Search results for "Calculus"

Tool-life modelling as a stochastic process

1998

Abstract In a previous paper [G. Galante, A. Lombardo, A. Passannanti, Proceedings of XXXVII Scientific Meeting of the Italian Statistical Society, 1994, p. 553] the Authors proposed to model cutting tool wear behaviour as a stochastic process with independent Gaussian increments plus drift. Such a model implies that the tool-life, i.e. the time to reach a fixed value of flank wear, has an inverse Gaussian probability distribution. The model has several practical and theoretical advantages. In fact, it is based on an easily and cheaply experimentally verifiable wear behaviour hypothesis, it is more flexible because it is not limited to a particular wear level and, finally, the data are bett…

Multi-State System in human reliability analysis

2009

Application of mathematical model of Multi-State System for human reliability analysis is considered in the paper. This paper describes new method for estimation of changes of more than one component states and they influence to Multi-State System reliability by Dynamic Reliability Indices. The Multi-State System failure is considered depending on decrease of some system component efficiency and the Multi-State System repair is declared depending on replacement of some failed components. The mathematical approach of Logical Differential Calculus is used for analysis of the Multi-State System reliability change that is caused by modifications of some system components states.

Oral health status in patients with moderate-severe and terminal renal failure.

2007

Aims. To evaluate the oral health status of patients with moderate-severe chronic renal failure (CRF) and with terminal renal failure (TRF). Design. The study group was formed of 50 patients: 22 (44%) with moderate-severe CRF and 28 (56%) with TRF included in a haemodialysis programme. The controls (n=64) presented similar characteristics with regard to sex, age, weight and educational level. A single dentist performed an intraoral examination on all the subjects, gathering information on: number of decayed, missing or filled teeth; supragingival plaque accumulation; calculus deposits; periodontal pockets in the Ramfjord teeth; and loss of insertion. Results. No significant differences were…

Personal Reflections on Dirk Jan Struik By Joseph W. Dauben

2018

Dirk Jan Struik, who taught for many years at the Massachusetts Institute of Technology and died on 21 October 2000 at the age of 106, was a distinguished mathematician and influential teacher. He was also widely known as a leading Marxist scholar and social activist. His early work on vector and tensor analysis, undertaken together with Jan Arnoldus Schouten, helped impart new mathematical techniques needed to master Einstein’s general theory of relativity. This collaboration lasted for over 20 years, but by the end of the 1930s, Struik came to realize that the heyday of the Ricci calculus had passed. After the Second World War, having now entered his 50s, he gave up mathematical research …

Geometry and “Metaphysics of Space” in Gauss and Riemann

1994

Gauss’s research on the principles of geometry and the axiom of parallels have been the subject of study for long time (e.g. Stackel 1933) which has shed light once and for all on his role in the early history of non-Euclidean geometry. It is therefore unnecessary to go through it all over again; what is more interesting here is to examine the development of Gauss’s ideas from another standpoint which emerges from the first testimony of his reflections on a subject that mathematicians had examined in vain right from antiquity: i.e. the possibility of proving the proposition that Euclid had taken as an axiom and formulated in the following terms: “That, if a straight line falling on two stra…

Rolle's Theorem Fails in l2

1996

Assessment of the capacity of a pyrophosphate-based mouth rinse to inhibit the formation of supragingival dental calculus. a randomized double-blind …

2019

Background This study aimed to analyze the efficacy of an anti-calculus mouth rinse and its possible adverse effects on the mucosa and teeth. Material and Methods This randomized double-blind placebo-controlled clinical trial included 40 patients with treated and managed periodontal disease, all with a history of rapid calculus formation. Patients used a pyrophosphate-based test mouth rinse (B) or a placebo (A). A range of parameters were measured for: saliva (saliva flow, pH and chemical composition); calculus (Volpe-Manhold [V-M] index, weight, and volume); adverse effects on mucosa and teeth; and the patients’ subjective perceptive of mouth rinse efficacy. Results The test mouth rinse B …

Analysis of Predisposing Factors for Rapid Dental Calculus Formation.

2020

Background: Calculus accumulation varies widely between individuals. Dental calculus has been associated with the principal periodontal diseases. The aim of this study was to analyze individual characteristics, and salivary and microbiological parameters among patients considered to be rapid calculus formers and patients who form calculus slowly. Methods: Individual characteristics were recorded in a sample of 74 patients (age, sex, smoking, periodontal diagnosis, and dental crowding), as well as salivary parameters (unstimulated saliva flow, pH, and biochemical analysis of saliva) and microbiological parameters (by means of semi-quantitative polymerase chain reaction (PCR) analysis). Resul…

On Obtaining Classification Confidence, Ranked Predictions and AUC with Tsetlin Machines

2020

Tsetlin machines (TMs) are a promising approach to machine learning that uses Tsetlin Automata to produce patterns in propositional logic, leading to binary (hard) classifications. In many applications, however, one needs to know the confidence of classifications, e.g. to facilitate risk management. In this paper, we propose a novel scheme for measuring TM confidence based on the logistic function, calculated from the propositional logic patterns that match the input. We then use this scheme to trade off precision against recall, producing area under receiver operating characteristic curves (AUC) for TMs. Empirically, using four real-world datasets, we show that AUC is a more sensitive meas…

xloops - Automated Feynman diagram calculation

1998

The program package xloops, a general, model independent tool for the calculation of high energy processes up to the two-loop level, is introduced. xloops calculates massive one- and two-loop Feynman diagrams in the standard model and related theories both analytically and numerically. A user-friendly Xwindows frontend is part of the package. xloops relies on the application of parallel space techniques. The treatment of tensor structure and the separation of divergences in analytic expressions is described in this scheme. All analytic calculations are performed with Maple. We describe the mathematical methods and computer algebra techniques xloops uses and give a brief introduction how to …