Association of Tooth Scaling with Acute Myocardial Infarction and Analysis of the Corresponding Medical Expenditure: A Nationwide Population-Based Study

Accumulating evidence has shown a significant correlation between periodontal diseases and systemic diseases. In this study, we investigated the association between the frequency of tooth scaling and acute myocardial infarction (AMI). Here, a group of 7164 participants who underwent tooth scaling was compared with another group of 7164 participants without tooth scaling through propensity score matching to assess AMI risk by Cox’s proportional hazard regression. The results show that the hazard ratio of AMI from the tooth scaling group was 0.543 (0.441, 0.670) and the average expenses of AMI in the follow up period was USD 265.76, while the average expenses of AMI in follow up period for control group was USD 292.47. The tooth scaling group was further divided into two subgroups, namely A and B, to check the influence of tooth scaling frequency on AMI risk. We observed that (1) the incidence rate of AMI in the group without any tooth scaling was 3.5%, which is significantly higher than the incidence of 1.9% in the group with tooth scaling; (2) the tooth scaling group had lower total medical expenditures than those of the other group because of the high medical expenditure associated with AMI; and (3) participants who underwent tooth scaling had a lower AMI risk than those who never underwent tooth scaling had. Therefore, the results of this study demonstrate the importance of preventive medicine.

Radiative MHD Sutterby Nanofluid Flow Past a Moving Sheet: Scaling Group Analysis

The present theoretical work endeavors to solve the Sutterby nanofluid flow and heat transfer problem over a permeable moving sheet, together with the presence of thermal radiation and magnetohydrodynamics (MHD). The fluid flow and heat transfer features near the stagnation region are considered. A new form of similarity transformations is introduced through scaling group analysis to simplify the governing boundary layer equations, which then eases the computational process in the MATLAB bvp4c function. The variation in the values of the governing parameters yields two different numerical solutions. One of the solutions is stable and physically reliable, while the other solution is unstable and is associated with flow separation. An increased effect of the thermal radiation improves the rate of convective heat transfer past the permeable shrinking sheet.

Charles Bouton and the Navier-Stokes Global Regularity Conjecture

The present article examines the Lie group invariants of the Navier-Stokes equation for incompressible fluids. This is accomplished by applying the invariant theory of Charles Bouton. His analyis shows that since the solutions of the NSE are relative invariants of the scaling group, they must be isobaric polynomials of x,y,z,t and thus infinitely differentiable. Then, bounded energy follows from conservation law. The total angular momentum per unit mass is a scale-invariant vector; it is analyzed and conclusions are drawn about its role in turbulence.

Shifts of group-like projections and contractive idempotent functionals for locally compact quantum groups

A one-to-one correspondence between shifts of group-like projections on a locally compact quantum group [Formula: see text] which are preserved by the scaling group and contractive idempotent functionals on the dual [Formula: see text] is established. This is a generalization of the Illie–Spronk’s correspondence between contractive idempotents in the Fourier–Stieltjes algebra of a locally compact group [Formula: see text] and cosets of open subgroups of [Formula: see text]. We also establish a one-to-one correspondence between nondegenerate, integrable, [Formula: see text]-invariant ternary rings of operators [Formula: see text], preserved by the scaling group and contractive idempotent functionals on [Formula: see text]. Using our results, we characterize coideals in [Formula: see text] admitting an atom preserved by the scaling group in terms of idempotent states on [Formula: see text]. We also establish a one-to-one correspondence between integrable coideals in [Formula: see text] and group-like projections in [Formula: see text] satisfying an extra mild condition. Exploiting this correspondence, we give examples of group-like projections which are not preserved by the scaling group.

Scaling Group Analysis of Mixed Bioconvective Flow in Nanofluid with Presence of Slips, MHD and Chemical Reactions

Bioconvective flows have attracted attention in recent years due to actual and potential applications. In this paper, we consider a steady and laminar convective MHD flow of a nanofluid with heat, mass and microorganism transfer with a heat source/sink present. In addition, we assume there exists a first order chemical reaction. The governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) using the scaling group transformation and the associated boundary value problem is then solved. The influences of selected governing parameters on the dimensionless velocity, temperature, nanoparticle concentration, density of motile microorganisms, skin friction, heat transfer, mass transfer, and motile microorganism density rates are computed and discussed