Loss of body height due to severe thoracic curvature does impact pulmonary testing results in adolescents with idiopathic scoliosis

A standing body height is a variable used to calculate pulmonary parameters during spirometry examination. In adolescents with idiopathic scoliosis, the loss of the body height is observed, and it may potentially influence the results of pulmonary testing. The study aimed to analyze pulmonary parameters in adolescents with idiopathic scoliosis in relation to the measured versus the corrected body height. Preoperative pulmonary testing and radiographic evaluation were performed in 39 children (29 females, 10 males) aged 12–17 years. Forced vital capacity (FVC) and forced expiratory volume in one second (FEV1) were measured. The single best effort was analyzed. Thoracic Cobb angle ranged 50°–104°. Corrected body height was calculated according to the Stokes’ formula. The subgroup analysis was performed for the subjects with curves 50°–74° (N=26) versus 75°–104° curves (N=13). Mean measured body height was 166.1±9.0 cm versus 168.9±8.9 cm mean corrected body height. The %FVC obtained for the measured height was significantly higher than obtained for the corrected height: 84.6% ±15.6 vs. 81.6% ±15.6, p<0.001. The %FEV1 obtained for the measured height was significantly higher than obtained for the corrected height: 79.8% ±16.3 vs. 77.35% ±15.9, p<0.001. The subgroup analysis revealed significant differences in %FVC and %FEV1 calculated for the measured versus the corrected body height, p<0.001. Corrected body height significantly influences the results of pulmonary parameters measurement. In consequence, it may influence the analysis of the pulmonary status of children with idiopathic scoliosis.

Applicability conditions of the Stokes formula

<abstract><p>In our research work on the microscopic properties of liquids in relation to biotechnical applications, we were led to use the Stokes formula to calculate the force exerted by a fluid on colloidal suspensions, and to look in the bibliography for the demonstration of this formula. The proofs that we have found are often partial and the applicability conditions not always explicit, which led us to resort to the initial demonstration made by Stokes ^{[<xref ref-type="bibr" rid="b1">1</xref>]} in 1850 with the mathematical formalism used in that time. Here we give the detailed demonstration by means of the vector analysis specific to this type of problem. We end the article with a brief discussion of low Reynolds number flows dominated by viscosity and where inertial effects are neglected.</p></abstract>

Discrete Hardy Spaces for Bounded Domains in $${\mathbb {R}}^{n}$$

Discrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional function theory to the case of arbitrary bounded domains in $${\mathbb {R}}^{n}$$ R n . On this way, discrete Stokes’ formula, discrete Borel–Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.

A semi-canonical reduction for periods of Kontsevich–Zagier

The [Formula: see text]-algebra of periods was introduced by Kontsevich and Zagier as complex numbers whose real and imaginary parts are values of absolutely convergent integrals of [Formula: see text]-rational functions over [Formula: see text]-semi-algebraic domains in [Formula: see text]. The Kontsevich–Zagier period conjecture affirms that any two different integral expressions of a given period are related by a finite sequence of transformations only using three rules respecting the rationality of the functions and domains: additions of integrals by integrands or domains, change of variables and Stokes formula. In this paper, we prove that every non-zero real period can be represented as the volume of a compact [Formula: see text]-semi-algebraic set obtained from any integral representation by an effective algorithm satisfying the rules allowed by the Kontsevich–Zagier period conjecture.

Unbiased least-squares modification of Stokes’ formula

As the KTH method for geoid determination by combining Stokes integration of gravity data in a spherical cap around the computation point and a series of spherical harmonics suffers from a bias due to truncation of the data sets, this method is based on minimizing the global mean square error (MSE) of the estimator. However, if the harmonic series is increased to a sufficiently high degree, the truncation error can be considered as negligible, and the optimization based on the local variance of the geoid estimator makes fair sense. Such unbiased types of estimators, derived in this article, have the advantage to the MSE solutions not to rely on the imperfectly known gravity signal degree variances, but only the local error covariance matrices of the observables come to play. Obviously, the geoid solution defined by the local least variance is generally superior to the solution based on the global MSE. It is also shown, at least theoretically, that the unbiased geoid solutions based on the KTH method and remove–compute–restore technique with modification of Stokes formula are the same.