共查询到20条相似文献,搜索用时 15 毫秒
1.
Holly J. Rosson 《Journal of Number Theory》2002,94(1):49-79
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Λ is an order of level M in H, we define theta series for each ideal I of Λ using the reduced norm on H. Using harmonic analysis on the completed algebra H∞ and the arithmetic of quaternion algebras, we establish a transformation law for these theta series. We also define analogs of the classical Hecke operators and show that in general, the Hecke operators map the theta series to a linear combination of theta series attached to different ideals, a generalization of the classical Eichler Commutation Relation. 相似文献
2.
Let k be a global function field over a finite field and let A be the ring of the elements in k regular outside a fixed place ∞. Let K be a global A-field of finite A-characteristic and let ? be a rank one Drinfeld A-module over K. Given any α∈K, we show that the set of places P of K for which α is a primitive root modulo P under the action of ? possesses a Dirichlet density. We also give conditions for this density to be positive. 相似文献
3.
Matteo Tommasini 《Topology and its Applications》2012,159(3):756-786
We define a 2-category structure (Pre-Orb) on the category of reduced complex orbifold atlases. We construct a 2-functor F from (Pre-Orb) to the 2-category (Grp) of proper étale effective groupoid objects over the complex manifolds. Both on (Pre-Orb) and (Grp) there are natural equivalence relations on objects: (a natural extension of) equivalence of orbifold atlases on (Pre-Orb) and Morita equivalence in (Grp). We prove that F induces a bijection between the equivalence classes of its source and target. 相似文献
4.
Christopher S. WithersSaralees Nadarajah 《Applied mathematics and computation》2011,218(5):2353-2363
Power series type solutions are given for a wide class of linear and q-dimensional nonlinear Volterra equations on Rp. The basic assumption on the kernel K(x, y) is that K(x, xt) has a power series in x. For example, this holds for any analytic kernel.The kernel may be strongly singular, provided certain constants are finite. One and only one such power series solution exists. Its coefficients are given by a simple iterative formula. In many cases this may be solved explicitly. In particular an explicit formula for the resolvent is given. 相似文献
5.
Michal Aharon Michael Elad Alfred M. Bruckstein 《Linear algebra and its applications》2006,416(1):48-67
A full-rank under-determined linear system of equations Ax = b has in general infinitely many possible solutions. In recent years there is a growing interest in the sparsest solution of this equation—the one with the fewest non-zero entries, measured by ∥x∥0. Such solutions find applications in signal and image processing, where the topic is typically referred to as “sparse representation”. Considering the columns of A as atoms of a dictionary, it is assumed that a given signal b is a linear composition of few such atoms. Recent work established that if the desired solution x is sparse enough, uniqueness of such a result is guaranteed. Also, pursuit algorithms, approximation solvers for the above problem, are guaranteed to succeed in finding this solution.Armed with these recent results, the problem can be reversed, and formed as an implied matrix factorization problem: Given a set of vectors {bi}, known to emerge from such sparse constructions, Axi = bi, with sufficiently sparse representations xi, we seek the matrix A. In this paper we present both theoretical and algorithmic studies of this problem. We establish the uniqueness of the dictionary A, depending on the quantity and nature of the set {bi}, and the sparsity of {xi}. We also describe a recently developed algorithm, the K-SVD, that practically find the matrix A, in a manner similar to the K-Means algorithm. Finally, we demonstrate this algorithm on several stylized applications in image processing. 相似文献
6.
This paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation AXB + CXTD = F. The basic idea is to decompose the matrix equation (system) under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving Ax = b and AXB = F. The analysis shows that when the matrix equation has a unique solution (under the sense of least squares), the iterative solution converges to the exact solution for any initial values. A numerical example verifies the proposed theorems. 相似文献
8.
Tom A. Fisher 《Journal of Number Theory》2003,98(1):105-155
We perform descent calculations for the families of elliptic curves whose m-torsion splits as μm×Z/mZ for m=3,4 or 5. These curves are parametrised by the modular curve X(m)?P1, whose cusps are arranged as the vertices of one of the Platonic solids. Following McCallum (Invent. Math. 93 (1988)) we write the Cassels-Tate pairing as a sum of local pairings. In the case m=5 our results extend the work of Beaver (J. Number Theory 82 (2000)). 相似文献
9.
Horst Herrlich 《Topology and its Applications》2009,156(11):1962-1965
For topological products the concept of canonical subbase-compactness is introduced, and the question analyzed under what conditions such products are canonically subbase-compact in ZF-set theory.Results: (1) Products of finite spaces are canonically subbase-compact iff AC(fin), the axiom of choice for finite sets, holds.(2) Products of n-element spaces are canonically subbase-compact iff AC(<n), the axiom of choice for sets with less than n elements, holds.(3) Products of compact spaces are canonically subbase-compact iff AC, the axiom of choice, holds.(4) All powers XI of a compact space X are canonically subbase compact iff X is a Loeb-space.These results imply that in ZF the implications
10.
A particular version of the singular value decomposition is exploited for an extensive analysis of two orthogonal projectors, namely FF† and F†F, determined by a complex square matrix F and its Moore-Penrose inverse F†. Various functions of the projectors are considered from the point of view of their nonsingularity, idempotency, nilpotency, or their relation to the known classes of matrices, such as EP, bi-EP, GP, DR, or SR. This part of the paper was inspired by Benítez and Rako?evi? [J. Benítez, V. Rako?evi?, Matrices A such that AA† − A†A are nonsingular, Appl. Math. Comput. 217 (2010) 3493-3503]. Further characteristics of FF† and F†F, with a particular attention paid on the results dealing with column and null spaces of the functions and their eigenvalues, are derived as well. Besides establishing selected exemplary results dealing with FF† and F†F, the paper develops a general approach whose applicability extends far beyond the characteristics provided therein. 相似文献
11.
Consider the system, of linear equations Ax = b where A is an n × n real symmetric, positive definite matrix and b is a known vector. Suppose we are given an approximation to x, ξ, and we wish to determine upper and lower bounds for ∥ x − ξ ∥ where ∥ ··· ∥ indicates the euclidean norm. Given the sequence of vectors {ri}ik = 0, where ri = Ari − 1 and r0 = b − Aξ, it is shown how to construct a sequence of upper and lower bounds for ∥ x − ξ ∥ using the theory of moments. 相似文献
12.
Y. MarkovA. Varchenko 《Advances in Mathematics》2002,166(1):100-147
The trigonometric KZ equations associated to a Lie algebra g depend on a parameter λ∈h where h⊂g is a Cartan subalgebra. A system of dynamical difference equations with respect to λ compatible with the KZ equations is introduced by V. Tarasov and the second author (2000, Internat. Math. Res. Notices15, 801-829). We prove that the standard hypergeometric solutions of the trigonometric KZ equations associated to slN also satisfy the dynamical difference equations. 相似文献
13.
We study a new mixed finite element of lowest order for general quadrilateral grids which gives optimal order error in the H(div)-norm. This new element is designed so that the H(div)-projection Πh satisfies ∇ · Πh = Phdiv. A rigorous optimal order error estimate is carried out by proving a modified version of the Bramble-Hilbert lemma for vector variables. We show that a local H(div)-projection reproducing certain polynomials suffices to yield an optimal L2-error estimate for the velocity and hence our approach also provides an improved error estimate for original Raviart-Thomas element of lowest order. Numerical experiments are presented to verify our theory. 相似文献
14.
In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwald frame. The geometry of such manifolds is controlled by three real invariants which live on T'M: two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular interest. Complex Berwald spaces coincide with Kähler spaces, in the two – dimensional case. We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the Kähler purely Hermitian spaces by the fact K = W = constant and I = 0. For the class of complex Berwald spaces we have K = W = 0. Finally, a classification of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained. 相似文献
15.
Jonq Juang 《Journal of Mathematical Analysis and Applications》2008,338(1):358-364
Let be a class of piecewise linear maps associated with a transition matrix A. In this paper, we prove that if fA,x∈LA, then the Liapunov exponent λ(x) of fA,x is equal to a measure theoretic entropy hmA,x of fA,x, where mA,x is a Markov measure associated with A and x. The Liapunov exponent and the entropy are computable by solving an eigenvalue problem and can be explicitly calculated when the transition matrix A is symmetric. Moreover, we also show that maxxλ(x)=maxxhmA,x=log(λ1), where λ1 is the maximal eigenvalue of A. 相似文献
16.
Erhard Aichinger 《Journal of Pure and Applied Algebra》2006,205(1):74-93
Let V be a finite expanded group, e.g., a ring or a group. We investigate the near-ring 〈C0(V);+,°〉 of zero-preserving congruence-preserving functions on V. We obtain some information on the structure of 〈C0(V);+,°〉 from the lattice of ideals of V: for example, the number of maximal ideals of 〈C0(V);+,°〉 is completely determined by the isomorphism class of the ideal lattice of V. 相似文献
17.
Alexandre B. Tchernev 《Advances in Mathematics》2007,208(1):75-134
Let k be a field, let R=k[x1,…,xm] be a polynomial ring with the standard Zm-grading (multigrading), let L be a Noetherian multigraded R-module, and let be a finite free multigraded presentation of L over R. Given a choice S of a multihomogeneous basis of E, we construct an explicit canonical finite free multigraded resolution T•(Φ,S) of the R-module L. In the case of monomial ideals our construction recovers the Taylor resolution. A main ingredient of our work is a new linear algebra construction of independent interest, which produces from a representation ? over k of a matroid M a canonical finite complex of finite dimensional k-vector spaces T•(?) that is a resolution of Ker?. We also show that the length of T•(?) and the dimensions of its components are combinatorial invariants of the matroid M, and are independent of the representation map ?. 相似文献
18.
For a given matrix A, a matrix P such that PA = A is said to be a local identity, and such that P2A = PA is said to be a local idempotent. In the paper, some simple properties of such operators are presented. Their relation to the best linear unbiased estimation in the general Gauss-Markov model is also demonstrated. 相似文献
19.
Let R and S be commuting n-tuples of operators. We will give some spectral relations between RS and SR that extend the case of single operators. We connect the Taylor spectrum, the Fredholm spectrum and some other joint spectra of RS and SR. Applications to Aluthge transforms of commuting n-tuples are also provided. 相似文献
20.