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1.
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
2.
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
3.
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
4.
Han Peters 《Mathematische Annalen》2007,337(1):1-13
Let F be an automorphism of which has an attracting fixed point. It is well known that the basin of attraction is biholomorphically equivalent to . We will show that the basin of attraction of a sequence of automorphisms f
1, f
2, . . . is also biholomorphic to if every f
n
is a small perturbation of the original map F. 相似文献
5.
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
6.
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
7.
Yu LI 《数学学报(英文版)》2008,24(2):285-304
Let G be a Lie group whose Lie algebra g is quadratic. In the paper "the non-commutative Weil algebra", Alekseev and Meinrenken constructed an explicit G-differential space homomorphism £, called the quantization map, between the Well algebra Wg = S(g^*) χ∧A(g^*) and Wg= U(g) χ Cl(g) (which they call the noncommutative Weil algebra) for g. They showed that £ induces an algebra isomorphism between the basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg). In this paper, we will interpret the quantization map .~ as the super Duflo map between the symmetric algebra S(Tg[1]) and the universal enveloping algebra U(Tg[1]) of a super Lie algebra T9[1] which is canonically associated with the quadratic Lie algebra g. The basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg) correspond exactly to S(Tg[1])^inv and U(Tg[1])^inv, respectively. So what they proved is equivalent to the fact that the super Duflo map commutes with the adjoint action of the super Lie algebra, and that the super Duflo map is an algebra homomorphism when restricted to the space of invariants. 相似文献
8.
Christoph Bohle G. Paul Peters Ulrich Pinkall 《Calculus of Variations and Partial Differential Equations》2008,32(2):263-277
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy
under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space
forms. In this paper we investigate more generally the critical points of arbitrary geometric functionals on the space of
immersions under the constraint that the admissible variations infinitesimally preserve the conformal structure. Besides constrained
Willmore surfaces we discuss in some detail examples of constrained minimal and volume critical surfaces, the critical points
of the area and enclosed volume functional under the conformal constraint.
C. Bohle, G. P. Peters and U. Pinkall are partially supported by DFG SPP 1154. 相似文献
9.
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
10.
A. R. D. Mathias 《Archive for Mathematical Logic》2007,46(1):43-50
We derive the schemes of from certain weak forms of the same. 相似文献
11.
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
12.
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
13.
Laguerre geometry of surfaces in is given in the book of Blaschke [Vorlesungen über Differentialgeometrie, Springer, Berlin Heidelberg New York (1929)], and has been studied by Musso and Nicolodi [Trans. Am. Math. soc. 348, 4321–4337 (1996); Abh. Math. Sem. Univ. Hamburg 69, 123–138 (1999); Int. J. Math. 11(7), 911–924 (2000)], Palmer [Remarks on a variation problem in Laguerre geometry. Rendiconti di Mathematica, Serie VII, Roma, vol. 19, pp. 281–293 (1999)] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in . For any umbilical free hypersurface with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invariant self-adjoint operator : TM → TM, and show that is a complete Laguerre invariant system for hypersurfaces in with n≥ 4. We calculate the Euler–Lagrange equation for the Laguerre volume functional of Laguerre metric by using Laguerre invariants. Using the Euclidean space , the semi-Euclidean space and the degenerate space we define three Laguerre space forms , and and define the Laguerre embeddings and , analogously to what happens in the Moebius geometry where we have Moebius space forms S
n
, and (spaces of constant curvature) and conformal embeddings and [cf. Liu et al. in Tohoku Math. J. 53, 553–569 (2001) and Wang in Manuscr. Math. 96, 517–534 (1998)]. Using these Laguerre embeddings we can unify the Laguerre geometry of hypersurfaces in , and . As an example we show that minimal surfaces in or are Laguerre minimal in .C. Wang Partially supported by RFDP and Chuang-Xin-Qun-Ti of NSFC. 相似文献
14.
15.
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
16.
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
17.
Juan A. Aledo José M. Espinar José A. Gálvez 《Calculus of Variations and Partial Differential Equations》2007,29(3):347-363
We study isometric immersions of surfaces of constant curvature into the homogeneous spaces and . In particular, we prove that there exists a unique isometric immersion from the standard 2-sphere of constant curvature
c > 0 into and a unique one into when c > 1, up to isometries of the ambient space. Moreover, we show that the hyperbolic plane of constant curvature c < −1 cannot be isometrically immersed into or .
J.A. Aledo was partially supported by Ministerio de Education y Ciencia Grant No. MTM2004-02746 and Junta de Comunidades de
Castilla-La Mancha, grant no. PAI-05-034.
J.M. Espinar and J.A. Gálvez were partially supported by Ministerio de Education y Ciencia grant no. MTM2004-02746 and Junta
de Andalucía Grant No. FQM325. 相似文献
18.
19.
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
20.
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