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1.
Brian Osserman 《Proceedings of the American Mathematical Society》2006,134(4):989-993
We note that the degeneration arguments given by the author in 2003 to derive a formula for the number of maps from a general curve of genus to with prescribed ramification also yields weaker results when working over the real numbers or -adic fields. Specifically, let be such a field: we see that given , , , and satisfying , there exists smooth curves of genus together with points such that all maps from to can, up to automorphism of the image, be defined over . We also note that the analagous result will follow from maps to higher-dimensional projective spaces if it is proven in the case , , and that thanks to work of Sottile, unconditional results may be obtained for special ramification conditions.
2.
Janko Marovt 《Proceedings of the American Mathematical Society》2006,134(4):1065-1075
Let be a compact Hausdorff space which satisfies the first axiom of countability, let and let , be the set of all continuous functions from to If , ,is a bijective multiplicative map, then there exist a homeomorphism and a continuous map such that for all and for all
3.
Barbara F. Csima Antonio Montalbá n 《Proceedings of the American Mathematical Society》2006,134(5):1499-1502
We construct a minimal pair of -degrees. We do this by showing the existence of an unbounded nondecreasing function which forces -triviality in the sense that is -trivial if and only if for all , .
4.
Gré gory Ginot Gilles Halbout 《Proceedings of the American Mathematical Society》2006,134(3):621-630
Let be the Hochschild complex of cochains on and let be the space of multivector fields on . In this paper we prove that given any -structure (i.e. Gerstenhaber algebra up to homotopy structure) on , and any -morphism (i.e. morphism of a commutative, associative algebra up to homotopy) between and , there exists a -morphism between and that restricts to . We also show that any -morphism (i.e. morphism of a Lie algebra up to homotopy), in particular the one constructed by Kontsevich, can be deformed into a -morphism, using Tamarkin's method for any -structure on . We also show that any two of such -morphisms are homotopic.
5.
Masahiro Shioya 《Proceedings of the American Mathematical Society》2006,134(6):1819-1821
Let be a -supercompact cardinal. We show that carries a normal ultrafilter with a property introduced by Menas. With it we give a transparent proof of Kamo's theorem that carries a normal ultrafilter with the partition property.
6.
Detlev W. Hoffmann 《Proceedings of the American Mathematical Society》2006,134(3):645-652
Let be a field of characteristic and let be a purely inseparable extension of exponent . We determine the kernel of the natural restriction map between the Witt rings of bilinear forms of and , respectively. This complements a result by Laghribi who computed the kernel for the Witt groups of quadratic forms for such an extension . Based on this result, we will determine for a wide class of finite extensions which are not necessarily purely inseparable.
7.
Hui June Zhu 《Proceedings of the American Mathematical Society》2006,134(2):323-331
We prove that for any pair of integers such that or 0$">, there exists a (hyper)elliptic curve over of genus and -rank whose automorphism group consists of only identity and the (hyper)elliptic involution. As an application, we prove the existence of principally polarized abelian varieties over of dimension and -rank such that .
8.
Frank Sottile Thorsten Theobald 《Proceedings of the American Mathematical Society》2005,133(10):2835-2844
Let and denote the dimension and the degree of the Grassmannian , respectively. For each there are (a priori complex) -planes in tangent to general quadratic hypersurfaces in . We show that this class of enumerative problems is fully real, i.e., for there exists a configuration of real quadrics in (affine) real space so that all the mutually tangent -flats are real.
9.
Let be a compact connected orientable Riemannian manifold of dimension and let be the -th positive eigenvalue of the Laplacian acting on differential forms of degree on . We prove that the metric can be conformally deformed to a metric , having the same volume as , with arbitrarily large for all .
Note that for the other values of , that is and , one can deduce from the literature that, 0$">, the -th eigenvalue is uniformly bounded on any conformal class of metrics of fixed volume on .
For , we show that, for any positive integer , there exists a metric conformal to such that, , , that is, the first eigenforms of are all exact forms.
10.
Francine Meylan 《Proceedings of the American Mathematical Society》2006,134(4):1023-1030
Let be a rational proper holomorphic map between the unit ball in and the unit ball in Write where and are holomorphic polynomials, with Recall that the degree of is defined by
deg
In this paper, we give a bound estimate for the degree of improving the bound given by Forstneric (1989). 11.
Farruh Mukhamedov Seyit Temir Hasan Akin 《Proceedings of the American Mathematical Society》2006,134(3):843-850
Akcoglu and Suchaston proved the following result: Let be a positive contraction. Assume that for the sequence converges weakly in . Then either or there exists a positive function , such that . In the paper we prove an extension of this result in a finite von Neumann algebra setting, and as a consequence we obtain that if a positive contraction of a noncommutative -space has no nonzero positive invariant element, then its mixing property implies the completely mixing property.
12.
Stephan Ramon Garcia 《Proceedings of the American Mathematical Society》2005,133(7):2051-2059
We study real Smirnov functions and investigate a certain -closed subalgebra of the Smirnov class containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space . This leads to a natural analog of the Riesz projection on a certain quotient space of for . We also study a Herglotz-like integral transform for singular measures on the unit circle .
13.
Sy D. Friedman 《Proceedings of the American Mathematical Society》2006,134(6):1823-1824
We show that ``saturation' of the universe with respect to forcing over with partial orders on is equivalent to the existence of .
14.
Xiaojie Gao S. L. Lee Qiyu Sun 《Proceedings of the American Mathematical Society》2006,134(4):1051-1057
A finitely supported sequence that sums to defines a scaling operator on functions a transition operator on sequences and a unique compactly supported scaling function that satisfies normalized with It is shown that the eigenvalues of on the space of compactly supported square-integrable functions are a subset of the nonzero eigenvalues of the transition operator on the space of finitely supported sequences, and that the two sets of eigenvalues are equal if and only if the corresponding scaling function is a uniform -spline.
15.
Boaz Tsaban 《Proceedings of the American Mathematical Society》2006,134(3):881-891
We construct several topological groups with very strong combinatorial properties. In particular, we give simple examples of subgroups of (thus strictly -bounded) which have the Menger and Hurewicz properties but are not -compact, and show that the product of two -bounded subgroups of may fail to be -bounded, even when they satisfy the stronger property . This solves a problem of Tkacenko and Hernandez, and extends independent solutions of Krawczyk and Michalewski and of Banakh, Nickolas, and Sanchis. We also construct separable metrizable groups of size continuum such that every countable Borel -cover of contains a -cover of .
16.
Stephen Allen David Pask Aidan Sims 《Proceedings of the American Mathematical Society》2006,134(2):455-464
Given a -graph and an element of , we define the dual -graph, . We show that when is row-finite and has no sources, the -algebras and coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the -theory of when is finite and strongly connected and satisfies the aperiodicity condition.
17.
We show that the -algebra associated to the tail-equivalence relation on a Bratteli diagram, according to a procedure recently introduced by the first-named author and A. Lopes, is isomorphic to the -algebra of the diagram. More generally we consider an approximately proper equivalence relation on a compact space for which the quotient maps are local homeomorphisms. We show that the algebra associated to under the above-mentioned procedure is isomorphic to the groupoid -algebra .
18.
Xiaojiang Yu 《Proceedings of the American Mathematical Society》2006,134(2):491-499
We prove that for any real expansive matrix , there exists a bounded -dilation wavelet set in the frequency domain (the inverse Fourier transform of whose characteristic function is a band-limited single wavelet in the time domain ). Moreover these wavelet sets can approximate a cube in arbitrarily. This result improves Dai, Larson and Speegle's result about the existence of (basically unbounded) wavelet sets for real expansive matrices.
19.
Let be the canonical AF subalgebra of a graph -algebra associated with a locally finite directed graph . For Brown and Voiculescu's topological entropy of the canonical completely positive map on , is known to hold for a finite graph , where is the loop entropy of Gurevic and is the block entropy of Salama. For an irreducible infinite graph , the inequality has recently been known. It is shown in this paper that
where is the graph with the direction of the edges reversed. Some irreducible infinite graphs 1)$"> with are also examined.
where is the graph with the direction of the edges reversed. Some irreducible infinite graphs 1)$"> with are also examined.
20.
Wlodzimierz Bak Andrzej Hulanicki 《Proceedings of the American Mathematical Society》2006,134(5):1467-1472
We prove that the spectrum of a convolution operator on a locally compact group by a self-adjoint -function is the same on and and consequently on all spaces, if and only if a Beurling algebra contains non-analytic functions on operating on into .