Disjoint Infinity-Borel Functions

This is a followup to a paper by the author where the disjointness relation for definable functions from ${^\omega \omega}$ to ${^\omega \omega}$ is analyzed. In that paper, for each $a \in {^\omega \omega}$ we defined a Baire class one function $f_a : {^\omega \omega} \to {^\omega \omega}$ which encoded $a$ in a certain sense. Given $g : {^\omega \omega} \to {^\omega \omega}$, let $\Psi(g)$ be the statement that $g$ is disjoint from at most countably many of the functions $f_a$. We show the consistency strength of $(\forall g)\, \Psi(g)$ is that of an inaccessible cardinal. We show that $\textrm{AD}^+$ implies $(\forall g)\, \Psi(g)$. Finally, we show that assuming large cardinals, $(\forall g)\, \Psi(g)$ holds in models of the form $L(\mathbb{R})[\mathcal{U}]$ where $\mathcal{U}$ is a selective ultrafilter on $\omega$.Comment: 16 page

Holy pharma! : healthism discourses in a pharmaceutical advertising website : a thesis presented in partial fulfillment of the requirements for the degree of Master of Arts in Psychology at Massey University

Pages 123 and 143 are missing from the original copy.Modern changes in the public health philosophy and government legislation reflect a desire of health for all. The changes support a new healthism ideology that controls the experience and definition of health. Scholars parallel the function of healthism to that of a religion that meets the needs of a modern secular culture. This study examines a pharmaceutical advertising website, taking a social constructionist stance to investigate dominant representations of healthism and any parallels to the values and practices of Western religion. The website selected is published by a pharmaceutical marketing group that has been disseminating health and product information for l0 years. The installment of March-April 2009 was examined in its entirety. A critical discourse analytic approach drawing on Durkheim and Foucault was adopted to analyse texts, images, and videos. Particular attention was given to the similarities and differences of healthism and religion in terms, meanings, subject positioning and function. Results show healthism to parallel religion in its construction as information, instruction and ritual practice. The expert discourse within healthism promotes a morality that parallels and deviates from religious values with a turn toward the value of the self. This expert discourse informs healthism discourses, constructing a doctrine of unquestionable behaviours that legitimate ritualized health practices. When viewed as an integral entity, the form, content, and function of healthism in pharmaceutical advertising takes on the religious connectivity of values, beliefs and practices that underlies all social life. The website is an intense concentration of coercive and symbolic power to inform the institutionalized social system ofs healthism

Tech Starts: High-Technology Business Formation and Job Creation in the United States

New and young businesses -- as opposed to small businesses generally -- play an outsized role in net job creation in the United States. But not all new businesses are the same -- the substantial majority of nascent entrepreneurs do not intend to grow their businesses significantly or innovate, and many more never do. Differentiating growth-oriented "startups" from the rest of young businesses is an important distinction that has been underrepresented in research on business dynamics and in small business policy.To advance the conversation, we contrast business and job creation dynamics in the entire U.S. private sector with the innovative high-tech sector -- defined here as the group of industries with very high shares of employees in the STEM fields of science, technology, engineering, and math. We highlight these differences at the national level, as well as detailing regions throughout the country where high-tech startups are being formed each year. The major findings include:* The high-tech sector and the information and communications technology (ICT) segment of high-tech are important contributors to entrepreneurship in the U.S. economy. During the last three decades, the high-tech sector was 23 percent more likely and ICT 48 percent more likely than the private sector as a whole to witness a new business formation.* High-tech firm births were 69 percent highe rin 2011 compared with 1980; they were 210 percent higher for ICT and 9 percent lower for the private sector as a whole during the same period. This is important because the productivity growth and job creation unleashed by these new and young firms -- aged less than five years -- require a continual flow of births each year.* Of new and young firms, high-tech companies play an outsized role in job creation. High-tech businesses start lean but grow rapidly in the early years, and their job creation is so robust that it offsets job losses from early-stage business failures. This is a key distinction from young firms across the entire private sector, where net job losses resulting from the high rate of early-stage failures are substantial.* Young firms exhibit an "up-or-out" dynamic,where they tend to either fail or grow rapidly in the early years. The job-creating strength of surviving young firms, while strong for young businesses across the private sector as a whole, is especially distinct for high-tech startups: the net job creation rate of these surviving young firms is twice as robust.* High-tech and ICT firm formations are becoming increasingly geographically dispersed. As technological advancement allows for the production of high-tech goods and services in a wider set of areas, many regions are catching up. The opposite has been true for the private sector as a whole, where new business growth has been occurring most in regions with already higher rates of new business formation

Weak Distributivity Implying Distributivity

Let $\mathbb{B}$ be a complete Boolean algebra. We show, as an application of a previous result of the author, that if $\lambda$ is an infinite cardinal and $\mathbb{B}$ is weakly $(\lambda^\omega, \omega)$-distributive, then $\mathbb{B}$ is $(\lambda, 2)$-distributive. Using a parallel result, we show that if $\kappa$ is a weakly compact cardinal such that $\mathbb{B}$ is weakly $(2^\kappa, \kappa)$-distributive and $\mathbb{B}$ is $(\alpha, 2)$-distributive for each $\alpha < \kappa$, then $\mathbb{B}$ is $(\kappa, 2)$-distributive.Comment: 12 page

Supergranules as Probes of Solar Convection Zone Dynamics

Supergranules are convection cells seen at the Sun's surface as a space filling pattern of horizontal flows. While typical supergranules have diameters of about 35 Mm, they exhibit a broad spectrum of sizes from ~10 Mm to ~100 Mm. Here we show that supergranules of different sizes can be used to probe the rotation rate in the Sun's outer convection zone. We find that the equatorial rotation rate as a function of depth as measured by global helioseismology matches the equatorial rotation as a function of wavelength for the supergranules. This suggests that supergranules are advected by flows at depths equal to their wavelengths and thus can be used to probe flows at those depths. The supergranule rotation profiles show that the surface shear layer, through which the rotation rate increases inward, extends to depths of ~50 Mm and to latitudes of at least 70 degrees. Typical supergranules are well observed at high latitudes and have a range of sizes that extend to greater depths than those typically available for measuring subsurface flows with local helioseismology. These characteristics indicate that probing the solar convection zone dynamics with supergranules can complement the results of helioseismology.Comment: 6 pages, 3 figures, Accepted for publication in The Astrophysical Journal Letter

Factors affecting the soil binding capacity of the root systems of some populus and salix clones : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Botany at Massey University

Man-induced changes in the vegetation of New Zealand over the last century have resulted in large areas of actively eroding land, both in the steeplands which still retain a form of forest cover, and in large areas of moderate to steep hill country cleared for pastoral use. By 1941, the seriousness of the problem had been recognised, and Catchment Authorities were constituted, under the auspices of the Soil Conservation and Rivers Control Council, to undertake river and erosion control programs. Many techniques were used in erosion control work, but most emphasis has been placed on the planting of trees, largely Populus and Salix species. The planting of trees has proven to have a beneficial effect on counteracting erosion by slumping and gullying, both in retired areas and in those still grazed. It may be assumed that this effect is due primarily to the reinforcing and binding effect of their root systems. The reduction of soil moisture by evapotranspiration is considered to be of secondary importance, as water loss from these deciduous trees is very low in winter, which is the period of maximum soil moisture content and thus maximum instability. In the past, the selection of poplars and willows for erosion control purposes has been based on the growth and characteristics of the shoot of the tree, while almost nothing was known of the root systems. Variations in morphology and strength of root systems obviously are important factors in the selection of the most suitable species or varieties for soil stabilisation purposes. Objectives of the study The primary objective of the study was to Investigate the morphology, anatomy, and soil binding capacity of the root systems of a representative number of Populus and Salix clones, in order to determine whether any of the clones were likely to be superior for soil stabilisation purposes, and to determine which characteristics of the root systems were most important for this purpose, as a basis for the selection of improved varieties