A New Comparison Principle for Impulsive Functional Differential Equations

通过归纳总结建立了一种关于具有有限时滞的脉冲泛函微分方程的新的比较原理,并利用这种比较原理,得到了几个时滞脉冲微分方程稳定性的充分条件。最后举出了一个例子来说明研究结果的有效性。In this paper,we establish a new comparison principle for impulsive differential systems with time delay,then,using this comparison principle,we obtain some sufficient conditions for several stabilities of impulsive delay differential equations.Finally,we present an example to show the effectiveness of our results

A Counterexample of the Approximate PoincaréMap

在WIggInS S.所著的书《glObAl bIfurCATIOnS And CHAOS》的第三章中分别讨论了在双曲奇点附近庞加莱映射与其线性逼近的误差,以及它们的导数之间的误差,即其证明了:P0-Pl0=Ο(ε2)与dP0-dPl0=O(ε2).针对该本书中提出来的庞卡莱映射线性逼近理论,构造出一个反例,通过利用等价关系和不等式等一些技巧,不仅说明了书中的上述两个逼近误差是错误的,而且指出了书中用来证明该线性逼近理论的引理都是不正确的.Wiggins S.,in his book " Global Bifurcations and Chaos",discussed the error between the Poincarémap and its linear approximation,and also the error between the derivations of those maps near the hyperbolic singular point in Chapter 3,respectively.In other words,he proved the conclusions: P0-PL0=O(ε2)and DP0-DPL0=O(ε2).In this paper,we present a counterexample in allusion to the linear approximation of Poincarémap in this book.Through utilizing some skills of the equivalence relation and some inequalities,not only do we illustrate the two approximation errors mentioned above are incorrect,but also the lemma,which is used to prove the theory of linear approximation,appears invalid

JUNO Sensitivity on Proton Decay p→νˉK+p\to \bar\nu K^+ Searches

The Jiangmen Underground Neutrino Observatory (JUNO) is a large liquid scintillator detector designed to explore many topics in fundamental physics. In this paper, the potential on searching for proton decay in $p\to \bar\nu K^+$ mode with JUNO is investigated.The kaon and its decay particles feature a clear three-fold coincidence signature that results in a high efficiency for identification. Moreover, the excellent energy resolution of JUNO permits to suppress the sizable background caused by other delayed signals. Based on these advantages, the detection efficiency for the proton decay via $p\to \bar\nu K^+$ is 36.9% with a background level of 0.2 events after 10 years of data taking. The estimated sensitivity based on 200 kton-years exposure is $9.6 \times 10^{33}$ years, competitive with the current best limits on the proton lifetime in this channel

JUNO sensitivity on proton decay p → ν K + searches*

The Jiangmen Underground Neutrino Observatory (JUNO) is a large liquid scintillator detector designed to explore many topics in fundamental physics. In this study, the potential of searching for proton decay in the $p\to \bar{\nu} K^+$ mode with JUNO is investigated. The kaon and its decay particles feature a clear three-fold coincidence signature that results in a high efficiency for identification. Moreover, the excellent energy resolution of JUNO permits suppression of the sizable background caused by other delayed signals. Based on these advantages, the detection efficiency for the proton decay via $p\to \bar{\nu} K^+$ is 36.9% ± 4.9% with a background level of $0.2\pm 0.05({\rm syst})\pm$$0.2({\rm stat})$ events after 10 years of data collection. The estimated sensitivity based on 200 kton-years of exposure is $9.6 \times 10^{33}$ years, which is competitive with the current best limits on the proton lifetime in this channel and complements the use of different detection technologies

Prediction of Energy Resolution in the JUNO Experiment

International audienceThis paper presents the energy resolution study in the JUNO experiment, incorporating the latest knowledge acquired during the detector construction phase. The determination of neutrino mass ordering in JUNO requires an exceptional energy resolution better than 3% at 1 MeV. To achieve this ambitious goal, significant efforts have been undertaken in the design and production of the key components of the JUNO detector. Various factors affecting the detection of inverse beta decay signals have an impact on the energy resolution, extending beyond the statistical fluctuations of the detected number of photons, such as the properties of liquid scintillator, performance of photomultiplier tubes, and the energy reconstruction algorithm. To account for these effects, a full JUNO simulation and reconstruction approach is employed. This enables the modeling of all relevant effects and the evaluation of associated inputs to accurately estimate the energy resolution. The study reveals an energy resolution of 2.95% at 1 MeV. Furthermore, the study assesses the contribution of major effects to the overall energy resolution budget. This analysis serves as a reference for interpreting future measurements of energy resolution during JUNO data taking. Moreover, it provides a guideline in comprehending the energy resolution characteristics of liquid scintillator-based detectors