Left Variables Research Articles

Cone-Beam Computed Tomographic Assessment of the Mandibular Condylar Volume in Different Skeletal Patterns: A Retrospective Study in Adult Patients.

The aim of this study was to assess the condylar volume in adult patients with different skeletal classes and vertical patterns using cone-beam computed tomography (CBCT). CBCT scans of 146 condyles from 73 patients (mean age 30 ± 12 years old; 49 female, 24 male) were selected from the archive of the Department of Dentistry and Maxillofacial Surgery of Fondazione IRCCS Ca’ Granda, Milan, Italy, and retrospectively analyzed. The following inclusion criteria were used: adult patients; CBCT performed with the same protocol (0.4 mm slice thickness, 16 × 22 cm field of view, 20 s scan time); no systemic diseases; and no previous orthodontic treatments. Three-dimensional cephalometric tracings were performed for each patient, the mandibular condyles were segmented and the relevant volumes calculated using Mimics Materialize 20.0® software (Materialise, Leuven, Belgium). Right and left variables were analyzed together using random-intercept linear regression models. No significant association between condylar volumes and skeletal class was found. On the other hand, in relation to vertical patterns, the mean values of the mandibular condyle volumes in hyperdivergent subjects (688 mm3) with a post-rotation growth pattern (625 mm3) were smaller than in hypodivergent patients (812 mm3) with a horizontal growth pattern (900 mm3). Patients with an increased divergence angle had smaller condylar volumes than subjects with normal or decreased mandibular plane divergence. This relationship may help the clinician when planning orthodontic treatment.

Analogues of Entropy in Bi-Free Probability Theory: Microstates

Abstract In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is defined. Properties essential to an entropy theory are developed, such as the behaviour of the entropy when transformations on the left variables or on the right variables are performed. In addition, the microstate bi-free entropy is demonstrated to be additive over bi-free collections provided additional regularity assumptions are included and is computed for all bi-free central limit distributions. Moreover, an orbital version of bi-free entropy is examined, which provides a tighter upper bound for the subadditivity of microstate bi-free entropy and provides an alternate characterization of bi-freeness in certain settings.

Impact of Urbanization on Household Economy Development in Sa Dec Flower Village, Dong Thap

Sa Dec Flower Village provides flowers for southern Vietnam and as a result makes an important contribution to the socio-economic development of the region, especially via tourism. This article aims to discern the factors affecting the economic and social changes of the Sa Dec Flower Village to establish appropriate development strategies. The impact on the economic changes of the flower village based on the following five key factors (1) Local orientation, (2) Urbanization, (3) Market economy, (4) Agricultural cooperative model, and (5) Traditional Flower Village engagement. There have been many previous related studies examining the relationship between these factors and household economic development in the context of urbanization; however, each study was done separately without combining all analyses in the same study. To test this impact, the paper applies the Exploratory Factor Analysis (EFA) model to find out which factors have the most impact on the dependent variable Household Economic Development. The study surveyed 350 cases in two areas of Tan Quy Dong ward and Tan Khanh Dong ward which have strong urbanization rate and a long history of development of ornamental flower craft villages as well as the largest flower production areas in Sa Dec flower village. The results show that factors of Urbanization, Market economy and Traditional Flower Village engagement (of which Urbanization is the strongest one) have the impact on the household economic development. The two left variables Local Development Orientation and Agricultural Cooperative Model do not have a significant relationship or impact on the dependent variable and are excluded from the regression model. Based on the research results presented, this paper suggests possible solutions to improve the efficiency of the economic development of Sa Dec flower village.

Harmonic analysis for the bi-free partial S-transform

We develop an analytic machinery to study Voiculescu's bi-free partial S-transform and then use the results to characterize the multiplicative bi-free infinite divisibility. It is shown that the class of infinitely divisible distributions coincides with the class of limit distributions for products of bi-free pairs of left and right infinitesimal unitaries, where the pairs are not required to be identically distributed but all left variables are assumed to commute with all right variables. Furthermore, necessary and sufficient conditions for convergence to a given infinitely divisible distribution are found.