Research on Stability of Impulsive Differential Systems with Complex Delays and Application Model

本文主要讨论具复杂时滞影响的脉冲微分系统的稳定性及其在脉冲递归神经网络上的应用. 全文的主要研究工作包括： 第一章主要介绍了脉冲时滞微分系统的研究背景和研究现状，提出了本文要研究的几个问题，并给出了本文的基本结构. 第二章探讨了具无穷时滞影响的脉冲微分系统的$\mu-$稳定性问题. 为更细致地刻画脉冲时滞微分系统的解以何种速率衰减至平衡解，分别从脉冲干扰角度(在一定的脉冲干扰下时滞微分系统可以保持其稳定性)和脉冲控制角度(在一定脉冲控制下确保时滞微分系统的稳定性)研究了时滞微分系统的$\mu-$稳定性.利用Lyapunov函数方法和Razumkin技巧，得到了保证脉冲时滞微分系...This paper mainly deals with the stability properties of impulsive differential systems with time delays and their applications to impulsive recurrent neural networks. It mainly includes: In Chapter 1, the background and present of the investigation of impulsive delay differential systems are firstly introduced. Then, we provide the problems and structure of the thesis. In Chapt...学位：理学博士院系专业：数学科学学院数学与应用数学系_应用数学学号：1902009015361

Asymptotic Expansion of a Kantorovich Variant of BBH Operators

研究了blEIMAnn-buTzEr-HAHn算子的kAnTOrOVICH型算子列k_n的逼近性质,作者运用分析和逼近论的方法以及不等式技巧得到了算子列k_n对可微函数类的渐进展开式与点态估计公式.特别地,作为结果的推论,建立了算子列k_n关于可微函数的一个VOnOrOVSkyA型渐进公式.The concern of this paper is some basic asymptotic properties of a Kantorovich variant of the Bleimann.Butzer and Hahn operators K_n.The asymptotic expansion and the rate of K_n convergence of for differentiable functions are presented by using some methods of analysis and inequation techniques.Specially,the Vonorovskya type asymptotic formula of K_n for differentiable functions is given in this paper as a deduction of the result.国家自然科学基金(10571145);厦门市科技计划项目(20083012

mu-stability of infinite delay functional differential systems with impulsive effects

In this article, a new concept of mu-stability for impulsive functional differential systems is proposed, which unifies uniform stability, uniform asymptotic stability, exponential stability, etc. Using the improved Razumikhin technique and Lyapunov functions, we obtain some sufficient conditions to ensure the mu-stability of functional differential systems with infinite delays under impulsive perturbations. The results obtained in this article improve and extend existing results and provide another set of criteria for determining the stability of impulsive infinite delay different systems. An example is given to illustrate the effectiveness and advantages of the results

Stability analysis of generalized impulsive functional differential equations

In this paper, the stability problem for a class of generalized impulsive functional differential equations in which the state variables on the impulses are related to the time delay is studied. By using Lyapunov functions and Razumikhin techniques, several global exponential stability and uniform stability criteria are derived, which can be applied to impulsive functional differential equations with any time delays. The results obtained improve and extend those in earlier publications. Moreover, our results show that delay differential equations can be exponentially stabilized by impulses in which the state variables are related to the time delay. Finally, two examples are given to illustrate the effectiveness and advantages of the results obtained. 漏 2011 Elsevier Ltd

A Case of Metastatic Testicular Cancer after Kidney Transplantation in which Complete Remission was Achieved

We report a case of testicular cancer after kidney transplantation in a 29-year-old man. Twenty-two years after the surgery, computed tomography (CT) showed a retroperitoneal mass 3 cm in diameter. Positron emission tomography (PET) -CT revealed high FDG uptake in both the right testis and retroperitoneal mass. Regarding serum tumor markers, α fetoprotein (AFP) was slightly elevated to 12.5 ng/ml. He underwent right radical orchiectomy, and pathological examination revealed pure seminoma. After surgery, the serum AFP level remained high (12. 9 ng/ml), and we initially considered this nonseminoma patient to have a good prognosis according to International Germ Cell Consensus Classification. During three cycles of a combination regimen including bleomycin, etoposide, and cisplatin (BEP), we performed adjustment of immunosuppressive therapy, treatment for Cytomegalovirus infection (valganciclovir hydrochloride), and that for other adverse events associated with systemic chemotherapy. The chemotherapy schedule was delayed, and bleomycin (third course, day 15) was skipped due to adverse effects. After 3 cycles of BEP, the retroperitoneal lymph node metastasis shrunk from 3.0 to 1.5 cm in diameter. In contrast to the good radiological response, the serum AFP level gradually increased during the treatment to 102.6 ng/ml. Therefore, we did not consider the AFP elevation to have derived from residual cancer, and decided to perform close follow-up. During the 3-year follow-up, AFP decreased to around 20 ng/ml, and PET-CT did not show any uptake in the retroperitoneal mass or other sites

Measurement of integrated luminosity of data collected at 3.773 GeV by BESIII from 2021 to 2024

We present a measurement of the integrated luminosity e+e- of collision data collected by the BESIII detector at the BEPCII collider at a center-of-mass energy of Ecm = 3.773 GeV. The integrated luminosities of the datasets taken from December 2021 to June 2022, from November 2022 to June 2023, and from October 2023 to February 2024 were determined to be 4.995±0.019 fb-1, 8.157±0.031 fb-1, and 4.191±0.016 fb-1, respectively, by analyzing large angle Bhabha scattering events. The uncertainties are dominated by systematic effects, and the statistical uncertainties are negligible. Our results provide essential input for future analyses and precision measurements

Determination of the number of ψ(3686) events taken at BESIII

The number of ψ(3686) events collected by the BESIII detector during the 2021 run period is determined to be (2259.3±11.1)×106 by counting inclusive ψ(3686) hadronic events. The uncertainty is systematic and the statistical uncertainty is negligible. Meanwhile, the numbers of ψ(3686) events collected during the 2009 and 2012 run periods are updated to be (107.7±0.6)×106 and (345.4±2.6)×106, respectively. Both numbers are consistent with the previous measurements within one standard deviation. The total number of ψ(3686) events in the three data samples is (2712.4±14.3)×10^