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1.
K. R. Apt 《Israel Journal of Mathematics》1978,29(2-3):221-238
The connections between inductive definability and models of comprehension are studied. Let
= 〈A, R
l, ...,R
n 〉 be an infinite structure and letI
φ
be a set inductively defined by a formulaφ of the second order language
. We prove that if
is a model of Δ
1
1
-Comprehension relativized toφ, andφ is
-absolute, then for everyη smaller than the height of
(h(
)),I
φ
is in
. If
is aβ-structure which satisfies Σ
1
1
-Comprehension relativized toφ and WF(X), and φ is
-absolute, thenI
φ
is in
and ‖φ| <h (
). These results imply that Barwise-Grilliot theorem is false in the case of uncountable acceptable structures. We also study
the notion of invariant definability over models1 of Δ
1
1
-Comprehension.
This paper is registered as Report ZW 69/76 of the Mathematical Centre. 相似文献
2.
Lars Hörmander 《Israel Journal of Mathematics》1973,16(1):103-116
Two extensions of a classical theorem of Rellich are proved: (1) LetP=P(−iϖ/ϖx) be a partial differential operator with constant coefficients in
, let the manifolds contained in
have codimension ≧k>0, and denote by Γ an open cone in
intersecting each normal plane of every such manifold. If
,Pu=0 and
it follows thatu=0. (2) Assume in addition that each irreducibe lfactor ofP van shes on a real hypersurface and that Γ contains both normal directions at some such point. If
andP(D) u has compact support, the same condition withk=1 implies thatu has compact support. In both results the hypotheses on the cone Γ and on the operatorP are minimal. 相似文献
3.
Daniel J. Rudolph 《Israel Journal of Mathematics》1978,30(3):255-263
LetT acting on (Ω, ℱ, μ) be afinite entropy Bernoulli shift. AT invariant factor
is “relatively finite” if a.e. fiber of
has a finite, hence constantk, number of points. We say two factors
, “sit the same” if there is a measurable measure preserving map ϕ with
and
. We show here that up to sitting the same there are only finitely many relatively finite factors withk point fibers in a Bernoulli shift, and that they are classified by a certain algebraic structure in the symmetric group onk-points.
This work was supported in part by the Miller Institute for Basic Research, U. C. Berkeley. 相似文献
4.
IfG is a finite group thend(G) denotes the minimal number of generators ofG. IfH andK are groups then the extension, 1 →H →G →K → 1, is called an outer extension ofK byH ifd(G)=d(H)+d(K). Let
be the class of groups containing all finitep-groupsG which has a presentation withd(G) = dimH
1(G,z
p
) generators andr(G)=dimH
2 (G,Z
p
) relations: in this article it is shown that ifK is a non cyclic group belonging to
andH is a finite abelian p-group then any outer extension ofK byH belongs to
. 相似文献
5.
Ehud Lehrer 《Israel Journal of Mathematics》1987,57(2):239-255
Every ergodic transformation (X, T, ℬ,μ) has an isomorphic system (Y, U,
ν) which is uniquely ergodic and topologically mixing.
This work is a part of an M.Sc. thesis written at The Hebrew University of Jerusalem under the supervision of Professor B.
Weiss to whom the author is greatly indebted. 相似文献
6.
William M. Kantor 《Israel Journal of Mathematics》1976,23(1):8-18
Generalized quadrangles
are studied in whichs ort is prime and Aut
has rank 3 on points.
This research was supported in part by NSF grant GP 37982X. 相似文献
7.
Evgeni Ja. Gabovič 《Semigroup Forum》1972,4(1):335-340
A semigroup S is calledE-semigroup (
-semigroup) if every (finitely generated) subsemigroup of S is an endomorphic image of S and Ē-semigroup (
-semigroup) if every subsemigroup of S is an E-semigroup
-semigroup. All classes X ε {Ē,
, E,
} are distinct even in the case of semilattices. It is established when a free band (semilattice) is an X-semigroup.
-,
- and Ē-chains and E-chains with identity or zero, Ē-and
, X-bands with identity and X-semigroups with identity and zero are found. 相似文献
8.
This paper is devoted to the first steps towards a systematic study of pro-p groups which are analytic over a commutative Noetherian local pro-p ring Λ, e.g. Λ=
. We restrict our attention to Λ-standard groups, which are pro-p groups arising from a formal group defined over Λ. Under some additional assumptions we show that these groups are of ‘intermediate
growth’ in various senses, strictly betweenp-adic analytic pro-p groups and free pro-p groups. This suggests a refinement of Lazard's theory which stresses the dichotomy betweenp-adic analytic pro-p groups and all the others. In the course of the discussion we answer a question posed in [LM1], and settle two conjectures
from [Bo]. 相似文献
9.
We show, for any operatorT from aC(K)-space into a Banach space with rank (T)≤n, the inequality
, whereC≤4.671 is a numerical constant. The factor (1+logn)1−1/p
is asymptotically correct. This inequality extends a result of Jameson top ≠ 2. Several applications are given — one is a positive solution of a conjecture of Rosenthal and Szarek: For 1≤p<q<2,
相似文献
10.
Roberto Magari 《Annali dell'Universita di Ferrara》1969,14(1):1-4
Riassunto Si dimostra che se
è una struttura algebrica priva di quozienti semplici, allora un’opportuna sottoalgebra di
ammette quozienti semplici. Ne segue il risultato del titolo.
Lavoro eseguito nell’ambito dell’attività del Comitato Nazionale per le Scienze Matematiche del C.N.R. (anno ’68–’69, programma 8). 相似文献
Summary Let be an algebraic structure with no simple quotients. Then there is a subalgebra of which possess simple quotients. Therefore every variety of algebras (=algebraic structures) has simple algebras.
Lavoro eseguito nell’ambito dell’attività del Comitato Nazionale per le Scienze Matematiche del C.N.R. (anno ’68–’69, programma 8). 相似文献
11.
Stephen H. Hechler 《Israel Journal of Mathematics》1973,14(2):115-148
For every uncountable cardinal κ define a metric spaceS to be κ-superuniversal iff for every metric spaceU of cardinality κ, every partial isometry intoS from a subset ofU of cardinality less than κ can be extended to all ofU. We prove that any such space must have cardinality at least
, and for each regular uncountable cardinal κ, we construct a κ-superuniversal metric space of cardinality
, It is proved that there is a unique κ-superuniversal metric space of cardinality κ iff
. Several decomposition theorems are also proved, e.g., every κ-superuniversal space contains a family of
disjoint κ-superuniversal subspaces. Finally, we consider some applications to more general topological spaces, to graph
theory, and to category theory, and we conclude with a list of open problems. 相似文献
12.
Le Tu Quoc Thang 《Discrete and Computational Geometry》1995,14(1):31-70
The existence of different kinds of local rules is established for many sets of pentagonal quasi-crystal tilings. For eacht∈ℝ there is a set
of pentagonal tilings of the same local isomorphism class; the caset=0 corresponds to the Penrose tilings. It is proved that the set
admits a local rule which does not involve any colorings (or markings, decorations) if and only ift=m+nτ. In other words, this set of tilings is totally characterized by patches of some finite radius, orr-maps. When
the set
admits a local rule which involvescolorings. For the set of Penrose tilings the construction here leads exactly to the Penrose matching rules. Local rules for the caset=1/2 are presented. 相似文献
13.
Gil Kalai 《Israel Journal of Mathematics》1983,45(4):337-351
Let
(n, k) be the class of all simplicial complexesC over a fixed set ofn vertices (2≦k≦n) such that: (1)C has a complete (k−1)-skeleton, (2)C has precisely (
k
n−1
)k-faces, (3)H
k
(C)=0. We prove that for
,H
k−1(C) is a finite group, and our main result is:
. This formula extends to high dimensions Cayley’s formula for the number of trees onn labelled vertices. Its proof is based on a generalization of the matrix tree theorem. 相似文献
14.
Liu Zongguang 《分析论及其应用》1999,15(4):64-70
The fractional maximal operator on homogeneous space (X, d, μ) is de fined as
. In this paper, the sufficient and necessary conditions for the
to be of weak type and extra weak type will be given.
In Memory of Professor M. T. Cheng 相似文献
15.
It
and
are two families of pairwise disjoint simple closed curves in the plane such that each curve in
intersects each curve in
, then the total number of points of intersection in
is at least 2(m−1)n, where
, and this bound is best possible. We use this to show that the cartesian product of two 5-cycles has crossing number 15. 相似文献
16.
吴畏 《中国科学A辑(英文版)》2001,44(1):67-73
We discuss the Krein-Milman-type problems in the C* -convexity theory for the generalized state space
of C*-algebraA. The main results are that every BW-compact, C*-convex subset of
possesses a C*-extreme point and every BW-compact, C* -convex subset of
is the C*-convex hull of its C*-extreme points. 相似文献
17.
Let
denote the Euler means of the Fourier series of the 2π-perodic function f(x). For an integer q>0, setting ℰ
nq
(ω)=sup‖f−ℰ
n
(q,f)‖, the precise value of
is obtained. 相似文献
18.
R. Schneider 《Discrete and Computational Geometry》1995,13(1):609-627
Let
be an infinite discrete system ofk-dimensional flats inn-dimensional Euclidean space. If the totalk-dimensional volume of the flats in
intersected with the ball of center 0 and radiusr, divided by the volume of that ball, tends to a limit forr→∞, then this limit is called thedensity of
. We consider isoperimetric problems of the following kind. If
is a hyperplane system of positive density, find sharp upper bounds for the density of the system ofk-flats (k∈{0, ...,n−2}) that are generated as intersections of hyperplanes in
. Ideas from the theory of uniform distribution of sequences are employed to define a large class of hyperplane systems, calleduniform, for which all necessary densities exist, isperimetric inequalities can be proved, and systems with extremal intersection
densities can be characterized. 相似文献
19.
Liu Zongguang 《逼近论及其应用》1999,15(4):64-70
The fractional maximal operator on homogeneous space (X, d, μ) is de fined as 相似文献
20.
M. G. Cimoroni 《分析论及其应用》1997,13(4):1-12
In this paper the author presents a method for the numerical solution of a 2-D Cauchy principal value of the form
where S is a domain with a continuous boundary. By using polar coordinates, the integral is reduced to the form
where
the finite-part of the integral. We construct the relative product rule based on quasi-inter polating splines.
Convergence results are proved and numerical examples are given. 相似文献