Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix

The key problems in discussing stochastic monotonicity and duality for continuous time Markov chains are to give the criteria for existence and uniqueness and to construct the associated monotone processes in terms of their infinitesimal q -matrices. In their recent paper, Chen and Zhang [6] discussed these problems under the condition that the given q-matrix Q is conservative. The aim of this paper is to generalize their results to a more general case, i.e., the given q-matrix Q is not necessarily conservative. New problems arise 'in removing the conservative assumption. The existence and uniqueness criteria for this general case are given in this paper. Another important problem, the construction of all stochastically monotone Q-processes, is also considered.

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.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

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.