| 1. |
- Andersson, Lars, et al.
(författare)
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Boundary and lens rigidity of Lorentzian surfaces
- 1996
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Ingår i: Transactions of the American Mathematical Society. - 0002-9947 .- 1088-6850. ; 348, s. 2307-2329
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Tidskriftsartikel (refereegranskat)abstract
- Let g be a Lorentzian metric on the plane ℝ2 that agrees with the standard metric g0 = -dx2 + dy2 outside a compact set and so that there are no conjugate points along any time-like geodesic of (ℝ2, g). Then (ℝ2, g) and (ℝ2, g0) are isometric. Further, if (M*, g*) and (M*, p*) are two dimensional compact time oriented Lorentzian manifolds with space-like boundaries and so that all time-like geodesies of (M, g) maximize the distances between their points and (M, g) and (M*, g*) are "boundary isometric", then there is a conformal diffeomorphism between (M, g) and (M*, g*) and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.
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| 2. |
- Angel, O., et al.
(författare)
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THE PHASE TRANSITION FOR DYADIC TILINGS
- 2014
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Ingår i: Transactions of the American Mathematical Society. - 0002-9947 .- 1088-6850. ; 366:2, s. 1029-1046
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Tidskriftsartikel (refereegranskat)abstract
- A dyadic tile of order n is any rectangle obtained from the unit square by n successive bisections by horizontal or vertical cuts. Let each dyadic tile of order n be available with probability p, independent of the others. We prove that for p sufficiently close to 1, there exists a set of pairwise disjoint available tiles whose union is the unit square, with probability tending to 1 as n -> infinity, as conjectured by Joel Spencer in 1999. In particular, we prove that if p = 7/8, such a tiling exists with probability at least 1 - (3/4)(n). The proof involves a surprisingly delicate counting argument for sets of unavailable tiles that prevent tiling.
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| 3. |
- Bauer, Thomas, et al.
(författare)
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Cyclic coverings and higher order embeddings of algebraic varieties
- 2001
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Ingår i: Transactions of the American Mathematical Society. - 0002-9947 .- 1088-6850. ; 353:3, s. 877-891
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Tidskriftsartikel (refereegranskat)abstract
- In the present paper we study higher order embeddings in the context of cyclic coverings. Analyzing the positivity of the line bundle downstairs and its relationship with the branch divisor, we provide criteria for its pull-back to define an embedding of given order. We show that the obtained criteria are sharp. Finally, we apply them to various - sometimes seemingly unrelated-problems in algebraic geometry.
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| 4. |
- Beidar, K.I., et al.
(författare)
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On Frobenius algebras and the quantum Yang-Baxter equation
- 1997
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Ingår i: Transactions of the American Mathematical Society. - 0002-9947 .- 1088-6850. ; 349:9, s. 3823-3836
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that every Frobenius algebra over a commutative ring determines a class of solutions of the quantum Yang-Baxter equation, which forms a subbimodule of its tensor square. Moreover, this subbimodule is free of rank one as a left (right) submodule. An explicit form of a generator is given in terms of the Frobenius homomorphism. It turns out that the generator is invertible in the tensor square if and only if the algebra is Azumaya.
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| 5. |
- Duits, Maurice, et al.
(författare)
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Powers of large random unitary matrices and toeplitz determinants
- 2010
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Ingår i: Transactions of the American Mathematical Society. - 0002-9947 .- 1088-6850. ; 362:3, s. 1169-1187
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Tidskriftsartikel (refereegranskat)abstract
- We study the limiting behavior of Tr U-k(n), where U is an n x n random unitary matrix and k(n) is a natural number that may vary with n in an arbitrary way. Our analysis is based on the connection with Toeplitz determinants. The central observation of this paper is a strong Szego limit theorem for Toeplitz determinants associated to symbols depending on 71 in a particular way. As a consequence of this result, we find that for each fixed m is an element of N, the random variables Tr U-kj(n)/root min(k(j)(n),n), j = 1,..., m, converge to independent standard complex normals.
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| 6. |
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| 9. |
- Zhang, Genkai, 1963
(författare)
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Radon transform on symmetric matrix domains
- 2009
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Ingår i: Transactions of the American Mathematical Society. - 0002-9947 .- 1088-6850. ; 361:3, s. 1351-1369
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Tidskriftsartikel (refereegranskat)abstract
- Let K = R, C, H be the field of real, complex or quaternionic numbers and Mp,q(K) the vector space of all p × q-matrices. Let X be the matrix unit ball in Mn-r,r(K) consisting of contractive matrices. As a symmetric space, X = G/K = O(n - r, r)/O(n - r) × O(r), U(n - r, r)/U(n - r) × U(r) and respectively Sp(n - r,r)/Sp(n - r) × Sp(r). The matrix unit ball y0 in Mr'-r,r with r' ≤ n - 1 is a totally geodesic submanifold of X and let Y be the set of all G-translations of the submanifold y0. The set Y is then a manifold and an affine symmetric space. We consider the Radon transform Rf(y) for functions f ∈ C ∞ 0(X) defined by integration of f over the subset y, and the dual transform Rt F(x),x ∈ X for functions F(y) on Y. For 2r
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| 10. |
- Arioli, Gianni, et al.
(författare)
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Multibump solutions and critical groups
- 2009
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Ingår i: Transactions of the American Mathematical Society. - 0002-9947 .- 1088-6850. ; 361:6, s. 3159-3187
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Tidskriftsartikel (refereegranskat)abstract
- We consider the Newtonian system $-\ddot q+B(t)q = W_q(q,t)$ with $B$, $W$ periodic in $t$, $B$ positive definite, and show that for each isolated homoclinic solution $q_0$ having a nontrivial critical group (in the sense of Morse theory) multibump solutions (with $2\le k\le\iy$ bumps) can be constructed by gluing translates of $q_0$. Further we show that the collection of multibumps is semiconjugate to the Bernoulli shift. Next we consider the Schr\"odinger equation $-\Delta u+V(x)u = g(x,u)$ in $\RN$, where $V$, $g$ are periodic in $x_1,\ldots,x_N$, $\sigma(-\Delta+V)\subset (0,\iy)$, and we show that similar results hold in this case as well. In particular, if $g(x,u)=|u|^{2^*-2}u$, $N\ge 4$ and $V$ changes sign, then there exists a solution minimizing the associated functional on the Nehari manifold. This solution gives rise to multibumps if it is isolated.
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