A semi-exact degree condition for Hamilton cycles in digraphs

The paper is concerned with directed versions of Posa's theorem and Chvatal's theorem on Hamilton cycles in graphs. We show that for each a>0, every digraph G of sufficiently large order n whose outdegree and indegree sequences d_1^+ \leq ... \leq d_n^+ and d_1^- \leq >... \leq d_n^- satisfy d_i^+, d_i^- \geq min{i + a n, n/2} is Hamiltonian. In fact, we can weaken these assumptions to (i) d_i^+ \geq min{i + a n, n/2} or d^-_{n - i - a n} \geq n-i; (ii) d_i^- \geq min{i + a n, n/2} or d^+_{n - i - a n} \geq n-i; and still deduce that G is Hamiltonian. This provides an approximate version of a conjecture of Nash-Williams from 1975 and improves a previous result of K\"uhn, Osthus and Treglown

The rediscovery of the role of the laity in the mission of the church – with reference to the Baptist Union of southern Africa (BUSA)

Please read the abstract in the section 00front of this document.Thesis (PhD)--University of Pretoria, 2009.Science of Religion and Missiologyunrestricte

Carbon monoxide formation during aerobic biostabilization of the organic fraction of municipal solid waste: the influence of technical parameters in a full-scale treatment system

The present study sought to investigate the formation of carbon monoxide (CO) during aerobic biostabilization (AB) of the organic fraction of municipal solid waste (OFMSW) in forced aerated piles. Understanding the factors influencing CO formation may be important not only for safety, but also for environmental and technical reasons. The objective of the study was to determine the effect of the technical parameters of the piles on the concentration of CO in the process gas during AB of the OFMSW in a full-scale waste treatment system: rate of waste aeration (from 3365 to 12,744 m3∙Mg−1), waste mass loads in the pile (from 391 to 702 Mg), thermal conditions, application of sidewalls as an element of pile bioreactor construction, concentration of O2 and CO2 in the waste piles and the duration of the process from 6 to 9 weeks. The temperature and concentration of O2, CO2, CO, CH4 were measured in each pile at weekly intervals. All six reactors provide stable thermal and aerobic conditions, but the presence of CO was observed, ranging from a few to over 2000 ppm, which demonstrated that ensuring optimum conditions for the process is not sufficient for CO to be eliminated. A moderate, non-linear rise in CO concentration was observed along with a rise in the temperature inside the reactors. Concentrations of CO were not highly correlated with those of O2 or CO2. An increase in waste mass loads increased the CO concentration in waste piles, while application of sidewalls decreased CO concentration. Increasing aeration rate had an influence on CO production, and the highest CO concentrations were noted under air flow rate 5.3 m3·Mg−1·h−1

The rediscovery of the role of the laity in the mission of the Church – with reference to the Baptist Union of Southern Africa (BUSA)

The role of the laity is at the cutting edge of Christian missions today. The author conducted a number of interviews and questionnaires to determine the status of the laity across denominations of the Christian faith in South Africa. His findings are in a number of instances startling: The picture of the laity, and what lay Christians in South Africa believe, run against general expectations. Some suggestions and proposals on how to empower the laity in general, and the churches of the Baptist Union in Southern Africa (BUSA) in particular, are made. The underlining motive for the research is to encourage the BUSA churches to become truly missional churches that make a difference in the world in which we live.The article is based on the first author’s PhD thesis on The rediscovery of the role of the laity in the mission of the Church – with reference to the Baptist Union of Southern Africa (BUSA), Department of Science of Religion and Missiology, University of Pretoria (April 2009), under the supervision of Professor P.G.J. Meiring.http://www.ve.org.zahttp://upetd.up.ac.za/thesis/available/etd-11032009-090915/nf201

On the Stability of a Periodic Solution of Distributed Parameters Biochemical System

International audienceThis paper studies the stability of periodic solutions of distributed parameters biochemical system with periodic input Sin(t). We prove that if Sin(t) is periodic then the system has a periodic solution that is input to state stable when small perturbations are acting on the input concentration Sin(t)

On prisms, M\"obius ladders and the cycle space of dense graphs

For a graph X, let f_0(X) denote its number of vertices, d(X) its minimum degree and Z_1(X;Z/2) its cycle space in the standard graph-theoretical sense (i.e. 1-dimensional cycle group in the sense of simplicial homology theory with Z/2-coefficients). Call a graph Hamilton-generated if and only if the set of all Hamilton circuits is a Z/2-generating system for Z_1(X;Z/2). The main purpose of this paper is to prove the following: for every s > 0 there exists n_0 such that for every graph X with f_0(X) >= n_0 vertices, (1) if d(X) >= (1/2 + s) f_0(X) and f_0(X) is odd, then X is Hamilton-generated, (2) if d(X) >= (1/2 + s) f_0(X) and f_0(X) is even, then the set of all Hamilton circuits of X generates a codimension-one subspace of Z_1(X;Z/2), and the set of all circuits of X having length either f_0(X)-1 or f_0(X) generates all of Z_1(X;Z/2), (3) if d(X) >= (1/4 + s) f_0(X) and X is square bipartite, then X is Hamilton-generated. All these degree-conditions are essentially best-possible. The implications in (1) and (2) give an asymptotic affirmative answer to a special case of an open conjecture which according to [European J. Combin. 4 (1983), no. 3, p. 246] originates with A. Bondy.Comment: 33 pages; 5 figure

Leading indicators of fiscal distress: evidence from extreme bounds analysis

Early warning systems (EWSs) are widely used to assess a country’s vulnerability to fiscal distress. A fiscal distress episode is identified as a period when government experiences extreme funding difficulties. Most EWSs employ a specific set of only fiscal leading indicators predetermined by the researchers, which casts doubt on their robustness. We revisit this issue using extreme bounds analysis, which allows identifying robust leading indicators of fiscal distress from a large set. A robust leading indicator’s effect does not strongly depend on the model specification. Consistent with the theoretical predictions of latest generation crisis models, we find that both fiscal and non-fiscal leading indicators are robust. In addition, we find that a fiscal vulnerability indicator based on fiscal and non-fiscal leading indicators offers a 29% gain in predictive power compared to a traditional one based only on fiscal leading indicators. This suggests that both fiscal and non-fiscal leading indicators should be taken into account when assessing country’s vulnerability to fiscal distress

Relational consequences of compulsive Internet use: A longitudinal study among newlyweds

This article examines how compulsive Internet use and marital well-being are related to each other. We suggest that they are negatively related and explore whether compulsive Internet use predicts marital well-being or vice versa. The relation between compulsive Internet use and marital well-being is tested in a two-wave prospective study among 190 newlywed couples. The results suggest that (a) compulsive Internet use predicts marital well-being, and not vice versa, (b) that this is a within- rather than a cross-partner effect, and (c) that the frequency of Internet use may be positively related to marital well-being. The results are discussed in terms of the mechanisms that underlie the link between compulsive Internet use and relationship quality