THE EIGEN-COMPLETE DIFFERENCE RATIO OF CLASSES OF GRAPHS- DOMINATION, ASYMPTOTES AND AREA

The energy of a graph   is related to the sum of Ï€ -electron energy in a molecule represented by a molecular graph, and originated by the  HMO (Hückel molecular orbital) theory.  Advances to this theory have taken place which includes the difference of the energy of graphs and the energy formation difference between a graph and its decomposable parts. Although the complete graph does not have the highest energy of all graphs, it is significant in terms of its easily accessible graph theoretical properties, and has a  high level of connectivity and robustness, for example. In this paper we introduce a ratio, the eigen-complete difference ratio, involving the difference in energy between the complete graph and any other connected graph G, which allows for the investigation of the effect of energy of G with respect to the complete graph when a large number of vertices are involved. This is referred to as the eigen-complete difference domination effect. This domination effect is greatest negatively (positively), for a strongly regular graph (star graphs with rays of length one), respectively, and zero for the lollipop graph. When this ratio is a function f(n), of the order of a graph, we attach the average degree of G to the Riemann integral to investigate the eigen-complete difference area aspect of classes of graphs.  We applied these eigen-complete aspects to complements of classes of graphs

An analysis of learners' engagement in mathematical task.

Thesis (M.Ed.) - University of Natal, Durban, 1988.The present project is part of a larger research programme focussed on the analysis of change; one aspect being educational transformation and in particular an emphasis on the explication of the contentless processes (eg. logical operations, reasoning styles, analysis and synthesis) which underlie both learning and teaching at university level. The present project is aimed at an analysis of the teaching-learning dialectic in mathematics courses. This analysis has two major focal points, that is, making explicit the often tacit and mostly inadequate and/or inappropriate rules for engaging in mathematical tasks which the under-prepared learner brings to the teaching-learning situation, and secondly the teaching strategies which may enable these learners to overcome their past (erroneous) knowledge and skills towards the development of effecient, autonomous mathematical problem-solving strategies. In order to remedy inadequate and inappropriate past learning and/or teaching, the present project presents a set of mediational strategies and regulative cues which function both for the benefit of the teacher and the learner in a problematic teaching-learning situation and on the meta and epistemic cognitive levels of information processing. Furthermore, these mediational strategies and regulative cues fall on a kind of interface between contentless processes and the particular content of the teaching-learning dialectic of mathematics in particular, as well as between the ideal components of any instructional process and the particular needs and demands of under-prepared learners engaged in mathematical tasks

The Victorian Newsletter (Fall 1981)

The Victorian Newsletter is sponsored for the Victorian Group of Modern Language Association by the Western Kentucky University and is published twice annually.Tennyson and Carlyle: A Source for "The Eagle" / Paul F. Mattheisen -- The Schooling of John Bull: Form and Moral in Talbot Baines Reed's Boys' Stories and in Kipling's Stalky & Co. / Patrick Scott -- How It Struck A Contemporary: Tennyson's "Lancelot and Elaine" and Pre-Raphaelite Art / Catherine Barnes Stevenson -- Amours de Voyage and Matthew Arnold in Love: An Inquiry / Eugene R. August -- Tennyson's "Ulysses" as Rhetorical Monologue / Mary Saunders -- The Mathematical References to the Adoption of the Gregorian Calendar in Lewis Carroll's Alice's Adventures in Wonderland / Laurence Dreyer -- Self-Helpers and Self-Seekers: Some Changing Attitudes to Wealth, 1840-1910 / J. L. Winte

Children's Oncology Group Trial AALL1231: A Phase III Clinical Trial Testing Bortezomib in Newly Diagnosed T-Cell Acute Lymphoblastic Leukemia and Lymphoma

PurposeTo improve the outcomes of patients with T-cell acute lymphoblastic leukemia (T-ALL) and lymphoblastic lymphoma (T-LL), the proteasome inhibitor bortezomib was examined in the Children's Oncology Group phase III clinical trial AALL1231, which also attempted to reduce the use of prophylactic cranial radiation (CRT) in newly diagnosed T-ALL.Patients and methodsChildren and young adults with T-ALL/T-LL were randomly assigned to a modified augmented Berlin-Frankfurt-Münster chemotherapy regimen with/without bortezomib during induction and delayed intensification. Multiple modifications were made to the augmented Berlin-Frankfurt-Münster backbone used in the predecessor trial, AALL0434, including using dexamethasone instead of prednisone and adding two extra doses of pegaspargase in an attempt to eliminate CRT in most patients.ResultsAALL1231 accrued 824 eligible and evaluable patients from 2014 to 2017. The 4-year event-free survival (EFS) and overall survival (OS) for arm A (no bortezomib) versus arm B (bortezomib) were 80.1% ± 2.3% versus 83.8% ± 2.1% (EFS, P = .131) and 85.7% ± 2.0% versus 88.3% ± 1.8% (OS, P = .085). Patients with T-LL had improved EFS and OS with bortezomib: 4-year EFS (76.5% ± 5.1% v 86.4% ± 4.0%; P = .041); and 4-year OS (78.3% ± 4.9% v 89.5% ± 3.6%; P = .009). No excess toxicity was seen with bortezomib. In AALL0434, 90.8% of patients with T-ALL received CRT. In AALL1231, 9.5% of patients were scheduled to receive CRT. Evaluation of comparable AALL0434 patients who received CRT and AALL1231 patients who did not receive CRT demonstrated no statistical differences in EFS (P = .412) and OS (P = .600).ConclusionPatients with T-LL had significantly improved EFS and OS with bortezomib on the AALL1231 backbone. Systemic therapy intensification allowed elimination of CRT in more than 90% of patients with T-ALL without excess relapse