Solutions of Schr\"odinger equations\\ with symmetry in orientation preserving tetrahedral group

We consider the nonlinear Schr\"odinger equation \begin{equation*} \Delta u = \big( 1 +\ve V_1(|y|)\big)u - |u|^{p-1}u \quad \text{in} \quad \mathbb{R}^N, \quad N\ge 3, \quad p \in \left(1, \frac{N+2}{N-2}\right).\end{equation*} The phenomenon of pattern formation has been a central theme in the study of nonlinear Schr\"odinger equations. However, the following nonexistence of $O(N)$ symmetry breaking solution is well-known: if the potential function is radial and radially nondecreasing, any positive solution must be radial. Therefore, solutions of interesting patterns, such as those with symmetry in a discrete subgroup of $O(N)$, can only exist after violating the assumptions. For a potential function that is radial but asymptotically decreasing, a solution with symmetry merely in a discrete subgroup of $O(2)$ has been presented. These observations pose the question of whether patterns of higher dimensions can appear. In this study, the existence of nonradial solutions whose symmetry group is a discrete subgroup of $O(3)$, more precisely, the orientation-preserving regular tetrahedral group is shown

Circuit Structure and Control Method to Reduce Size and Harmonic Distortion of Interleaved Dual Buck Inverter

A new circuit structure and control method for a high power interleaved dual-buck inverter are proposed. The proposed inverter consists of six switches, four diodes and two inductors, uses a dual-buck structure to eliminate zero-cross distortion, and operates in an interleaved mode to reduce the current stress of switch. To reduce the total harmonic distortion at low output power, the inverter is controlled using discontinuous-current-mode control combined with continuous-current-mode control. The experimental inverter had a power-conversion efficiency of 98.5% at output power = 1300 W and 98.3% at output power = 2 kW, when the inverter was operated at an input voltage of 400 V-DC, output voltage of 220 V-AC/60 Hz, and switching frequency of 20 kHz. The total harmonic distortion was < 0.66%, which demonstrates that the inverter is suitable for high-power dc-ac power conversion.11Ysciescopu

The effect of multileaf collimator leaf width on the radiosurgery planning for spine lesion treatment in terms of the modulated techniques and target complexity

PURPOSE: We aim to evaluate the effects of multileaf collimator (MLC) leaf width (5 mm vs. 2.5 mm) on the radiosurgery planning for the treatment of spine lesions according to the modulated techniques (intensity-modulated radiotherapy [IMRT] vs. volumetric-modulated arc therapy [VMAT]) and the complexity of the target shape. METHODS: For this study, artificial spinal lesions were contoured and used for treatment plans. Three spinal levels (C5, T5, and L2 spines) were selected, and four types of target shapes reflecting the complexity of lesions were contoured. The treatment plans were performed using 2.5-mm and 5-mm MLCs, and also using both static IMRT and VMAT. In total, 48 treatment plans were established. The efficacy of each treatment plan was compared using target volume coverage (TVC), conformity index (CI), dose gradient index (GI), and V(30%). RESULTS: When the 5-mm MLC was replaced by the 2.5-mm MLC, TVC and GI improved significantly by 5.68% and 6.25%, respectively, while CI did not improve. With a smaller MLC leaf width, the improvement ratios of the TVC were larger in IMRT than VMAT (8.38% vs. 2.97%). In addition, the TVC was improved by 14.42-16.74% in target type 4 compared to the other target types. These improvements were larger in IMRT than in VMAT (27.99% vs. 6.34%). The V(30%) was not statistically different between IMRT and VMAT according to the MLC leaf widths and the types of target. CONCLUSION: The smaller MLC leaf width provided improved target coverage in both IMRT and VMAT, and its improvement was larger in IMRT than in VMAT. In addition, the smaller MLC leaf width was more effective for complex-shaped targets

Peroxisome Proliferators-Activated Receptor (PPAR) Modulators and Metabolic Disorders

Overweight and obesity lead to an increased risk for metabolic disorders such as impaired glucose regulation/insulin resistance, dyslipidemia, and hypertension. Several molecular drug targets with potential to prevent or treat metabolic disorders have been revealed. Interestingly, the activation of peroxisome proliferator-activated receptor (PPAR), which belongs to the nuclear receptor superfamily, has many beneficial clinical effects. PPAR directly modulates gene expression by binding to a specific ligand. All PPAR subtypes (α, γ, and σ) are involved in glucose metabolism, lipid metabolism, and energy balance. PPAR agonists play an important role in therapeutic aspects of metabolic disorders. However, undesired effects of the existing PPAR agonists have been reported. A great deal of recent research has focused on the discovery of new PPAR modulators with more beneficial effects and more safety without producing undesired side effects. Herein, we briefly review the roles of PPAR in metabolic disorders, the effects of PPAR modulators in metabolic disorders, and the technologies with which to discover new PPAR modulators

Unveiling the Role of Ruthenium in Layered Sodium Cobaltite Toward High-Performance Electrode Enabled by Anionic and Cationic Redox

The effect of Ru substitution on the structure and electrochemical properties of P2-type Na0.67CoO2 is investigated. The first-discharge capacities of Na0.67CoO2 and Na0.6 [Co0.78Ru0.22]O2 materials are 128 and 163 mAh g−1 (23.5 mA g−1), respectively. Furthermore, the rate capability is improved due to the electro-conducting nature of Ru doping. Operando X-ray diffraction analysis reveals that the Na0.67CoO2 does not undergo a phase transition; however, multiple Na+/vacancy ordered superstructures within the P2 phase appear during Na+ extraction/insertion. In contrast, the Na0.6[Co0.78Ru0.22]O2 material undergoes a P2–OP4 phase transition during desodiation, with no formation of Na+/vacancy ordering within the P2 phase. The increased discharge capacity of Na0.6[Co0.78Ru0.22]O2 is most likely associated with additional cationic Ru4+/Ru5+ redox and increased anionic O2−/(O2n−) redox participation. Combined experimental (galvanostatic cycling, X-ray absorption spectroscopy, differential electrochemical mass spectrometry) and theoretical (density functional theory calculations) studies confirm that Ru substitution provokes the oxygen-redox reaction and that partial O2 release from the oxide lattice is the origin of the reaction. The findings provide new insight for improving the electrode performance of cathode materials via 4d Ru substitution and motivate the development of a new strategy for the design of high-capacity cathode materials for sodium-ion batteries.</p