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1.
Ján Jakubík 《Mathematica Slovaca》2008,58(2):143-154
For an MV-algebra
let J
0(
) be the system of all closed ideals of
; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV-algebras will be called a K-radical class iff, whenever
∈ X and
is an MV-algebra with J
0(
) ≅ J
0(
), then
∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that
there is a one-to-one correspondence between K-radical classes of MV-algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV-algebras; product radical classes of lattice ordered groups were studied by Ton.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information,
Grant I/2/2005. 相似文献
2.
Ján Jakubík 《Czechoslovak Mathematical Journal》2008,58(4):1129-1143
The notion of bounded commutative residuated ℓ-monoid (BCR ℓ-monoid, in short) generalizes both the notions of MV-algebra and of BL-algebra. Let
be a BCR ℓ-monoid; we denote by ℓ(
) the underlying lattice of
. In the present paper we show that each direct product decomposition of ℓ(
) determines a direct product decomposition of
. This yields that any two direct product decompositions of
have isomorphic refinements. We consider also the relations between direct product decompositions of
and states on
.
This work was supported by Slovak Research and Development Agency under the contract No APVV-0071-06.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information
(grant I/2/2005). 相似文献
3.
Ján Jakubík 《Mathematica Slovaca》2008,58(3):289-300
In a previous author’s paper, sequential convergences on an MV-algebra
have been studied; the Urysohn’s axiom was assumed to be valid. The system of all such convergences was denoted by Conv
. In the present paper we investigate analogous questions without supposing the validity of the Urysohn’s axiom; the corresponding
system of convergences is denoted by conv
. Both Conv
and conv
are partially ordered by the set-theoretical inclusion. We deal with the properties of conv 289-6 and the relations between conv
and Conv
. We prove that each interval of conv
is a distributive lattice. The system conv
has the least element, but it does not possess any atom. Hence it is either a singleton set or it is infinite. We consider
also the relations between conv
and conv G, where (G, u) is a unital lattice-ordered group with
= Γ (G, u).
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence — Physics of
Information, Grant 1/2/2005. 相似文献
4.
Yu Cheng Li 《数学学报(英文版)》2008,24(10):1737-1750
In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f(z) = z^ng(z) (n ≥1), g(z) = b0 + b1z^p1 +b2z^p2 +.. , bk ≠ 0 (k = 0, 1, 2,...), our main result is =A′(Mf) = A′(Mzn)∩A′(Mg) = A′(Mz^s), where s = g.c.d.(n,p1,p2,...). In the last section, we study the relation between strongly irreducible curve and the winding number W(f,f(α)), α ∈ D. 相似文献
5.
The authors define strongly Gauduchon spaces and the class■■, which are generalization of strongly Gauduchon manifolds in complex spaces. Comparing with the case of Kahlerian, the strongly Gauduchon space and the class■are similar to the Kahler space and the Fujiki class■■ respectively. Some properties about these complex spaces are obtained. Moreover, the relations between the strongly Gauduchon spaces and the class■■ are studied. 相似文献
6.
If X is a space that can be mapped onto a metric space by a one-to-one mapping, then X is said to have a weaker metric topology.
In this paper, we give characterizations of sequence-covering compact images and sequentially-quotient compact images of spaces
with a weaker metric topology. The main results are that
(1) Y is a sequence-covering compact image of a space with a weaker metric topology if and only if Y has a sequence
of point-finite cs-covers such that
for each y ∈ Y.
(2) Y is a sequentially-quotient compact image of a space with a weaker metric topology if and only if Y has a sequence
of point-finite cs*-covers such that
for each y ∈ Y.
Supported by the NNSF(10471084) of China. 相似文献
7.
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
8.
Ming DING 《Frontiers of Mathematics in China》2011,6(2):231-240
We extend the definition of a quantum analogue of the Caldero-Chapoton map defined by D. Rupel. When Q is a quiver of finite type, we prove that the algebra (Q) generated by all cluster characters is exactly the quantum cluster algebra (Q). 相似文献
9.
A partial Steiner (k,l)-system is a k-uniform hypergraph
with the property that every l-element subset of V is contained in at most one edge of
. In this paper we show that for given k,l and t there exists a partial Steiner (k,l)-system such that whenever an l-element subset from every edge is chosen, the resulting l-uniform hypergraph contains a clique of size t. As the main result of this note, we establish asymptotic lower and upper bounds on the size of such cliques with respect
to the order of Steiner systems.
Research of the second author partially supported by NSERC grant OGP0025112. 相似文献
10.
The degree conjecture for the Selberg class
of L-functions states that the degree d
F
of every F ∈
is an integer. Moreover, it is expected that every F ∈
has polynomial Euler product, and that the degree ∂
F
of such an Euler product coincides with d
F
. In this note we prove that a suitable continuity assumption on the degree d
F
implies that ∂
F
= d
F
for all F ∈
with polynomial Euler product.
相似文献
11.
Sergiy Maksymenko 《Central European Journal of Mathematics》2009,7(2):272-298
Let F be a C
∞ vector field defined near the origin O ∈ ℝ
n
, F(O) = 0, and (F
t
) be its local flow. Denote by
the set of germs of orbit preserving diffeomorphisms h: ℝ
n
→ ℝ
n
at O, and let
, (r ≥ 0), be the identity component of
with respect to the weak Whitney W
r
topology. Then
contains a subset
consisting of maps of the form F
α(x)(x), where α: ℝ
n
→ ℝ runs over the space of all smooth germs at O. It was proved earlier by the author that if F is a linear vector field, then
=
.
In this paper we present a class of examples of vector fields with degenerate singularities at O for which
formally coincides with
, i.e. on the level of ∞-jets at O.
We also establish parameter rigidity of linear vector fields and “reduced” Hamiltonian vector fields of real homogeneous polynomials
in two variables.
相似文献
12.
LiHua Yang 《中国科学A辑(英文版)》2008,51(12):2217-2230
In this paper, a new distribution space
is constructed and the definition of the classical Hilbert transform is extended to it. It is shown that
is the biggest subspace of
on which the extended Hilbert transform is a homeomorphism and both the classical Hilbert transform for L
p
functions and the circular Hilbert transform for periodic functions are special cases of the extension. Some characterizations
of the space
are given and a class of useful nonlinear phase signals is shown to be in
. Finally, the applications of the extended Hilbert transform are discussed.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 60475042, 10631080) 相似文献
13.
Zhi Xiang Wu 《数学学报(英文版)》2009,25(8):1337-1352
We define a new kind quantized enveloping algebra of a generalized Kac-Moody algebra by adding a new generator J satisfying jm = j for some integer m. We denote this algebra by wUqT(A). This algebra is a weak Hopf algebra if and only if m = 2,3. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usual quantum envelope algebra Uq (A) of a generalized Kac-Moody algebra A. 相似文献
14.
Michael Kohlhase 《Mathematics in Computer Science》2008,2(2):279-304
One of the great problems of Mathematical Knowledge Management (MKM) systems is to obtain access to a sufficiently large corpus
of mathematical knowledge to allow the management/search/navigation techniques developed by the community to display their
strength. Such systems usually expect the mathematical knowledge they operate on in the form of semantically enhanced documents,
but mathematicians and publishers in Mathematics have heavily invested into the format and workflow.
We analyze the current practice of semi-semantic markup in documents and extend it by a markup infrastructure that allows to embed semantic annotations into documents without changing their visual appearance. This collection of macro packages is called (semantic ) as it allows to markup documents semantically without leaving the time-tried workflow, essentially turning into an MKM format. At the heart of is a definition mechanism for semantic macros for mathematical objects and a non-standard scoping construct for them, which
is oriented at the semantic dependency relation rather than the document structure.
We evaluate the macro collection on a large case study: the course materials of a two-semester course in Computer Science was annotated semantically
and converted to the OMDoc MKM format by Bruce Miller’s LaTeXML system.
相似文献
15.
Let (, d, μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we consider the behavior on × ⋯ × for the m-linear singular integral operators with nonsmooth kernels which were first introduced by Duong, Grafakos and Yan. 相似文献
16.
Measure theory of statistical convergence 总被引:2,自引:0,他引:2
The question of establishing measure theory for statistical convergence has been moving closer to center stage, since a kind
of reasonable theory is not only fundamental for unifying various kinds of statistical convergence, but also a bridge linking
the studies of statistical convergence across measure theory, integration theory, probability and statistics. For this reason,
this paper, in terms of subdifferential, first shows a representation theorem for all finitely additive probability measures
defined on the σ-algebra
of all subsets of N, and proves that every such measure can be uniquely decomposed into a convex combination of a countably additive probability
measure and a statistical measure (i.e. a finitely additive probability measure μ with μ(k) = 0 for all singletons {k}). This paper also shows that classical statistical measures have many nice properties, such as: The set
of all such measures endowed with the topology of point-wise convergence on
forms a compact convex Hausdorff space; every classical statistical measure is of continuity type (hence, atomless), and
every specific class of statistical measures fits a complementation minimax rule for every subset in N. Finally, this paper shows that every kind of statistical convergence can be unified in convergence of statistical measures.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 10771175, 10471114) 相似文献
17.
Cheng Jun Hou 《数学学报(英文版)》2008,24(6):983-996
We introduce two notions of the pressure in operator algebras, one is the pressure Pα(π, T) for an automorphism α of a unital exact C^*-algebra A at a self-adjoint element T in A with respect to a faithful unital *-representation π the other is the pressure Pτ,α(T) for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T. 相似文献
18.
Ján Jakubík 《Czechoslovak Mathematical Journal》2009,59(1):183-196
In this paper we deal with a pseudo effect algebra
possessing a certain interpolation property. According to a result of Dvurečenskij and Vettterlein,
can be represented as an interval of a unital partially ordered group G. We prove that
is projectable (strongly projectable) if and only if G is projectable (strongly projectable). An analogous result concerning weak homogeneity of
and of G is shown to be valid.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence—Physics of Information
(grant I/2/2005). 相似文献
19.
Jia Feng Lü 《数学学报(英文版)》2009,25(6):1015-1030
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
20.
R. Rimányi V. Schechtman V. Tarasov A. Varchenko 《Functional Analysis and Its Applications》2011,45(4):252-264
We interpret the equivariant cohomology HGLn *H_{GL_n }^* (ℱ
λ
,ℂ) of a partial flag variety ℱ
λ
parametrizing chains of subspaces 0 = F
0 ⊂ F
1 ⊂ … ⊂ F
N
= ℂ
n
, dimF
i
/F
i−1 = λ
i
, as the Bethe algebra of the -weight subspace of a [t]-module . 相似文献