The algebro-geometric solutions for Degasperis-Procesi hierarchy

Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the associated Baker-Akhiezer functions, meromorphic function and Dubrovin-type equations are established. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker-Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DP hierarchy.Comment: 65 pages. arXiv admin note: text overlap with arXiv:solv-int/9809004 by other author

Algebro-geometric Solutions for the Degasperis--Procesi Hierarchy

Though the completely integrable Camassa--Holm (CH) equation and Degasperis--Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we derive the DP hierarchy with the help of Lenard recursion operators. Based on the characteristic polynomial of a Lax matrix for the DP hierarchy, we introduce a third order algebraic curve $\mathcal{K}_{r-2}$ with genus $r-2$, from which the associated Baker--Akhiezer functions, meromorphic function and Dubrovin-type equations are established. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker--Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DP hierarchy

A GPU-Based Transient Stability Simulation Using Runge-Kutta Integration Algorithm

Abstract Graphics processing units (GPU) have been investigated to release the computational capability in various scientific applications. Recent research shows that prudential consideration needs to be given to take the advantages of GPUs while avoiding the deficiency. In this paper, the impact of GPU acceleration to implicit integrators and explicit integrators in transient stability is investigated. It is illustrated that implicit integrators, although more numerical stable than explicit ones, are not suitable for GPU acceleration. As a tradeoff between numerical stability and efficiency, an explicit 4th order Runge-Kutta integration algorithm is implemented for transient stability simulation based on hybrid CPU-GPU architecture. The differential equations of dynamic components are evaluated in GPU, while the linear network equations are solved in CPU using sparse direct solver. Simulation on IEEE 22-bus power system with 6 generators is reported to validate the feasibility of the proposed method

Nonlinear vibration modeling and bifurcation characteristic study of a planetary gear train processing device

In this paper, a nonlinear torsional vibration model with meshing errors, time varying meshing stiffness, damping coefficients and gear backlashes was established and dimensionless equations of the system are derived in the planetary gear train processing device. The paper analyzed the nonlinear dynamic behavior of the device which was used to machine the Circular-Arc-Tooth-Trace cylindrical gear. By using the method of numerical integration, the bifurcation diagrams are obtained and the results indicate that the processing device has abundant bifurcation characteristics with the change of the dimensionless speed, and the damping ratios, gear backlashes and meshing errors of meshing pairs could influence the vibration greatly. The bifurcation diagrams reveal that increasing the damping ratios can change the bifurcation and the chaos can be avoid when the damping ratios are bigger enough, reducing the gear backlashes can reduce the dimensionless displacement amplitudes, increasing the meshing errors can make the bifurcation diagrams shift left for a distance, and alternating load torque with large amplitude will cause complex chaos phenomenon. The study can help to avoid the fatigue failure and instabilities caused by chaos and it also contribute to improving the performance of the processing device

MUX64, an analogue 64-to-1 multiplexer ASIC for the ATLAS High Granularity Timing Detector

We present the design and the performance of MUX64, a 64-to-1 analogue multiplexer ASIC for the ATLAS High Granularity Timing Detector (HGTD). The MUX64 transmits one of its 64 inputs selected by six address lines for the voltages or temperatures being monitored to an lpGBT ADC channel. The prototype ASICs fabricated in TSMC 130 nm CMOS technology were prepared in wire-bonding and QFN88 packaging format. A total of 280 chips was examined for functionality and quality assurance. The accelerated aging test conducted at 85 degrees celsius shows negligible degradation over 16 days

Manipulating Multiple Order Parameters via Oxygen Vacancies: The case of Eu0.5Ba0.5TiO3-{\delta}

Controlling functionalities, such as magnetism or ferroelectricity, by means of oxygen vacancies (VO) is a key issue for the future development of transition metal oxides. Progress in this field is currently addressed through VO variations and their impact on mainly one order parameter. Here we reveal a new mechanism for tuning both magnetism and ferroelectricity simultaneously by using VO. Combined experimental and density-functional theory studies of Eu0.5Ba0.5TiO3-{\delta}, we demonstrate that oxygen vacancies create Ti3+ 3d1 defect states, mediating the ferromagnetic coupling between the localized Eu 4f7 spins, and increase an off-center displacement of Ti ions, enhancing the ferroelectric Curie temperature. The dual function of Ti sites also promises a magnetoelectric coupling in the Eu0.5Ba0.5TiO3-{\delta}.Comment: Accepted by Physical Review B, 201

Health-related quality of life as measured with EQ-5D among populations with and without specific chronic conditions: A population-based survey in Shaanxi province, China

© 2013 Tan et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Introduction: The aim of this study was to examine health-related quality of life (HRQoL) as measured by EQ-5D and to investigate the influence of chronic conditions and other risk factors on HRQoL based on a distributed sample located in Shaanxi Province, China. Methods: A multi-stage stratified cluster sampling method was performed to select subjects. EQ-5D was employed to measure the HRQoL. The likelihood that individuals with selected chronic diseases would report any problem in the EQ-5D dimensions was calculated and tested relative to that of each of the two reference groups. Multivariable linear regression models were used to investigate factors associated with EQ VAS. Results: The most frequently reported problems involved pain/discomfort (8.8%) and anxiety/depression (7.6%). Nearly half of the respondents who reported problems in any of the five dimensions were chronic patients. Higher EQ VAS scores were associated with the male gender, higher level of education, employment, younger age, an urban area of residence, access to free medical service and higher levels of physical activity. Except for anemia, all the selected chronic diseases were indicative of a negative EQ VAS score. The three leading risk factors were cerebrovascular disease, cancer and mental disease. Increases in age, number of chronic conditions and frequency of physical activity were found to have a gradient effect. Conclusion: The results of the present work add to the volume of knowledge regarding population health status in this area, apart from the known health status using mortality and morbidity data. Medical, policy, social and individual attention should be given to the management of chronic diseases and improvement of HRQoL. Longitudinal studies must be performed to monitor changes in HRQoL and to permit evaluation of the outcomes of chronic disease intervention programs. © 2013 Tan et al.National Nature Science Foundation (No. 8107239

AMPK Phosphorylates and Inhibits SREBP Activity to Attenuate Hepatic Steatosis and Atherosclerosis in Diet-Induced Insulin-Resistant Mice

SummaryAMPK has emerged as a critical mechanism for salutary effects of polyphenols on lipid metabolic disorders in type 1 and type 2 diabetes. Here we demonstrate that AMPK interacts with and directly phosphorylates sterol regulatory element binding proteins (SREBP-1c and -2). Ser372 phosphorylation of SREBP-1c by AMPK is necessary for inhibition of proteolytic processing and transcriptional activity of SREBP-1c in response to polyphenols and metformin. AMPK stimulates Ser372 phosphorylation, suppresses SREBP-1c cleavage and nuclear translocation, and represses SREBP-1c target gene expression in hepatocytes exposed to high glucose, leading to reduced lipogenesis and lipid accumulation. Hepatic activation of AMPK by the synthetic polyphenol S17834 protects against hepatic steatosis, hyperlipidemia, and accelerated atherosclerosis in diet-induced insulin-resistant LDL receptor-deficient mice in part through phosphorylation of SREBP-1c Ser372 and suppression of SREBP-1c- and -2-dependent lipogenesis. AMPK-dependent phosphorylation of SREBP may offer therapeutic strategies to combat insulin resistance, dyslipidemia, and atherosclerosis

Pump-controlled wavelength switchable dissipative soliton mode-locked Yb-doped fiber laser using a 45° tilted fiber grating

We demonstrate a pump-controlled wavelength switchable Yb-doped fiber laser (YDFL) by nonlinear polarization rotation (NPR) for the first time. The polarizer replaced by a 45° tilted fiber grating (45°-TFG) combines with a section of polarization maintaining fiber (PMF) to form a fiber-based birefringent filter. Stable dissipative soliton (DS) with center wavelength of 1068.39 nm is generated under the mode-locked threshold of 277 mW. The operating wavelength switching between 1046.51 nm and 1067.90 nm can be realized via increasing the pump power simply while keeping the polarization controllers (PCs) in a fixed state. The laser maintains stable mode-locking operation at each wavelength, which can be regarded as a type of multi-wavelength ultrafast light source with precise control and integration potential

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements