Local polynomial convexity of the union of two totally real surfaces at their intersection

We consider the following question: Let $S_1$ and $S_2$ be two smooth, totally-real surfaces in $\mathbb{C}^2$ that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is $S_1 \cup S_2$ locally polynomially convex at the origin? If $T_0S_1 \cap T_0S_2=\{0\}$, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dimension of $T_0S_1 \cap T_0S_2$ over the field of real numbers is 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.Comment: 18 page

Uniform algebras generated by holomorphic and close-to-harmonic functions

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc closure(D) generated by z and h --- where h is a nowhere-holomorphic harmonic function on D that is continuous up to the boundary --- equals the algebra of continuous functions on closure(D). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h+R, where R is a non-harmonic perturbation whose Laplacian is "small" in a certain sense.Comment: 6 pages; added an important remark on page 2 and a reference; to appear in Proc. Amer. Math. So

Function theory and holomorphic maps on symmetric products of planar domains

We show that the $\bar{\partial}$-problem is globally regular on a domain in $\mathbb{C}^n$, which is the $n$-fold symmetric product of a smoothly bounded planar domain. Remmert-Stein type theorems are proved for proper holomorphic maps between equidimensional symmetric products and proper holomorphic maps from cartesian products to symmetric products. It is shown that proper holomorphic maps between equidimensional symmetric products of smooth planar domains are smooth up to the boundar

The Dynamics of Social Seclusion in the Select Short Stories of Manju Bala

The paper intends to study Manju Bala’s short stories such as Conflict, The Housemaid Special, Discrimination in the light of dalitism. Bala being a Bengali Dalit woman writer portrays the grim condition of the marginalized women in Bengal with her empirical study. In all three stories, we happen to witness caste-based discrimination, gender biasness, social injustice, domestic violence and so on. The female protagonists may be seen as transgressing the conventionality but society in large biased towards gender roles. Women are seen only as objects, peace providers, calm and quiet so on. They as we see are not provided with any emancipatory spirit even by their kith and kin but they have tried to go beyond with such obstacles. And throughout their journey, the characters face multiple dilemmas, troubles and conflicting emotion. The discriminatory practice is not something external or physical but cognitive. This mental dilemma is quite noticeable. We attempt to observe how economic stability fails to secure self-esteem and social prestige not only due to caste discrimination but also gender expectation. Patriarchy always runs high in controlling the minds that of the uncontrolled. Patriarchy, somehow, interpellates that women need not to be educated and provided with what the males in particular are provided. From early childhood till maturity, we see how the characters are marginalized and bullied by others. The term Dalit comes in contact in this paper to suggest any kind of exploitation faced by anybody. Thus, this paper tends to highlight all such issues which are silently nurtured by society

Mujeres de las colinas en la poca de las guerras tribales: Una lectura de cuentos populares del noreste de la India

What we know about women in traditional tribal societies in Northeast India is based on what oral traditions tell us about them. Although they were more resourceful and respected than the women of the plains societies, their disadvantages in a world teeming with tribal feuds were considerable. Ruthless enemies destroyed villages and killed everyone, but sometimes they spared the lives of women. When two hostile villages agreed to a truce, the women enjoyed freedom of movement, but only within the village. Kidnappings were frequent, and it was unsafe for women to leave the village unaccompanied by men. Their vulnerability prompted tribes to adopt measures such as face tattooing and the practice of tribe or village endogamy. Based on the evidence in oral traditions, mostly folk tales, this paper reconstructs the position of women in the tribal societies of Northeast India during the period of inter-tribal wars.Lo que sabemos sobre las mujeres en las sociedades tribales tradicionales del noreste de la India se basa en lo que las tradiciones orales nos cuentan sobre ellas. Aunque eran más ingeniosas y respetadas que las mujeres de las sociedades de las llanuras, sus desventajas en un mundo plagado de disputas tribales eran considerables. Enemigos despiadados destruyeron pueblos y mataron a todos, pero a veces perdonaron la vida de las mujeres. Cuando dos pueblos hostiles acordaron una tregua, las mujeres disfrutaron de libertad de movimiento, pero solo dentro del pueblo. Los secuestros eran frecuentes y no era seguro para las mujeres abandonar el pueblo sin la compañía de hombres. Su vulnerabilidad llevó a las tribus a adoptar medidas como el tatuaje facial y la práctica de la endogamia de la tribu o la aldea. Basado en la evidencia de las tradiciones orales, en su mayoría cuentos populares, este artículo reconstruye la posición de las mujeres en las sociedades tribales del noreste de la India durante el período de las guerras intertribales