χ Value in the Chi-square distribution used to test for significant differences between three (or more) independent groups when using the Kruskall-Wallis non-parametric analysis of variance where the dependent variable is measured on an ordinal scale. p Probability of making a type I decision error. U Critical value in the Mann-Whitney U test to test for significant differences between two inde...

INTRODUCTION The antimicrobial efficacy of root canal irrigant plays an important role in increasing the success of root canal treatment (RCT). The aim of the present experimental study was to compare the antimicrobial activity of Triphala (a plant-derived solution) with 0.5, 1, 2.5 and 5% concentrations of sodium hypochlorite (NaOCl), against Enterococcus faecalis (E. faecalis). METHODS AND ...

Proof. This theorem is a corollary of the (much more general) Kruskal-Katona theorem. The Kruskal-Katona theorem has a very hands-on proof, based on iteratively modifying the graph. We will see a linear-algebraic proof. Let A be the n×n adjacency matrix of G (Auv = 1 if vertex u is adjacent to vertex v, and Auv = 0 otherwise). Note that A is symmetric. It turns out that e and t are both fundame...

Calculating the statistical linear response of turbulent dynamical systems to the change in external forcing is a problem of wide contemporary interest. Here the authors apply linear regression models with memory, AR(p) models, to approximate this statistical linear response by directly fitting the autocorrelations of the underlying turbulent dynamical system without further computational exper...

OBJECTIVE The aim of this study was 2-fold. The first aim was to evaluate the effects of mixing technique (hand-mixing or auto-mixing) on bacterial attachment to polyether impression materials. The second aim was to determine whether bacterial attachment to these materials was affected by length of exposure to disinfection solutions. MATERIALS AND METHODS Polyether impression material samples...

The problem of the rectification curves and calculation (for which we shall adopt more geometric term “flattening”) surface a rotating solid generated by curve, once rotation axis has been fixed, were treated John Wallis in two short inter-related tracts on cycloids cissoids 1659. In this work, focus parabola, an ancient reproposed 17th century, solution obtained using particular series that re...