where angels fear to tread : Tracing the Journey of the Female Poet in Aurora Leigh

Through Aurora Leigh, Elizabeth Barrett Browning explores the role of female poets as agents of social change in the Victorian society. During the Victorian period, the role of women was largely confined to the domestic setting. While women were allowed to write, female writers were limited to the realm of novels, which was perceived by the Victorian society to be the less distinguished genre. In writing Aurora Leigh, Barrett Browning challenged this gender stereotype by producing a novel-poem that unites the feminine voice with masculine authority and superiority. Like Barrett Browning, Aurora Leigh, in her fictional role as a writer, also challenges the same stereotypes. She seeks to redefine poetry, which is the domain of man. In rejecting Romney’s initial marriage proposal, Aurora Leigh also rebels against the stereotypical gender roles. At the same time, in doing so, she inadvertently rejects Romney’s plan for social change that involves only the physical aspect. Instead, in pursuing her career as a poet, Aurora Leigh finds herself in a position to bring about social change on a level that transcends the physical. By telling the story of Marian Erle, Aurora Leigh has the power to change the plight of women in the Victorian society. Finally, being women themselves, both Barrett Browning and Aurora Leigh can speak up for the Victorian women even more effectively

Commutators and Anti-Commutators of Idempotents in Rings

We show that a ring $\,R\,$ has two idempotents $\,e,e'\,$ with an invertible commutator $\,ee'-e'e\,$ if and only if $\,R \cong {\mathbb M}_2(S)\,$ for a ring $\,S\,$ in which $\,1\,$ is a sum of two units. In this case, the "anti-commutator" $\,ee'+e'e\,$ is automatically invertible, so we study also the broader class of rings having such an invertible anti-commutator. Simple artinian rings $\,R\,$ (along with other related classes of matrix rings) with one of the above properties are completely determined. In this study, we also arrive at various new criteria for {\it general\} $\,2\times 2\,$ matrix rings. For instance, $R\,$ is such a matrix ring if and only if it has an invertible commutator $\,er-re\,$ where $\,e^2=e$.Comment: 21 page

On vanishing sums of m \,m\,th roots of unity in finite fields

In an earlier work, the authors have determined all possible weights $n$ for which there exists a vanishing sum $\zeta_1+\cdots +\zeta_n=0$ of $m$th roots of unity $\zeta_i$ in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic $p$. For given $m$ and $p$, results are obtained on integers $n_0$ such that all integers $n\geq n_0$ are in the ``weight set'' $W_p(m)$. The main result $(1.3)$ in this paper guarantees, under suitable conditions, the existence of solutions of $x_1^d+\cdots+x_n^d=0$ with all coordinates not equal to zero over a finite field

Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau [arXiv:1006.3614]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.Comment: 8 pages in Revtex 4.1 preprint format, to appear in Journal of Inequalities and Application