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1.
Alain Rivière 《Geometriae Dedicata》2001,85(1-3):217-235
For a separable Hilbert space E whose dimension is 2 and for an open subset of E, not empty and different from E, let
be the set of all points of which have at least two projections on the close set E\, and let
be the set of all the centres of the open balls contained in and which are maximal for inclusion. We show that the Hausdorff dimension dimH(
) of
may be any real value s such that 0sdim E; we also show that can be chosen so that
is everywhere dense in and so that we have dimH(
)=1.Associons à un ouvert d'un espace de Hilbert séparable E de dimension 2, non vide et distinct de E, l'ensemble
des points de admettant plusieurs projections sur le fermé E\, et l'ensemble
des centres des boules ouvertes inclues dans et maximales pour l'inclusion. Nous montrons d'une part que la dimension de Hausdorff dimH(
) de
peut prendre toute valeur réelle s telle que 0sdim E, et d'autre part qu'on peut choisir de sorte que
soit dense dans et qu'on ait dimH(
)=1. 相似文献
2.
Let (, , ) be a complete measure space, L0 the vector lattice of -measurable real functions on , : L0 [0, )] a lattice semimodular,
the corresponding modular space, S0 the ideal generated by
and
0,{\text{ }}\exists {\text{ }}s \in {\text{ }}S_{\text{0}} {\text{ such that }}\rho \left( {\frac{{x - s}}{\user1{\lambda }}} \right) < \infty } \right\}$$
" align="middle" border="0">
. In X consider the distance
0:\rho \left( {\frac{{x - y}}{\user1{\lambda }}} \right) \leqq \user1{\lambda }} \right\}$$
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and, if is convex, the distances dL, do subordinated to the Luxemburg and Amemiya-Orlicz norms, respectively. We give necessary and sufficient conditions for H(So) in order to be proximinal in X with the distances d, dL and do. 相似文献
3.
Considering mixed-norm sequence spaces lp,q, p, q 1, C. N. Kellogg proved the following theorem: if 1 < p 2 then
lp,2 and lp,2
, where 1/p + 1/p = 1. This result extends the Hausdorff-Young Theorem.We introduce here multiple mixed-norm sequence spaces
, examine their properties and characterize the multipliers of spaces of the form lp,[s;n],q, with the index s repeated n times. By an interpolation-type argument we prove that
(l,[2;n],2, lp,[1;n],1) for 1 < p 2. Using these results we obtain a further generalization of the Hausdorff-Young Theorem: if 1 < p 2 then
lp,[2;n] and lp,[2;n]
for each n = 0, 1, 2, ¨. The spaces lp,[2;n] decrease and lp,[2;n] increase properly with n for 1 < p < 2 and 1/p + 1/p = 1. We also extend a theorem of J. H. Hedlund on multiplers of Hardy spaces
and deduce other results. 相似文献
4.
In this paper we define a lattice order on a set F of binary functions. We then provide necessary and sufficient conditions for the resulting algebra
F to be a distributive lattice or a Boolean algebra. We also prove a Cayley theorem for distributive lattices by showing that for every distributive lattice
, there is an algebra
F of binary functions, such that
is isomorphic to
F and we show that
F is a distributive lattice iff the operations and are idempotent and cummutative, showing that this result cannot be generalized to non-distributive lattices or quasilattices without changing the definitions of and . We also examine the equational properties of an Algebra
for which
, now defined on the set of binary
-polynomials is a lattice or Boolean algebra. 相似文献
5.
Patrick Headley 《Journal of Algebraic Combinatorics》1997,6(4):331-338
Let be an irreducible crystallographic rootsystem in a Euclidean space V, with + theset of positive roots. For ,
, let
be the hyperplane
. We define a set of hyperplanes
. This hyperplane arrangement is significant inthe study of the affine Weyl groups. In this paper it is shown that thePoincaré polynomial of
is
, where n is the rank of and h is the Coxeter number of the finiteCoxeter group corresponding to . 相似文献
6.
F. Morits 《Mathematical Notes》1975,17(2):127-133
Let {Xi}
–
be a sequence of random variables, E(Xi) 0. If 1, estimates for the -th moments
can be derived from known estimates
of the -th moment. Here we generalized the Men'shov-Rademacher inequality for =2 for orthonormal Xi, to the case 1 and dependent random variables. The Men'shov-Payley inequality >2 for orthonormal Xi) is generalized for >2 to general random variables. A theorem is also proved that contains both the Erdös -Stechkin theorem and Serfling's theorem withv > 2 for dependent random variables.Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 219–230, February, 1975.This article was written while the author was working in the V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR. 相似文献
7.
R. Vosylius 《Lithuanian Mathematical Journal》2003,43(2):210-220
In the canonical smooth fiber bundles : n+1 n endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups
and construct
-invariant generalizations of differentiable connections. In both regular and special cases of the representations of the relevant groups
, we found all the affine nonholonomic 1-, 2-, and 1, 2-connections of the first order (see [4]) possessing the local Lie groups of transformations
and also described the respective
-invariant planar connections. 相似文献
8.
Luise Unger 《manuscripta mathematica》1986,57(1):1-31
Let
be the path algebra for some representation-infinite quiver
over some field k. There exists a bound
such that mI is faithful for all indecomposable injective
-modules I and all
, and such that there exists an indecomposable injective
-module J satisfying that
J is not faithful, denotes the Auslander-Reiten-translation. Let m() be the maximum of the
taken over all possible orientations of the underlying graph . In this article we determine the bounds m() for representation-infinite quivers
for which is a tree. 相似文献
9.
Andrzej Nowik 《Czechoslovak Mathematical Journal》2000,50(4):865-877
We prove the following theorems:1. There exists an -covering with the property s
0.2. Under cov
there exists X such that
is not an -covering orX \ B is not an -covering].3. Also we characterize the property of being an -covering. 相似文献
10.
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
11.
Zusammenfassung Es wird die Fortpflanzung elastisch-plastischer Spannungswellen in einem unendlichen Medium betrachtet, welches einer idealen Spannungs-Verformungs-Kurve folgt, Trescas Fliesskriterium unterworfen ist und einen sphärischen Hohlraum enthält, wobei an der Fläche des Hohlraumes ein Stoss
angenommen wird. Ein rechnerisches Verfahren, basiert auf endliche Differenzen, wird entwickelt and ein Beispiel gegeben.
Notation radial stress - tangential stress - K yield stress - rr non-dimensional radial stress ( /K) - non-dimensional tangential stress ( /K) - , Lame's constants - K b Bulk constant (=(3+2)/3) - v Poisson's constant - Material density - C Elastic wave velocity (=((+2)/)1/2) - C p Plastic wave velocity (=(K b /)1/2) - distance from center of cavity - r 0 cavity radius - v non-dimensional radial co-ordinate (= /r 0) - time - t non-dimensional time (=C /r 0) - radial displacement - u non-dimensional radial displacement (=/r 0) - particle velocity - v non-dimensional particle velocity (= /C) - pressure - P(t) non-dimensional pressure (= /K) 相似文献
Notation radial stress - tangential stress - K yield stress - rr non-dimensional radial stress ( /K) - non-dimensional tangential stress ( /K) - , Lame's constants - K b Bulk constant (=(3+2)/3) - v Poisson's constant - Material density - C Elastic wave velocity (=((+2)/)1/2) - C p Plastic wave velocity (=(K b /)1/2) - distance from center of cavity - r 0 cavity radius - v non-dimensional radial co-ordinate (= /r 0) - time - t non-dimensional time (=C /r 0) - radial displacement - u non-dimensional radial displacement (=/r 0) - particle velocity - v non-dimensional particle velocity (= /C) - pressure - P(t) non-dimensional pressure (= /K) 相似文献
12.
Damjan Kobal 《K-Theory》1999,17(2):113-140
The goal of this paper is to present a new view on the link between the well known K-theory of finitely generated projective modules and much less understood K-theory of Hermitian forms on finitely generated projective modules.For a given Hermitian ring (R, , ), we obtain the K-theory space KR equipped with an involution and the Hermitian K-theory space KHerm(R, , ). The fixed subspace
2 is homotopy equivalent to the Hermitian K-theory space KHerm(R,, , ). We construct the Karoubi Tower diagram, which is obtained by iterating Karoubi's construction of the homotopy fibers of the forgetful and hyperbolic maps. Using an interesting factorization of these maps, we prove various homotopy properties of the Karoubi Tower. The homotopy inverse limit of the Karoubi Tower is homotopy equivalent to the homotopy fibre of the inclusion of the fixed set
2 into the homotopy fixed set
h
2. Considering Karoubi's fundamental periodicity theorem, the Karoubi Tower generalizes the low dimensional connections between Hermitian K-theory and K-theory groups. Illustrative examples of the Karoubi Tower are given by the finite field case and the classical Hermitian rings over
,
and
. Considering topological K-theory for these cases, the Karoubi Tower comprises the classical Bott periodicity.Another important application of the Karoubi Tower is an elegant and comprehensive generalization of the classical invariants of quadratic forms. 相似文献
13.
Let X and Y be two Hilbert spaces, and
the space of bounded linear transformations from X into Y. Let {A
}
be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (1991). In this work we proceed further to characterize {A
n} by a positive measure and a number T of
-valued functions a
0, . . . ,a
T–1; in the spectral form
, where
and is an
-valued Borel set function on [0, 2) such that
相似文献
14.
We investigate the problem of the boundedness of the following recurrence sequence in a Banach space B:
where |y
n} and |
n
} are sequences bounded in B, and A
k, k 1, are linear bounded operators. We prove that if, for any > 0, the condition
is satisfied, then the sequence |x
n} is bounded for arbitrary bounded sequences |y
n} and |
n
} if and only if the operator
has the continuous inverse for every z C, |z| 1. 相似文献
15.
Michel Matthey 《K-Theory》2001,24(1):87-107
Let be a group, F the free
-module on the set of finite order elements in , with acting by conjugation, and
the ring extension of
by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaWaaiWaaeaada% WcaaqaaiaaigdaaeaatCvAUfKttLearyGqLXgBG0evaGqbciab-5ga% UbaaieaacaGFLbGaaGOmaiaabc8acqWFPbqAcaqGVaGae8NBa42aaq% qaaeaacqGHdicjcqaHZoWzcqGHiiIZcqqHtoWrcaqGGaGaae4Baiaa% bAgacaqGGaGaae4BaiaabkhacaqGKbGaaeyzaiaabkhacaqGGaGae8% NBa4gacaGLhWoaaiaawUhacaGL9baaaaa!563E!\[\left\{ {\frac{1}{n}e2{\text{\pi }}i{\text{/}}n\left| {\exists \gamma \in \Gamma {\text{ of order }}n} \right.} \right\}\]. For a ring R with
, we build an injective assembly map
, detected by the Dennis trace map. This is proved by establishing a delocalization property for the assembly map
in Hochschild homology, namely providing a gluing of simpler assembly maps (i.e. localized at the identity of ) to build
, and by delocalizing a known assembly map in K-theory to define
. We also prove the delocalization property in cyclic homology and in related theories. 相似文献
16.
I. I. Mel'nik 《Mathematical Notes》1973,14(5):962-966
On the lattice of manifolds of all algebras L we study the operator of nilpotent closure
, where
is a nilpotent manifold of -algebras. With a given system of identities defining, we construct a system *, giving the manifold
It is proved that if does not contain
, then the lattice of submanifolds of
is the double of the lattice of submanifolds of. We describe the free and subdirect indecomposable manifolds of algebras
. Let
and A be adense retract of B. We denote by (B) the lattice of congruences on B. The theorem is proved: (B) is a complemented lattice if and only if (A) is a complemented lattice.Translated from Matematicheskie Zametki, Vol. 14, No. 5, pp. 703–712, November, 1973. 相似文献
17.
Hauke Klein 《Geometriae Dedicata》1999,77(3):271-277
We consider a four-dimensional compact projective plane
whose collineation group is six-dimensional and solvable with a nilradical N isomorphic to Nil×R, where Nil denotes the three-dimensional, simply connected, non-Abelian, nilpotent Lie group. We assume that fixes a flag p W, acts transitively on
and fixes no point in the set W\p. Under these conditions, we will prove that either contains a three-dimensional group of elations or acts doubly transitively on
. 相似文献
18.
Micheline Vigué-Poirrier 《manuscripta mathematica》1986,56(2):177-191
Let X be a nilpotent space such that it exists k1 with Hp (X,) = 0 p > k and Hk (X,) 0, let Y be a (m–1)-connected space with mk+2, then the rational homotopy Lie algebra of YX (resp.
is isomorphic as Lie algebra, to H* (X,) (* (Y) ) (resp.+ (X,) (* (Y) )). If X is formal and Y -formal, then the spaces YX and
are -formal. Furthermore, if dim * (Y) is infinite and dim H* (Y,Q) is finite, then the sequence of Betti numbers of
grows exponentially. 相似文献
19.
Hans Fuchs 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1970,21(1):115-119
Summary Lyon's formula for heat transfer to liquid metals for constant wall heat flux (Nu=7+0.025 ( Pe)0.8) is compared with results of Reichardt and Elser (Nu=5.2+0.025 ( Pe)0.8).The difference is shown to be due to the adopted distribution of radial heat flux—both Reichardt and Elser tacitly assuming constant wall temperature. Their results lend therefore support to the Seban-Shimazaki formula (Nu=5+0.025 Pe0.8). Differences between experimental values and Lyon's formula can possibly be explained by inaccuracies of Nikuradse's velocity profiles for low Re number.
Symbole Temperaturleitfähigkeit - c p Spezifische Wärme - D=2R Rohrdurchmesser - q Wärmestromdichte - r laufender Radius - T Temperatur - mittlere Temperatur - u Geschwindigkeit - mittlere Geschwindigkeit - x Längskoordinate - Wärmeübergangszahl - H , M eddy diffusivity for heat/momentum - Wärmeleitfähigkeit - kinemat. Zähigkeit - =r/R dimensionsloser Radius - Dichte - Schubspannung - Nusselt-Zahl - Pe=Re Pr Péclet-Zahl - Prandtl-Zahl - Reynolds-Zahl - Index Wand 相似文献
Symbole Temperaturleitfähigkeit - c p Spezifische Wärme - D=2R Rohrdurchmesser - q Wärmestromdichte - r laufender Radius - T Temperatur - mittlere Temperatur - u Geschwindigkeit - mittlere Geschwindigkeit - x Längskoordinate - Wärmeübergangszahl - H , M eddy diffusivity for heat/momentum - Wärmeleitfähigkeit - kinemat. Zähigkeit - =r/R dimensionsloser Radius - Dichte - Schubspannung - Nusselt-Zahl - Pe=Re Pr Péclet-Zahl - Prandtl-Zahl - Reynolds-Zahl - Index Wand 相似文献
20.
Milos Arsenovic 《Integral Equations and Operator Theory》1988,11(1):1-9
H. O. Cordes investigated a C*-algebra C of singular integral operators on a polycylinder =n×B and defined symbol homomorphisms
where
is a certain compact space,
and Cx is the Laplace comparison algebra of the compact space B (cf. [2]). We give a characterization of the Frechet algebra CC obtained as the closure of a certain algebra of dos in the topology generated by all HS norms. We define B:L(HS)L(HS)(S) by analogy with [4, 7] and prove that B maps C into C continuously. As a corollary we get
, generalizing surjectivity results from [4] and [7]. It seems that no characterization of (C) is known, but it is clear that
where
is the Frechet algebra studied in [1] and [7]. 相似文献