“Debiteure” van die bedryfsekonomie*

Business Economics is a relatively young science, yet this fact presents a challenge to those who want to he called “debtors" of Business Economics. For the Christian businessman or the lecturer in Business Economics it means a reformulation of the basic principle of Economics and an acknowledgement of the fact that economic decisions involve more than economic norms only. Accounts receivables represent I.O.U.’s and in order to evaluate credit risk one must consider the five c’s of credit: character, capacity, collateral, capital and condition. If the liabilities, according to the requirements of the five c’s, are met, the “debtors” will appear in their rightful place on the balance sheet, that is under the assets. Then and then only can “debtors" generate a “profit"'

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

The applicability of some marketing principles to the Gospel

The primary objective of this study irav to test the applicability of some marketing principles to the Gospel. The secondary objective was to ascertain a correlation between the growing and declining churches and their respective adherence to or rejection of marketing principles. A new concept of marketing - the stewardship marketing concept - had to be formulated to satisfy the unique character of the Gospel. This broadened stewardship marketing concept allows the Gospel to be described as an intangible product which can be promoted, distributed and exchanged for scarce resources. Man's inability to 'sell' an excellent product like the Gospel dearly asks for a new distribution system to promote the Gospel This new distribution system, defined as a multi-channel vertical marketing system, can supplement and does not necessarily become a substitute for existing church structures

Generation and detection of very high frequency acoustic waves in solids Final report

Techniques for generation and detection of very high frequency acoustic waves in solid

Effect of Extending the Original Eligibility Criteria for the CROSS Neoadjuvant Chemoradiotherapy on Toxicity and Survival in Esophageal Cancer

Patients with curable esophageal cancer (EC) who proceed beyond the original Chemoradiotherapy for Oesophageal Cancer Followed by Surgery Study (CROSS) eligibility criteria are also treated with neoadjuvant chemoradiotherapy (nCRT). This study assessed the effect that extending the CROSS eligibility criteria for nCRT has on treatment-related toxicity and overall survival (OS) in EC. The study enrolled 161 patients with locally advanced EC (T1N1-3/T2-4aN0-3/M0) treated with the CROSS schedule followed by esophagectomy. Group 1 consisted of 89 patients who met the CROSS criteria, and group 2 consisted of 72 patients who met the extended eligibility criteria, i.e. a tumor length greater than 8 cm (n = 24), more than 10% weight loss (n = 35), more than 2-4 cm extension in the stomach (n = 21), celiac lymph node metastasis (n = 13), and/or age over 75 years (n = 2). The study assessed the differences in nCRT-associated toxicity [National Cancer Institute's Common Terminology Criteria for Adverse Events (CTCAE) grade3] and 90-day postoperative mortality. Moreover, the prognostic value for OS was assessed with multivariate Cox regression analysis. No difference was found in nCRT-associated toxicity (P = 0.117), postoperative complications (P = 0.783), and 90-day mortality (P = 0.492). The OS differed significantly (P = 0.004), with a median of 37.3 months [95% confidence interval (CI), 10.4-64.2 months] for group 1 and 17.2 months (95% CI 13.8-20.7 months) for group 2. Pathologic N stage (P = 0.023), pathologic T stage (P = 0.043), and group 2 (P = 0.008) were independent prognostic factors for OS. Extension of the CROSS study eligibility criteria for nCRT did not affect nCRT-associated toxicity, postoperative complications, and postoperative mortality, but was prognostic for OS