A dissertation presented to the Faculty of Health, Durban University of Technology, for the Masters Degree in Technology: Chiropractic, 2009. / Background: The International Classification of Diseases (ICD) provides codes to classify diseases in such a manner, that every health condition is assigned to a unique category. Some of the most common diagnoses made by chiropractors are not included in the ICD-10 coding system, as it is mainly medically orientated and does not accommodate these diagnoses. This can potentially lead to reimbursement problems for chiropractors in future and create confusion for medical aid schemes as to what conditions chiropractors actually diagnose and treat. Aim: To determine the level of compliancy of chiropractors, in South Africa, to the ICD-10 coding procedure and the factors that may influence the use of correct ICD-10 codes. As well as to determine whether the ICD-10 diagnoses chiropractors commonly submit to the medical aid schemes, reflect the actual diagnoses made in practice. Method: The study was a retrospective survey of a quantitative nature. A self-administered questionnaire was e-mailed and posted to 380 chiropractors, practicing in South Africa. The electronic questionnaires were sent out four times at two week intervals for the duration of eight weeks; and the postal questionnaires sent once. A response rate of 16.5% (n = 63) was achieved. Raw data was received from the divisional manager of the coding unit of Discovery Health (Pty) Ltd. in the form of an excel spreadsheet containing the most common ICD-10 diagnoses made by chiropractors in South Africa, for the period June 2006 to July 2007, who had submitted claims to the Medical Scheme. The spreadsheet also contained depersonalised compliance statistics of chiropractors to the ICD-10 system from July 2006 to October 2008. SPSS version 15 was used for descriptive statistical data analysis (SPSS Inc., Chicago, Ill, USA). Results: The age range of the 63 participants who responded to the questionnaire was 26 to 79 years, with an average of 41 years. The majority of the participants were male (74.6%, n = 47). KwaZulu-Natal had 25 participants (39.6%), Gauteng 17 (26.9%), Western Cape 12 (19%), Eastern Cape four (6.3%), Free State and Mpumalanga two (3.1%) each and North West one (1.5%). The mean knowledge score for ICD-10 coding was 43.5%, suggesting a relatively low level of knowledge. The total percentage of mistakes for electronic claims was higher for both the primary and unlisted claims (3.93% and 2.18%), than for manual claims iv (1.57% and 1.59%). The total percentage of mistakes was low but increased marginally each year for both primary claims (1.43% in 2006; 1.99% in 2007; 2.33% in 2008) and unlisted claims (0% in 2006; 2.61% in 2007; 3.07% in 2008). CASA members were more likely to be aware of assistance offered, in terms of ICD-10 coding through the medical schemes and the association (p = 0.131), than non-members. There was a non-significant trend towards participants who had been on an ICD-10 coding course (47.6%; n = 30), having a greater knowledge of the ICD-10 coding procedures (p = 0.147). Their knowledge was almost 10% higher than those who had not been on a course (52.4%; n = 33). Most participants (38.1%; n = 24) did not use additional cause codes when treating cases of musculoskeletal trauma, nor did they use multiple codes (38.7%; n = 24) when treating more than one condition in the same patient. Nearly 70% of participants (n = 44) used the M99 code in order to code for vertebral subluxation and the majority (79.4%; n = 50) believed the definition of subluxation used in ICD-10 coding to be the same as that which chiropractors use to define subluxation. According to the medical aid data, the top five diagnoses made by chiropractors from 2006 to 2007 were: Low back pain, lumbar region, M54.56 (8996 claims); Cervicalgia, M54.22 (6390 claims); Subluxation complex, cervical region, M99.11 (2895 claims); Other dorsalgia, multiple sites in spine, M54.80 (1524 claims) and Subluxation complex, sacral region, M99.14 (1293 claims). According to the questionnaire data, the top five diagnoses (Table 4.24) were: Lumbar facet syndrome, M54.56 (25%); Lumbar facet syndrome, M99.13 (23.3%); Cervical facet syndrome, M99.11 (21.7%); Cervicogenic headache, G44.2 (20%) and Cervicalgia, M54.22 (20%). Conclusion: The sample of South African chiropractors were fairly compliant to the ICD-10 coding system. Although the two sets of data (i.e. from the medical aid scheme and the questionnaire) regarding the diagnoses that chiropractors make on a daily basis correlate well with each other, there is no consensus in the profession as to which codes to use for chiropractic specific diagnoses. These chiropractic specific diagnoses (e.g. facet syndrome) are however, the most common diagnoses made by chiropractors in private practice. Many respondents indicated that because of this they sometimes use codes that they know will not be rejected, even if it is the incorrect code. For more complicated codes, the majority of respondents indicated that they did not know how to or were not interested in submitting the correct codes to comply with the level of specificity required by the medical aid schemes. The challenge is to make practitioners aware of the advantages of correct coding for the profession.

The Poincaré series, Py(f) of a polynomial f was first introduced by Borevich and Shafarevich in [BS66], where they conjectured, that the series is always rational. Denef and Igusa independently proved this conjecture. However it is still of interest to explicitly compute the Poincaré series in special cases. In this direction several people looked at diagonal polynomials with restrictions on the coefficients or the exponents and computed its Poincaré series. However in this dissertation we consider a general diagonal polynomial without any restrictions and explicitly compute its Poincaré series, thus extending results of Goldman, Wang and Han. In a separate chapter some new results are also presented that give a criterion for an element to be an mth power in a complete discrete valuation ring.

This dissertation explores the robust confluence of syntactic and cultural factors involved in the structure and content of chéngyǔ. It unpacks a number of structural tendencies in the data sample, and illuminates selected underlying cultural themes. The presence of syntactic and semantic parallelism within chéngyǔ in the dataset, as an expression of the correlative Chinese philosophy of the wǔxíng (五行 ‘Five Phases’ or ‘Five Elements’ of the universe), is a recurring point. Syntactic parallelism is demonstrated via chéngyǔ with invertible elements and by the overwhelming preference for syntactic parallelism, in particular the # N # N structure. Semantic parallelism is demonstrated via content words with related semantic fields or separable content words. The Chinese philosophical concepts of yīn and yáng are shown to have a clear impact on the use of numbers within chéngyǔ. Yīn and yáng are preferably arranged in balance with each other. If only one is present, however, then yáng is considered to be preferable over yīn. The interaction between the numbers within chéngyǔ has several pragmatic effects. For example, the combination of the numbers qī (七 'seven') and bā (八 'eight') is used to suggest disorder, untidiness or physical or emotional disturbance (Pellatt 2007:96). Bàn (半 ‘half’) may be used in chéngyǔ to denote the meaning of ‘a proportion.’ It also may be used together with yī (一 ‘one’) to indicate ‘any at all’ as well as a cluster of closely related concepts generally indicating ‘the existence of a small amount.’ Numbers also often have the effect of highlighting the contrast between two content words. Some chéngyǔ have a clearcut syntactic analysis, others do not. This is due to their highly elliptical and idiomatic nature, the fact that many lexemes can fall into more than one word class, and the fact that chéngyǔ are frozen expressions that often preserve some grammatical structures from Classical Chinese. Additionally, chéngyǔ do include conceptual metaphors, from the standpoint of the conceptual theory of metaphor launched with Lakoff and Johnson (1980). / Department of English

The crossing number of a graph is the minimum number of pairwise edge crossings in a drawing of a graph. A graph $G$ is $k$-crossing-critical if it has crossing number at least $k$, and any subgraph of $G$ has crossing number less than $k$. A consequence of Kuratowski's theorem is that 1-critical graphs are subdivisions of $K_{3,3}$ and $K_{5}$. The graph $V_{2n}$ is a $2n$-cycle with $n$ diameters. Bokal, Oporowski, Richter and Salazar found in \cite{bigpaper} all the critical graphs except the ones that contain a $V_{8}$ minor and no $V_{10}$ minor. We show that a 4-connected graph $G$ has crossing number at least 2 if and only if for each pair of disjoint edges there are two disjoint cycles containing them. Using a generalization of this result we found limitations for the 2-crossing-critical graphs remaining to classify. We showed that peripherally 4-connected 2-crossing-critical graphs have at most 4001 vertices. Furthermore, most 3-connected 2-crossing-critical graphs are obtainable by small modifications of the peripherally 4-connected ones.

This research is aimed at the formulation of a model for the processing of demography as a determinant of the education system. The inadequate understanding of demography in the education system causes flawed management of the target group by educational providers worldwide. Enrolment rates, school life expectancy, put-through rates and school completion rates (especially in developing countries) are not up to standard in most countries. Although developed regions manage most of these imperatives satisfactory, other education system aspects are experienced as challenges, for example inclusivety and equality. To steer the formulation of the model for the processing, a literature study was undertaken to elucidate demography in the context of the education system. The concept demography is investigated from a theoretical perspective. Research about the worldwide demographic tendencies was undertaken and the different aspects concerning demographic challenges were exposed. This was followed by a study concerning demographic challenges with respect to the four components of the education system. The literature clearly showed that the way in which demographic imperatives influence the four components, determines the criteria according to which a particular education system might measure it's success. Within this context demography as determinant of the education system is explained and an awareness is cultivated about how demographic demands of the target group can be approached by the education provider. A local investigation was undertaken to understand demographic demands in regional context. The North-West Province was used as a case study to present a local perspective of demographic demands on the education system. As the North-West Province is one of the nine provinces of South Africa, it was also necessary to indicate the wider South African demographic trends. Although the North-West Province does experience certain demographic challenges similar to those of the South African set-up as a whole, it also possesses has a number of unique aspects, for instance its geography and economy, which have direct demographic influence on the education system. The general population data and the education data of the province was scrutinised in the context of the educational region to emphasis the implications for the Department of Education. Typical examples of demographic imperatives (especially migration between regions of the province and migration to and from the province) which operate in the North-West Province can be attributed to the farming and mining activities prevalent in the province. The empirical investigation of the research was aimed at the experiences of schools in the North-West Province concerning demographic challenges. The investigation is focused on the leadership of schools and the management of the school leaders regarding demography. The demographic impact in the school- and regional context is also investigated in detail. Administrative problems experienced by principals as a result of inefficient planning are investigated and a policy analysis is done from a management perspective. The responses regarding the above-mentioned aspects show the challenges facing the Department of Education because of the demographic impact. A model is formulated with general demographic guidelines, relevant demographic imperatives and a structural education system approach. Suggestions are made about the adequate application of the model. This contribution to demographic processing is intended to broaden the understanding of educational providers regarding demography as a determinant of the education system and to address the gaps in educational provision and management. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2005.

For a given graph, G, the crossing number crₐ(G) denotes the minimum number of edge crossings when a graph is drawn on an orientable surface of genus a. The sequence cr₀(G), cr₁(G), ... is said to be the crossing sequence of a G. An equivalent definition exists for non-orientable surfaces. In 1983, Jozef Širáň proved that for every decreasing, convex sequence of non-negative integers, there is a graph G such that this sequence is the crossing sequence of G. This main result of this thesis proves the existence of a graph with non-convex crossing sequence of arbitrary length.

Thesis (M. Sc.)--University of Adelaide, 1979. / Bibliographies: leaves ii & 146-150.

Thesis (Ph.D.)--Tufts University, 2001. / Adviser: Marjorie G. Hahn. Submitted to the Dept. of Mathematics. Includes bibliographical references (leaves44-46). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph.D.)--McMaster University, 2002. / Adviser: Manfred Kolster. Includes bibliographical references. Also available via World Wide Web.

Thesis (Ph.D.)--McMaster University, 2002. / Adviser: Manfred Kolster. Includes bibliographical references. Also available via World Wide Web.