On the additive theory of prime numbers II

The undecidability of the additive theory of primes (with identity) as well as the theory Th(N,+, n -> p\_n), where p\_n denotes the (n+1)-th prime, are open questions. As a possible approach, we extend the latter theory by adding some extra function. In this direction we show the undecidability of the existential part of the theory Th(N, +, n -> p\_n, n -> r\_n), where r\_n is the remainder of p\_n divided by n in the euclidian division

Contextualising fisheries policy in the Lower Mekong Basin

Development policies for fishery resources within the Mekong River Basin are increasingly divided between aquaculture and capture fisheries. The modern production orientation of aquaculture has been adopted by government and NGOs and justified by the rhetoric of poverty alleviation and rural development. In contrast, capture fisheries has been subjugated as an activity that reaffirms the dependency of the rural poor on natural resources. This paper critically analyses the division between aquaculture and capture fisheries in Cambodia, Thailand and Lao PDR by tracing the emergence and influence of `development narratives¿ used to justify contemporary policy and practice

A Method for Establishing Outdoor Recreation Project Priorities in Alaska

The authors thank Theodore Smith, Edward Kramer and Nat Goodhue of the Division of Parks for information and comments supplied during this study, and Frank Orth, Charles Marsh, Ed Kramer, C.E. Logsdon, and Frank Wooding for reviewing the manuscript. Thanks is also due the Department of Business Administration, University of Alaska, Fairbanks, Dale Swanson, Head, for their cooperation in this research project.The objectives of this study are to define outdoor recreation benefits to the public and to develop a priority ranking method for proposed outdoor recreation projects. A careful analysis of the benefits which people derive from outdoor recreation provides a frame of reference for evaluating a recreational facility. A project should supply those benefits which are most highly demanded by the public. Fifteen benefits of recreation are defined and discussed. They are divided into two major categories; those which accrue to recreational participants and those which accrue to non-participants.This research was supported by a grant from the Division of Parks, State of Alaska

Introduction: Analytic, Continental and the question of a bridge

This is the peer reviewed version of the following article: Introduction: Analytic, Continental and the question of a bridge, which has been published in final form at 10.1177/1474885115582078. This article may be used for non-commercial purposes in accordance with SAGE’s Terms and Conditions for Self-Archiving.In philosophy and political theory, divisions come and go, but some persist despite beingobviously problematic. The analytic and Continental divide is one such division. Inpolitical philosophy and political theory, the division has been particularly pronounced.Analytic and Continental thinkers are divided not only over substantial issues but also over the very nature of political theorising. In spite of this fundamental nature, theorists often seem to assume that, as a division, the analytic/Continental divide requires no explanation. We suggest that, as a central division within political theory, and despite being acknowledged as problematic for quite some time, it has persisted because it has not been adequately examined. Once examined, the division turns out to be operationally weaker than it once was. In recent years, there has been a growing interest in engaging thinkers from the other side. This has been accompanied by a corresponding tendency, among both analytic and Continental philosophers and political thinkers, to reflect on the nature of their own tradition and ‘philosophy’. Both traditions have entered a self-conscious period of meta-reflection. Such questioning indicates the possibility of transformation within both groups, in the absence of settled frameworks and divisions. However, it is also clear that such signs are the beginning of the possibility of a new relation rather than a sign of the eclipse of the division. The continued institutional separation and the space between their respective philosophical vocabularies suggest that, while the time is ripe for work here, there is still much to be done

Motivation Cards to Support Students’ Understanding on Fraction Division

This design research aims to develop a learning activity which supports the fifth-grade students to understand measurement fraction division problems (A whole number divided by a fraction that result in a whole number answer) conceptually. Furthermore, how students solve the fraction division problem using models is also analyzed.  Data for the retrospective analysis is collected through two teaching experiments in the form of students’ work, field notes, and some part of classroom discussions. The important findings in this research are: 1) the developed learning activity namely Motivation Cards support students understand that  3 divided by one-half means how many one-half are in 3 through models. However, when the divisor is not a unit fraction they could not directly relate the unshaded part in area model for example. 2) area model is proper model to be firstly introduced when the students work on fraction division. 3) understanding this kind of fraction division help students understand other measurement fraction division where both divisor and dividend are fractions. 4) the learning activity supports the development of character values for students.   

Symbiotic Cell Differentiation and Cooperative Growth in Multicellular Aggregates

As cells grow and divide under a given environment, they become crowded and resources are limited, as seen in bacterial biofilms and multicellular aggregates. These cells often show strong interactions through exchanging chemicals, as in quorum sensing, to achieve mutualism. Here, to achieve stable division of labor, three properties are required. First, isogenous cells differentiate into several types. Second, this aggregate of distinct cell types shows better growth than that of isolated cells, by achieving division of labor. Third, this cell aggregate is robust in the number distribution of differentiated cell types. We here address how cells acquire the ability of cell differentiation and division of labor simultaneously, which is also connected with the robustness of a cell society. For this purpose, we developed a dynamical-systems model of cells consisting of chemical components with intracellular catalytic reaction dynamics. The reactions convert external nutrients into internal components for cellular growth, and the divided cells interact via chemical diffusion. We found that cells sharing an identical catalytic network spontaneously differentiate via induction from cell-cell interactions, and then achieve division of labor, enabling a higher growth rate than that in the unicellular case. This symbiotic differentiation emerged for a class of reaction networks with limited resources and strong cell-cell interactions. Then, robustness in the cell type distribution was achieved, while instability of collective growth could emerge even among the cooperative cells when the internal reserves of products were dominant. The present mechanism is simple and general as a natural result of interacting cells with resource limitation, and is consistent with the observed behaviors and forms of several aggregates of unicellular organisms.Comment: 14 pages, 6 figure