Existence of Solutions for a Quasilinear Schrödinger Equation with Potential Vanishing

Acta Mathematicae Applicatae Sinica, English Series - We study the following quasilinear Schrödinger equation $$ - \Delta u + V(x)u - \Delta ({u^2})u = K(x)g(u),\,\,\,\,\,\,\,\,x \in...     

Extension Operators Preserving Biholomorphic Mappings on Hartogs Domains*

In this paper, the authors extend the Roper-Suffridge operator on the generalized Hartogs domains. They mainly research the properties of the extended operator.By the characteristics of Hartogs domains and the geometric properties of subclasses of spirallike mappings, they obtain the extended Roper-Suffridge operator preserving almost starlikeness of complex order λ, almost spirallikeness of type β and order α, parabolic spirallikeness of type β and order ρ on the Hartogs domains in different co...     

Hα∞到Hβ∞复合算子的线性组合

设B是N维复空间C^N中的开单位球,φ_i为B上的解析自映射,H_α^∞表示定义在单位球上的加权解析函数空间.本文主要研究的是从空间H_α^∞到H_β^∞上的复合算子线性组合■的紧致性,其中λ_i(i=1,2,…,M)是非零常数.另外,根据紧致性等价条件,得出算子差分对(C_φ1-C_φ2)-(C_φ3-C_φ1)是紧致的当且仅当C_φ1-C_φ2与C_φ3-C_φ1都是紧致的算子.     

呼吸声分类技术研究及检测系统设计*

患有呼吸问题的病人由于呼吸道腺体不受意识控制、异物或者其本身肺部病变等原因会出现呼吸异常。医护人员通过病人的呼吸状况可以找寻和分析病人出现这种呼吸状况的原因。而以往呼吸声的诊断方式是专业的医护人员通过使用听诊器对病人进行肺部听诊。但是听诊的结果取决于医护人员的经验与相关参数。在初级诊断治疗阶段,初级医生识别听诊声的效率以及准确率很低,一般从20%到80%不等。因此会存在10%到20%的高误诊率（漏诊、错诊和延误）。本文提出了一种利用PVDF薄膜传感器提取语声特征的检测系统,该检测系统根据病人发出声音的不同,提取呼吸声特征值判断病人的呼吸状况。通过PVDF传感器采集的微弱呼吸声再经过KNN算法分类之后其识别率可达90.6%,对于细分种较类多的湿罗声,其识别率在80.2%左右。综上表明相比于传统听诊方式通过PVDF传感器采集识别的结果具有更高的准确性和可靠性,其判断呼吸状况的结果可以为医护人员提供参考,更好的为患有呼吸疾病的病人提供监测。     

Characterization of the low-temperature oxidation chemistry of an unsaturated aldehyde 2-butenal in a Jet-stirred reactor

Unsaturated aldehydes such as butenal are essential intermediates in the combustion of various alkenes and oxygenated biofuels. 2-Butenal is a typical intermediate included in the core mechanism, containing a C=C double bond adjacent to an aldehyde group. In the present work, the oxidation of 2-butenal is studied in a jet-stirred reactor (JSR) at atmospheric pressure under temperature ranging from 500 to 850 K. The synchrotron vacuum ultraviolet photoionization mass spectrometry is employed to identify the key intermediates. A kinetic model for 2-butenal oxidation is developed and validated against the experimental datasets. Fuel flux and sensitivity analyses are performed to clarify reactions governing the reactivity of 2-butenal. OH addition to the C=C double bond is essential for fuel reactivity at the initial stage. A combination of experimental observations and kinetic simulations is used to illuminate the Waddington mechanism initiated by OH addition. The resonance-stabilized feature of fuel radicals facilitates their interactions with HO₂ radicals, which replenishes a large amount of OH radicals and contributes to the formation of CO₂.     

A functional-group-based approach to modeling real-fuel combustion chemistry – III: Application to biodiesels

Real biodiesel fuels are mixtures comprising many high molecular weight components, making it a challenge to predict their combustion chemistry with detailed kinetic models. Our group previously proposed a functional-group approach (FGMech) to model the combustion chemistry of real gasoline and jet fuels; this approach has now been extended to model real biodiesel combustion and mixtures with petroleum fuels. As in our previous work, a decoupling philosophy is adopted for construction of the model. A lumped reaction mechanism describes the (oxidative) pyrolysis of fuels, while a detailed base chemistry model represents the oxidation of key pyrolysis intermediates. However, due to the presence of the ester group, several oxygenated species are identified as additional primary products and incorporated into the lumped reaction steps. In addition to the lumped reactions initiated by unimolecular decomposition and H-atom abstraction reactions, a lumped H-atom addition-elimination reaction is also incorporated as a new reaction class to account for the presence of double bonds. Stoichiometric parameters are obtained based on a multiple linear regression (MLR) model, which establishes relationships between the fuel's functional group distributions and the stoichiometric parameters of the lumped reactions. Global rate constants are developed from consistent rate rules obtained from pure fuels. New pyrolysis experimental data for methyl pentanoate/methyl nonanoate and methyl heptanoate/n-heptane mixtures (50%/50% in mol) are obtained in a jet-stirred reactor at atmospheric pressure. In general, kinetic models developed using the FGMech approach can reasonably reproduce all the validation targets obtained in this work, as well as those in the literature, confirming that functional-group-modeling is a promising approach to simulate combustion behavior of diesel/biodiesel surrogate fuels and real biodiesels.     

High- and low-temperature ignition delay time study and modeling efforts on vinyl acetate

Although esters in general have received much attention over the last decade of combustion research, the combustion of vinyl esters have yet not been studied in detail. Recent studies on ethyl acetate show that vinyl acetate is a major intermediate but its combustion is not well understood. This may be due to the fact that vinyl acetate itself can presumably not be used as a fuel or fuel additive, but both the fundamental understanding of vinyl ester combustion and the improvement of the ethyl ester modeling motivate the present study. Building on the work on ethyl acetate, a first kinetic model for the high- and low-temperature combustion of vinyl acetate is proposed, which includes reactions and intermediates that have not been considered before. These reactions are based on low-level quantum mechanical calculations as well as analogies drawn to mainly ethyl acetate. Seven additional species are considered compared to the ethyl acetate study for which the thermochemical data is derived by ab-initio calculations. The vinyl acetate kinetic model is validated against ignition delay times obtained in a shock tube and a rapid compression machine at pressures of 20 and 40 bar and temperatures ranging from 850 to 1250 K. Overall, a satisfactory agreement between the predictions of the kinetic model and the experimental data was found for all investigated conditions. Rate of production and brute force sensitivity analyses were performed to identify the most relevant reaction pathways, which underline the strong connection between the vinyl acetate and ethyl acetate chemistry.     

An analysis of the in-cylinder soots generated from the main- and post-injection combustion in diesel engines

In modern diesel engines, the exhaust soot primarily comes from the main-injection combustion and post-injection combustion. Therefore, to reduce the diesel soot emissions, it is essential to better understand the soots generated from the main-injection combustion (main-soot) and from the post-injection combustion (post-soot). This work focused on the properties of the main-soot and post-soot during the combustion process, including the primary particle size, nanostructure and soot mass. The in-cylinder soot samples were obtained using a self-developed total cylinder sampling system, and the primary particle size and nanostructure were determined using high-resolution transmission electron microscopy. The isolation of the post-soot was achieved by adding dimethyl ether to the intake gas instead of the real main-injection to create a simulated main-injection combustion environment for post-soot formation. Combustion analysis and numerical simulation results showed that the simulated combustion environment for post-soot formation generated by the DME combustion was very similar to that generated by the real main-injection combustion. During the combustion process, although the main-soot and post-soot exhibit similar variations in the primary particle size, the maximum primary particle size of the post-soot is smaller than that of the main-soot (23.38 nm for the main-soot and 20.51 nm for the post-soot). The main-soot and post-soot show almost the same trends in the nanostructure, as characterized by the fringe length, separation and tortuosity, throughout the combustion process. The introduction of the post-injection accelerates the reduction of the primary particle size of the main-soot and the increase in the structural order of the main-soot. Because a large number of the main-soot particles are oxidized during the post-injection combustion, the post-soot accounts for a considerable proportion in the engine-out soot (i.e., 42%).     

Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model

In this paper, a version of the Polyakov-Nambu-Jona-Lasinio (PNJL) model based on nonextensive statistical mechanics is presented. This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs (BG) statistics to a dimensionless nonextensivity parameter q. Thus, when q tends to 1, it returns to the BG case. Within the nonextensive PNJL model, we found that as q increases, the location of the critical end point (CEP) exhibits non-monotonic behavior. That is, for \begin{document}$ q<1.15 $\end{document}, CEP moves in the direction of lower temperature and larger quark chemical potential. However, for \begin{document}$ q>1.15 $\end{document}, CEP turns to move in the direction of lower temperature and lower quark chemical potential. In addition, we studied the moments of the net-baryon number distribution, that is, variance (\begin{document}$ \sigma^{2} $\end{document}), skewness (S), and kurtosis (κ). Our results are generally consistent with the latest experimental data reported, especially for \begin{document}$ \sqrt{S_{NN}}>19.6\ \mathrm{GeV} $\end{document}, when q is set to \begin{document}$ 1.07 $\end{document}.     

Insights into the nature of X(3872) through B meson decays

We study the \begin{document}$ B_{c,u,d}\to X(3872)P $\end{document} decays in the perturbative QCD (PQCD) approach, involving the puzzling resonance \begin{document}$ X(3872) $\end{document}, where P represents a light pseudoscalar meson (K or π). Assuming \begin{document}$ X(3872) $\end{document} to be a \begin{document}$ 1^{++} $\end{document} charmonium state, we obtain the following results. (a) The branching ratios of the \begin{document}$ B^+_c\to X(3872)\pi^+ $\end{document} and \begin{document}$ B^+_c\to X(3872) K^+ $\end{document} decays are consistent with the results predicted by the covariant light-front approach within errors; however, they are larger than those given by the generalized factorization approach. (b) The branching ratio of the \begin{document}$ B^+\to X(3872)K^+ $\end{document} decay is predicted as \begin{document}$ (3.8^{+1.1}_{-1.0})\times10^{-4} $\end{document}, which is smaller than the previous PQCD calculation result but still slightly larger than the upper limits set by Belle and BaBar. Hence, we suggest that the\begin{document}$ B^{0,+}\to X(3872)K^{0,+} $\end{document} decays should be precisely measured by the LHCb and Belle II experiments to help probe the inner structure of \begin{document}$ X(3872) $\end{document}. (c) Compared with the \begin{document}$ B_{u,d}\to X(3872)K $\end{document}decays, the \begin{document}$ B_{u,d}\to X(3872)\pi $\end{document} decays have significantly smaller branching ratios, which drop to values as low as \begin{document}$ 10^{-6} $\end{document}. (d) The direct CP violations of these considered decays are small (\begin{document}$ 10^{-3}\sim 10^{-2} $\end{document}) because the penguin contributions are loop suppressed compared to the tree contributions. The mixing-induced CP violation of the \begin{document}$ B\to X(3872)K^0_S $\end{document} decay is highly consistent with the current world average value \begin{document}$ \sin2\beta=(69.9\pm1.7)$\end{document}%. Experimentally testing the results for the branching ratios and CP violations, including the implicit \begin{document}$S U(3)$\end{document} and isospin symmetries of these decays, helps probe the nature of \begin{document}$ X(3872) $\end{document}.