共查询到20条相似文献,搜索用时 24 毫秒
1.
Tobias Ekholm John Etnyre Michael Sullivan 《Transactions of the American Mathematical Society》2007,359(7):3301-3335
A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form , where is an exact symplectic manifold, is established. The class of such contact manifolds includes 1-jet spaces of smooth manifolds. As an application, contact homology is used to provide (smooth) isotopy invariants of submanifolds of and, more generally, invariants of self transverse immersions into up to restricted regular homotopies. When , this application is the first step in extending and providing a contact geometric underpinning for the new knot invariants of Ng.
2.
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.
3.
Rü diger W. Braun Reinhold Meise B. A. Taylor 《Transactions of the American Mathematical Society》2004,356(4):1315-1383
The local Phragmén-Lindelöf condition for analytic subvarieties of at real points plays a crucial role in complex analysis and in the theory of constant coefficient partial differential operators, as Hörmander has shown. Here, necessary geometric conditions for this Phragmén-Lindelöf condition are derived. They are shown to be sufficient in the case of curves in arbitrary dimension and of surfaces in . The latter result leads to a geometric characterization of those constant coefficient partial differential operators which are surjective on the space of all real analytic functions on .
4.
Russell G. Miller Andre O. Nies Richard A. Shore 《Transactions of the American Mathematical Society》2004,356(8):3025-3067
The three quantifier theory of , the recursively enumerable degrees under Turing reducibility, was proven undecidable by Lempp, Nies and Slaman (1998). The two quantifier theory includes the lattice embedding problem and its decidability is a long-standing open question. A negative solution to this problem seems out of reach of the standard methods of interpretation of theories because the language is relational. We prove the undecidability of a fragment of the theory of that lies between the two and three quantifier theories with but includes function symbols.
Theorem. The two quantifier theory of , the r.e. degrees with Turing reducibility, supremum and infimum (taken to be any total function extending the infimum relation on ) is undecidable.
The same result holds for various lattices of ideals of which are natural extensions of preserving join and infimum when it exits.
5.
Yu. I. Lyubich 《Proceedings of the American Mathematical Society》2008,136(11):3953-3956
The isometric embeddings (, ) over a field are considered, and an upper bound for the minimal is proved. In the commutative case ( ) the bound was obtained by Delbaen, Jarchow and Pełczyński (1998) in a different way.
6.
Daniel M. Oberlin 《Proceedings of the American Mathematical Society》2004,132(4):1195-1199
We establish a uniform Fourier restriction estimate for certain hypersurfaces in .
7.
Alexandru D. Ionescu Stephen Wainger 《Journal of the American Mathematical Society》2006,19(2):357-383
We prove that if is a Calderón-Zygmund kernel and is a polynomial of degree with real coefficients, then the discrete singular Radon transform operator extends to a bounded operator on , . This gives a positive answer to an earlier conjecture of E. M. Stein and S. Wainger.
8.
Roger Bielawski 《Transactions of the American Mathematical Society》2006,358(9):3997-4019
We study manifolds arising as spaces of sections of complex manifolds fibering over with the normal bundle of each section isomorphic to .
9.
S. Prashanth 《Proceedings of the American Mathematical Society》2007,135(1):201-209
Let denote the closure of in the norm Let and define the constants and Let We consider the following problem for We show an exact multiplicity result for for all small .
10.
Piotr Gajda Youming Li Leszek Plaskota Grzegorz W. Wasilkowski. 《Mathematics of Computation》2004,73(246):813-825
We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain . The algorithm and its desirable theoretical properties are derived based on certain stochastic assumptions about the integrands. It is easy to implement, enjoys convergence rate, and uses only standard random number generators. Numerical results are also included.
11.
We prove that every real ellipsoid admits at least four umbilical points, which can be compared to the result of Webster that a generic real ellipsoid in with does not admit any umbilical point.
12.
Siqi Fu 《Proceedings of the American Mathematical Society》2007,135(3):725-730
The spectrum of the -Neumann Laplacian on a polydisc in is explicitly computed. The calculation exhibits that the spectrum consists of eigenvalues, some of which, in particular the smallest ones, are of infinite multiplicity.
13.
Tavan T. Trent 《Proceedings of the American Mathematical Society》2004,132(8):2429-2432
We find the maximal invariant subspaces for on -valued Bergman-type spaces.
14.
Shulim Kaliman Sté phane Vé né reau Mikhail Zaidenberg 《Transactions of the American Mathematical Society》2004,356(2):509-555
The Abhyankar-Sathaye Problem asks whether any biregular embedding can be rectified, that is, whether there exists an automorphism such that is a linear embedding. Here we study this problem for the embeddings whose image is given in by an equation , where and . Under certain additional assumptions we show that, indeed, the polynomial is a variable of the polynomial ring (i.e., a coordinate of a polynomial automorphism of ). This is an analog of a theorem due to Sathaye (1976) which concerns the case of embeddings . Besides, we generalize a theorem of Miyanishi (1984) giving, for a polynomial as above, a criterion for when .
15.
We derive sharp injectivity criteria for mappings in terms of Ahlfors' definition of the Schwarzian derivative for such mappings.
16.
Dalide Pontoni 《Transactions of the American Mathematical Society》2007,359(11):5419-5448
We compute the small quantum cohomology of Hilb and determine recursively most of the big quantum cohomology. We prove a relationship between the invariants so obtained and the enumerative geometry of hyperelliptic curves in . This extends the results obtained by Graber (2001) for Hilb and hyperelliptic curves in .
17.
Petr Holicky Tamá s Keleti 《Proceedings of the American Mathematical Society》2005,133(6):1851-1859
It is known that the sets of extreme and exposed points of a convex Borel subset of are Borel. We show that for there exist convex subsets of such that the sets of their extreme and exposed points coincide and are of arbitrarily high Borel class. On the other hand, we show that the sets of extreme and of exposed points of a convex set of additive Borel class are of ambiguous Borel class . For proving the latter-mentioned results we show that the union of the open and the union of the closed segments of are of the additive Borel class if is a convex set of additive Borel class .
18.
Gabriel Acosta Ricardo G. Durá n 《Proceedings of the American Mathematical Society》2004,132(1):195-202
For convex domains with diameter we prove
for any with zero mean value on . We also show that the constant in this inequality is optimal.
for any with zero mean value on . We also show that the constant in this inequality is optimal.
19.
Richard F. Bass Takashi Kumagai 《Transactions of the American Mathematical Society》2008,360(4):2041-2075
We consider symmetric Markov chains on where we do not assume that the conductance between two points must be zero if the points are far apart. Under a uniform second moment condition on the conductances, we obtain upper bounds on the transition probabilities, estimates for exit time probabilities, and certain lower bounds on the transition probabilities. We show that a uniform Harnack inequality holds if an additional assumption is made, but that without this assumption such an inequality need not hold. We establish a central limit theorem giving conditions for a sequence of normalized symmetric Markov chains to converge to a diffusion on corresponding to an elliptic operator in divergence form.
20.
Daniel M. Oberlin 《Proceedings of the American Mathematical Society》2008,136(1):213-217
We study convolution and Fourier restriction estimates for some degenerate curves in .