Die persoonlike geloofsdaad van die Nagmaalsgebruiker

The act of personal faith of the Communicant The aim of this article is to determine the nature of the communicant’s act of faith in the Three Formulae of Unity. The main theses are:Holy communion is only instituted for the reborn to nourish their spiritual and heavenly life.The only food that can strengthen the new life is the exalted, living Christ, also in accordance with his human nature.The most important act which occurs during Holy Communion is Christ’s act of giving Himself. In fact the reborn partakes of the true Christ with the Holy Spirit and is thus nourished.Because Christ is in heaven, the communicant must raise his heart towards heaven to partake of Christ and to make Him his own

Improved bounds for the crossing numbers of K_m,n and K_n

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing number cr(K_n) of the complete graph K_n equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In this paper we show the following improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values: (i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1); (ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and (iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83. The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8, respectively. These improved bounds are obtained as a consequence of the new bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to set up a quadratic program on 6! variables whose minimum p satisfies cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic optimization techniques combined with a bit of invariant theory of permutation groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure

Die hermeneuse van die skrif met die oog op hedendaagse kerklik-etiese vraagstukke

Ons verstaan Hermeneutiek in die tradisionele sin. Ons gebruik die term dus nie in die sin van die sg. Nuwere Hermeneutiek, wat bykans die hele teologie onder “Hermeneutiek” as die hele proses van “verstaan” van die Skrifte wil insluk nie

New approximations for the cone of copositive matrices and its dual

We provide convergent hierarchies for the cone C of copositive matrices and its dual, the cone of completely positive matrices. In both cases the corresponding hierarchy consists of nested spectrahedra and provide outer (resp. inner) approximations for C (resp. for its dual), thus complementing previous inner (resp. outer) approximations for C (for the dual). In particular, both inner and outer approximations have a very simple interpretation. Finally, extension to K-copositivity and K-complete positivity for a closed convex cone K, is straightforward.Comment: 8

A dinocephalian therapsid fauna on the Ecca–Beaufort contact in Eastern Cape Province, South Africa

Systematic exploration of outcrops of the lowermost Beaufort Group for fossils of the oldest terrestrial vertebrates of South Africa, known only from the Permian age Eodicynodon Assemblage Zone in Western Cape Province, has resulted in the discovery of a therapsid fauna in Eastern Cape Province that is dominated by advanced dinocephalians. The new discoveries include the skull and partial skeleton of a juvenile Anteosaurus, skull and skeletal elements of tapinocephalids, as well as the skull of a scylacosaurid therocephalian. The combined presence of advanced tapinocephalid dinocephalians, the anteosaur Anteosaurus, and scylacosaurid therocephalians suggests that the rocks of the lowermost Beaufort Group in the Eastern Cape Province can be assigned to the Tapinocephalus Assemblage Zone, rather than to the Eodicynodon Assemblage Zone, which appears to be restricted to the southwestern part of the Karoo Basin. This biozone identity permits the recognition of a younger age for the Ecca-Beaufort contact eastwards along the southern margin of the basin, thus demonstrating the diachronous nature of the Ecca-Beaufort contact in the southern Karoo

Perspektiewe vanuit die psigologie en sosiale wetenskappe vir kerklike bediening aan die adolossent. Deel 2: Ondersoek na die leefw�reld van die adolessent

In this article meta-theoretical� perspectives for youth ministry are obtained specifically from the fields of psychology and sociology. In the first place, the various psychological development phases of the adolescent are determined, as well as how they have to be accounted for in youth ministry.� In the second place, the characteristics of the world in which the adolescent lives are indicated together with their influence on the adolescents