On the weakening of the convergence of Newton’s method using recurrent functions

We use Newton’s method to approximate a locally unique solution of an equation in a Banach space setting. We introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton’s method than before [J. Appell, E. De Pascale, J.V. Lysenko, P.P. Zabrejko, New results on Newton–Kantorovich approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optim. 18 (1997) 1–17; I.K. Argyros, The theory and application of abstract polynomial equations, in: Mathematics Series, St. Lucie/CRC/Lewis Publ., Boca Raton, Florida, USA, 1998; I.K. Argyros, Concerning the “terra incognita” between convergence regions of two Newton methods, Nonlinear Anal. 62 (2005) 179–194; I.K. Argyros, Convergence and Applications of Newton-Type Iterations, Springer-Verlag Publ., New York, 2008; S. Chandrasekhar, Radiative Transfer, Dover Publ., New York, 1960; F. Cianciaruso, E. De Pascale, Newton–Kantorovich approximations when the derivative is Hölderian: Old and new results, Numer. Funct. Anal. Optim. 24 (2003) 713–723; N.T. Demidovich, P.P. Zabrejko, Ju.V. Lysenko, Some remarks on the Newton–Kantorovich method for nonlinear equations with Hölder continuous linearizations, Izv. Akad. Nauk Belorus 3 (1993) 22–26. (in Russian); E. De Pascale, P.P. Zabrejko, Convergence of the Newton–Kantorovich method under Vertgeim conditions: A new improvement, Z. Anal. Anwendvugen 17 (1998) 271–280; L.V. Kantorovich, G.P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982; J.V. Lysenko, Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations, Dokl. Akad. Nauk BSSR 38 (1994) 20–24. (in Russian); B.A. Vertgeim, On conditions for the applicability of Newton’s method, (Russian), Dokl. Akad. Nauk., SSSR 110 (1956) 719–722; B.A. Vertgeim, On some methods for the approximate solution of nonlinear functional equations in Banach spaces, Uspekhi Mat. Nauk 12 (1957) 166–169. (in Russian); English transl.:; Amer. Math. Soc. Transl. 16 (1960) 378–382] provided that the Fréchet-derivative of the operator involved is p$p$-Hölder continuous (p∈(0,1]$p\in (0,1]$).     

采用连续电位阶跃方法研究聚吡咯在电解质水溶液中的氧化还原稳定性

连续电位阶跃方法是一种研究氧化还原稳定性的有效方法. 本文采用连续电位阶跃方法研究了以对甲苯磺酸钠为掺杂剂的聚吡咯(ppy)膜的电化学氧化还原稳定性, 通过计算聚吡咯在阶跃电位下的还原电量(Q_red), 还原和氧化电量的比值(Q_red/Q_ox)考察聚吡咯在H₂SO₄、Na₂SO₄和NaOH溶液中在不同电位下的氧化还原可逆性. 结果发现聚吡咯过氧化的发生强烈依赖支持电解质的pH值和阶跃电位. 在H₂SO₄溶液中, 过氧化的起始电位为0.8 V, 而在Na₂SO₄溶液中, 过氧化的起始电位为0.5 V. 在NaOH溶液中, 过氧化在任何电位均可发生, 表明溶液中OH^- 的存在是过氧化发生的直接原因.     

A NOTE ON RECURRENT SETS

ＡＮＯＴＥＯＮＲＥＣＵＲＲＥＮＴＳＥＴＳ￥ＷＥＮＺＨＩＹＩＮＧ；ＷＵＬＩＭＩＮＧ；ＺＨＯＮＧＨＯＮＧＬＩＵ（ＤｅｐａｒｔｍｅＤｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙｓＷｕｈａｎ４３００７２，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｔｈｅ...     

Indole-3-Carbinol for recurrent respiratory papillomatosis: long-term results

We report the results of a clinical study using Indole-3-Carbinol (I3C) for the treatment of recurrent respiratory papillomatosis (RRP). I3C is abundant in cruciferous vegetables and has been shown to decrease papillomatous growth in cell cultures and be effective in an animal model of RRP. This is a prospective, open-label study design. Patients with RRP were enrolled from September 1996 to August 2001 and treated with I3C (adult dose of 200 mg PO BID). All patients underwent complete surgical removal and then started I3C. Further surgery was performed on an as-needed basis. Patients were categorized as having a complete, partial, or no response to I3C. Thirty-three patients treated with I3C were available for long-term follow-up (mean=4.8 years), whereas 12 patients were lost to follow-up. Eleven (33%) patients experienced remission of papillomatous growth and did not require surgery while on I3C. Ten (30%) patients had a reduction in papillomatous growth that resulted in less frequent surgery. Twelve patients (36%) had no clinical response. No patients experienced a worsening of their RRP. Of the 9 pediatric patients available, 1 experienced a complete response, 3 a partial response, and 5 had no response to I3C. Twelve patients with a positive response (partial or complete) to I3C are still taking I3C. Seven positive responders discontinued I3C, 3 of which have remained disease-free, whereas 4 continue to have RRP. No immediate or long-term side effects related to I3C were found. I3C has been found to be a successful treatment option for RRP. I3C's efficacy in pediatric patients merits further study.     

复发口疮治疗前后血清SOD,MDA等改变研究

选取了３５例ＲＡＵ患者与３０例正常对照，作锌、铁制剂辅助中草药雷公藤、丹参片治疗前后血清ＳＯＤ、ＭＤＡ的改变，实验组与对照组有显著性差异（Ｐ〈０．０１），治疗前后对比又有显著性差异（Ｐ〈０．０１）。而ＰＥＧ－ＣＩＣ的改变，实验组比对照组有显著性增高（Ｐ〈０．０１），治疗前后对比又有显著性差异（Ｐ〈０．０１）。     

反馈型自联想记忆神经网络

自联想记忆神经网络具有类似于大脑的记忆和联想的特性．在Hopfield网络的理论基础上，提出了一种反馈型的自联想记忆神经网络．和Hopfield模型不同的是，这种神经网络增加了一个隐含层来扩大网络的存储容量，并采用局部相连的拓扑结构来代替全相连，从而减少了计算复杂度．在网络的学习过程中，各神经元之间的权值按照学习规则不断地进行调整，使回忆后的输出结果更加接近期望输出、     

New results on input-to-state convergence for recurrent neural networks with variable inputs

In this paper, we study a class of recurrent neural networks (RNNs) arising from optimization problems. By constructing appropriate Lyapunov functions, we prove two new results on input-to-state convergence of RNNs with variable inputs. Numerical simulations are also given to demonstrate the convergence of the solutions.     

Comparing the Long-Term Outcome of Immediate Postoperative Facial Nerve Dysfunction and Vocal Fold Immobility After Parotid and Thyroid Surgery

SUMMARY: Hypothesis: The long-term recovery rate of immediate postoperative facial nerve dysfunction with an electrophysiologically and anatomically intact facial nerve is higher than the long-term recovery rate of immediate postoperative vocal fold immobility with an electrophysiologically and anatomically intact recurrent laryngeal nerve. Methods: A retrospective review of parotid and thyroid surgery with electrophysiologic monitoring of the facial and recurrent laryngeal nerves, respectively. Results: Forty-five consecutive patients had electrophysiologic and anatomic integrity of the facial nerve at the conclusion of the parotidectomy. Eight of 45 (18%) patients developed a postoperative facial nerve dysfunction. All eight patients with facial nerve dysfunction had complete return of facial nerve function within 3 months. A total of 102 consecutive patients underwent dissection of the recurrent laryngeal nerve during thyroid surgery. Seven of 102 (7%) had immediate unilateral vocal fold dysfunction. All 102 had electrophysiologic and anatomic integrity of the recurrent laryngeal nerve at the conclusion of the procedure. Two of 102 (2%) have clinically complete permanent vocal fold dysfunction. Five of seven (71%) with immediate complete vocal fold immobility had complete return of mobility. Conclusions: A higher immediate postoperative rate of transient facial nerve dysfunction is reported compared with vocal fold immobility in parotid and thyroid surgery, respectively (P < 0.05). Immediate postoperative facial nerve dysfunction with an electrophysiologically response at 1 mA and an anatomically intact facial nerve during parotid surgery resulted in a complete return of function in all cases in this series. Immediate postoperative vocal fold immobility with an electrophysiological response at 1 mA and an anatomically intact recurrent laryngeal nerve had a 30% rate of being permanent in this series.