Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Birth-death processes with an instantaneous reflection barrier

A new structure with the special property that an instantaneous reflection barrier is imposed on the ordinary birth-death processes is considered. An easy-checking criterion for the existence of such Markov processes is first obtained. The uniqueness criterion is then established. In the nonunique case, all the honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. It is proved that honest processes are always ergodic without necessarily imposing any extra conditions. Equilibrium distributions for all these ergodic processes are established. Several examples are provided to illustrate our results.

Birth-death processes with disaster and instantaneous resurrection

A new structure with the special property that instantaneous resurrection and mass disaster are imposed on an ordinary birth-death process is considered. Under the condition that the underlying birth-death process is exit or bilateral, we are able to give easily checked existence criteria for such Markov processes. A very simple uniqueness criterion is also established. All honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. Surprisingly, it can be proved that all the honest processes are not only recurrent but also ergodic without imposing any extra conditions. Equilibrium distributions are then established. Symmetry and reversibility of such processes are also investigated. Several examples are provided to illustrate our results.

Two-machine shop scheduling: Compromise between flexibility and makespan value

In this paper, we consider the problem of providing flexibility to solutions of two-machine shop scheduling problems. We use the concept of group-scheduling to characterize a whole set of schedules so as to provide more choice to the decision-maker at any decision point. A group-schedule is a sequence of groups of permutable operations defined on each machine where each group is such that any permutation of the operations inside the group leads to a feasible schedule. Flexibility of a solution and its makespan are often conflicting, thus we search for a compromise between a low number of groups and a small value of makespan. We resolve the complexity status of the relevant problems for the two-machine flow shop, job shop and open shop. A number of approximation algorithms are developed and their worst-case performance is analyzed. For the flow shop, an effective heuristic algorithm is proposed and the results of computational experiments are reported.

Assessment of the nutritional value of wild leafy vegetables consumed in the Buhera District of Zimbabwe: a preliminary study

Wild leafy vegetables play a vital role in the livelihoods of many communities in Africa. The focus of this study was to investigate the nutritional value of wild vegetables commonly consumed by the people of Buhera District in the Manicaland province of Zimbabwe. A variety of vegetables including Amaranthus hybridus, Cleome gynandra, Bidens pilosa, Corchorus tridens, and Adansonia digitata were collected during a survey in Buhera District. Samples were processed employing traditional methods of cooking and drying, then subjected to proximate and micronutrient analyses. The results indicate that these vegetables were particularly high in calcium, iron, and vitamin C. Compared with Brassica napus (rape), Amaranthus hybridus contained twice the amount of calcium, with other nutrients almost in the same range. Compared with Spinacia oleracea (spinach), Amaranthus hybridus contained three times more vitamin C (44 mg/100 g). Calcium levels were 530 mg/100 g. Amaranthus hybridus was also found to contain 7, 13, and 20 times more vitamin C, calcium, and iron respectively compared with Lactuca sativa (lettuce). Cleome gynandra contained 14 mg/100 g, 115 mg/100 g, 9 mg/100 g of vitamin C, calcium, and iron respectively. Bidens pilosa was found to be a valuable source of vitamin C (63 mg/100 g), iron (15 mg/100 g), and zinc (19 mg/100 g), compared with Brassica oleracea (cabbage). The leaves of Corchorus tridens were an excellent source of vitamin C (78 mg/100 g), calcium (380 mg/100 g), and iron (8 mg/100 g). The Adansonia digitata leaves were also rich in vitamin C (55 mg/100 g), iron (23 mg/ 100 g), and calcium (400 mg/100 g). Based on these nutrient contents, the above vegetables will have potential benefits as part of feeding programmes, as well as their promotion as part of composite diet for vulnerable groups.

What is the value of technology? Toward a labour theory of technology change

Economic analysis of technology treats it as given exogenously, while determined endogenously. This paper examines the conceptual conflict. The paper outlines an alternative conceptual framework. This uses a 'General Vertical Division of Labour' into conceptual and executive parts to facilitate a coherent political economic explanation of technological change. The paper suggests that we may acquire rather than impose an understanding of technological change. It also suggests that we may re-define and reassess the efficiency of technological change, through the values inculcated into it.

An inquiry concerning the acceptance of intrinsic value theories of nature

This study empirically assesses the extent to which intrinsic value theories of nature are accepted and acknowledged outside the realm of academic environmental ethics. It focuses on twenty of the largest landowning organisations in England, including both conservation and non-conservation organisations and investigates the environmental philosophical beliefs and values held by representative individuals of these groups. An in-depth interview was held with a representative from each organisation. The interviews were analysed using qualitative data analysis software and the results compared against a backdrop of academic philosophical positions. The study found that an ecocentric position which acknowledges nature's intrinsic value was adopted by the majority of respondents, both from conservation and non-conservation organisations. However, it was also found that individuals felt the idea of nature's intrinsic value was generally not reflected in organisational policy.