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1.
G. G. Braichev 《Mathematical Notes》1976,19(2):135-140
In this paper it is shown that under conditions of applicability of the operator
to the class [,] =(I,s), 2 1, 2), 1, 2< the equation
y=f has a particular solution of this class vf[, ]. The general form of a solution of the homogeneous equation
y=0 is established. The growth of a solution is investigated by means of a system of conjugate orders and a system of conjugate types. A solvability result is also obtained in the class
, where T is a certain set in R
+
2
depending on the operator
.Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 225–236, February, 1976.In conclusion, the author would like to express his thanks to his adviser, Yu. F. Korobeinik. 相似文献
2.
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
3.
G. Akrivis 《Numerische Mathematik》1984,44(2):261-278
Summary We consider Gauss quadrature formulaeQ
n
,n, approximating the integral
,w an even weight function. Let
be analytic inK
r
:={z:|z|<r},r>1, and
. The error functionalR
n
:=I-Q
n
is continuous with respect to |·|r and the relation
, q2k
(x):=x
2k
holds.In this paper estimates for R
n
are given. To this end we first derive two new representations of R
n
which are essential for our further investigations. The R
n
=r
2
R
n
(), with (x):=1/(r
2-x
2), is estimated in various ways by using the best uniform approximation of in P2n-1, and also the expansion of with respect to Chebyshe polynomials of the first and second kind. Forw(x)=(1-x
2), =±1/2, R
n
is calculated. The asymptotic behaviour, forr1+, of R
n
and of the derived error bounds is also discussed. Finally, we compare different error bounds and give numerical examples. 相似文献
4.
Let {\bold x}[] be a stationary Gaussian process with zero mean and spectral density f, let
be the -algebra induced by the random variables {\bold x}[], D(R1), and let
t, t > 0, be the -algebra induced by the random variables x[],supp [-t,t]. Denote by
(f) the Gaussian measure on
generated by {\bold x}. Let
t(f) be the restriction of
(f) to
t. Let f and g be nonnegative functions such that the measures
t(f) and
t(g) are absolutely continuous. Put
For a fixed g(u) and for f(u)= ft(u) close to g(u) in some sense, the asymptotic normality of
t(f,g) is proved under some regularity conditions. Bibliography: 14 titles. 相似文献
5.
B. F. Skubenko 《Journal of Mathematical Sciences》1984,26(3):1922-1930
This paper proves three theorems concerning the simultaneous approximation of numbers from a totally real algebraic number field. It is shown that for two given numbers 1 and 2 from a totally real algebraic number field, the constant 12 can be explicitly calculated, this being the upper limit of the numbers c12 such that the inequality max (q1, q2)(qc12)–1/2 holds for infinitely many natural numbers q; likewise for the constant a12 such that the inequality q1·q2< a12(qlogq) holds for infinitely many natural numbers q. It is shown that there exist n –1 numbers 1, ..., n–1 in an algebraic number field of degree n and discriminant d such that the inequality
holds only for finitely many natural numbers q if
2^{ - \left[ {\tfrac{{n - 1}}{2}} \right]} \sqrt d $$
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. is fixed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 142–154, 1982. 相似文献
6.
7.
Let H be a real Hilbert space, :H [0, + ] a proper l.s.c., convex function with Lk:={u H; u2 + (u) k} compact for every k > 0, let > 0 be a given constant and
. We prove an existence result for strong solutions to a class of functional differential equations of the form
相似文献
8.
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
9.
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
10.
D. M. Smirnov 《Algebra and Logic》2005,44(2):109-116
Let be the set of all primes,
the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as
, and
, where AD is a variety of -divisible Abelian groups with unique taking of the pth root p(x) for every p ,
is a variety of
-modules over a normal field
, contained in
, and Gn is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that
, and
are distributive lattices, with
and
where
ub and
ubf are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005. 相似文献
11.
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
12.
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
13.
The main result is the following theorem. Let
be a commutative Banach algebra with radical R, where the factor algebra
is isomorphic to the algebra of all continuous functions on a totally disconnected compact space. If rn1 /n 0 as n uniformly for r R, rl, then the algebra
is strongly decomposable, i.e., there exists a closed subalgebra B
isomorphic to
such that
=BR.This is a strengthening of the theorem of A. Ya. Khelemskii, who assumed
. There are 4 references.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 589–592, December, 1967. 相似文献
14.
We consider a conformally invariant regularization of an Abelian gauge theory in an Euclidean space of even dimension D 4 and regularized skeleton expansions for vertices and higher Green's functions. We set the respective regularized fields
and
with the scaling dimensions
and
into correspondence to the gauge field A
and Euclidean current j
. We postulate special rules for the limiting transition 0. These rules are different for the transversal and longitudinal components of the field
and the current
. We show that in the limit 0, there appear conformally invariant fields A
and j
each of which is transformed by a direct sum of two irreducible representations of the conformal group. Removing the regularization, we obtain a well-defined skeleton theory constructed from conformal two- and three-point correlation functions. We consider skeleton equations on the transversal component of the vertex operator and of the spinor propagator in conformal quantum electrodynamics. For simplicity, we restrict the consideration to an Abelian gauge field A
, but generalization to a non-Abelian theory is straightforward. 相似文献
15.
Peter Brinkmann 《Geometriae Dedicata》2002,93(1):191-203
We present necessary and sufficient conditions for the existence of a splitting over of the mapping torus
of a free group automorphism . 相似文献
16.
Victor Kaftal 《Integral Equations and Operator Theory》1982,5(1):50-70
LetA be a von Neumann algebra,J be the ideal of compact operators relative toA and letF
+ be the left-Fredholm class ofA. We call almost left-Fredholm the class
= {A A: if P A is a projection and AP J then P J}. Then
and the inclusion is proper unlessA is semifinite and has a non-large center.
satisfies all of the algebraic properties ofF
+ but it is generally not open. IfA is semifinite then A
iff there are central projectionsG
with G = I such that AG F+(AG). Let :A A/J. Then the left almost essential spectrum ofA A,
, coincides with the set of eigenvalues of (A) 相似文献
17.
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
18.
We study Banach spaces of the form
We call such a space a p-space, p[1,), if for every k the space
is isomorphic to pk and the sequence (pk) strictly decreases to p. We examine the finite block representability of the spaces r in a p-space proving that it depends not only on p but also on the sequences (pk) and (nk). Assuming that i ni
1/q decreases to 0, where q is the conjugate exponent of p, we prove the existence of an asymptotic biorthogonal system in X and also that c
0 is finitely representable in X. Moreover we investigate the modified versions of p-spaces proving that, if nkm1/pkm-1/pkm-1 increases to infinity for a subsequence (nkm) , then 1 embeds into X. We also investigate complemented minimality for the class of spaces
where
is either a subsequence of the sequence of Schreier classes (
n)n N or a subsequence of (
n)n N. 相似文献
19.
A. S. Chani 《Journal of Mathematical Sciences》1993,67(4):3229-3233
We consider finite-dimensional homogeneous stochastic semigroups X
s
t
, 0 s t < assuming values in the space of real square matrices. For stochastic semigroups assuming values in the class of upper triangular matrices we compute the index of exponential growth
, where · is the operator norm of a matrix. The answer is given in terms of the characteristic Yt of the generating process Yt of the semigroup Xs
t:x=–(1/2), where is the smallest eigenvalue of the matrix B which defines the characteristic Yt=Bt.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 78–84, 1988. 相似文献
20.
For any probability on the space of d×d stochastic matrices we associate a probability
; on a finite group—a subgroup of the permutation group—related to the kernel of the semigroup generated by the support of . We show that n converges iff
n converges. 相似文献
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