DOCSLIB.ORG

LASALLE TYPE STATIONARY OSCILLATION THEOREMS for AFFINE-PERIODIC SYSTEMS Hongren Wang Xue Yang Yong Li Xiaoyue Li

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
LASALLE TYPE STATIONARY OSCILLATION THEOREMS for AFFINE-PERIODIC SYSTEMS Hongren Wang Xue Yang Yong Li Xiaoyue Li DISCRETE AND CONTINUOUS doi:10.3934/dcdsb.2017156 DYNAMICAL SYSTEMS SERIES B Volume 22, Number 7, September 2017 pp. 2907{2921 LASALLE TYPE STATIONARY OSCILLATION THEOREMS FOR AFFINE-PERIODIC SYSTEMS Hongren Wang College of mathematics, Jilin Normal University Jilin 136000, China College of Mathematics, Jilin University Changchun 130012, China Xue Yang School of Mathematics and Statistics, Northeast Normal University Changchun 130024, China Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University Changchun 130024, China College of Mathematics, Jilin University Changchun 130012, China Institute of Mathematics, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing 100190, China Yong Li∗ School of Mathematics and Statistics, Northeast Normal University Changchun 130024, China Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University Changchun 130024, China College of Mathematics, Jilin University Changchun 130012, China Xiaoyue Li School of Mathematics and Statistics, Northeast Normal University Changchun 130024, China (Communicated by Yuan Lou) Abstract. The paper concerns the existence of affine-periodic solutions for affine-periodic (functional) differential systems, which is a new type of quasi- periodic solutions if they are bounded. Some more general criteria than LaSalle's one on the existence of periodic solutions are established. Some applications are also given. 2010 Mathematics Subject Classification. Primary: 34C27; Secondary: 34C25. Key words and phrases. LaSalle type stationary oscillation principle, Q-affine T -periodic solu- tions, asymptotic stability. The second author is supported by NSFC (grant No. 11201173). The third author is supported by National Basic Research Program of China (grant No. 2013CB834100), NSFC (grant No. 11571065) and NSFC (grant No. 11171132). ∗ Corresponding author: Yong Li. 2907 2908 HONGREN WANG, XUE YANG, YONG LI AND XIAOYUE LI 1. Introduction. As is well known, regular solutions of differential equations are generally split into the following types: stationary, periodic, quasi-periodic, almost periodic, almost automorphic or recurrent ones. It is an important topic what conditions, for example, stability, can guarantee the existence of such solutions. Some classical results of this aspect can be found in books [27] and [1]. Here we would like to mention LaSalle's stationary oscillation theorem [13], which is a simple but flexible criterion in applications. More precisely, consider the equation d x_ = f(t; x)(· ≡ ); (1) dt where f : R1 ×Rn ! Rn is continuous, T -periodic in t, and satisfies some regularity conditions. 1 1 Theorem 1.1. (LaSalle stationary oscillation principle, [13]) Let a : R+ ! R+ nf0g be continuous and satisfy lim a(t) = 0. Assume f(t; x) is Lipschitz in x, T -periodic t!1 1 in t, and all solutions are bounded on R+; moreover jx(t; x0) − x(t; y0)j ≤ a(t)jx0 − y0j 8t ≥ 0; where x(t; x0) denotes the solution of system (1) with the initial value x(0) = x0. Then system (1) has a unique asymptotically stable T -periodic solution. Some systems exhibit the following affine periodicity: −1 1 n f(t + T; x) = Qf(t; Q x) 8t 2 R ; x 2 R ; where Q is a nonsingular n × n matrix. When Q = I (the identity matrix), system (1) is just a usual T -periodic one; when Q is an orthogonal matrix, system (1) is a quasi-periodic one. From physics' views it is natural to ask whether system (1) admits a solution x(t) with the following property x(t + T ) = Qx(t) 8t; where f(t; x) possesses the affine periodicity. We call such a solution x(t) a Q-affine T -periodic solution of (1). As mentioned above, a Q-affine T -periodic solution x(t) might be T -periodic if Q = I, quasi- periodic if Q is orthogonal, even unbounded like eλty(t) with quasi-periodic y(t) if Q is only nonsingular. For periodic solutions and anti-periodic solutions, some works can be found in [2, 4, 5, 7, 8, 10, 11, 12, 15, 16, 17, 18, 19, 21, 22, 25, 26]. Recently, there have been some literature in studying the existence of affine-periodic solutions, see, for example, [3, 14, 20, 23, 24, 28]. In this paper, we will prove similar stationary oscillation theorems for Q-affine periodic systems with orthogonal matrix Q, make some discusses about more general stationary oscillation conditions, and give more flexible versions. The paper is organized as follows. In Section 2, we state a stationary oscillation theorem on Q-affine T periodic solutions. Section 3 provides an analogous result for functional differential equations. In Section 4, we illustrate some applications. 2. Stationary oscillation theorem for ODE (1). From now on we always as- sume Q is an orthogonal matrix. In this section, we will prove the following LaSalle type theorem on Q-affine T periodic solutions for system (1). Theorem 2.1. Consider the Q-affine T -periodic system (1), and assume f : R1 × n n 1 1 R ! R is continuous. Let a : R+ ! R+ n f0g be continuous and satisfy r = LASALLE TYPE STATIONARY OSCILLATION THEOREMS 2909 lim a(kT ) < 1. Assume the following hold: k!1 1) There exists a solution z(t) of system (1) defined on [0;T ]; 2) Any two solutions x(t) and y(t) satisfy jx(t) − y(t)j ≤ a(t)jx(0) − y(0)j whenever they exist. Then system (1) has a unique asymptotically stable Q-affine T periodic solution. Lemma 2.2. Assume the Q-affine T -periodic system (1) admits the uniqueness to initial value problems. Let x(t; x0) be a solution of (1) with the initial value 1 condition x(0) = x0 defined on R+. Then −1 −1 Q x(t + T; x0) ≡ x(t; Q x(T; x0)): 1 Proof. Note that for t 2 R+, Z t+T x(t + T; x0) = x0 + f(s; x(s; x0))ds 0 Z T Z t+T = x0 + f(s; x(s; x0))ds + f(s; x(s; x0))ds 0 T Z t = x(T; x0) + f(s + T; x(s + T; x0))ds 0 Z t −1 = x(T; x0) + Q f(s; Q x(s + T; x0))ds; 0 which together with the uniqueness of solutions to the initial value problem implies that −1 −1 Q x(t + T; x0) ≡ x(t; Q x(T; x0)): We now give the proof of Theorem 2.1. Proof. We take the following three steps: 1 Step 1. Prove that z(t) is extensible on R+. Once done, by 2), it follows that jx(t; x0) − z(t)j ≤ a(t)jx0 − z(0)j 8t ≥ 0: 1 Hence all the solutions x(t; x0) of system (1) are defined on R+. By 2), x(t; x0) is uniquely determined by the initial value x0, i.e., the equation admits the continuous dependence of solutions with respect to initial values. By Peano's theorem and 2), (1) has a unique solution w(t) with the initial value condition w(0) = Q−1z(T ), and it exists on [0;T ]. Note that dQw(t − T ) dQw(t − T ) = dt d(t − T ) = Qf(t − T;Q−1Qw(t − T )) = f(t; Qw(t − T )) 8t 2 [T; 2T ]: Therefore, Qw(t − T ) is the solution of (1) with the initial value condition z(T ) on [T; 2T ]. 2910 HONGREN WANG, XUE YANG, YONG LI AND XIAOYUE LI Define 8 < z(t); t 2 [0;T ]; z(t) = : Qw(t − T ); t 2 [T; 2T ]: Hence z(t) exists on [T; 2T ]. Repeating this procedure, we obtain that z(t) exists 1 on R+. Step 2. Prove that the equation has Q-affine T periodic solutions. We define the Poincar´emap P : Rn ! Rn by −1 n P (x0) = Q x(T; x0) 8x0 2 R ; and P is well-defined. By the definition of r, there exist positive integer K and r 2 (r; 1) such that a(kT ) ≤ r 8k ≥ K: By induction and the uniqueness of solutions to initial value problem, we have j j−1 −j P (x0) = P ◦ P (x0) = Q x(jT; x0) 8j ≥ 1: In fact, j j−1 −1 j−1 P (x0) = P ◦ P (x0) = Q x(T;P x0) 8j ≥ 1: Note that Z t+T x(t + T; x0) = x0 + f(s; x(s; x0))ds 0 Z t+T = x(T; x0) + f(s; x(s; x0))ds: T Therefore Z t −1 −1 −1 Q x(t + T; x0) = Q x(T; x0) + f(s; Q x(s + T; x0))ds: 0 Further we have Z t −1 −1 −1 x(t; Q x(T; x0)) = Q x(T; x0) + f(s; x(s; Q x(T; x0)))ds: 0 From the above, we can see −2 −1 −1 Q x(t + T; x0) = Q x(t; Q x(T; x0)): In the same manner, it follows that j −j P (x0) = Q x(jT; x0) 8j ≥ 1: Thus K K −K −K jP (x0) − P (y0)j = jQ x(KT; x0) − Q x(KT; y0)j = jx(KT; x0) − x(KT; y0)j n ≤ rjx0 − y0j 8x0; y0 2 R : Therefore P is a r-contraction mapping of order K. Now, by Banach's contraction n mapping fixed point theorem, P has a unique fixed point x∗ 2 R , i.e., −1 Q x(T; x∗) = x∗: Again by the uniqueness of solutions to the initial value problem, we have x(t + T; x∗) ≡ Qx(t; x∗) 8t; LASALLE TYPE STATIONARY OSCILLATION THEOREMS 2911 which shows that x(t; x∗) is a unique Q-affine T periodic solution of the system. Step 3. Prove the stability and the asymptotic stability. Let us prove the following estimate inductively: m jx(t + mKT; x∗) − x(t + mKT; x0)j ≤ a(t)jx∗ − x0jr 8t ≥ 0; m ≥ 1: Firstly, for m = 1, by Lemma 1 and assumption 2), we have jx(t + KT; x∗) − x(t + KT; x0)j −1 −1 =jQ x(t + KT; x∗) − Q x(t + KT; x0)j −1 −1 =jx(t + (K − 1)T;Q x(T; x∗)) − x(t + (K − 1)T;Q x(T; x0))j −1 −1 −1 −1 =jQ x(t + (K − 1)T;Q x(T; x∗)) − Q x(t + (K − 1)T;Q x(T; x0))j −1 −1 =jx(t + (K − 2)T;Q x(T;Q x(T; x∗))) −1 −1 − x(t + (K − 2)T;Q x(T;Q x(T; x0)))j −2 −2 =jx(t + (K − 2)T;Q x(2T; x∗)) − x(t + (K − 2)T;Q x(2T; x0))j = :::::: −K −K =jx(t; Q x(KT; x∗)) − x(t; Q x(KT; x0))j ≤a(t)jx(KT; x∗) − x(KT; x0)j ≤a(t)a(KT )jx∗ − x0j ≤a(t)jx∗ − x0jr: Secondly, suppose that for k = m − 1, the estimate holds.
Load more

Recommended publications
  • A Discussion of Differences Between Hand Shao Yin and Hand Jue Yin
    March 2014 NAJOM A Discussion of Differences Channel treat its own disease symptom patterns? eye system,” the Divergent Channel “travels along Is there a difference between the indications of the throat, and emerges to the face.” Between Hand Shao Yin the Heart and Pericardium channels? It is a meaningful exercise to conduct a compara- and Hand Jue Yin Channel An answer to these questions can be approached tive analysis between the channel pathways to Indications from two perspectives – a theoretical perspective, understand the disease symptom patterns, and and from the standard textbook explanation. From the indication and actions of the points of these these two sources, the indications for the Hand two channels. by Wang Hong Min Shao Yin and hand Jue Yin channels are very similar and are related to the heart, chest, and psycho- Advisor: Wang Ju-yi 2. Anatomy and Physiology of emotional disorders, including illnesses related the Heart to the channel pathways. In addition, from recent clinical research there are reports that use both The heart is a hollow viscera and the cardiac wall Abstract Heart and Pericardium channel points to treat heart is comprised of three membrane layers – from the disease. Rarely is further research conducted to interior to the exterior they are the endocardium, The Nei-Jing cites indications governed by the distinguish between these channels. myocardium and epicardium. The structure of the Hand Shao Yin Heart Channel and Hand Jue Yin endocardium includes the endothelium, subendo- Pericardium Channel. The author developed an Wang Ju-yi’s descriptions of the unique structures thelial layer, endothecium, and subendocardium.
    [Show full text]
  • Guo, Ning Et. Al. Complaint
    UNITED STATES DISTRICT COURT DISTRICT OF NEW JERSEY UNITED STATES OF AMERICA Hon. Cathy L. Waldor v. NING GUO, alk/a "Danny," alk/a "Peter," alk/a Crim. No. 12-7060 "The Beijing Kid," GUO HUA ZHANG, alk/a. "Leo," alk/a "Alex," WAN PING REN, alk/a "Helen," CRIMINAL COMPLAINT YI JIAN CHEN, alk/a "Kenny," JIAN ZHI MO, alk/a "Jimmy," YUAN FENG LAI, alk/a "Leo," YUAN BO LAI, alk/a "Paul," KONG BIAO WANG, alk/a "Karl Wang," HUI HUANG, alk/a "Rick Wang," MING ZHENG, alk/a "Uncle Mi," GOU QIANG ZHAO, and BASSIROU ISSOUFOU, alk/a "Butch" I, the undersigned complainant, being duly sworn, state the following is true and correct to the best of my knowledge and belief. From at least as early as in or about August 2008 to in or about February 2012, in Essex and Union Counties, in the District of New Jersey and elsewhere, the defendants listed on Attachment A, did: SEE ATTACHMENT A I further state that I am a Special Agent with the Federal Bureau of Investigation, and that this complaint is based on the following facts: SEE ATTACHMENT B continued on the attached page and made a part hereof. ent ation Sworn to before me and subscribed in my presence, March 1, 2012, at Newark, New Jersey HONORABLE CATHY W. WALDOR UNITED STATES MAGISTRATE JUDGE Signature of Judicial Officer ATTACHMENT A Count 1 - Conspiracy to Traffic in Counterfeit Goods From at least as early as in or about August 2008 to in or about February 2012, in Essex and Union Counties, in th~ District of New Jersey, and elsewhere, defendants NING GUO, a/k/a "Danny," a/k/a "Peter," a/k/a "The
    [Show full text]
  • Third Edition 中文听说读写
    Integrated Chinese Level 1 Part 1 Textbook Simplified Characters Third Edition 中文听说读写 THIS IS A SAMPLE COPY FOR PREVIEW AND EVALUATION, AND IS NOT TO BE REPRODUCED OR SOLD. © 2009 Cheng & Tsui Company. All rights reserved. ISBN 978-0-88727-644-6 (hardcover) ISBN 978-0-88727-638-5 (paperback) To purchase a copy of this book, please visit www.cheng-tsui.com. To request an exam copy of this book, please write [email protected]. Cheng & Tsui Company www.cheng-tsui.com Tel: 617-988-2400 Fax: 617-426-3669 LESSON 1 Greetings 第一课 问好 Dì yī kè Wèn hǎo SAMPLE LEARNING OBJECTIVES In this lesson, you will learn to use Chinese to • Exchange basic greetings; • Request a person’s last name and full name and provide your own; • Determine whether someone is a teacher or a student; • Ascertain someone’s nationality. RELATE AND GET READY In your own culture/community— 1. How do people greet each other when meeting for the fi rst time? 2. Do people say their given name or family name fi rst? 3. How do acquaintances or close friends address each other? 20 Integrated Chinese • Level 1 Part 1 • Textbook Dialogue I: Exchanging Greetings SAMPLELANGUAGE NOTES 你好！ 你好！(Nǐ hǎo!) is a common form of greeting. 你好！ It can be used to address strangers upon fi rst introduction or between old acquaintances. To 请问，你贵姓？ respond, simply repeat the same greeting. 请问 (qǐng wèn) is a polite formula to be used 1 2 我姓 李。你呢 ？ to get someone’s attention before asking a question or making an inquiry, similar to “excuse me, may I 我姓王。李小姐 ， please ask…” in English.
    [Show full text]
  • Kathy Siyu Xue, Ph.D., MPH 120 Pine Bark Ln Athens, GA 30605 (706) 353-7609 [email protected]
    Kathy Siyu Xue, Ph.D., MPH 120 Pine Bark Ln Athens, GA 30605 (706) 353-7609 [email protected] EDUCATION Doctorate of Philosophy 2012-2017 Interdisciplinary Toxicology Program Athens, GA Department of Environmental Health Sciences University of Georgia Master of Public Health 2014-2017 University of Georgia Athens, GA Bachelor of Science 2008-2012 Cell and Molecular Biology Austin, TX University of Texas – Austin WORK EXPERIENCE 2017- present Postdoctoral Researcher, University of Georgia, Athens, GA. Mentor: Dr. Jia-Sheng Wang Jun. 2016 – Aug. 2016 Internship, United State Department of Agriculture Toxicology and Mycotoxin Research Unit, Athens, GA Site Supervisor: Dr. Kenneth Voss 2012-2017 Research Assistant, University of Georgia, Athens, GA. Advisor: Dr. Jia-Sheng Wang Aug.2013- Dec. 2013 Teaching Assistant, University of Georgia, Athens, GA. Taking roll, organizing student seminars, coordinating speakers Mar. 2012 – May 2012 Undergraduate Research Volunteer, Dr. Mueller Lab University of Texas – Austin, TX 2010 – 2012 Student Volunteer, Athens Regional Medical Center, Athens, GA 2010-2011 Student Research Assistant, University of Georgia – Athens, GA Dr. Jia-sheng Wang Lab Refill pipette tips, organize chemicals, shadowing research scientists. Additional work including culturing and toxicity testing for C elegans, assistance in oxidative damage biomarker analysis. 2004-2007 Student Volunteer, Texas Tech University – Lubbock, TX Dr. Jia-Sheng Wang Lab HONOR AND AWARDS 2017 Induction into Beta Chi Chapter of Delta Omega Honorary Society
    [Show full text]
  • The Later Han Empire (25-220CE) & Its Northwestern Frontier
    University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2012 Dynamics of Disintegration: The Later Han Empire (25-220CE) & Its Northwestern Frontier Wai Kit Wicky Tse University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Asian History Commons, Asian Studies Commons, and the Military History Commons Recommended Citation Tse, Wai Kit Wicky, "Dynamics of Disintegration: The Later Han Empire (25-220CE) & Its Northwestern Frontier" (2012). Publicly Accessible Penn Dissertations. 589. https://repository.upenn.edu/edissertations/589 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/589 For more information, please contact [email protected]. Dynamics of Disintegration: The Later Han Empire (25-220CE) & Its Northwestern Frontier Abstract As a frontier region of the Qin-Han (221BCE-220CE) empire, the northwest was a new territory to the Chinese realm. Until the Later Han (25-220CE) times, some portions of the northwestern region had only been part of imperial soil for one hundred years. Its coalescence into the Chinese empire was a product of long-term expansion and conquest, which arguably defined the egionr 's military nature. Furthermore, in the harsh natural environment of the region, only tough people could survive, and unsurprisingly, the region fostered vigorous warriors. Mixed culture and multi-ethnicity featured prominently in this highly militarized frontier society, which contrasted sharply with the imperial center that promoted unified cultural values and stood in the way of a greater degree of transregional integration. As this project shows, it was the northwesterners who went through a process of political peripheralization during the Later Han times played a harbinger role of the disintegration of the empire and eventually led to the breakdown of the early imperial system in Chinese history.
    [Show full text]
  • Self-Study Syllabus on China’S Domestic Politics
    Self-Study Syllabus on China’s domestic politics www.mandarinsociety.org PrefaceAbout this syllabus. syllabus aspires to guide interested non-specialists in Thisthe study of some of the most salient and important aspects of the contemporary Chinese domestic political scene. The recommended readings survey basic features of China’s political system as well as important developments in politics, ideology, and domestic policy under Xi Jinping. Some effort has been made to promote awareness of the broad array of available English language scholarship and analysis. Reflecting the authors’ belief that study of official documents remains a critical skill for the study of Chinese politics, an effort has been made as well to include some of these important sources. This syllabus is organized to build understanding in a step-by-step fashion based on one hour of reading five nights a week for four weeks. We assume at most a passing familiarity with the Chinese political system. The syllabus also provides a glossary of key terms and a list of recommended reading for books and websites for those seeking to engage in deeper study. American Mandarin Society 1 Week One: Building the Foundation The organization, ideology, and political processes of China’s governance • “Chinese Politics Has No Rules, But It May Be Good if Xi Jinping Breaks Them” Overview ,Christopher Johnson, Center for Strategic and International Studies, August 9, 2017. Mr. Johnson argues that the institutionalization of This week’s readings review some of the basic and most distinctive features of China’s Chinese politics was less than many foreign political system.
    [Show full text]
  • 中国人的姓名 王海敏 Wang Hai Min
    中国人的姓名 王海敏 Wang Hai min last name first name Haimin Wang 王海敏 Chinese People’s Names Two parts Last name First name 姚明 Yao Ming Last First name name Jackie Chan 成龙 cheng long Last First name name Bruce Lee 李小龙 li xiao long Last First name name The surname has roughly several origins as follows: 1. the creatures worshipped in remote antiquity . 龙long, 马ma, 牛niu, 羊yang, 2. ancient states’ names 赵zhao, 宋song, 秦qin, 吴wu, 周zhou 韩han，郑zheng, 陈chen 3. an ancient official titles 司马sima, 司徒situ 4. the profession. 陶tao，钱qian, 张zhang 5. the location and scene in residential places 江jiang，柳 liu 6.the rank or title of nobility 王wang，李li • Most are one-character surnames, but some are compound surname made up of two of more characters. • 3500Chinese surnames • 100 commonly used surnames • The three most common are 张zhang, 王wang and 李li What does my name mean? first name strong beautiful lively courageous pure gentle intelligent 1.A person has an infant name and an official one. 2.In the past,the given names were arranged in the order of the seniority in the family hierarchy. 3.It’s the Chinese people’s wish to give their children a name which sounds good and meaningful. Project:Search on-Line www.Mandarinintools.com/chinesename.html Find Chinese Names for yourself, your brother, sisters, mom and dad, or even your grandparents. Find meanings of these names. ----What is your name? 你叫什么名字？ ni jiao shen me ming zi? ------ 我叫王海敏 wo jiao Wang Hai min ------ What is your last name? 你姓什么? ni xing shen me? （你贵姓？）ni gui xing? ------ 我姓 王，王海敏。 wo xing wang, Wang Hai min ----- What is your nationality? 你是哪国人？ ni shi na guo ren? ----- I am chinese/American 我是中国人/美国人 Wo shi zhong guo ren/mei guo ren 百家 姓 bai jia xing 赵(zhào) 钱(qián) 孙(sūn) 李(lǐ) 周(zhōu) 吴(wú) 郑(zhèng) 王(wán 冯(féng) 陈(chén) 褚(chǔ) 卫(wèi) 蒋(jiǎng) 沈(shěn) 韩(hán) 杨(yáng) 朱(zhū) 秦(qín) 尤(yóu) 许(xǔ) 何(hé) 吕(lǚ) 施(shī) 张(zhāng).
    [Show full text]
  • The Case of Wang Wei (Ca
    _full_journalsubtitle: International Journal of Chinese Studies/Revue Internationale de Sinologie _full_abbrevjournaltitle: TPAO _full_ppubnumber: ISSN 0082-5433 (print version) _full_epubnumber: ISSN 1568-5322 (online version) _full_issue: 5-6_full_issuetitle: 0 _full_alt_author_running_head (neem stramien J2 voor dit article en vul alleen 0 in hierna): Sufeng Xu _full_alt_articletitle_deel (kopregel rechts, hier invullen): The Courtesan as Famous Scholar _full_is_advance_article: 0 _full_article_language: en indien anders: engelse articletitle: 0 _full_alt_articletitle_toc: 0 T’OUNG PAO The Courtesan as Famous Scholar T’oung Pao 105 (2019) 587-630 www.brill.com/tpao 587 The Courtesan as Famous Scholar: The Case of Wang Wei (ca. 1598-ca. 1647) Sufeng Xu University of Ottawa Recent scholarship has paid special attention to late Ming courtesans as a social and cultural phenomenon. Scholars have rediscovered the many roles that courtesans played and recognized their significance in the creation of a unique cultural atmosphere in the late Ming literati world.1 However, there has been a tendency to situate the flourishing of late Ming courtesan culture within the mainstream Confucian tradition, assuming that “the late Ming courtesan” continued to be “integral to the operation of the civil-service examination, the process that re- produced the empire’s political and cultural elites,” as was the case in earlier dynasties, such as the Tang.2 This assumption has suggested a division between the world of the Chinese courtesan whose primary clientele continued to be constituted by scholar-officials until the eight- eenth century and that of her Japanese counterpart whose rise in the mid- seventeenth century was due to the decline of elitist samurai- 1) For important studies on late Ming high courtesan culture, see Kang-i Sun Chang, The Late Ming Poet Ch’en Tzu-lung: Crises of Love and Loyalism (New Haven: Yale Univ.
    [Show full text]
  • Lǎoshī Hé Xuéshēng (Teacher and Students)
    © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. CHAPTER Lǎoshī hé Xuéshēng 1 (Teacher and Students) Pinyin Text English Translation (A—Dīng Yī, B—Wáng Èr, C—Zhāng Sān) (A—Ding Yi, B—Wang Er, C—Zhang San) A: Nínhǎo, nín guìxìng? A: Hello, what is your honorable surname? B: Wǒ xìng Wáng, jiào Wáng Èr. Wǒ shì B: My surname is Wang. I am called Wang Er. lǎoshī. Nǐ xìng shénme? I am a teacher. What is your last name? A: Wǒ xìng Dīng, wǒde míngzi jiào Dīng Yī. A: My last name is Ding and my full name is Wǒ shì xuéshēng. Ding Yi. I am a student. 老师 老師 lǎoshī n. teacher 和 hé conj. and 学生 學生 xuéshēng n. student 您 nín pron. honorific form of singular you 好 hǎo adj. good 你(您)好 nǐ(nín)hǎo greeting hello 贵 貴 guì adj. honorable 贵姓 貴姓 guìxìng n./v. honorable surname (is) 我 wǒ pron. I; me 姓 xìng n./v. last name; have the last name of … 王 Wáng n. last name Wang 叫 jiào v. to be called 二 èr num. two (used when counting; here used as a name) 是 shì v. to be (any form of “to be”) 10 © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher.
    [Show full text]
  • Chiquan Guo the University of Texas Rio Grande Valley Department of Marketing (956) 665-7339 Email: [email protected]
    Dr. Chiquan Guo The University of Texas Rio Grande Valley Department of Marketing (956) 665-7339 Email: [email protected] Education PhD, Southern Illinois University - Carbondale, 2002. Major: Business Administration Title: Market Orientation and Customer Satisfaction: An Empirical Investigation MBA, University of Wisconsin - Oshkosh, 1996. Major: Business Administration BA, University of Wisconsin - Green Bay, 1994. Major: Economics Employment History Academic - Post-Secondary Associate Professor of Marketing, The University of Texas Rio Grande Valley. (September 2015 - Present). Licensures and Certifications UTRGV's Sustainable Faculty Development Webinar Sessions, The University of Texas Rio Grande Valley Office for Sustainability. (May 2019 - Present). QM Rubric Update Sixth Edition (RU), Quality Matters (QM). (January 8, 2019 - Present). Study of Exchange: Comprehension of Local History and Culture, B3 Institure & Center for Teaching Excellence at The University of Texas Rio Grande Valley. (2018 - Present). Independent Applying the QM Rubric (APPQMR), Quality Matters (QM). (December 9, 2016 - Present). Majors Fair, The University of Texas-Pan American. (September 23, 2014 - Present). Teaching Excellence, College of Business Administration at The University of Texas-Pan American. (May 2014 - Present). Majors Fair, Coordinator of Majors Fair Committee at The University of Texas Rio Grande Valley. (September 24, 2013 - Present). Teaching Online Certification - Blackboard Learn, Center for Online Learning, Teaching & Technology at The University of Texas-Pan American. (April 8, 2013 - Present). Responsible Conduct of Research; Social and Behavioral Responsible Conduct of Research Course 1; 1 - Basic Course, CITI Program. (February 20, 2019 - February 19, 2023). Report Generated on September 13, 2021 Page 1 of 8 Basic/Refresher Course - Human Subjects Research; Social Behavioral Research Investigators and Key Personnel; 1 - Basic Course, CITI Program.
    [Show full text]
  • Names of Chinese People in Singapore
    101 Lodz Papers in Pragmatics 7.1 (2011): 101-133 DOI: 10.2478/v10016-011-0005-6 Lee Cher Leng Department of Chinese Studies, National University of Singapore ETHNOGRAPHY OF SINGAPORE CHINESE NAMES: RACE, RELIGION, AND REPRESENTATION Abstract Singapore Chinese is part of the Chinese Diaspora.This research shows how Singapore Chinese names reflect the Chinese naming tradition of surnames and generation names, as well as Straits Chinese influence. The names also reflect the beliefs and religion of Singapore Chinese. More significantly, a change of identity and representation is reflected in the names of earlier settlers and Singapore Chinese today. This paper aims to show the general naming traditions of Chinese in Singapore as well as a change in ideology and trends due to globalization. Keywords Singapore, Chinese, names, identity, beliefs, globalization. 1. Introduction When parents choose a name for a child, the name necessarily reflects their thoughts and aspirations with regards to the child. These thoughts and aspirations are shaped by the historical, social, cultural or spiritual setting of the time and place they are living in whether or not they are aware of them. Thus, the study of names is an important window through which one could view how these parents prefer their children to be perceived by society at large, according to the identities, roles, values, hierarchies or expectations constructed within a social space. Goodenough explains this culturally driven context of names and naming practices: Department of Chinese Studies, National University of Singapore The Shaw Foundation Building, Block AS7, Level 5 5 Arts Link, Singapore 117570 e-mail: [email protected] 102 Lee Cher Leng Ethnography of Singapore Chinese Names: Race, Religion, and Representation Different naming and address customs necessarily select different things about the self for communication and consequent emphasis.
    [Show full text]
  • Historical Background of Wang Yang-Ming's Philosophy of Mind
    Ping Dong Historical Background of Wang Yang-ming’s Philosophy of Mind From the Perspective of his Life Story Historical Background of Wang Yang-ming’s Philosophy of Mind Ping Dong Historical Background of Wang Yang-ming’s Philosophy of Mind From the Perspective of his Life Story Ping Dong Zhejiang University Hangzhou, Zhejiang, China Translated by Xiaolu Wang Liang Cai School of International Studies School of Foreign Language Studies Zhejiang University Ningbo Institute of Technology Hangzhou, Zhejiang, China Zhejiang University Ningbo, Zhejiang, China ISBN 978-981-15-3035-7 ISBN 978-981-15-3036-4 (eBook) https://doi.org/10.1007/978-981-15-3036-4 © The Editor(s) (if applicable) and The Author(s) 2020. This book is an open access publication. Open Access This book is licensed under the terms of the Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 International License (http://creativecommons.org/licenses/by-nc- nd/4.0/), which permits any noncommercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if you modified the licensed material. You do not have permission under this license to share adapted material derived from this book or parts of it. The images or other third party material in this book are included in the book’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
    [Show full text]