Tight bounds for break minimization

We consider round-robin sports tournaments with n teams and n − 1 rounds. We construct an infinite family of opponent schedules for which every home-away assignment induces at least 1/4 n(n−2) breaks. This construction establishes a matching lower bound for a corresponding upper bound from the literature

Lossy gossip and composition of metrics

We study the monoid generated by n-by-n distance matrices under tropical (or min-plus) multiplication. Using the tropical geometry of the orthogonal group, we prove that this monoid is a finite polyhedral fan of dimension n(n-1)/2, and we compute the structure of this fan for n up to 5. The monoid captures gossip among n gossipers over lossy phone lines, and contains the gossip monoid over ordinary phone lines as a submonoid. We prove several new results about this submonoid, as well. In particular, we establish a sharp bound on chains of calls in each of which someone learns something new.Comment: Minor textual edits, final versio

Vanwaar die kragtige invloed van die optrede en prediking van Jesus?

No Abstract

Kajian Awal Penyusunan Algoritma Perhitungan Luas Tanah dan Faktor Koreksi dengan Metode Poligon Terbuka dan Tertutup

Data for land squares area and land volumes are strongly needed for private company neither is the government. Nowadays, the calculations of land squares are done manually, which need long and repetitive calculations. It is unfortunately risky for the researches. On the other side, none of the standard methods is used to calculate the volume of land burying. One of the alternatives when we intend to minimize the error of the calculation and measurement process is to integrate the step of calculation and measurement processes themselves. The underlined means to practice the automation on the recitation of several measurement output, and then the calculation of land squares, contour drawing, and land volumes can automatically be done. On the calculation of area squares, contour drawing, and land volumes, data of the measurements are put into calculation algorithm and are expected to be directly used in calculating the land squares, contour drawing, and land volumes, also automatically make the correction on the errors in order to minimize them. In this research, no hardware development is being developed. The author intended only to compose a calculation of algorithm to calculate land squares.Keywords: Land Squares, Algorithm, Integrat

Non-axisymmetric oscillations of stratified coronal magnetic loops with elliptical cross-sections

We study non-axisymmetric oscillations of a straight magnetic tube with an elliptic cross-section and density varying along the tube. The governing equations for kink and fluting modes in the thin tube approximation are derived. We found that there are two kink modes, polarised along the large and small axes of the elliptic cross-section. We have shown that the ratio of frequencies of the first overtone and fundamental harmonic is the same for both kink modes and independent of the ratio of the ellipse axes. On the basis of this result we concluded that the estimates of the atmospheric scale height obtained using simultaneous observations of the fundamental harmonic and first overtone of the coronal loop kink oscillations are independent of the ellipticity of the loop cross-section

On General Axial Gauges for QCD

General Axial Gauges within a perturbative approach to QCD are plagued by 'spurious' propagator singularities. Their regularisation has to face major conceptual and technical problems. We show that this obstacle is naturally absent within a Wilsonian or 'Exact' Renormalisation Group approach and explain why this is so. The axial gauge turns out to be a fixed point under the flow, and the universal 1-loop running of the gauge coupling is computed.Comment: 4 pages, latex, talk presented by DFL at QCD'98, Montpellier, July 2-8, 1998; to be published in Nucl. Phys. B (Proc. Suppl.

On the nature of kink MHD waves in magnetic flux tubes

Magnetohydrodynamic (MHD) waves are often reported in the solar atmosphere and usually classified as slow, fast, or Alfv\'en. The possibility that these waves have mixed properties is often ignored. The goal of this work is to study and determine the nature of MHD kink waves. This is done by calculating the frequency, the damping rate and the eigenfunctions of MHD kink waves for three widely different MHD waves cases: a compressible pressure-less plasma, an incompressible plasma and a compressible plasma with non-zero plasma pressure which allows for MHD radiation. In all three cases the frequency and the damping rate are for practical purposes the same as they differ at most by terms proportional to $(k_z R)^2$. In the magnetic flux tube the kink waves are in all three cases, to a high degree of accuracy incompressible waves with negligible pressure perturbations and with mainly horizontal motions. The main restoring force of kink waves in the magnetised flux tube is the magnetic tension force. The total pressure gradient force cannot be neglected except when the frequency of the kink wave is equal or slightly differs from the local Alfv\'{e}n frequency, i.e. in the resonant layer. Kink waves are very robust and do not care about the details of the MHD wave environment. The adjective fast is not the correct adjective to characterise kink waves. If an adjective is to be used it should be Alfv\'{e}nic. However, it is better to realize that kink waves have mixed properties and cannot be put in one single box

Education and training as a social science : some empirical evidence in the Rosebank Business Precinct of Auckland New Zealand

Tertiary institutions should seek continuous feedback from industries to keep track of the needs of businesses to provide education and training. Academics should stay in touch with businesses by networking and consulting. Holland and De Cieri (2006) refer to theories of child learning (pedagogy) to inform their understanding of andragogy, the study of adult learning. Adult learners would be continuous learners and would move in and out of formal education according to individual needs or life circumstances, job requirements or career development. In designing programmes and up-grading curricula, these are important factors to bear in mind so that programmes &ldquo;cater&rdquo; for these learners as well.This study was financed by Auckland City Council focussing on Auckland&rsquo;s Rosebank Business Precinct (ARBP). The surrounding communities, particularly M&auml;ori, Pacific peoples and recent migrants, experience disparities in employment. Our research questions were:&bull; Is there a skills match between the present-day workforce and actual business needs over the medium term?&bull; What can these data tell us about Rosebank&rsquo;s trajectory as a skilled business cluster and about its future workforce requirements?&bull; What education and training will be necessary for these organisations to maintain their competitive advantage and profit margins?The target population were the 500-600 businesses operating on Rosebank Road. A total of 529 businesses were identified. Interviews with 102 companies with a 36-question questionnaire were conducted. The sampling frame was owner-managers (senior, non-shareholding managers). Of the respondent firms, 68.75% had vacancies for up to 3 months and 31.24% vacancies for 6 months.This paper highlights areas identified in the ARBP for developing programmes and curricula for tertiary institutions to provide employable students with the right knowledge, skills and attributes (KSAs) to grow existing ventures. A fine balance must be struck between human and organisational needs. In the analysis and discussion we point out what education or training is necessary for the ARBP to provide greater efficiencies and subsequent improvement to their profit levels by current and future employees entering the workforce; well &ldquo;equipped&rdquo; employees with knowledge and skills to add value in their organisations. Recommendations, future perspectives and conclusions form the last part of this paper<br /