On discrete analytic functions: Products, Rational Functions, and some Associated Reproducing Kernel Hilbert Spaces

We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the Cauchy-Kovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis

A new realization of rational functions, with applications to linear combination interpolation

We introduce the following linear combination interpolation problem (LCI): Given $N$ distinct numbers $w_1,\ldots w_N$ and $N+1$ complex numbers $a_1,\ldots, a_N$ and $c$, find all functions $f(z)$ analytic in a simply connected set (depending on $f$) containing the points $w_1,\ldots,w_N$ such that $$\sum_{u=1}^Na_uf(w_u)=c.$$ To this end we prove a representation theorem for such functions $f$ in terms of an associated polynomial $p(z)$. We first introduce the following two operations, $(i)$ substitution of $p$, and $(ii)$ multiplication by monomials $z^j, 0\le j < N$. Then let $M$ be the module generated by these two operations, acting on functions analytic near $0$. We prove that every function $f$, analytic in a neighborhood of the roots of $p$, is in $M$. In fact, this representation of $f$ is unique. To solve the above interpolation problem, we employ an adapted systems theoretic realization, as well as an associated representation of the Cuntz relations (from multi-variable operator theory.) We study these operations in reproducing kernel Hilbert space): We give necessary and sufficient condition for existence of realizations of these representation of the Cuntz relations by operators in certain reproducing kernel Hilbert spaces, and offer infinite product factorizations of the corresponding kernels

Concurrent Enrollment Programs and Acquired Social Capital for Students from Impoverished Backgrounds: An Examination of High School and College Outcomes

Poverty has been linked to reduced workforce opportunities, reduced collegegoing rates, increased social-emotional challenges, and even negative health consequences. Postsecondary educational opportunities, offered during high school, that contribute to the acquisition of social capital may improve academic outcomes for students from impoverished backgrounds. The Colorado concurrent enrollment legislation, provides one opportunity for students to enroll in college level coursework and receive college credits with tuition being paid through state funding while in high school. Concurrent enrollment (CE) programs support the college application, financial aid and enrollment processes. Most importantly, they also support the development of social networks that may foster beneficial secondary and postsecondary outcomes. This dissertation examines the participation and representation rates of free and reduced lunch (FRL) students in CE programs at the state and local level. Next, the impact of CE participation on secondary and postsecondary outcomes in students from impoverished backgrounds is examined. The quasi-experimental research design included a matched control group generated by logistic regression and propensity score matching techniques. A sensitivity analysis was conducted to estimate unaccounted for variance that may have contributed to any observed between-group differences. Between-group differences were examined for a range of outcomes at the high school and postsecondary level. The study analysis was replicated utilizing two additional groups of program participants across two years to increase confidence in the obtained findings. Overall, the findings indicate that FRL students were underrepresented as concurrent enrollment participants during the 2010 and 2011 academic years. A limited number of local education agencies had FRL student participation rates that exceeded enrollment expectations. Statistical analysis indicated that FRL students earned CE credits at a lower rate than their non-eligible peers. In contrast, the FRL students enrolled for a larger number of CE credits than non-eligible students. Additional analysis revealed that a number of positive secondary and postsecondary outcomes were related to concurrent enrollment participation for economically disadvantaged students. The results of sensitivity analyses indicate that other, unaccounted for variables were unlikely to have impacted the obtained findings. The findings of this study indicate that concurrent enrollment opportunities may mitigate some of the deleterious impacts of poverty by improving academic achievement and college-going rates. The beneficial role of social capital for achievement of postsecondary success is discussed

Relative reproducing kernel Hilbert spaces

We introduce a reproducing kernel structure for Hilbert spaces of functions where differences of point evaluations are bounded. The associated reproducing kernels are characterized in terms of conditionally negative functions

Mining narratives and multiple geographies in Papua New Guinea: Ok Tedi, the emerald cave and Lost Tribes

Mining in Papua New Guinea has been accompanied by an efflorescence of origin tales that often serve as justifications for local claims to land rights or benefits arising from specific projects. While many of these narratives or myths have a clear instrumental function, there are many other elements of these tales that cannot be accounted for in these terms. In this article the author describes a recent origin story that emerged around the Ok Tedi mine, and places it in the context of traditional mythology, a changing system of regional relations, and circulating evangelical discourses. He argues that the story is best interpreted as an attempt to articulate a local position in relation to multiple geographies in which mining and Christianity are linked across scales ranging from the regional to the global.L’exploitation minière en Papouasie Nouvelle-Guinée a vu émerger de nombreuses histoires des origines, servant souvent à justifier des revendications locales quant au droit foncier et aux bénéfices relatifs à des projets précis. Bien qu’une large part de ces récits et mythes ait une fonction clairement instrumentale, cette dernière interprétation ne peut rendre compte de tous les éléments constitutifs de ces histoires. Dans cet article, l’auteur décrit une histoire des origines récente, qui a émergé dans le contexte de la mine Ok Tedi. Il replace cette histoire dans le contexte de la mythologie traditionnelle, d’un système de relations sociales régionales en évolution, et des discours évangéliques qui circulent dans la zone. Il défend l’idée que ce récit doit être interprété comme une tentative d’articuler une posture locale avec les géographies multiples qui relient exploitation minière et christianisme, selon des échelles qui varient du régional au global

On Discrete Analytic Functions: Products, Rational Functions, and Reproducing Kernels

We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the Cauchy-Kovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis

Composting hoop structure bedding/manure

Tom Richard has conducted composting research on ISU\u27s Rhodes Research Farm using cornstalk-bedded manure from a finishing hoop. The manure is partially composted in the building. Manure inside the hooped structure varies in moisture content and nitrogen. The wet areas where pigs dung are high in nitrogen; dry areas are low in nitrogen

Understanding the mechanisms underlying biological control of Fusarium diseases in cereals

Many Fusarium species cause serious diseases for cereal cultivation. These include Fusarium head blight and crown rot on wheat and bakanae disease on rice. These represent a major concern both in terms of food security and food safety. The latter is connected with the risk of mycotoxin contamination of grains. Biological control has proven its potential for controlling head blight and crown rot diseases of cereals caused by Fusarium species in a number of studies, and indeed several commercial products are under development. We review current knowledge of the mechanisms underlying biological control with a focus on fungal biocontrol agents, and also include challenges related to co-occurrence of Fusarium species. Several of the established biological control mechanisms (antibiosis, competition, hyperparasitism and induced resistance) can act simultaneously, thus resulting in disease control and, consequently, reduction of mycotoxin contamination. We also review the biological roles of some of the many mycotoxins produced by Fusarium species, and the mechanisms by which they are detoxified by cereal enzymes or by other fungi and how biological control agents (BCAs) can stimulate their degradation. Finally, the effect of biocontrol agents on the resident microbiota, as well as the effect of the resident microbiota on the performances of BCAs, are discussed. New perspectives on the use of biocontrol agents for the management of Fusarium diseases on cereals

Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey

We report the discovery of five very cool white dwarfs in the Sloan Digital Sky Survey (SDSS). Four are ultracool, exhibiting strong collision induced absorption (CIA) from molecular hydrogen and are similar in color to the three previously known coolest white dwarfs, SDSS J1337+00, LHS 3250 and LHS 1402. The fifth, an ultracool white dwarf candidate, shows milder CIA flux suppression and has a color and spectral shape similar to WD 0346+246. All five new white dwarfs are faint (g > 18.9) and have significant proper motions. One of the new ultracool white dwarfs, SDSS J0947, appears to be in a binary system with a slightly warmer (T_{eff} ~ 5000K) white dwarf companion.Comment: 15 pages, 3 figures, submitted to ApJL. Higher resolution versions of finding charts are available at http://astro.uchicago.edu/~gates/findingchart