaussian measure on H. Given any abstract Wiener space (H,B,) over H, and for every Hilbert–Schmidt operator T: HBH which is (|{}|,)-continuous, where |{}| stands for the (Gross-measurable) norm on B, we construct an Ornstein–Uhlenbeck process : (,F,P)×[0,1](B,|{}|) as a pathwise solution of the following infinite-dimensional Langevin equation d
t
=db
t
+T(
t
)dt with the initial data 0=0, where b is a B-valued Brownian motion based on the abstract Wiener space (H,B,). The richness of the probability space (,F,P) then implies the following consequences: the probability space is independent of the abstract Wiener space (H,B,) (in the sense that (,F,P) does not depend on the choice of the Gross-measurable norm |{}|) and the space C
B
consisting of all continuous B-valued functions on [0,1] is identical with the set of all paths of . Finally, we present a way to obtain pathwise continuous solutions :d
t
=
db
t
+
t
dt
with initial data 0=0, where ,R,0 and 0<. 相似文献
8.
Е. П. долженко 《Analysis Mathematica》1976,2(3):191-201
LetG be a domain inC
n
,EG, mes
E=0 for (r)=r
2n–1(r), where (r) is a nondecreasing non-negative function (r>0). Iff(z) is holomorphic inGE and (,f, GE)(), C=const, thenf(z) is holomorphic inG.The impossibility of the relaxation of the stipulations on () and(r) is also established.The statement above is a corollary to a more general result about the representation of a holomorphic function from a certain class in the form of an integral with respect to -measure, extended over the set of singular points of the function. 相似文献
9.
Characterization theorem of generalized polynomial of best approximation having bounded coefficients
Shusheng Xu 《应用数学学报(英文版)》1989,5(4):361-366
Let the set of generalized polynomials having bounded coefficients beK={p=
jgj.
j
j
j,j=1, 2, ...,n}, whereg
1,g
2, ...,g
n are linearly independent continuous functions defined on the interval [a, b],
j,
j are extended real numbers satisfying
j<+,
j>-, and
j
j. Assume thatf is a continuous function defined on a compact setX [a, b]. This paper gives the characterization theorem forp being the best uniform approximation tof fromK, and points out that the characterization theorem can be applied in calculating the approximate solution of best approximation tof fromK. 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.
Summary This paper is concerned with the rate of convergence to zero of theL
pmetrics
np1p, constructed out of differences between distribution functions, for departure from normality for normed sums of independent and identically distributed random variables with zero mean and unit variance. It is shown that the
np are, under broad conditions, asymptotically equivalent in the strong sense that, for 1p, p,
np/np is universally bounded away from zero and infinity asn. 相似文献
12.
N. M. Ivochkina 《Journal of Mathematical Sciences》1984,26(6):2349-2359
One proves that a priori boundedness of the norm
of the solution of the problem det(Uxx)=f(x,u,ux)>>0,u¦=0. The magnitudes of the exponents,() depends on whether the arguments u p occur or not in f (x,u,p).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 74–90, 1983. 相似文献
13.
Jan -Cees van der Meer Richard Cushman 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1986,37(3):402-424
Summary Consider a Hamiltonian system (H, 2n
,). LetM be a symplectic submanifold of (2n
,). The system (H, 2n
,) constrained toM is (HM, M, M). In this paper we give an algorithm which normalizes the system on 2n
in such a way that restricted toM we have normalized the constrained system. This procedure is then applied to perturbed Kepler systems such as the lunar problem and the main problem of artificial satellite theory.
Zusammenfassung Wir betrachten ein Hamiltonisches System (H, 2n ,). SeiMein symplectisches Submanifold von (2n ,). Das System (H, 2n ,), aufM beschränkt, ist (HM,M,M). In der vorliegenden Arbeit wird ein Algorithmus vorgeschlagen, der dieses System so auf 2n normalisiert, daß das aufM beschränkte System auch normalisiert ist. Dieser Algorithmus wird dann auf gestörte Keplersysteme, wie z. B. das Hill-sche Mondproblem und das Hauptproblem der Theorie der künstlichen Satelliten, angewendet.相似文献
14.
M. I. Freidlin 《Mathematical Notes》1968,3(1):50-54
This paper concerns the investigation of the stabilization of solutions of the Cauchy problem for a system of equations of the form u/t = u + fi(u, v); v/t = v + F2(u, v). It is proved that under certain assumptions the behavior of solutions as t is determined by mutual arrangement of the set of initial conditions {(u, v): u = f1(x), v =f
2(x), xRn} and the trajectories of the system of ordinary differential equations du/dt = F1(u, v), dv/dt = F2(u, v). The question of stabilization of the solutions of a single quasilinear parabolic equation is also considered.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 85–92, January, 1968. 相似文献
15.
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
16.
ONBAHADURASYMPTOTICEFFICIENCYINASEMIPARAMETRICREGRESSIONMODELLIANGHUA(梁华);CHENGPING(成平)(InstituteofSystemsScience,theChineseA... 相似文献
17.
许树声 《应用数学学报(英文版)》1994,10(3):262-273
ALTERNATIONTHEORYINAPPROXIMATIONBYPOLYNOMIALSHAVINGBOUNDEDCOEFFICIENTSXUSHUSHENG(许树声)(JiangnanUniversity,Wuxi214063,China)Abs... 相似文献
18.
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
19.
Summary We consider the problem of comparing large finite and infinite systems with locally interacting components, and present a general comparison scheme for the case when the infinite system is nonergodic. We show that this scheme holds for some specific models. One of these is critical branching random walk onZ
d
. Let
t
denote this system, and let
t
N
denote a finite version of
t
defined on the torus [–N,N]
d
Z
d
. Ford3 we prove that for stationary, shift ergodic initial measures with density , that ifT(N) andT(N)/(2N+1)d s[0,] asN, then {v
}, 0 is the set of extremal invariant measures for the infinite system
t
andQ
s
is the transition function of Feller's branching diffusion. We prove several extensions and refinements of this result. The other systems we consider are the voter model and the contact process.Work supported in part by the National Science Foundation under Grant DMS-8802055, by the U.S. Army Research Office through the Mathematical Sciences Institute at Cornell University and by the Deutsche Forschungsgemeinschaft through the SFB 123 at the Universität Heidelberg 相似文献
20.
Zoran Vondraček 《Journal of Theoretical Probability》1991,4(2):457-464
Let (Y
t, Qx) be a strong Markov process in a bounded Lipschitz domainD with continuous paths up to its lifetime , and let (X
t, Px) be a Brownian motion inD. IfY
– exists in D andQ
x(Y– C)=Px(X– C) for all Borel subsetsC of D and allx, thenY is a time change ofX. 相似文献