Stabilization in HR∞(D)H^\infty_{\mathbb{R}}(\mathbb{D})

In this paper we prove the following theorem: Suppose that f_1,f_2\in H^\infty_\R(\D), with \norm{f_1}_\infty,\norm{f_2}_{\infty}\leq 1, with \inf_{z\in\D}(\abs{f_1(z)}+\abs{f_2(z)})=\delta>0. Assume for some $\epsilon>0$ and small, $f_1$ is positive on the set of $x\in(-1,1)$ where \abs{f_2(x)}0 sufficiently small. Then there exists g_1, g_1^{-1}, g_2\in H^\infty_\R(\D) with \norm{g_1}_\infty,\norm{g_2}_\infty,\norm{g_1^{-1}}_\infty\leq C(\delta,\epsilon) and f_1(z)g_1(z)+f_2(z)g_2(z)=1\quad\forall z\in\D. Comment: v1: 22 pages, 2 figures, to appear in Pub. Mat; v2: 32 pages, 5 figures. The earlier version incorrectly claimed a characterization, as was pointed out by R. Mortini. A key hypothesis was strengthened with the main result remaining the sam

COMPETITIVE STRATEGIES OF BIOTECHNOLOGY FIRMS: IMPLICATIONS FOR U.S. AGRICULTURE

The agricultural biotechnology industry has evolved from a focus on outstanding science to a more mature phase where firms focus on near-term products and building businesses. Understanding complex relationships and distribution channels and a global perspective are crucial to commercialization. Yet, leading-edge technology and early identification of key traits will be critical to developing superior products that ensure competitiveness in the marketplace. Monsanto is organizing around a life sciences model where seed, crop chemicals, pharmaceuticals, and food ingredient businesses will exploit mutual synergies driven by basic science and discovery.Biotechnology, Monsanto, Strategies, Research and Development/Tech Change/Emerging Technologies,

Bergman-type Singular Operators and the Characterization of Carleson Measures for Besov--Sobolev Spaces on the Complex Ball

The purposes of this paper are two fold. First, we extend the method of non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle "Bergman--type" singular integral operators. The canonical example of such an operator is the Beurling transform on the unit disc. Second, we use the methods developed in this paper to settle the important open question about characterizing the Carleson measures for the Besov--Sobolev space of analytic functions $B^\sigma_2$ on the complex ball of $\mathbb{C}^d$. In particular, we demonstrate that for any $\sigma> 0$, the Carleson measures for the space are characterized by a "T1 Condition". The method of proof of these results is an extension and another application of the work originated by Nazarov, Treil and the first author.Comment: v1: 31 pgs; v2: 31 pgs, title changed, typos corrected, references added; v3: 33 pages, typos corrected, references added, presentation improved based on referee comments

Becoming a Scientist: Using First-Year Undergraduate Science Courses to Promote Identification with Science Disciplines

In this qualitative study, we examined how two professors (a physicist and biochemist) of first year college students perceived their students’ development of identification in biochemistry or physics and how they actively supported this development. The professors described students who entered college with different levels of domain identification and different expectations for their college science experience depending upon whether they were in a biochemistry or physics major. Although neither professor was familiar with research related to the concept of domain identification, their beliefs about their students’ identification and academic support strategies generally aligned with the Osborne and Jones (2011) model of academic identification