Under study are some conditions for the weakly regular modules to be closed under direct sums and the rings over which all modules are weakly regular. For an arbitrary right R-module M, we prove that every module in the category σ(M) is weakly regular if and only if each module in σ(M) is either semisimple or contains a nonzero M-injective submodule. We describe the normal rings over which all modules are weakly regular. 相似文献
We prove that for two elements x, y in a Hilbert C*-module V over a C*-algebra the C*-valued triangle equality |x + y| = |x| + |y| holds if and only if 〈x, y〉 = |x| |y|. In addition, if has a unit e, then for every x, y ∊ V and every ɛ > 0 there are contractions u, υ ∊ such that |x + y| ≦ u|x|u* + υ|y|υ* + ɛe.
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It is shown that a ring R is a GM-ring if and only if there exists a complete orthogonal set { e1,...,en} of idempotents such that all eiRei are GM-rings. We also investigate GM-rings for Morita contexts, module extensions and power series rings.This work was supported by the Natural Science Foundation of Zhejiang Province. 相似文献
In this paper we extend the notion of n-weak amenability of a Banach algebra
when n ∈ ℕ. Technical calculations show that when
is Arens regular or an ideal in
**, then
* is an
(2n)-module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of n-weak amenability to n ∈ ∕. 相似文献
Let A be a compact set in of Hausdorff dimension d. For s ∈ (0,d) the Riesz s-equilibrium measure μs is the unique Borel probability measure with support in A that minimizes
over all such probability measures. If A is strongly -rectifiable, then μs converges in the weak-star topology to normalized d-dimensional Hausdorff measure restricted to A as s approaches d from below.
This research was supported, in part, by the U. S. National Science Foundation under grants DMS-0505756 and DMS-0808093. 相似文献
In this paper, we get W1,p(Rn)-boundedness for tangential maximal function and nontangential maximal function, which improves J.Kinnunen, P.Lindqvist and
Tananka’s results.
Supported by the key Academic Discipline of Zhejiang Province of China under Grant No.2005 and the Zhejiang Provincial Natural
Science Foundation of China. 相似文献
For any nontrivial connected graph F and any graph G, the F-degree of a vertex v in G is the number of copies of F in G containing v. G is called F-continuous if and only if the F-degrees of any two adjacent vertices in G differ by at most 1; G is F-regular if the F-degrees of all vertices in G are the same. This paper classifies all P4-continuous graphs with girth greater than 3. We show that for any nontrivial connected graph F other than the star K1,k, k ⩾ 1, there exists a regular graph that is not F-continuous. If F is 2-connected, then there exists a regular F-continuous graph that is not F-regular.
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The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈ W H J^d(A) if and only if M admits a filtration of submodules: 0 belong to U0 belong to U1 belong to ... belong to Up = M such that all Ui/Ui-1 are d-Koszul-type modules, from which we obtain that the finitistic dimension conjecture holds in W H J^d(A) in a special case. Let M ∈ W H J^d(A). It is proved that the Koszul dual E(M) is Noetherian, Hopfian, of finite dimension in special cases, and E(M) ∈ gr0(E(A)). In particular, we show that M ∈ W H J^d(A) if and only if E(G(M)) ∈ gr0(E(A)), where G is the associated graded functor. 相似文献
In this paper we study the Lp-discrepancy of digitally shifted Hammersley point sets. While it is known that the (unshifted) Hammersley point set (which
is also known as Roth net) with N points has Lp-discrepancy (p an integer) of order (log N)/N, we show that there always exists a shift such that the digitally shifted Hammersley point set has Lp-discrepancy (p an even integer) of order
which is best possible by a result of W. Schmidt. Further we concentrate on the case p = 2. We give very tight lower and upper bounds for the L2-discrepancy of digitally shifted Hammersley point sets which show that the value of the L2-discrepancy of such a point set mostly depends on the number of zero coordinates of the shift and not so much on the position
of these.
This work is supported by the Austrian Research Fund (FWF), Project P17022-N12 and Project S8305. 相似文献
We determine the Lp discrepancy of the two-dimensional Hammersley point set in base b. These formulas show that the Lp discrepancy of the Hammersley point set is not of best possible order with respect to the general (best possible) lower bound
on Lp discrepancies due to Roth and Schmidt. To overcome this disadvantage we introduce permutations in the construction of the
Hammersley point set and show that there always exist permutations such that the Lp discrepancy of the generalized Hammersley point set is of best possible order. For the L2 discrepancy such permutations are given explicitly.
F.P. is supported by the Austrian Science Foundation (FWF), Project S9609, that is part of the Austrian National Research
Network “Analytic Combinatorics and Probabilistic Number Theory”. 相似文献
In this paper LJ-spaces are introduced and studied. They are a common generalization of Lindelöf spaces and J-spaces researched by E. Michael. A space X is called an LJ-space if, whenever {A, B} is a closed cover of X with A ∩ B compact, then A or B is Lindelöf. Semi-strong LJ-spaces and strong LJ-spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors. 相似文献
Lp approximation capability of radial basis function (RBF) neural networks is investigated. If g: R+1 → R1 and ∈ Llocp(Rn) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in Lp(K) with any accuracy for any compact set K in Rn, if and only if g(x) is not an even polynomial.
Partly supported by the National Natural Science Foundation of China (10471017) 相似文献
The following results are proved. In Theorem 1, it is stated that there exist both finitely presented and not finitely presented
2-generated nonfree groups which are k-free-like for any k ⩾ 2. In Theorem 2, it is claimed that every nonvirtually cyclic (resp., noncyclic and torsion-free) hyperbolic m-generated group is k-free-like for every k ⩾ m + 1 (resp., k ⩾ m). Finally, Theorem 3 asserts that there exists a 2-generated periodic group G which is k-free-like for every k ⩾ 3.
Supported by NSF (grant Nos. DMS 0455881 and DMS-0700811). (A. Yu. Olshanskii, M. V. Sapir)
Supported by RFBR project No. 08-01-00573. (A. Yu. Olshanskii)
Supported by BSF grant (USA–Israel). (M. V. Sapir)
Translated from Algebra i Logika, Vol. 48, No. 2, pp. 245–257, March–April, 2009. 相似文献
We classify graph C*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph, up to
strict isomorphism. This is done by a purely graph theoretical calculation of the K-theory of the C*-algebras and the method also provides an independent proof of the classification up to Morita equivalence and stable equivalence
of such algebras, without using the boundary operator algebra. A direct relation is given between the K1-group of the algebra and the cycle space of the graph.
We thank Jakub Byszewski for his input in Sect. 2.8. The position of the unit in K0(
Ч) was guessed based on some example calculations by Jannis Visser in his SCI 291 Science Laboratory at Utrecht University
College. 相似文献
The relation between the inseparable prime C^*-algebras and primitive C^*-algebras is studied,and we prove that prime AW^*-algebras are all primitive C^*-algebras. 相似文献
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ1, ..., ϕr)T is unknown, g is a given vector of compactly supported functions on ℝs, a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite
interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕn, n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ0. We characterize the Lp-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness
property of the solutions of the refinement equations associated with the homogeneous refinement equation.
This project is supported by the NSF of China under Grant No. 10071071 相似文献
The rank of a q-ary code C is the dimension of the subspace spanned by C. The kernel of a q-ary code C of length n can be defined as the set of all translations leaving C invariant. Some relations between the rank and the dimension of the kernel of q-ary 1-perfect codes, over
as well as over the prime field
, are established. Q-ary 1-perfect codes of length n=(qm − 1)/(q − 1) with different kernel dimensions using switching constructions are constructed and some upper and lower bounds for the dimension of the kernel, once the rank is given, are established.Communicated by: I.F. Blake 相似文献
We prove the existence of the computable families of finite sets and general recursive functions with no e-principal numbering. We give a series of examples of e-degrees such that the p-degrees of their computable numberings include no top p-degree. 相似文献
Let
be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are presented: (1) G ∈
if and only if there is a normal subgroup H such that G/H ∈
and every maximal subgroup of all Sylow subgroups of H is either c-normal or S-quasinormally embedded in G. (2) G ∈
if and only if there is a normal subgroup H such that G/H ∈
and every maximal subgroup of all Sylow subgroups of F*(H), the generalized Fitting subgroup of H, is either c-normal or S-quasinormally embedded in G. (3) G ∈
if and only if there is a normal subgroup H such that G/H ∈
and every cyclic subgroup of F*(H) of prime order or order 4 is either c-normal or S-quasinormally embedded in G.
Supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi Autonomous Region (No.
0249001).
Corresponding author. Supported in part by the Natural Science Foundation of China (10571181), NSF of Guangdong Province (06023728)
and ARF(GDEI). 相似文献