Center Manifold Analysis of Delayed Lienard Equation and Its Applications

Lienard Equations serve as the elegant models for oscillating circuits. Motivated by this fact, this thesis addresses the stability property of a class of delayed Lienard equations. It shows the existence of the Hopf bifurcation around the steady state. It has both practical and theoretical importance in determining the criticality of the Hopf bifurcation. For such purpose, center manifold analysis on the bifurcation line is required. This thesis uses operator differential equation formulation to reduce the infinite dimensional delayed Lienard equation onto a two-dimensional manifold on the critical bifurcation line. Based on the reduced two-dimensional system, the so called Poincare-Lyapunov constant is analytically determined, which determines the criticality of the Hopf bifurcation. Numerics based on a Matlab bifurcation toolbox (DDE-Biftool) and Matlab solver (DDE-23) are given to compare with the theoretical calculation. Two examples are given to illustrate the method

Sustainable energy technologies for energy saving and carbon emission reduction

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Fault location of distribution network with distributed generation based on Karrenbauer transform and support vector machine regression

As the capacity and scale of distribution networks continue to expand, and distributed generation technology is increasingly mature, the traditional fault location is no longer applicable to an active distribution network and "two-way" power flow structure. In this paper, a fault location method based on Karrenbauer transform and support vector machine regression (SVR) is proposed. Firstly, according to the influence of Karrenbauer transformation on phase angle difference before and after section fault in a low-voltage active distribution network, the fault regions and types are inferred preliminarily. Then, in the feature extraction stage, combined with the characteristics of distribution network fault mechanism, the fault feature sample set is established by using the phase angle difference of the Karrenbauer current. Finally, the fault category prediction model based on SVR was established to solve the problem of a single-phase mode transformation modulus and the indistinct identification of two-phase short circuits, then more accurate fault segments and categories were obtained. The proposed fault location method is simulated and verified by building a distribution network system model. The results show that compared with other methods in the field of fault detection, the fault location accuracy of the proposed method can reach 98.56%, which can enhance the robustness of rapid fault location

Clinical value of preferred endoscopic ultrasound-guided antegrade surgery in the treatment of extrahepatic bile duct malignant obstruction

Objectives: To explore the clinical value of preferred ultrasound endoscopic guided biliary drainage in patients with extrahepatic biliary obstruction with intrahepatic biliary ectasis. Methods: A total of 58 patients with malignant obstruction and intrahepatic bile duct expansion, including 32 males, 26 females and median age 65 (58‒81) were selected. A prospective randomized controlled study was randomized into EUS-AG and ERCP-BD, with 28 patients in EUS-AG and 30 in ERCP-BD. The efficacy of the two treatments, operation success rate, operation time, the incidence of complications, hospitalization days, cost, unimpeded stent duration, and survival time were compared. Results: 1) The surgical success rate in group EUS-AG was 100%, and in group, ERCP-BD was 96.67%. There was no statistical difference in surgical success rate in the two groups (p>0.05). 2) Average operating time in EUS-AG was (23.69±11.57) min, and in ERCP-BD was (36.75±17.69) min. The difference between the two groups has statistical significance (p<0.05). 3) The clinical symptoms of successful patients were significantly relieved. Compared with the preoperative procedure, the differences in group levels had statistical significance (p<0.05); TBIL, ALP, WBC and CRP levels, no statistical significance difference in groups (p>0.05). Conclusion: EUS-AG operation has short time, low incidence of complications, safe, effective, and can be used as the preferred treatment plan for patients with extrahepatic biliary duct malignant obstruction associated with intrahepatic biliary duct expansion; EUS-AG operation has more unique clinical advantages for patients with altered gastrointestinal anatomy or upper gastrointestinal obstruction

Adjusting for genetic confounders in transcriptome-wide association studies improves discovery of risk genes of complex traits

Many methods have been developed to leverage expression quantitative trait loci (eQTL) data to nominate candidate genes from genome-wide association studies. These methods, including colocalization, transcriptome-wide association studies (TWAS) and Mendelian randomization-based methods; however, all suffer from a key problem—when assessing the role of a gene in a trait using its eQTLs, nearby variants and genetic components of other genes’ expression may be correlated with these eQTLs and have direct effects on the trait, acting as potential confounders. Our extensive simulations showed that existing methods fail to account for these ‘genetic confounders’, resulting in severe inflation of false positives. Our new method, causal-TWAS (cTWAS), borrows ideas from statistical fine-mapping and allows us to adjust all genetic confounders. cTWAS showed calibrated false discovery rates in simulations, and its application on several common traits discovered new candidate genes. In conclusion, cTWAS provides a robust statistical framework for gene discovery

Spin-Induced Disk Precession in the Supermassive Black Hole at the Galactic Center

Sgr A* is a compact radio source at the Galactic Center, thought to be the radiative manifestation of a $2.6\times 10^6 M_\odot$ supermassive black hole. At least a portion of its spectrum--notably the mm/sub-mm ``bump''--appears to be produced within the inner portion ($r< 10 r_S$) of a hot, magnetized Keplerian flow, whose characteristics are also consistent with the $\sim 10$ linear polarization detected from this source at mm wavelengths. (The Schwarzschild radius, $r_S$, for an object of this mass $M$ is $2GM/c^2\approx 7.7\times 10^{11}$ cm, or roughly 1/20 A.U.) The recent detection of a 106-day cycle in Sgr A*'s radio variability adds significant intrigue to this picture, since it may signal a precession of the disk induced by the spin $a$ of the black hole. The dynamical time scale near the marginally stable orbit around an object with this mass is $\approx 20$ mins. Thus, since the physical conditions associated with the disk around Sgr A* imply rigid-body rotation, a precession period of 106 days may be indicative of a small black hole spin if the circularized flow is confined to a region $\sim 30 r_S$, for which $a\approx (M/10) (r_o/30 r_S)^{5/2}$. The precession of a larger structure would require a bigger black hole spin. We note that a small value of $a/M$ ($< 0.1$) would be favored if the non-thermal ($\sim 1-20$ cm) portion of Sgr A*'s spectrum is powered with energy extracted via a Blandford-Znajek type of process, for which the observed luminosity would correspond to an outer disk radius $r_o\sim 30 r_S$. Such a small disk size is also suggested by earlier hydrodynamical simulations, and is implied by Sgr A*'s spectral and polarimetric characteristics.Comment: 12 pages, 1 figure. Accepted for publicaton in ApJ Letter

Advanced Geological Prediction

Due to the particularity of the tunnel project, it is difficult to find out the exact geological conditions of the tunnel body during the survey stage. Once it encounters unfavorable geological bodies such as faults, fracture zones, and karst, it will bring great challenges to the construction and will easily cause major problems, economic losses, and casualties. Therefore, it is necessary to carry out geological forecast work in the tunnel construction process, which is of great significance for tunnel safety construction and avoiding major disaster accident losses. This lecture mainly introduces the commonly used methods of geological forecast in tunnel construction, the design principles, and contents of geological forecast and combines typical cases to show the implementation process of comprehensive geological forecast. Finally, the development direction of geological forecast theory, method, and technology is carried out. Prospects provide a useful reference for promoting the development of geological forecast of tunnels

Highly enhanced catalytic stability of copper by the synergistic effect of porous hierarchy and alloying for selective hydrogenation reaction

Supported copper has a great potential for replacing the commercial palladium-based catalysts in the field of selective alkynes/alkadienes hydrogenation due to its excellent alkene selectivity and relatively high activity. However, fatally, it has a low catalytic stability owing to the rapid oligomerization of alkenes on the copper surface. In this study, 2.5 wt% Cu catalysts with various Cu:Zn ratios and supported on hierarchically porous alumina (HA) were designed and synthesized by deposition–precipitation with urea. Macropores (with diameters of 1 μm) and mesopores (with diameters of 3.5 nm) were introduced by the hydrolysis of metal alkoxides. After in situ activation at 350 °C, the catalytic stability of Cu was highly enhanced, with a limited effect on the catalytic activity and alkene selectivity. The time needed for losing 10% butadiene conversion for Cu1Zn3/HA was ~40 h, which is 20 times higher than that found for Cu/HA (~2 h), and 160 times higher than that found for Cu/bulky alumina (0.25 h). It was found that this type of enhancement in catalytic stability was mainly due to the rapid mass transportation in hierarchically porous structure (i.e., four times higher than that in bulky commercial alumina) and the well-dispersed copper active site modified by Zn, with identification by STEM–HAADF coupled with EDX. This study offers a universal way to optimize the catalytic stability of selective hydrogenation reactions