Resolution of Singularities for a Class of Hilbert Modules

Let M be the completion of the polynomial ring C(z) under bar] with respect to some inner product, and for any ideal I subset of C (z) under bar], let I] be the closure of I in M. For a homogeneous ideal I, the joint kernel of the submodule I] subset of M is shown, after imposing some mild conditions on M, to be the linear span of the set of vectors {p(i)(partial derivative/partial derivative(w) over bar (1),...,partial derivative/partial derivative(w) over bar (m)) K-I] (., w)vertical bar(w=0), 1 <= i <= t}, where K-I] is the reproducing kernel for the submodule 2] and p(1),..., p(t) is some minimal ``canonical set of generators'' for the ideal I. The proof includes an algorithm for constructing this canonical set of generators, which is determined uniquely modulo linear relations, for homogeneous ideals. A short proof of the ``Rigidity Theorem'' using the sheaf model for Hilbert modules over polynomial rings is given. We describe, via the monoidal transformation, the construction of a Hermitian holomorphic line bundle for a large class of Hilbert modules of the form I]. We show that the curvature, or even its restriction to the exceptional set, of this line bundle is an invariant for the unitary equivalence class of I]. Several examples are given to illustrate the explicit computation of these invariants.

The Tetrablock as a Spectral Set

The tetrablock, roughly speaking, is the set of all linear fractional maps that map the open unit disc to itself. A formal definition of this inhomogeneous domain is given below. This paper considers triples of commuting bounded operators (A,B,P) that have the tetrablock as a spectral set. Such a triple is named a tetrablock contraction. The motivation comes from the success of model theory in another inhomogeneous domain, namely, the symmetrized bidisc F. A pair of commuting bounded operators (S,P) with Gamma as a spectral set is called a Gamma-contraction, and always has a dilation. The two domains are related intricately as the Lemma 3.2 below shows. Given a triple (A, B, P) as above, we associate with it a pair (F-1, F-2), called its fundamental operators. We show that (A,B,P) dilates if the fundamental operators F-1 and F-2 satisfy certain commutativity conditions. Moreover, the dilation space is no bigger than the minimal isometric dilation space of the contraction P. Whether these commutativity conditions are necessary, too, is not known. what we have shown is that if there is a tetrablock isometric dilation on the minimal isometric dilation space of P. then those commutativity conditions necessarily get imposed on the fundamental operators. En route, we decipher the structure of a tetrablock unitary (this is the candidate as the dilation triple) and a tertrablock isometry (the restriction of a tetrablock unitary to a joint invariant sub-space). We derive new results about r-contractions and apply them to tetrablock contractions. The methods applied are motivated by 11]. Although the calculations are lengthy and more complicated, they beautifully reveal that the dilation depends on the mutual relationship of the two fundamental operators, so that certain conditions need to be satisfied. The question of whether all tetrablock contractions dilate or not is unresolved.

Similarity of Matrices Over Local Rings of Length Two

Let R be a (commutative) local principal ideal ring of length two, for example, the ring R = Z/p(2)Z with p prime. In this paper, we develop a theory of normal forms for similarity classes in the matrix rings M-n (R) by interpreting them in terms of extensions of R t]-modules. Using this theory, we describe the similarity classes in M-n (R) for n <= 4, along with their centralizers. Among these, we characterize those classes which are similar to their transposes. Non-self-transpose classes are shown to exist for all n > 3. When R has finite residue field of order q, we enumerate the similarity classes and the cardinalities of their centralizers as polynomials in q. Surprisingly, the polynomials representing the number of similarity classes in M-n (R) turn out to have non-negative integer coefficients.

Factors associated with 2009 pandemic influenza A (H1N1) vaccination acceptance among university students from India during the post-pandemic phase

Background: There was a low adherence to influenza A (H1N1) vaccination program among university students and health care workers during the pandemic influenza in many parts of the world. Vaccination of high risk individuals is one of the recommendations of World Health Organization during the post-pandemic period. It is not documented about the student's knowledge, attitude and willingness to accept H1N1 vaccination during the post-pandemic period. We aimed to analyze the student's knowledge, attitude and willingness to accept H1N1 vaccination during the post-pandemic period in India. Methods: Vaccine against H1N1 was made available to the students of Vellore Institute of Technology, India from September 2010. The data are based on a cross-sectional study conducted during October 2010 to January 2011 using a self-administered questionnaire with a representative sample of the student population (N = 802). Results: Of the 802 respondents, only 102/802 (12.7%) had been vaccinated and 105/802 (13%) planned to do so in the future, while 595/802 (74%) would probably or definitely not get vaccinated in the future. The highest coverage was among the female (65/102, 63.7%) and non-compliance was higher among men in the group (384/595; 64.5%) (p < 0.0001). The representation of students from school of Bio-sciences and Bio-technology among vaccinees is significantly higher than that of other schools. Majority of the study population from the three groups perceived vaccine against H1N1 as the effective preventive measure when compared to other preventive measures. 250/595 (42%) of the responders argued of not being in the risk group. The risk perception was significantly higher among female (p < 0.0001). With in the study group, 453/802 (56.4%) said that they got the information, mostly from media. Conclusions: Our study shows that the vaccination coverage among university students remains very low in the post-pandemic period and doubts about the safety and effectiveness of the vaccine are key elements in their rejection. Our results indicate a need to provide accessible information about the vaccine safety by scientific authorities and fill gaps and confusions in this regard.

Standardizing Patent Data Cleaning in a University Technology Transfer Office

There are multiple goals of a technology transfer office (TTO) based in a university system. Whilst commercialization is a critical goal, maintenance and cleaning of the TTO's database needs detailing. Literature in the area is scarce and only some researchers make reference to TTO data cleaning. During an attempt to understand the commercial strategy of a university TTO in Bangalore the challenge of data cleaning was encountered. This paper describes a case study of data cleaning at an Indian university based TTO. 382 patent records were analyzed in the study. The case study first describes the back ground of the university system. Second, the method to clean the data and the experiences encountered are highlighted. Insights drawn indicate that patent data cleaning in a TTO is a specialized area which needs attention. Overlooking this activity can have legal implications and may result in an inability to commercialize the patent. Two levels of patent data cleaning are discussed in this case study. Best practices of data cleaning in academic TTOs are discussed.

Conceptualization of a Behavior Modification Tool for University Systems and Doctoral Students

This paper describes a university based system relevant to doctoral students who have problems with themselves, their peers and research supervisors. Doctoral students have various challenges to solve and these challenges contribute to delays in their thesis submission. This tool aims at helping them think through their problem in a pre-counseling stage. The tool uses narratives and hypothetical stories to walk a doctoral student through options of responses he or she can make given the situation in the narrative. Narratives were developed after a preliminary survey (n=57) of doctoral students. The survey indicated that problems they experienced were: busy supervisors, negative competition from peers and laziness with self. The narrative scenarios in the tool prompt self-reflection and provide for options to chose from leading to the next scenario that will ensue. The different stages of the stimulus-response cycles are designed based on Thomas-Kilmann conflict resolution techniques (collaboration and avoidance). Each stimulus-response cycle has a score attached that reflects the student's ability to judge a collaborative approach. At the end of all the stages a scorecard is generated indicating either a progressive or regressive outcome of thesis submission.