共查询到20条相似文献,搜索用时 31 毫秒
1.
So Ryoung Park Jinsoo Bae Hyun Gu Kang Iickho Song. 《Mathematics of Computation》2008,77(262):1135-1151
In this paper, it is shown that the number of partitions of a nonnegative integer with parts can be described by a set of polynomials of degree in , where denotes the least common multiple of the integers and denotes the quotient of when divided by . In addition, the sets of the polynomials are obtained and shown explicitly for and .
2.
We study Noether's problem for various subgroups of the normalizer of a group generated by an -cycle in , the symmetric group of degree , in three aspects according to the way they act on rational function fields, i.e., , and . We prove that it has affirmative answers for those containing properly and derive a -generic polynomial with four parameters for each . On the other hand, it is known in connection to the negative answer to the same problem for that there does not exist a -generic polynomial for . This leads us to the question whether and how one can describe, for a given field of characteristic zero, the set of -extensions . One of the main results of this paper gives an answer to this question.
3.
Karim Belabas Francisco Diaz y Diaz Eduardo Friedman. 《Mathematics of Computation》2008,77(262):1185-1197
Assuming the Generalized Riemann Hypothesis, Bach has shown that the ideal class group of a number field can be generated by the prime ideals of having norm smaller than . This result is essential for the computation of the class group and units of by Buchmann's algorithm, currently the fastest known. However, once has been computed, one notices that this bound could have been replaced by a much smaller value, and so much work could have been saved. We introduce here a short algorithm which allows us to reduce Bach's bound substantially, usually by a factor 20 or so. The bound produced by the algorithm is asymptotically worse than Bach's, but favorable constants make it useful in practice.
4.
Harald Meyer. 《Mathematics of Computation》2008,77(263):1801-1821
Let be a prime. We denote by the symmetric group of degree , by the alternating group of degree and by the field with elements. An important concept of modular representation theory of a finite group is the notion of a block. The blocks are in one-to-one correspondence with block idempotents, which are the primitive central idempotents of the group ring , where is a prime power. Here, we describe a new method to compute the primitive central idempotents of for arbitrary prime powers and arbitrary finite groups . For the group rings of the symmetric group, we show how to derive the primitive central idempotents of from the idempotents of . Improving the theorem of Osima for symmetric groups we exhibit a new subalgebra of which contains the primitive central idempotents. The described results are most efficient for . In an appendix we display all primitive central idempotents of and for which we computed by this method.
5.
Vassil Dimitrov Laurent Imbert Pradeep K. Mishra. 《Mathematics of Computation》2008,77(262):1075-1104
We describe an algorithm for point multiplication on generic elliptic curves, based on a representation of the scalar as a sum of mixed powers of and . The sparseness of this so-called double-base number system, combined with some efficient point tripling formulae, lead to efficient point multiplication algorithms for curves defined over both prime and binary fields. Side-channel resistance is provided thanks to side-channel atomicity.
6.
Valeriu Soltan 《Proceedings of the American Mathematical Society》2008,136(3):1071-1081
We show that the boundary of an -dimensional closed convex set , possibly unbounded, is a convex quadric surface if and only if the middle points of every family of parallel chords of lie in a hyperplane. To prove this statement, we show that the boundary of is a convex quadric surface if and only if there is a point such that all sections of by 2-dimensional planes through are convex quadric curves. Generalizations of these statements that involve boundedly polyhedral sets are given.
7.
Lidia Angeleri Hü gel Silvana Bazzoni Dolors Herbera 《Transactions of the American Mathematical Society》2008,360(5):2409-2421
Let be a commutative domain. We prove that an -module is projective if and only if for any torsion module . This answers in the affirmative a question raised by Kaplansky in 1962.
8.
B. C. Carlson. 《Mathematics of Computation》2008,77(263):1615-1621
The 12 inverse Jacobian elliptic functions are expanded in power series by using properties of the symmetric elliptic integral of the first kind. Suitable notation allows three series to include all 12 cases, three of which have been given previously. All coefficients are polynomials in the modulus that are homogeneous variants of Legendre polynomials. The four series in each of three subsets have the same coefficients in terms of .
9.
Sunil K. Chebolu J. Daniel Christensen Já n Miná c 《Proceedings of the American Mathematical Society》2008,136(4):1171-1179
A ghost in the stable module category of a group is a map between representations of that is invisible to Tate cohomology. We show that the only non-trivial finite -groups whose stable module categories have no non-trivial ghosts are the cyclic groups and . We compare this to the situation in the derived category of a commutative ring. We also determine for which groups the second power of the Jacobson radical of is stably isomorphic to a suspension of .
10.
Baris Coskunuzer 《Proceedings of the American Mathematical Society》2008,136(4):1427-1432
Let be a Gromov hyperbolic -space with cocompact metric, and the sphere at infinity of . We show that for any simple closed curve in , there exists a properly embedded least area plane in spanning . This gives a positive answer to Gabai's conjecture from 1997. Soma has already proven this conjecture in 2004. Our technique here is simpler and more general, and it can be applied to many similar settings.
11.
Oliver Jenkinson 《Proceedings of the American Mathematical Society》2008,136(3):1023-1027
For an irrational number , let denote its -th continued fraction inverse complete quotient, obtained by deleting the first partial quotients. For any positive real number , we establish the optimal linear bound on the sum of the -th powers of the first complete quotients. That is, we find the smallest constants such that for all and all irrationals .
12.
Sé rgio Mendonç a Heudson Mirandola 《Proceedings of the American Mathematical Society》2008,136(3):1065-1070
Let be an immersion of an -dimensional connected manifold in an -dimensional connected complete Riemannian manifold without conjugate points. Assume that the union of geodesics tangent to does not cover . Under these hypotheses we have two results. The first one states that is simply connected provided that the universal covering of is compact. The second result says that if is a proper embedding and is simply connected, then is a normal graph over an open subset of a geodesic sphere. Furthermore, there exists an open star-shaped set such that is a manifold with the boundary .
13.
Daniel H. Luecking 《Proceedings of the American Mathematical Society》2008,136(5):1717-1723
Given a complex Borel measure with compact support in the complex plane the sesquilinear form defined on analytic polynomials and by , determines an operator from the space of such polynomials to the space of linear functionals on . This operator is called the Toeplitz operator with symbol . We show that has finite rank if and only if is a finite linear combination of point masses. Application to Toeplitz operators on the Bergman space is immediate.
14.
Ariane M. Masuda Michael E. Zieve 《Proceedings of the American Mathematical Society》2008,136(4):1403-1408
We find all polynomials over a field such that and are linear and . We also solve the same problem for rational functions , in case the field is algebraically closed.
15.
Nihat Gö khan Gö gü s 《Transactions of the American Mathematical Society》2008,360(5):2693-2707
A bounded domain is called -regular if the plurisubharmonic envelope of every continuous function on extends continuously to . We show using Gauthier's Fusion Lemma that a domain is locally -regular if and only if it is -regular.
16.
Steffen Sagave 《Transactions of the American Mathematical Society》2008,360(5):2767-2808
We construct and examine the universal Toda bracket of a highly structured ring spectrum . This invariant of is a cohomology class in the Mac Lane cohomology of the graded ring of homotopy groups of which carries information about and the category of -module spectra. It determines for example all triple Toda brackets of and the first obstruction to realizing a module over the homotopy groups of by an -module spectrum.
For periodic ring spectra, we study the corresponding theory of higher universal Toda brackets. The real and complex -theory spectra serve as our main examples.
17.
David R. Pitts 《Proceedings of the American Mathematical Society》2008,136(5):1757-1768
We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if and are operator algebras, then any bounded epimorphism of onto is completely bounded provided that contains a norming -subalgebra. We use this result to give some insights into Kadison's Similarity Problem: we show that every faithful bounded homomorphism of a -algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a -algebra is similar to a -representation precisely when the image operator algebra -norms itself. We give two applications to isometric isomorphisms of certain operator algebras. The first is an extension of a result of Davidson and Power on isometric isomorphisms of CSL algebras. Secondly, we show that an isometric isomorphism between subalgebras of -diagonals () satisfying extends uniquely to a -isomorphism of the -algebras generated by and ; this generalizes results of Muhly-Qiu-Solel and Donsig-Pitts.
18.
Let be an imaginary quadratic field with ring of integers , where is a square free integer such that , and let is a linear code defined over . The level theta function of is defined on the lattice , where is the natural projection. In this paper, we prove that:
i) for any such that , and have the same coefficients up to ,
ii) for , determines the code uniquely,
iii) for , there is a positive dimensional family of symmetrized weight enumerator polynomials corresponding to .
19.
Let be a Riemannian compact -manifold. We know that for any , there exists such that for any , , being the smallest constant possible such that the inequality remains true for any . We call the ``first best constant'. We prove in this paper that it is possible to choose and keep a finite constant. In other words we prove the existence of a ``second best constant' in the exceptional case of Sobolev inequalities on compact Riemannian manifolds.
20.
In this paper, we establish two fixed point theorems of Krasnoselskii type for the sum of , where is a compact operator and may not be injective. Our results extend previous ones. As an application, we apply such results to obtain some existence results of periodic solutions for delay integral equations and then give three instructive examples.