STABILITY CRITERIA FOR THE SYSTEM OF DELAY DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS

In this paper, we consider the asymptotic stability for the system of linear delay differential equations. Because of the complicated interactions induced by the delay effects of the system, there are few results of the asymptotic stability for the system of the delay differential equations with multiple delays. Given this fact, we propose the new stability conditions for the system and apply these conditions to some mathematical models for the population dynamics and neural network system described by the system of delay differential equations

Organocatalytic depolymerization of poly(trimethylene carbonate)

Aliphatic polycarbonates have attracted attention as degradable and sustainable materials contributing to the circular plastic economy. Their chemical recycling has not been sufficiently studied. In this study, the efficacy of organocatalysts for depolymerization of poly(trimethylene carbonate) (PTMC), a representative aliphatic polycarbonate, is investigated using several organic acids and bases. The hydrolysis of PTMC produces the water-soluble degradates propane-1,3-diol (PD) and CO2. A phosphazene base P2-t-Bu shows high activity for the hydrolysis, yielding up to 31% and 89% of PD in the homogeneous reaction at around 27°C and the inhomogeneous reaction under the reflux condition, respectively. By contrast, 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) exhibits exceptionally high catalytic activity for the methanolysis of PTMC, producing PD and dimethyl carbonate. This is because of dual hydrogen-bonding activation, which completes the inhomogeneous reaction in a few hours at around 27°C while yielding more than 90% of PD. The reaction rate of the TBD-catalyzed methanolysis depends on the concentration of the nucleophile and catalyst, and the ratio of the nucleophile to the substrate affects the PD yield. These results provide a highly promising standard for chemical recycling of functionalized aliphatic polycarbonates that could potentially be applied to sustainable materials in the future

Charge-Order Pattern of the Low-Temperature Phase of NaV2O5 Uniquely Determined by Resonant X-Ray Scattering from Monoclinic Single Domain

The present resonant x-ray scattering from each of monoclinically-split single domains of NaV2O5 has critically enhanced contrast between V4+ and V5+ ions strong enough to lead to unambiguous conclusion of the charge-order pattern of its low-temperature phase below Tc = 35 K. The zig-zag type charge-order patterns in the $ab$-plane previously confirmed have four kinds of configurations (A, A', B and B') and the stacking sequence along the c-axis is determined as the AAA'A' type by comparison with model calculations. By assigning the A and A' configurations to Ising spins, one can reasonably understand the previously discovered "devil's staircase"-type behavior with respect to the modulation of the layer-stacking sequences at high pressures and low temperatures, which very well resembles the global phase diagram theoretically predicted by the ANNNI model.Comment: 4 pages, 3 figure

Stand-to-sit motion in older women

Objectives : The aims of this study were to examine the biomechanics of StandTS movements in older adults and to identify their optimal StandTS motion by measuring sitting impact forces. Methods : Healthy older women (n = 17) and healthy young women (n = 18) were asked to perform SitTS and StandTS motions at a natural speed using a chair. We measured the ground reaction forces from the participants’ feet and the chair, the angle of the trunk and ankle, vertical velocity, and postural muscle activities using a force plate, motion analyzer, and electromyography, respectively. Results : Sitting impact force was significantly greater in the older women than in the young women during the StandTS motion. There was a significant difference between the trunk angle and the ankle angle during the StandTS motion and sitting impact force had a significant negative correlation with the ankle joint motion in the older women. Conclusions : The ankle joint strategy was characterized by body sway resembling a single-segment-inverted pendulum and suggests that this response is less developed in the older adult. These results indicate that the ankle joint strategy may be an important factor involved in the sitting impact force

Microwave hinge states in a simple-cubic-lattice photonic crystal insulator

We numerically and experimentally demonstrated a higher-order topological state in a three-dimensional (3D) photonic crystal (PhC) with a complete photonic bandgap. Two types of cubic lattices were designed with different topological invariants, which were theoretically and numerically confirmed by the finite difference of their Zak phases. Topological boundary states in the two-dimensional interfaces and hinge states in the one-dimensional corners were formed according to the higher-order of bulk-boundary correspondence. Microwave measurements of the fabricated 3D PhC containing two boundaries and one corner showed a localized intensity, which confirmed the boundary and hinge states.Comment: 8 pages, 6 figure

Broadband X-ray Spectral Study of Nuclear Structure in Local Obscured Radio Galaxies

Radio galaxies are a key population to understand the importance of relativistic jets in AGN feedback. We present the results of a systematic, broadband X-ray spectral analysis of hard X-ray selected radio galaxies to investigate their nuclear structures. In this study, we focus on the seven most radio-loud, X-ray obscured narrow line radio galaxies in the \textit{Swift}/BAT 70 month AGN catalog. The spectra from 0.5 keV up to 66 keV obtained with \textit{Suzaku} and \textit{NuSTAR} of six objects are newly analyzed here by utilizing the X-ray clumpy torus model (XCLUMPY), whereas we refer to Ogawa et al. (2021) for the results of Centaurus A. We find that these radio galaxies have similar torus covering fractions compared with radio quiet AGNs at the same Eddington ratios ($-3 < \log \lambda_{\rm Edd} < -1$). This result implies that (1) the torus structure is not an important factor that determines the presence of jets and (2) AGN jets have physically little effect on the torus.Comment: 10 pages (4 tables/14 figures in the main text), accepted in MNRA

Clinical Application of the Ratio of Serum Bone Isoform to Total Alkaline Phosphatase in General Practice

Alkaline phosphatase (ALP) is an enzyme that is expressed in a variety of tissues. Among the isoforms of ALP, bone-specific alkaline phosphatase (BAP) is used as a marker for evaluating bone metabolism. We investigated the clinical usefulness of the ratio of serum BAP to total ALP for the diagnosis of various disorders in general practice. We retrospectively analyzed the cases of 107 Japanese patients whose serum BAP levels were exam-ined, focusing on clinical characteristics. We observed that the BAP/ALP ratios of the patients with fever and those with inflammatory diseases were significantly lower than the ratios of other patient groups. The BAP/ALP ratios of the patients with osteoporosis and those with metabolic bone diseases were higher than those of the patients with other conditions. The BAP/ALP ratio was found to be negatively correlated with age, a cor-relation that has not been found in other ethnicities. The serum BAP/ALP ratio was inversely correlated with serum CRP levels but was positively correlated with serum albumin levels and hemoglobin concentrations. Collectively, our results suggest that the BAP/ALP ratio could be a useful predictor for important geriatric con-ditions seen in general practice

Evaluation of two-dimensional electronic portal imaging device using integrated images during volumetric modulated arc therapy for prostate cancer

Background: The aim of the study was to evaluate analysis criteria for the identification of the presence of rectal gas during volumetric modulated arc therapy (VMAT) for prostate cancer patients by using electronic portal imaging device (EPID)-based in vivo dosimetry (IVD). Materials and methods: All measurements were performed by determining the cumulative EPID images in an integrated acquisition mode and analyzed using PerFRACTION commercial software. Systematic setup errors were simulated by moving the anthropomorphic phantom in each translational and rotational direction. The inhomogeneity regions were also simulated by the I’mRT phantom attached to the Quasar phantom. The presence of small and large air cavities (12 and 48 cm3) was controlled by moving the Quasar phantom in several timings during VMAT. Sixteen prostate cancer patients received EPID-based IVD during VMAT. Results: In the phantom study, no systematic setup error was detected in the range that can happen in clinical ( &lt; 5-mm and &lt; 3 degree). The pass rate of 2% dose difference (DD2%) in small and large air cavities was 98.74% and 79.05%, respectively, in the appearance of the air cavity after irradiation three quarter times. In the clinical study, some fractions caused a sharp decline in the DD2% pass rate. The proportion for DD2% &lt; 90% was 13.4% of all fractions. Rectal gas was confirmed in 11.0% of fractions by acquiring kilo-voltage X-ray images after the treatment. Conclusions: Our results suggest that analysis criteria of 2% dose difference in EPID-based IVD was a suitable method for identification of rectal gas during VMAT for prostate cancer patients