基于纤维丛表述的李变换群延拓群算子

本文提出积流形李变换群延拓群的概念，并应用纤维丛方法解决延拓群算子中的系数问题，进而讨论其在黎曼流形中的一个应用．     

带作用的群系的临界结构

在本文中，我们讨论了带作用群的群系的临界结构，给出了处理允许某些作用群的群的问题的一般方法，作为应用，我们特别给出了关于幂零群及ｐ－幂零群的一些结果。     

关于n-亚换位子群

本文从n-亚换位子群的定义出发，得到了它的几条重要性质，作为应用，给出了一个群为n-Abelian群的一个充要条件及p-Abelian群的一个判别法。     

Coleman自同构群的投射极限

在这篇注记中，利用群的投射极限性质给出了有限可解群的Coleman自同构群的一个具体构造.作为应用，证明了二面体群的Coleman外自同构群或者是1或者是一个初等阿贝尔2-群.     

酉群的热核及应用

本文显式构造出了酉群Ｕ（ｎ），特殊酉群的ＳＵ（ｎ）的热核，作为应用定出了酉群的谱．     

粗糙不变子群的若干性质与粗糙商群

讨论粗糙集理论在代数系统——群上的应用。基于有关粗糙群、粗糙子群和粗糙不变子群的基本概念以及粗糙子群的一些性质和有关粗糙不变子群的定理，讨论了粗糙不变子群的若干性质和粗糙商群的概念，并给出了这些性质的严格证明。     

Coxter群中二阶元的判定及其在仿射Weyl群中的应用

本文首先给出Coxter群中二阶元的判定方法，应用到E6型有限wey1群及A21^(1)型仿射Wey1群，给出了其二阶元的共轭标准形与共轭类数．     

张量积的代数K－理论及其应用

本文研究了两个代数张量积的Ｇｒｏｔｈｅｎｄｉｅｃｋ群和Ｗｈｉｔｅｈｅａｄ群首先构作三个群同态，并证明：若Ｒ为增广Ａ－代数，则存在的子群Ｃ使得，并存在的子群Ｄ使得．然后给出在群代数和包络代数方面的应用，最后考虑的增广代数的情形．     

有限值l-群与特殊值l-群等价的一个充要条件

G是l-群，本文主要证明：G是有限值的当且仅当G是特殊值的且C（G）＝K（G），作为应用，我们证明了G是有基的l-群，则两者之间是等价的。     

高校应用数学学报──第9卷（1994年）B辑（英文版）第4期目次和提要

高校应用数学学报──第９卷（１９９４年）Ｂ辑（英文版）第４期目次和提要微分方程的对称和群不变解田畴（中国科技大学数学系）该文首先给出微分方程的对称和单参数不变群的关系的一个证明；其次给出微分方程的对称和群不变解的关系；最后，作为应用对Ｋｄｖ方程讨论了...     

Transformation formula for a double Clausenian hypergeometric series,its q-analogue,and its invariance group

A transformation formula for a double basic hypergeometric series of type Φ_0:2;2^1:2;2 is derived. This transformation yields a double series analogue of Sears’ transformation for a terminating ₃Φ₂ series. In the limit q→1, the formula reduces to a transformation for a terminating double Clausenian hypergeometric series of unit argument (one of the proper Kampé de Fériet series, F_0:2;2^1:2;2(1,1)). This formula is a double series analogue of Whipple's terminating ₃F₂ transformation. This transformation gives rise to a transformation group (the invariance group) acting on the parameters of the double series. The invariance group is examined and shown to be a subgroup of a double copy of the symmetries of the square.     

Elementary derivations of identities for bilateral basic hypergeometric series

We give elementary derivations of several classical and some new summation and transformation formulae for bilateral basic hypergeometric series. For motivation, we review our previous simple proof (Proc. Amer. Math. Soc. 130 (2002), 1103-1111) of Bailey's very-well-poised ₆y₆_6\psi_6 summation. Using a similar but different method, we now give elementary derivations of some transformations for bilateral basic hypergeometric series. In particular, these include M. Jackson's very-well-poised ₈y₈_8\psi_8 transformation, a very-well-poised ₁₀y₁₀_{10}\psi_{10} transformation, by induction, Slater's general transformation for very-well-poised _2ry_2r_{2r}\psi_{2r} series, and Slater's transformation for general _ry_r_{r}\psi_{r} series. Finally, we derive some new transformations for bilateral basic hypergeometric series of a specific type.     

The Kμ-Transformation on McBride's Spaces of Generalized Functions

In this paper we define the K_μ- transformation on certain spaces of generalized functions introduced by A.C. McBride by employing the kernel method. we also establish relations between the generalized K_μ- transformation and certain fractional integral operators.     

An elliptic hypergeometric integral with <Emphasis Type="Italic">W</Emphasis>(<Emphasis Type="Italic">F</Emphasis><Subscript>4</Subscript>) symmetry

In this article we give a new transformation between elliptic hypergeometric beta integrals, which gives rise to a Weyl group symmetry of type F ₄. The transformation is a generalization of a series transformation discovered by Langer, Schlosser, and Warnaar (SIGMA 5:055, 2009). Moreover we consider various limits of this transformation to basic hypergeometric functions obtained by letting p tend to 0.     

On one transformation of parameter-spaces of real interpolation method

In connection with estimation of interpolation orbits and coorbits we introduce a new transformation acting in the class of all parameter-space of real interpolation K-method. We “calculate” the result of the transformation of classical parameters. It is revealed that the transformation of weighted L₁-spaces leads to Orlicz spaces.     

On projective equivalence of invariant subspace lattices

For i = 1,2, let A_i be a linear transformation on a complex vector space and let σ be a lattice isomorphism from the invariant subspace lattice of A₁ onto the invariant subspace lattice of A₂. We determine the conditions under which σ is implemented by a linear or conjugate linear transformation (or a sum of these two kinds).     

Darboux Transformation and Exact Solutions for Two Dimensional A 2n−1 (2) Toda Equations

The Darboux transformation for the two dimensional A⁽²⁾_2n-1 Toda equations is constructed so that it preserves all the symmetries of the corresponding Lax pair. The expression of exact solutions of the equation is obtained by using Darboux transformation.     

Resolution of Corank 1 Singularities of a Generic Front

We construct a resolution of singularities for wave fronts having only stable singularities of corank 1. It is based on a transformation that takes a given front to a new front with singularities of the same type in a space of smaller dimension. This transformation is defined by the class A_µ of Legendre singularities. The front and the ambient space obtained by the A_µ-transformation inherit topological information on the closure of the manifold of singularities A_µ of the original front. The resolution of every (reducible) singularity of a front is determined by a suitable iteration of A_µ-transformations. As a corollary, we obtain new conditions for the coexistence of singularities of generic fronts.     

A classification of maximal idempotent-generated subsemigroups of finite orientation-preserving singular partial transformation semigroups

In this paper we describe the maximal idempotent-generated subsemigroups of the finite orientation-preserving singular partial transformation semigroup SPOP _n and obtain their complete classification. We also obtain a classification of the maximal idempotent-generated subsemigroups of the finite order-preserving singular partial transformation semigroup PO^k_n\mathit{PO}^{k}_{n} with respect to ≤ _k .     

A transformation from Hausdorff to Stieltjes moment sequences

We introduce a non-linear injective transformation τ from the set of non-vanishing normalized Hausdorff moment sequences to the set of normalized Stieltjes moment sequences by the formulaT[(a _n ) _n=1 ^∞ ] _n = 1/a₁ ...a _n . Special cases of this transformation have appeared in various papers on exponential functionals of Lévy processes, partly motivated by mathematical finance. We give several examples of moment sequences arising from the transformation and provide the corresponding measures, some of which are related toq-series.