共查询到20条相似文献,搜索用时 15 毫秒
1.
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases correspond to the type of equations where the commutative property of the coefficient matrices with respect to the dependent variables and the first-order derivatives in the considered system does not hold. A discussion of the results as well as a note on the extension to linear systems of second-order ordinary differential equations with more than two equations are given. 相似文献
2.
Vladislav V. Goldberg 《Acta Appl Math》2004,80(1):35-55
We investigate the linearizability problem for different classes of 4-webs in the plane. In particular, we apply the linearizability conditions, recently found by Akivis, Goldberg and Lychagin, to confirm that a 4-web MW (Mayrhofer's web) with equal curvature forms of its 3-subwebs and a nonconstant basic invariant is always linearizable (this result was first obtained by Mayrhofer in 1928; it also follows from the papers of Nakai). Using the same conditions, we further prove that such a 4-web with a constant basic invariant (Nakai's web) is linearizable if and only if it is parallelizable. Next we study four classes of the so-called almost parallelizable 4-webs APW
a
,a=1,2,3,4 (for them the curvature K=0 and the basic invariant is constant on the leaves of the web foliation X
a
), and prove that a 4-web APW
a
is linearizable if and only if it coincides with a 4-web MW
a
of the corresponding special class of 4-webs MW. The existence theorems are proved for all the classes of 4-webs considered in the paper. 相似文献
3.
S. Moyo S.V. Meleshko G.F. Oguis 《Communications in Nonlinear Science & Numerical Simulation》2013,18(11):2972-2983
We give a complete group classification of the general case of linear systems of two second-order ordinary differential equations excluding the case of systems which are studied in the literature. This paper gives the initial step in the study of nonlinear systems of two second-order ordinary differential equations. It can also be extended to systems of equations with more than two equations. Furthermore the complete group classification of a system of two linear second-order ordinary differential equations is done. Four cases of linear systems of equations with inconstant coefficients are obtained. 相似文献
4.
Stavros Kontogiorgis Christodoulos Sophocleous 《Mathematical Methods in the Applied Sciences》2017,40(5):1746-1756
Group classification of a class of systems of diffusion equations is carried out. Arbitrary elements that appear in the system depend on two variables. All forms of the arbitrary elements that provide additional Lie symmetries are determined. Equivalence transformations are used to simplify the analysis. Examples of similarity reductions are presented. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
5.
Yanyan Gao 《代数通讯》2013,41(7):2800-2812
Let KG be the group ring of a group G over a field K. Let * be an involution of a group G extended linearly to the group ring KG. Suppose that G is a torsion group without 2-elements and K is a field with characteristic different from 2. We prove that KG is Lie *-nilpotent if and only if KG is Lie nilpotent. 相似文献
6.
Meena Sahai 《代数通讯》2013,41(3):817-828
ABSTRACT Let K be a field of characteristic p ≠ 2 and let G be any group. A characterization of group algebras KG satisfying the Lie identity [[x,y],[u,v],[z,t]] = 0 for all x,y,u,v,z,t ? KG is obtained. 相似文献
7.
8.
Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal
subspaces associated to the standard modules for
satisfy certain classical recursion formulas of Rogers and Selberg. These recursions were exploited by Andrews in connection
with Gordon’s generalization of the Rogers–Ramanujan identities and with Andrews’ related identities. The present work generalizes
the authors’ previous work on intertwining operators and the Rogers–Ramanujan recursion.
2000 Mathematics Subject Classification Primary—17B69, 39A13
S. Capparelli gratefully acknowledges partial support from MIUR (Ministero dell’Istruzione, dell’Università e della Ricerca).
J. Lepowsky and A. Milas gratefully acknowledge partial support from NSF grant DMS-0070800. 相似文献
9.
Let G be a group and let K be a field of characteristic p>0. Lie nilpotent group algebras of strong Lie nilpotency index up to 11 have already been classified. In this paper, our aim is to classify the group algebras KG which are strongly Lie nilpotent of index 12 or 13. 相似文献
10.
本文给出三体在—般情形下的伴随李群系与守恒量,并在特殊的力势函数下求出了三体扩展的伴随李群系,进一步利用这个扩展的伴随李群系求出除10个经典守恒外的更多守恒量. 相似文献
11.
旗传递t-设计的分类是代数组合学的一个重要课题.本文主要讨论了旗传递5-(v,k,3)设计.由P.J.Cameron和C.E.Praeger的结论可知,此时设计的自同构群是3-齐次群.本文利用3-齐次群的分类,证明了设计的自同构群不能是仿射型群. 相似文献
12.
Zeng Guangxing 《代数通讯》2013,41(12):5847-5856
The aim of this paper is to develop the study of modules in real algebra. By introducing two kinds of reality for modules over commutative rings, we establish some results on semireal modules and real modules. Our results involve real radicals of submodules and orderings on modules. 相似文献
13.
14.
Chaudry Masood Khalique Abdullahi R. Adem 《Applied mathematics and computation》2010,216(10):2849-2496
In this paper, Lie group analysis is employed to derive some exact solutions of a generalized (3 + 1)-dimensional Kadomtsev-Petviashvili equation which describes the dynamics of solitons and nonlinear waves in plasmas and superfluids. 相似文献
15.
Timothy J. Ford 《代数通讯》2013,41(9):3277-3298
We study algebra classes and divisor classes on a normal affine surface of the form z 2 = f(x, y). The affine coordinate ring is T = k[x, y, z]/(z 2 ? f), and if R = k[x, y][f ?1] and S = R[z]/(z 2 ? f), then S is a quadratic Galois extension of R. If the Galois group is G, we show that the natural map H1(G, Cl(T)) → H1(G, Pic(S)) factors through the relative Brauer group B(S/R) and that all of the maps are onto. Sufficient conditions are given for H1(G, Cl(T)) to be isomorphic to B(S/R). The groups and maps are computed for several examples. 相似文献
16.
17.
Ignacio Bajo 《Geometriae Dedicata》1997,66(3):281-291
Lie groups with bi-invariant semi-Riemannian metrics are considered. We study the decomposition of the algebra of prederivations of a direct sum of Lie algebras and derive some results on the isotropy group of a bi-invariant product Lie group. We also give necessary and sufficient conditions to ensure that all isometries of a complex Lie group, endowed with a bi-invariant Norden metric, are holomorphic. 相似文献
18.
Zsolt Balogh 《代数通讯》2013,41(2):315-324
In this article the Lie derived length and the strong Lie derived length of group algebras are determined in the case when the derived subgroup of the basic group is cyclic of odd order. As a consequence, we have the characterization of the group algebras of minimal strong Lie derived length. 相似文献
19.
二步幂零Lie群上sub-Laplace算子的谱 总被引:1,自引:0,他引:1
本文首先研究包括Greiner算子和二步幂零Lie群上sub Laplace算子L在内的广义齐次线性偏微分算子的谱,然后利用酉表示理论确定了算子L的谱结构,并深化了K.Furutani,K.Sagami,N.Otsuki关于Laplace算子的有关结果. 相似文献
20.
We study nonlinear heat and wave equations on a Lie group. The noise is assumed to be a spatially homogeneous Wiener process. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise. 相似文献