Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data

We establish a global existence result for the rotating Navier-Stokes equations with ondecaying initial data in a critical space which includes a large class of almost periodic unctions. The scaling invariant function space we introduce is given as the divergence of the pace of 3×3 fields of Fourier transformed finite Radon measures. The smallness condition n initial data for global existence is explicitly given in terms of the Reynolds number. The ondition is independent of the size of the angular velocity of rotation

Uniform local solvability for the Navier-Stokes equations with the Coriolis force

The unique local existence is established for the Cauchy problem of the incompressible Navier-Stokes equations with the Coriolis force. The Coriolis operator restricted to divergence free vector fields is a zero order pseudodifferential operator with the skew-symmetric matrix symbol related to the Riesz operator. It leads to the additional term in the Navier-Stokes equations which has real parameter being proportional to the speed of rotation. For initial data as Fourier preimage of the space of all finite Radon measures with no point mass at the origin we prove uniform estimate for the existence time in the speed of rotation

Global solvabiliy of the Navier-Stokes equations in spaces based on sum-closed frequency sets

We prove existence of global regular solutions for the 3D Navier-Stokes quations with (or without) Coriolis force for a class of initial data u0 in he space FM¾;± , i.e. for functions whose Fourier image bu0 is a vector-valued adon measure and that are supported in sum-closed frequency sets with istance ± from the origin. In our main result we establish an upper bound or admissible initial data in terms of the Reynolds number, uniform on the oriolis parameter ­. In particular this means that this upper bound is inearly growing in ±. This implies that we obtain global in time regular olutions for large (in norm) initial data u0 which may not decay at space nfinity, provided that the distance ± of the sum-closed frequency set from he origin is sufficiently large

Primordial black holes and gravitational waves induced by exponential-tailed perturbations

Primordial black holes (PBHs) whose masses are in $\sim[10^{-15}M_\odot,10^{-11}M_{\odot}]$ have been extensively studied as a candidate of whole dark matter (DM). One of the probes to test such a PBH-DM scenario is scalar-induced stochastic gravitational waves (GWs) accompanied with the enhanced primordial fluctuations to form the PBHs with frequency peaked in the mHz band being targeted by the LISA mission. In order to utilize the stochastic GWs for checking the PBH-DM scenario, it needs to exactly relate the PBH abundance and the amplitude of the GWs spectrum. Recently in Kitajima et al., the impact of the non-Gaussianity of the enhanced primordial curvature perturbations on the PBH abundance has been investigated based on the peak theory, and they found that a specific non-Gaussian feature called the exponential tail significantly increases the PBH abundance compared with the Gaussian case. In this work, we investigate the spectrum of the induced stochastic GWs associated with PBH DM in the exponential-tail case. In order to take into account the non-Gaussianity properly, we employ the diagrammatic approach for the calculation of the spectrum. We find that the amplitude of the stochastic GW spectrum is slightly lower than the one for the Gaussian case, but it can still be detectable with the LISA sensitivity. We also find that the non-Gaussian contribution can appear on the high-frequency side through their complicated momentum configurations. Although this feature emerges under the LISA sensitivity, it might be possible to obtain information about the non-Gaussianity from GW observation with a deeper sensitivity such as the DECIGO mission.Comment: 33 pages, 19 figure

Navier-Stokes Equations in a Rotating Frame in R3{\mathbb R}^3 with Initial Data Nondecreasing at Infinity

Three-dimensional rotating Navier-Stokes equations are considered with a constant Coriolis parameter $\Omega$ and initial data nondecreasing at infinity. In contrast to the non-rotating case ($\Omega=0$), it is shown for the problem with rotation ($\Omega \neq 0$) that Green's function corresponding to the linear problem (Stokes + Coriolis combined operator) does not belong to $L^1({\mathbb R}^3)$. Moreover, the corresponding integral operator is unbounded in the space $L^{\infty}_{\sigma}({\mathbb R}^3)$ of solenoidal vector fields in ${\mathbb R}^3$ and the linear (Stokes+Coriolis) combined operator does not generate a semigroup in $L^{\infty}_{\sigma}({\mathbb R}^3)$. Local in time, uniform in $\Omega$ unique solvability of the rotating Navier-Stokes equations is proven for initial velocity fields in the space $L^{\infty}_{\sigma,a}({\mathbb R}^3)$ which consists of $L^{\infty}$ solenoidal vector fields satisfying vertical averaging property such that their baroclinic component belongs to a homogeneous Besov space ${\dot B}_{\infty,1}^0$ which is smaller than $L^\infty$ but still contains various periodic and almost periodic functions. This restriction of initial data to $L^{\infty}_{\sigma,a}({\mathbb R}^3)$ which is a subspace of $L^{\infty}_{\sigma}({\mathbb R}^3)$ is essential for the combined linear operator (Stokes + Coriolis) to generate a semigroup. The proof of uniform in $\Omega$ local in time unique solvability requires detailed study of the symbol of this semigroup and obtaining uniform in $\Omega$ estimates of the corresponding operator norms in Banach spaces. Using the rotation transformation, we also obtain local in time, uniform in $\Omega$ solvability of the classical 3D Navier-Stokes equations in ${\mathbb R}^3$ with initial velocity and vorticity of the form \mbox{\bf{V}}(0)=\tilde{\mbox{\bf{V}}}_0(y) + \frac{\Omega}{2} e_3 \times y, \mbox{curl} \mbox{\bf{V}}(0)=\mbox{curl} \tilde{\mbox{\bf{V}}}_0(y) + \Omega e_3 where \tilde{\mbox{\bf{V}}}_0(y) \in L^{\infty}_{\sigma,a}({\mathbb R}^3)

Comparison of scapular upward rotation during arm elevation in the scapular plane in healthy volunteers and patients with rotator cuff tears pre- and post-surgery.

[Background] Function loss caused by rotator cuff tears alters the scapular orientation, however, few prior studies have reported on scapular movements after rotator cuff repair. The purpose was to determine the scapular orientations before and after rotator cuff repair. [Methods] We recruited 14 healthy controls, 10 small and six massive rotator cuff tear in patients. The scapular upward rotation during arm elevation was analyzed using fluoroscopic imaging. [Findings] Before surgery, both rotator cuff groups demonstrated greater scapular upward rotation compared to healthy controls. Two months postoperation, the analyses showed significant differences between the patients with small rotator cuff tears and healthy controls at arm elevations of 90°, and between patients with both rotator cuff tear groups and healthy controls at arm elevations of 120°. At five months post-operation, significant differences still existed between the healthy controls and both rotator cuff groups. In regard to the temporal effects in the patients with small rotator cuff tears, the scapular upward rotation decreased significantly over time (2–5 months postoperation) at arm elevations of 120°. We did not identify a main effect owing to time in the patients with massive rotator cuff tears. [Interpretation] In patients with small rotator cuff tears, scapular upward rotation was reduced over the period of 2–5 months postoperation, however, the patients with massive rotator cuff tears showed greater scapular upward rotation throughout the experimental period. The results suggested that the execution of the rehabilitation program should consider that the tear size could affect scapular motion

Agreement in rotator cuff muscles measurement between ultrasonography and magnetic resonance imaging

[Background/objective] It is important to assess the atrophy of the rotator cuff to better understand shoulder function and pain. Previously, magnetic resonance imaging has been used for the evaluation of atrophy of rotator cuff muscles, which is time consuming. Therefore, a measurement tool requiring little time and easy accessibility is clinically desirable to be used frequently in rehabilitation. Recently, rotator cuff muscles have been evaluated using ultrasonography. However, little is known about the agreement of evaluation in rotator cuff muscles between magnetic resonance imaging and ultrasonography. The purpose of this study was to demonstrate the agreement between the muscle thickness measurements of supraspinatus, infraspinatus, and teres minor muscles by ultrasonography and the cross-sectional area measured by magnetic resonance imaging in the patient with rotator cuff tears. [Methods] A total of 47 patients with rotator cuff tears were enrolled. There were the 37 small tears, four medium tears, and six large tears, and the involved rotator cuff muscles were the supraspinatus in 37 shoulders, and the supraspinatus and infraspinatus in 10 shoulders. The measuring variables were muscle thickness and cross-sectional area of supraspinatus, infraspinatus, and teres minor muscles by using magnetic resonance imaging. Further, the muscle thickness of the rotator cuff were assessed using ultrasonography. A single regression model was used for demonstrating the agreement between the cross-sectional area measurement by magnetic resonance imaging and the muscle thickness measured using ultrasonography and magnetic resonance imaging of rotator cuff muscles. Additionally, the Bland-Altman plots between magnetic resonance imaging and ultrasonography was analyzed. [Results] The cross-sectional area were correlated with the muscle thickness measurement of rotator cuff muscles by magnetic resonance imaging, significantly (supraspinatus: r = 0.84, infraspinatus: ρ = 0.63, teres minor: ρ = 0.61, all p < 0.001). There were significant agreements between the cross-sectional area measured by magnetic resonance imaging and muscle thickness measured by ultrasonography (supraspinatus: r = 0.80, infraspinatus: ρ = 0.78, teres minor: ρ = 0.74, all p < 0.001). Bland-Altman plots revealed significant correlations between the average and the difference of the two measurements in supraspinatus (r = 0.36, p = 0.012), infraspinatus (r = 0.38, p < 0.001), and teres minor (r = 0.42, p < 0.001). These results clarified the proportional bias between MRI and US. [Conclusion] This study showed that, similar to magnetic resonance imaging, ultrasonography is a useful tool for assessing muscle atrophy of supraspinatus, infraspinatus, and teres minor muscles

Rikkunshito Ameliorates Cancer Cachexia Partly through Elevation of Glucarate in Plasma

Cancer cachexia, which is characterized by decreased food intake, weight loss and systemic inflammation, increases patient’s morbidity and mortality. We previously showed that rikkunshito (RKT), a Japanese traditional herbal medicine (Kampo), ameliorated the symptoms of cancer cachexia through ghrelin signaling-dependent and independent pathways. To investigate other mechanisms of RKT action in cancer cachexia, we performed metabolome analysis of plasma in a rat model bearing the Yoshida AH-130 hepatoma. A total of 110 metabolites were detected in plasma and RKT treatment significantly altered levels of 23 of those metabolites in cachexia model rats. Among them, glucarate, which is known to have anticarcinogenic activity through detoxification of carcinogens via inhibition of β-glucuronidase, was increased in plasma following administration of RKT. In our AH-130 ascites-induced cachexia rat model, administration of glucarate delayed onset of weight loss, improved muscle atrophy, and reduced ascites content. Additionally, glucarate reduced levels of plasma interferon-γ (IFN-γ) in tumor-bearing rats and was also found to suppress LPS-induced IFN-γ expression in splenocytes in vitro. These results suggest that glucarate has anti-inflammatory activity via a direct effect on immune host cells and suggest that RKT may also ameliorate inflammation partly through the elevation of glucarate in plasma

Supplementary material for the article: Beškoski, V. P.; Yamamoto, A.; Nakano, T.; Yamamoto, K.; Matsumura, C.; Motegi, M.; Beškoski, L. S.; Inui, H. Defluorination of Perfluoroalkyl Acids Is Followed by Production of Monofluorinated Fatty Acids. Science of the Total Environment 2018, 636, 355–359. https://doi.org/10.1016/j.scitotenv.2018.04.243

Supplementary material for: [https://doi.org/10.1016/j.scitotenv.2018.04.243]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/2168

Supplementary material for the article: Beškoski, V. P.; Yamamoto, A.; Nakano, T.; Yamamoto, K.; Matsumura, C.; Motegi, M.; Beškoski, L. S.; Inui, H. Defluorination of Perfluoroalkyl Acids Is Followed by Production of Monofluorinated Fatty Acids. Science of the Total Environment 2018, 636, 355–359. https://doi.org/10.1016/j.scitotenv.2018.04.243

Supplementary material for: [https://doi.org/10.1016/j.scitotenv.2018.04.243]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/2168