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1.
The Bochner-Riesz means of order 0 for suitable test functions on N are defined via the Fourier transform by . We show that the means of the critical index , do not mapL p,( N ) intoL p,( N ), but they map radial functions ofL p,( N ) intoL p,( N ). Moreover, iff is radial and in theL p,( N ) closure of test functions,S R f(x) converges, asR+, tof(x) in norm and for almost everyx in N . We also observe that the means of the function|x| –N/p, which belongs toL p,( N ) but not to the closure of test functions, converge for nox.  相似文献   

2.
, , , . , . , , x(0,1),x2j ,j=1,2,..., 2 n . , ka k 0 k k. , (0, 1) , , , , . , .  相似文献   

3.
Summary We discuss in this paper a non-homogeneous Poisson process A driven by an almost periodic intensity function. We give the stationary version A * and the Palm version A 0 corresponding to A *. Let (T i ,i) be the inter-point distance sequence in A and (T i 0 ,i) in A 0. We prove that forj, the sequence (T i+j,i) converges in distribution to (T i 0 ,i). If the intensity function is periodic then the convergence is in variation.  相似文献   

4.
Summary Discretization of the Theodorsen integral equation (T) yields the discrete Theodorsen-equation (T d ), a system of 2N nonlinear equations. A so-called -condition may be fulfilled. It is known that (T) has exactly one continuous solution. This solution gives the boundary correspondence of the normalized conformal map of the unit disc onto a given domainG. It is also known that (T d ) has one and only one solution if <1 and at least one solution if 1. We show here that for every 1 and N\ {1} there is a domainG satisfying an -condition such that (T d ) has an infinite number of solutions. Moreover, givenK>0 and any domainG that fulfills an -condition, we will construct a domainG 1 in the neighbourhood ofG that fulfills a max (1, +K)-condition such that (T d ) forG 1 has an infinite number of solutions. The underlying idea of the construction of those domains allows also to give important new facts about iterative methods for the solution of (T d ), even in the case <1.
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5.
LetR be a commutative ring with 1 andM anR-module. If:M R MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR M; in particular, we are interested in some homological properties ofR M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM *, where the isomorphism is given by the adjoint of.  相似文献   

6.
7.
In the open unit disk E={z, ¦z¦<1} we consider the class of regular functions q(z) = 1 + 2(1 = )e1zn + 2pn+kzn+k + ..., Re q(z)>, , [0, 1), [0, 2] and fixed, n, kN; fixing zE, we construct the range of the functional I0=q(z). We find an analog of V. A. Zmorovich's variational formula for the expression zp'(z) and point out some applications.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 6, pp. 813–820, June, 1991.  相似文献   

8.
Summary For the Prandtl numberP in the rangeP 1/3 1 ( is the ratio between the thermal conductivities of the boundary and of the fluid) two-dimensional rolls are preferred in contrast to square-pattern convection that represents the preferred stable convection in the rangeP 1/3.
Zussammenfasung Für PrandtlzahlenP, die der RelationP 1/3 1 genügen (\ ist das Verhältnis zwischen den thermischen Leitfähigkeiten der Wand und des Fluid), sind zweidimensionale Rollen bevorzugt im Gegensatz zur quadratartigen Konvektion, welche die bevorzugte stabile Konvektionsform im BereichP 1/3 darstellt.
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9.
The paper considers control of the heat conduction process ut — u = g from the initial state u(x, 0) to the final state u(x, t1) in a fixed (finite) time t1 via the coefficient (z) in the boundary condition Bu = (u/n) + (x)u. A uniqueness theorem is proved for the problem to find the process—control pair (u, ). The control problem is posed in terms of the coefficient in a boundary condition of the form Bu = (u/n) + (t)u.Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 3, pp. 93–97, 1993.  相似文献   

10.
We define a distance d on the set of r-spaces of an n-space. By the transfer of d to the GraßmannianG=G(n, r) we obtain a distinguished class of normal rational curves of order 1, the 1-distance lines, 1=1,..., r, which are in 1–1-correspondence to the so-called generalized reguli of type (r, 1).To every chain geometry there are subspaces T and Z of the surrounding space ofG, such that forV=GT andW = VZ we have a projective representation of on V\W as pointset, where the chains of are exactly the r-distance lines on V\W.Dedicated to Prof.A. Barlotti on occasion of his 60 birthday  相似文献   

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