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1.
Ohne Zusammenfassung
Zusatz bei der Korrektur: Ein vollständiger und korrekter Beweis für die Entscheidbarkeit der eingangs angeführten Aanderaaschen Klasse ((0, ), (, , ...)) erscheint demnächst im JSL (S.O. Aanderaa/H.R.Lewis: Prefix classes of Krom formulas). Ebendort wird auch die Reduktionstypeneigenschaft für ((0, ), (0, 0, )) und ((0, )), (0, 0, )) nachgewiesen, während ((0, ), (, )) sich als entscheidbar herausgestellt hat (s. E. Börger: Eine entscheidbare Klasse von Kromformeln. ZMLG 19 (1973), 117–120.) Der Kromsche Reduktionstyp konnte mittlerweile einerseits zu ((0, ), (0, 4)) verschärft werden (s. D. Rödding, E. Börger: The undecidability of (0, 4)-formulae with binary disjunctions, vorgetragen auf dem Logic Coll. Bristol 1973, ein abstract erscheint im JSL), andererseits kündigt H.R.Lewis die Reduktionstypeneigenschaft für ((0, ), (0, 1)) an (s. H.R.Lewis: Krom formulas with one dyadic predicate letter. Notices AMS 20, 5 (1973) A-500, abstr. no. 73T-E78.)Dieser Aufsatz geht aus der Dissertation [2] hervor, die dem Fachbereich Mathematik der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Münster im Sommersemester 1971 vorgelegt worden ist. Die Ergebnisse stammen aus dem Wintersemester 1970/71. Eine Ankündigung der hauptsächlichen Resultate ist in den Notices of the American Mathematical Society 19, 2 (1972) A-333 unter der abstract no. * 72T-E24 erschienen. 相似文献
2.
Let L be a distributive lattice characterized by a ternary operation (, ,), where (a,b,c)=(ab)(bc)(ac)=(ab)(ac)(bc), a,b,cL. The note considers convex sublattices of L, called generalized ideals of L generated by the operation (, ,). Some remarks have been stated about the graph of a distributive lattice. 相似文献
3.
B
p,
(r)
( R
n
) l
l
p
. B
p,
(r)
( R
n
) «» . 相似文献
4.
. , A
0, A
1,— - lim sup A
j
- H,
. , - - . , , ; , , . - . - . 相似文献
5.
We will establish the following improved Krasnosel'skii theorems for the dimension of the kernel of a starshaped set: For each k and d, 0 k d, define f(d,k) = d+1 if k = 0 and f(d,k) = max{d+1,2d–2k+2} if 1 k d.Theorem 1. Let S be a compact, connected, locally starshaped set in R d, S not convex. Then for a k with 0 k d, dim ker S k if and only if every f(d, k) lnc points of S are clearly visible from a common k-dimensional subset of S.Theorem 2. Let S be a nonempty compact set in R d. Then for a k with 0 k d, dim ker S k if and only if every f (d, k) boundary points of S are clearly visible from a common k-dimensional subset of S. In each case, the number f(d, k) is best possible for every d and k. 相似文献
6.
Analogues are formulated of the well-known, in the theory of analytic functions, Phragmen-Lindelöf theorem for the gradients of solutions of a broad class of quasilinear equations of elliptic type. Examples are given illustrating the accuracy of the results obtained for the gradients of solutions of the equations of the form div(|U| –2u)=f(x, u, u), where f(x, u, u) is a function locally bounded in 2n+1. f(x, 0, u)=0, uf(x, u, u) c¦u¦1+q(1+ ¦u|), > 1, c > 0, q > 0, is an arbitrary real number, and n >- 2. The basic role in the technique employed in the paper is played by the apparatus of capacitary characteristics.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1376–1381, October, 1992.The author sincerely appreciates E. M. Landis's permanent attention and numerous useful discussions. 相似文献
7.
W
p
r
(1 p<) , . - r -1. =1 r-2. 相似文献
8.
The number of subgroups of type and cotype in a finite abelian p-group of type is a polynomialg
with integral coefficients. We prove g
has nonnegative coefficients for all partitions and if and only if no two parts of differ by more than one. Necessity follows from a few simple facts about Hall-Littlewood symmetric functions; sufficiency relies on properties of certain order-preserving surjections that associate to each subgroup a vector dominated componentwise by . The nonzero components of ( H) are the parts of , the type of H; if no two parts of differ by more than one, the nonzero components of – ( H) are the parts of , the cotype of H. In fact, we provide an order-theoretic characterization of those isomorphism types of finite abelian p-groups all of whose Hall polynomials have nonnegative coefficients. 相似文献
9.
. , , –1< <0. .
The present work was written on the basis of two earlier works received by Analysis Mathematica on January 16, 1979, and July 20, 1979. 相似文献
10.
For n2 we consider the Stokes problem in n, -u + p= f, -div u= g, in weighted Soboiev spaces H
6
m,r
, where the weights are proportional to (1+| x|) . We prove the existence of weak solutions for any K, where K is a discrete set of critical values. Furthermore, we characterize the solutions of the homogeneous problem.This research was supported by the DFG research group Equations of Hydrodynamics, Universities of Bayreuth and Paderborn. 相似文献
11.
Summary The aim of this paper is to generalize the well-known Eulerian numbers, defined by the recursion relation E(n, k) = (k + 1)E(n – 1, k) + (n – k)E(n – 1, k – 1), to the case that n is replaced by . It is shown that these Eulerian functions E(, k), which can also be defined in terms of a generating function, can be represented as a certain sum, as a determinant, or as a fractional Weyl integral. The E(, k) satisfy recursion formulae, they are monotone in k and, as functions of , are arbitrarily often differentiable. Further, connections with the fractional Stirling numbers of second kind, the S(, k), > 0, introduced by the authors (1989), are discussed. Finally, a certain counterpart of the famous Worpitzky formula is given; it is essentially an approximation of x
in terms of a sum involving the E(, k) and a hypergeometric function.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth. 相似文献
12.
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
13.
In the category p b of p-convex vector spaces and linear maps preserving bounded sets a p-bornological topology will be introduced on the tensor product of two spaces, likewise on the spaces of morphisms Hom(E,F). Thus one gets a pair of adjoint functors from p to p , p being the category of p-bornological spaces and continuous linear maps, and the topologies being introduced will be characterized by extreme properties with respect to the adjoint transformations.
Dieser Arbeit liegt ein Teil der Dissertation des Autors, Kiel 1967, zugrunde. 相似文献
14.
Let M n denote an n-dimensional Riemannian manifold. Its metric is called -strongly spherical if at every point Q M n there exists a -dimensional subspace Q
T QM n such that the curvature operator of the metric of M n satisfies R(X, Y) Z = k(< Y, Z > X < X, Z > Y), where k = const > 0, Y Q
, X, Z #x2208; T QM n. The number is called the index of sphericity and k the exponent of sphericity. The following theorems are proved in the paper. THEOREM 1. Let the Sasakian metric of T 1M n be -strongly spherical with exponent of sphericity k. The following assertions hold: a) = 1 if and only if M 2 has constant Gaussian curvature K 1 and k = K 2/4; b) = 3 if and only if M 2 has constant curvature K = 1 and k = 1/4; c) = 0, otherwise. THEOREM 2. Let the Sasakian metric of T 1M n (n M n) be -strongly spherical with exponent of sphericity k. If k > 1/3 and k 1, then = 0. Let us denote by (M n, K) a space of constant curvature K. THEOREM 3. Let the Sasakian metric of T 1(M n, K) (n 3) be -strongly spherical with exponent of sphericity k. The following assertions hold: a) = 1 if and only if K = 1/4; b) = 0, otherwise. In dimension n = 3 Theorem 2 is true for k {1/4, 1}.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 150–159, 1992. 相似文献
15.
Summary Approximations for the function implicitly defined by (u)=(u, (u)) are obtained via the iterative scheme n(u)=(u, n–1(u)). In this paper the uniform convergence of high order derivatives of n to the corresponding derivatives of is proved. This result yields a high order approximation theorem for the input-output map generated by a nonlinear control system, using linear combinations of iterated integrals of the control.Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R. 相似文献
16.
Let K be a compact Hausdorff space and let FK be a peak interpolation set for a function algebra AC(K). Let be a map from K to the family of all convex subsets of such that the set { (z, x)zK, x(z)} is open in K×C and such that g(z)(z) (zK) for some gA. We prove that every fC(F) satisfying f(s)(s) (sF) (f(s)closure (s) (sF)) admits an extension fAA} satisfying f(z)(z) (zK) (f(z))}closure (z) (zK), respectively). We prove a more general theorem of this kind and present various applications which generalize known dominated interpolation theorems for subspaces of C(K). 相似文献
17.
In this paper we shall study the Fredholm determinant and related trace formulas for a class of operators which correspond to the restriction of integral operators with kernels of the form k(x,y) = (x)g v(x–y)+[1–(x)]f v(x–y) to the square |x|,|y| T and shall evaluate the limit as T . Here denotes the indicator function of the right half-line [0,) . The results obtained generalize the well known formulas of M. Kac for the classical convolution operator in which g = f . 相似文献
18.
A necessary and sufficient condition is found for the function to ensure absolute convergence of the Haar—Fourier series of all functions (f) provided that the Haar—Fourier series of f converges absolutely. Absolute convergence means absolute convergence of the series of coefficients, and the condition is that should be in Lip 1.
— 相似文献
19.
Let X be a real or complex infinite dimensional Banach space and A a standard operator algebra on X. Denote by B(X) the algebra of all bounded linear operators on X. Let : + + be a function with the property lim
t (t)t
–1=0. Assume that a mapping D: A B(X) satisfies D(AB)–AD(B)–D(A)B<( A B) for all operators A, B D (no linearity or continuity of D is assumed). Then D is of the form D(A)=AT–TA for some TB(X).This work was supported by the Research Council of Slovenia 相似文献
20.
Let u(x,t) be a solution, uA|u| p for xIR 3, t0 where is the d'Alembertian, and A, p are constants with A>0, 1 0–|x–x0|, if the initial data u(x,0), ut(x,0) have their support in the ball |x–x0|t0. In particular global solutions of u=A|u|p with initial data of compact support vanish identically. On the other hand for A>0, p>1+2 global solutions of u=A|u|p exist, if the initial data are of compact support and u is sufficiently small in a suitable norm. For p=2 the time at which u becomes infinite is of order u–2.Dedicated to Hans Lewy and Charles B. Morrey, Jr.The research for this paper was performed at the Courant Institute and supported by the Office of Naval Research under Contract No. N00014-76-C-0301. Reproduction in whole or part is permitted for any purpose of the United States Government. 相似文献
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