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131.
We analyze the decomposition rank (a notion of covering dimensionfor nuclear C*-algebras introduced by E. Kirchberg and the author)of subhomogeneous C*-algebras. In particular, we show that asubhomogeneous C*-algebra has decomposition rank n if and onlyif it is recursive subhomogeneous of topological dimension n,and that n is determined by the primitive ideal space. As an application, we use recent results of Q. Lin and N. C.Phillips to show the following. Let A be the crossed productC*-algebra coming from a compact smooth manifold and a minimaldiffeomorphism. Then the decomposition rank of A is dominatedby the covering dimension of the underlying manifold. 2000 MathematicsSubject Classification 46L85, 46L35. 相似文献
132.
Radosav?Dordevi? Miodrag? Ra?kovi? Zoran?Ognjanovi?Email author 《Archive for Mathematical Logic》2004,43(4):557-563
A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form Ps (with the intended meaning the probability is at least s). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories.This research was supported by Ministarstvo za nauku, tehnologije i razvoj Republike Srbije, through Matematiki institut, under grant 1379Mathematics Subject Classification (2000): 03C70, 03B48 相似文献
133.
Antonio Ros 《Journal of the American Mathematical Society》2004,17(2):373-388
Given a cubic space group (viewed as a finite group of isometries of the torus ), we obtain sharp isoperimetric inequalities for -invariant regions. These inequalities depend on the minimum number of points in an orbit of and on the largest Euler characteristic among nonspherical -symmetric surfaces minimizing the area under volume constraint (we also give explicit estimates of this second invariant for the various crystallographic cubic groups ). As an example, we prove that any surface dividing into two equal volumes with the same (orientation-preserving) symmetries as the A. Schoen minimal Gyroid has area at least (the conjectured minimizing surface in this case is the Gyroid itself whose area is ).
134.
Alexander Postnikov Boris Shapiro 《Transactions of the American Mathematical Society》2004,356(8):3109-3142
For a graph , we construct two algebras whose dimensions are both equal to the number of spanning trees of . One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis elements correspond to -parking functions that naturally came up in the abelian sandpile model. These ideals are instances of the general class of monotone monomial ideals and their deformations. We show that the Hilbert series of a monotone monomial ideal is always bounded by the Hilbert series of its deformation. Then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals. In some cases these resolutions coincide with Scarf resolutions. We prove several formulas for Hilbert series of monotone monomial ideals and investigate when they are equal to Hilbert series of deformations. In the appendix we discuss the abelian sandpile model.
135.
V. F. Murzina 《Algebra and Logic》2003,42(3):181-191
A modal logic associated with the
-spaces introduced by Ershov is examined. We construct a modal calculus that is complete w.r.t. the class of all strictly linearly ordered
-frames, and the class of all strictly linearly ordered
-frames. 相似文献
136.
We consider Ribaucour transformations between minimal surfaces and we relate such transformations to generating planar embedded ends. Applying Ribaucour transformations to Enneper's surface and to the catenoid, we obtain new families of complete, minimal surfaces, of genus zero, immersed in R
3, with infinitely many embedded planar ends or with any finite number of such ends. Moreover, each surface has one or two nonplanar ends. A particular family is obtained from the catenoid, for each pair (n,m), nm, such that n
m0 is an irreducible rational number. For any such pair, we get a 1-parameter family of finite total curvature, complete minimal surfaces with n+2 ends, n embedded planar ends and two nonplanar ends of geometric index m, whose total curvature is –4(n+m). The analytic interpretation of a Ribaucour transformation as a Bäcklund type transformation and a superposition formula for the nonlinear differential equation = e-2 is included. 相似文献
137.
Minimal Length Elements of Thompson's Group F 总被引:1,自引:1,他引:0
S. Blake Fordham 《Geometriae Dedicata》2003,99(1):179-220
Elements of the group are represented by pairs of binary trees and the structure of the trees gives insight into the properties of the elements of the group. The review section presents this representation and reviews the known relationship between elements of F and binary trees. In the main section we give a method of determining the minimal lengths of elements of Thompson's group F in the two generator presentation
This method is an effective algorithm in that its order is linear in the size of the trees representing an element of F. We also give a method for constructing all minimal length representatives of an element in F. 相似文献
138.
A surface x: M S
n
is called a Willmore surface if it is a criticalsurface of the Willmore functional
M
(S – 2H
2)dv, where H isthe mean curvature and S is the square of the length of the secondfundamental form. It is well known that any minimal surface is aWillmore surface. The first nonminimal example of a flat Willmoresurface in higher codimension was obtained by Ejiri. This example whichcan be viewed as a tensor product immersion of S
1(1) and a particularsmall circle in S
2(1), and therefore is contained in S
5(1) gives anegative answer to a question by Weiner. In this paper we generalize theabove mentioned example by investigating Willmore surfaces in S
n
(1)which can be obtained as a tensor product immersion of two curves. We inparticular show that in this case too, one of the curves has to beS
1(1), whereas the other one is contained either in S
2(1) or in S
3(1). In the first case, we explicitly determine the immersion interms of elliptic functions, thus constructing infinetely many newnonminimal flat Willmore surfaces in S
5. Also in the latter casewe explicitly include examples. 相似文献
139.
We present an alternative, purely semantical and relatively simple, proof of the Statman's result that both intuitionistic propositional logic and its implicational fragment are PSPACE-complete.This paper was supported by grant 401/01/0218 of the Grant Agency of the Czech Republic. %
Mathematics Subject Classification (2000): 相似文献
140.
L''. Holá 《Set-Valued Analysis》2003,11(2):133-151
Our paper studies the topology of uniform convergence on compact sets on the space of densely continuous forms (introduced by Hammer and McCoy (1997)), usco and minimal usco maps. We generalize and complete results from Hammer and McCoy (1997) concerning the space D(X,Y) of densely continuous forms from X to Y. Let X be a Hausdorff topological space, (Y,d) be a metric space and D
k
(X,Y) the topology of uniform convergence on compact sets on D(X,Y). We prove the following main results: D
k
(X,Y) is metrizable iff D
k
(X,Y) is first countable iff X is hemicompact. This result gives also a positive answer to question 4.1 of McCoy (1998). If moreover X is a locally compact hemicompact space and (Y,d) is a locally compact complete metric space, then D
k
(X,Y) is completely metrizable, thus improving a result from McCoy (1998). We study also the question, suggested by Hammer and McCoy (1998), when two compatible metrics on Y generate the same topologies of uniform convergence on compact sets on D(X,Y). The completeness of the topology of uniform convergence on compact sets on the space of set-valued maps with closed graphs, usco and minimal usco maps is also discussed. 相似文献