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

Preliminary Investigation on Bamboo Pulping

A preliminary investigation on bamboo pulping by Semi-Keebra process reveals that a higher pulp yield than that obtained by most of the known methods of pulping bamboo can be attained by Semi-Keebra process.* The chemical requirement for pulping is lower than the conventional processes and the spent liquor also contains a higher per cent of solids. The pulp obtained by Semi-Keebra pulp would also require a considerable lesser time for obtaining the desired freeness value, resulting in lower power consumption for stock preparation, than that for the conventional sulphate bamboo pulp of bleachable grade. A comparison of the various hand-sheet properties of the two pulps show that all properties other than density and breaking length are, however, lower in the case of Semi-Keebra bamboo pulp. It is, however, hoped that further investigation on optimum condition of Semi-Keebra process for bamboo pulping would show some further improvement in the strength properties

Ex post implementation in environments with private goods

We prove by construction that ex post incentive compatible mechanisms exist in a private goods setting with multi-dimensional signals and interdependent values. The mechanism shares features with the generalized Vickrey auction of one-dimensional signal models. The construction implies that for environments with private goods, informational externalities (i.e., interdependent values) are compatible with ex post equilibrium in the presence of multi-dimensional signals.Ex post incentive compatibility, multi-dimensional information, interdependent values

Birkhoff-James orthogonality and applications : A survey

In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficient conditions for Birkhoff-James orthogonality in certain Banach spaces are mentioned. Their applications in studying the geometry of normed spaces are given. The connections between this concept of orthogonality, and the Gateaux derivative and the subdifferential set of the norm function are provided. Several interesting distance formulas can be obtained using the characterizations of Birkhoff-James orthogonality, which are also mentioned. In the end, some new results are obtained.Comment: To appear in : Springer/Birkh\"auser Verlag book series Operator Theory: Advances and Applications. Number of pages : 1

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