A System of Multivariable Krawtchouk Polynomials and a Probabilistic Application

The one variable Krawtchouk polynomials, a special case of the $_2F_1$ function did appear in the spectral representation of the transition kernel for a Markov chain studied a long time ago by M. Hoare and M. Rahman. A multivariable extension of this Markov chain was considered in a later paper by these authors where a certain two variable extension of the $F_1$ Appel function shows up in the spectral analysis of the corresponding transition kernel. Independently of any probabilistic consideration a certain multivariable version of the Gelfand-Aomoto hypergeometric function was considered in papers by H. Mizukawa and H. Tanaka. These authors and others such as P. Iliev and P. Tertwilliger treat the two-dimensional version of the Hoare-Rahman work from a Lie-theoretic point of view. P. Iliev then treats the general $n$-dimensional case. All of these authors proved several properties of these functions. Here we show that these functions play a crucial role in the spectral analysis of the transition kernel that comes from pushing the work of Hoare-Rahman to the multivariable case. The methods employed here to prove this as well as several properties of these functions are completely different to those used by the authors mentioned above

The Role of Economic Factors, Including the Level of Tuition, in Individual University Participation Decisions in Canada

The study uses individual data from the Canadian Labour Force Survey to consider economic factors in university participation decisions by persons aged 17-24 from 1976 to 2003. The level of real tuition is one economic factor that may affect the university participation decision. There is also regional variation in the opportunity cost of university attendance; in the reduction in the probability of unemployment after obtaining a university degree; and in the proportion of university budgets used for financial support of students. In addition, there is some national variation by gender and over time in the return to a university education. This study finds that higher tuition levels in the 1990s did reduce the probability of university participation by persons aged 17,18 or 19 relative to a province-specific trend increase in university participation. Before drawing a policy conclusion from this result, it would be necessary to consider what the trend terms represent in the university participation decision.tuition fees; enrollment

How Vulnerable are Bangladesh’s Indigenous People to Climate Change?

This paper compares the vulnerabilities to climate change and climate variability of the indigenous people with the Bengali population of Bangladesh. It distinguishes between (a) individual vulnerabilities that are related to an individual’s capability to adapt to climate change and; (b) spatial vulnerabilities, that is, vulnerabilities that are related to the location of a person (like the exposure to climate change-induced disasters). While an individual’s capability to adapt to climate change is determined by many factors, some relatively simple approximation is to look at poverty, landlessness, and illiteracy. Spatial vulnerabilities are reviewed by looking at drought hazard maps, flood hazard maps, landslide hazard maps, and cyclone hazard maps. Hence, the paper compares levels of poverty, landlessness, illiteracy, and the more direct though also more subjective exposures to increased droughts, floods, landslides, and cyclones across the two population groups. The paper concludes with some broad suggestions on adaptation strategies of indigenous people as well as suggestions for policy interventions to reduce climate change-induced vulnerabilities for indigenous people in the Chittagong Hill Tracts (CHT).Bangladesh, climate change, vulnerability

Inferring an Indeterminate String from a Prefix Graph

An \itbf{indeterminate string} (or, more simply, just a \itbf{string}) \s{x} = \s{x}[1..n] on an alphabet $\Sigma$ is a sequence of nonempty subsets of $\Sigma$. We say that \s{x}[i_1] and \s{x}[i_2] \itbf{match} (written \s{x}[i_1] \match \s{x}[i_2]) if and only if \s{x}[i_1] \cap \s{x}[i_2] \ne \emptyset. A \itbf{feasible array} is an array \s{y} = \s{y}[1..n] of integers such that \s{y}[1] = n and for every $i \in 2..n$, \s{y}[i] \in 0..n\- i\+ 1. A \itbf{prefix table} of a string \s{x} is an array \s{\pi} = \s{\pi}[1..n] of integers such that, for every $i \in 1..n$, \s{\pi}[i] = j if and only if \s{x}[i..i\+ j\- 1] is the longest substring at position $i$ of \s{x} that matches a prefix of \s{x}. It is known from \cite{CRSW13} that every feasible array is a prefix table of some indetermintate string. A \itbf{prefix graph} \mathcal{P} = \mathcal{P}_{\s{y}} is a labelled simple graph whose structure is determined by a feasible array \s{y}. In this paper we show, given a feasible array \s{y}, how to use \mathcal{P}_{\s{y}} to construct a lexicographically least indeterminate string on a minimum alphabet whose prefix table \s{\pi} = \s{y}.Comment: 13 pages, 1 figur

Antimicrobial Diterpenes: Recent Development From Natural Sources

Antimicrobial resistance has been posing an alarming threat to the treatment of infectious diseases over the years. Ineffectiveness of the currently available synthetic and semisynthetic antibiotics has led the researchers to discover new molecules with potent antimicrobial activities. To overcome the emerging antimicrobial resistance, new antimicrobial compounds from natural sources might be appropriate. Secondary metabolites from natural sources could be prospective candidates in the development of new antimicrobial agents with high efficacy and less side effects. Among the natural secondary metabolites, diterpenoids are of crucial importance because of their broad spectrum of antimicrobial activity, which has put it in the center of research interest in recent years. The present work is aimed at reviewing recent literature regarding different classes of natural diterpenes and diterpenoids with significant antibacterial, antifungal, antiviral, and antiprotozoal activities along with their reported structure–activity relationships. This review has been carried out with a focus on relevant literature published in the last 5 years following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. A total of 229 diterpenoids from various sources like plants, marine species, and fungi are summarized in this systematic review, including their chemical structures, classification, and significant antimicrobial activities together with their reported mechanism of action and structure–activity relationships. The outcomes herein would provide researchers with new insights to find new credible leads and to work on their synthetic and semisynthetic derivatives to develop new antimicrobial agents

High yield fusion in a Staged Z-pinch

We simulate fusion in a Z-pinch; where the load is a xenon-plasma liner imploding onto a deuterium-tritium plasma target and the driver is a 2 MJ, 17 MA, 95 ns risetime pulser. The implosion system is modeled using the dynamic, 2-1/2 D, radiation-MHD code, MACH2. During implosion a shock forms in the Xe liner, transporting current and energy radially inward. After collision with the DT, a secondary shock forms pre-heating the DT to several hundred eV. Adiabatic compression leads subsequently to a fusion burn, as the target is surrounded by a flux-compressed, intense, azimuthal-magnetic field. The intense-magnetic field confines fusion $\alpha$-particles, providing an additional source of ion heating that leads to target ignition. The target remains stable up to the time of ignition. Predictions are for a neutron yield of $3.0\times 10^{19}$ and a thermonuclear energy of 84 MJ, that is, 42 times greater than the initial, capacitor-stored energy