Approximative compactness of linear combinations of characteristic functions

2020 ◽  
Vol 257 ◽  
pp. 105435
Author(s):  
Paul C. Kainen ◽  
Věra Kůrková ◽  
Andrew Vogt
Author(s):  
Andrew Gelman ◽  
Deborah Nolan

Descriptive statistics is the typical starting point for a statistics course, and it can be tricky to teach because the material is more difficult than it first appears. The activities in this chapter focus more on the topics of data displays and transformations, rather than the mean, median, and standard deviation, which are covered easily in a textbook and on homework assignments. Specific topics include: distributions and handedness scores; extrapolation of time series and world record times for the mile run; linear combinations and economic indexes; scatter plots and exam scores; and logarithmic transformations and metabolic rates.


Bernoulli ◽  
2013 ◽  
Vol 19 (5A) ◽  
pp. 1776-1789 ◽  
Author(s):  
Xiaoqing Pan ◽  
Maochao Xu ◽  
Taizhong Hu

Medicina ◽  
2021 ◽  
Vol 57 (8) ◽  
pp. 772
Author(s):  
Alexandra-Cristina Măroiu ◽  
Cosmin Sinescu ◽  
Virgil-Florin Duma ◽  
Florin Topală ◽  
Anca Jivănescu ◽  
...  

1. Background and Objectives: Ceramic veneers represent the most appropriate treatment option for minimally invasive aesthetic rehabilitation. For long-term clinical success, the accurate marginal and internal adaptation of dental restorations are of paramount importance. The aim of this in vitro study is to assess the effect of a novel (patented) design of veneers compared to conventional ones on their marginal and internal gap to the prepared tooth surface. 2. Materials and Methods: Twenty-four lithium disilicate ceramic veneers are obtained using Computer-Aided-Design (CAD) and then milled using Computer-Aided-Manufacturing (CAM). The samples are divided into two groups: 12 conventional (CO) veneers (i.e., with a linear marginal contour) and 12 crenelated (CR) veneers, the latter with the novel sinusoidal marginal design. All samples are bonded to frontal teeth, and the adhesive interfaces are analyzed using two methods, optical microscopy and micro-Computed Tomography (CT): the former for the accuracy of the marginal gap and the latter for the internal gap (as well as for the homogeneity of the luting cement) of ceramic veneers. 3. Results: STATA and one-way ANOVA tests reveal significant differences between CO and CR veneers: (i) the marginal gap is smaller for CR (64 μm) than for CO veneers (236 μm); (ii) the internal adaptation is better for CR veneers: for a cement width of up to 120 μm, the covered surface for the CR group is 81.5%, while for the CO group it is 64.5%; (iii) the mean of the porosities within the cement is not significantly different (3.4 × 106 μm3 for CO and 3.9 × 106 μm3 for CR veneers), with a higher standard deviation for the CO group. Analytical modeling is achieved for internal gaps using the micro-CT results. The characteristic functions obtained allow us to compare the volume of luting cement for the two types of veneers. 4. Conclusion: The novel veneers design produces an improvement in the marginal and internal adaptation of the restorations to the prepared tooth surface. Thus, it provides favorable premises for better clinical performances.


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