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81.
Vincenzo de Filippis 《数学学报(英文版)》2009,25(12):1965-1974
Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g(x) = x for all x ∈ R, or char(R) = 2, R satisfies the standard identity s4(x1, x2, x3, x4), L is commutative and u2 ∈ Z(R), for any u C L. We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set [I, I], where I is a non-zero right ideal of R. 相似文献
82.
George E. Andrews 《数学学报(英文版)》2009,25(9):1437-1442
A variety of interesting connections with modular forms, mock theta functions and Rogers- Ramanujan type identities arise in consideration of partitions in which the smaller integers are repeated as summands more often than the larger summands. In particular, this concept leads to new interpretations of the Rogers Selberg identities and Bailey's modulus 9 identities. 相似文献
83.
We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form. 相似文献
84.
In this paper we will use the residue theorem of elliptic functions to prove some theta function identities of Ramanujan. We also derive some new identities by this method. 相似文献
85.
In this paper we shall first introduce the Pascal k-eliminated functional matrices Pn,k[xyz] and CPn,k[xyz]. Then, using these matrices we obtain several important combinatorial identities. Finally, using the matrix inversion of Pn,k[xyz] and CPn,k[xyz], we derive an interesting formula for Eulerian numbers [7] 相似文献
86.
Peter J. Wood 《Proceedings of the American Mathematical Society》2000,128(2):445-451
In this paper we provide a necessary condition for a closed ideal in the Fourier algebra of a locally compact amenable group to be completely complemented. The classification of completely complemented ideals is completed in the case of an amenable discrete group. We also investigate the ideals possessing a bounded approximate identity.
87.
Versions of Bailey's lemma which change the base from q to q
2 or q
3 are given. Iterates of these versions give many new versions of multisum Rogers-Ramanujan identities. 相似文献
88.
Using a new graphical representation for partitions, the author obtains a family of partition identities associated with partitions into distinct parts of an arithmetic progression, or, more generally, with partitions into distinct parts of a set that is a finite union of arithmetic progressions associated with a modular sum-free Sidon set. Partition identities are also constructed for sets associated with modular sum-free sets. 相似文献
89.
The present paper offers two likely neglected applications of the classical Lagrange expansion formula.One is a unified approach to some age-old derivative identities originally due to Pfaff and Cauchy.Another is two explicit matrix inversions which may serve as common generalizations of some known inverse series relations. 相似文献
90.
利用算符代数中的分析方法,得到了多模海森堡(Heisenberg)代数中的BCH公式和压缩算符的展开式。 相似文献