共查询到10条相似文献,搜索用时 93 毫秒
1.
Luis Paris 《Proceedings of the American Mathematical Society》1997,125(3):731-738
Let be a Coxeter system, and let be a subset of . The subgroup of generated by is denoted by and is called a parabolic subgroup. We give the precise definition of the commensurator of a subgroup in a group. In particular, the commensurator of in is the subgroup of in such that has finite index in both and . The subgroup can be decomposed in the form where is finite and all the irreducible components of are infinite. Let be the set of in such that for all . We prove that the commensurator of is . In particular, the commensurator of a parabolic subgroup is a parabolic subgroup, and is its own commensurator if and only if .
2.
Jø rgen Ellegaard Andersen 《Proceedings of the American Mathematical Society》1997,125(5):1511-1515
Let be a compact oriented surface with or without boundary components. In this note we prove that if then there exist infinitely many integers such that there is a point in the moduli space of irreducible flat connections on which is fixed by any orientation preserving diffeomorphism of . Secondly we prove that for each orientation preserving diffeomorphism of and each there is some such that has a fixed point in the moduli space of irreducible flat connections on . Thirdly we prove that for all there exists an integer such that the 'th power of any diffeomorphism fixes a certain point in the moduli space of irreducible flat connections on .
3.
Diane Benjamin 《Proceedings of the American Mathematical Society》1997,125(10):2831-2837
Given a finite solvable group , we say that has property if every set of distinct irreducible character degrees of is (setwise) relatively prime. Let be the smallest positive integer such that satisfies property . We derive a bound, which is quadratic in , for the total number of irreducible character degrees of . Three exceptional cases occur; examples are constructed which verify the sharpness of the bound in each of these special cases.
4.
5.
W. Bulla F. Gesztesy W. Renger B. Simon 《Proceedings of the American Mathematical Society》1997,125(5):1487-1495
We study the eigenvalue spectrum of Dirichlet Laplacians which model quantum waveguides associated with tubular regions outside of a
bounded domain. Intuitively, our principal new result in two dimensions asserts that any domain obtained by adding an arbitrarily small ``bump' to the tube (i.e., , open and connected, outside a bounded region) produces at least one positive eigenvalue below the essential spectrum of the Dirichlet Laplacian . For sufficiently small ( abbreviating Lebesgue measure), we prove uniqueness of the ground state of and derive the ``weak coupling' result using a Birman-Schwinger-type analysis. As a corollary of these results we obtain the following surprising fact: Starting from the tube with Dirichlet boundary conditions at , replace the Dirichlet condition by a Neumann boundary condition on an arbitrarily small segment , , of . If denotes the resulting Laplace operator in , then has a discrete eigenvalue in no matter how small is.
bounded domain. Intuitively, our principal new result in two dimensions asserts that any domain obtained by adding an arbitrarily small ``bump' to the tube (i.e., , open and connected, outside a bounded region) produces at least one positive eigenvalue below the essential spectrum of the Dirichlet Laplacian . For sufficiently small ( abbreviating Lebesgue measure), we prove uniqueness of the ground state of and derive the ``weak coupling' result using a Birman-Schwinger-type analysis. As a corollary of these results we obtain the following surprising fact: Starting from the tube with Dirichlet boundary conditions at , replace the Dirichlet condition by a Neumann boundary condition on an arbitrarily small segment , , of . If denotes the resulting Laplace operator in , then has a discrete eigenvalue in no matter how small is.
6.
Gennady Lyubeznik 《Proceedings of the American Mathematical Society》1997,125(7):1941-1944
We show that for fixed and the set of Bernstein-Sato polynomials of all the polynomials in at most variables of degrees at most is finite. As a corollary, we show that there exists an integer depending only on and such that generates as a module over the ring of the -linear differential operators of , where is an arbitrary field of characteristic 0, is the ring of polynomials in variables over and is an arbitrary non-zero polynomial of degree at most .
7.
Tejinder S. Neelon 《Proceedings of the American Mathematical Society》1997,125(9):2531-2535
Analyticity of solutions , of systems of real analytic equations , is studied. Sufficient conditions for and power series solutions to be real analytic are given in terms of iterative Jacobian ideals of the analytic ideal generated by . In a special case when the 's are independent of , we prove that if a solution satisfies the condition , then is necessarily real analytic.
8.
Hypersurfaces in a sphere with constant mean curvature 总被引:13,自引:0,他引:13
Zhong Hua Hou 《Proceedings of the American Mathematical Society》1997,125(4):1193-1196
Let be a closed hypersurface of constant mean curvature immersed in the unit sphere . Denote by the square of the length of its second fundamental form. If , is a small hypersphere in . We also characterize all with .
9.
Gabriel Navarro Wolfgang Willems 《Proceedings of the American Mathematical Society》1997,125(6):1589-1591
Let and be distinct prime numbers and let be a finite group. If is a -block of and is a -block, we study when the set of ordinary irreducible characters in the blocks and coincide.
10.
Pavlos Tzermias 《Proceedings of the American Mathematical Society》1997,125(3):663-668
Let denote the Jacobian of the Fermat curve of exponent 5 and let . We compute the groups , , , where is the unique quadratic subfield of . As an application, we present a new proof that there are no -rational points on the 5-th Fermat curve, except the so called ``points at infinity".