The Second Condition for Equilibrium

Vietnam national university, HanoiCollege of foreign languagesPost-Graduate Department----------------------------------------------Duong Thi haoDesigning an esp syllabus for the second-year students of library study at the national teachers training college Thiết kế giáo trình tiếng Anh chuyên ngành cho sinh viên năm thứ hai ngành Th viện trờng Cao Đẳng S Phạm Trung ơngMA. minor thesisMajor: English language teaching methodologyCode: 601014 Vietnam national university, HanoiCollege of foreign languagesPost-Graduate Department------------------------------------------------Duong Thi haoDesigning an esp syllabus for the second year students of library study at the national teachers training college Thiết kế giáo trình tiếng Anh chuyên ngành cho sinh viên năm thứ hai ngành Th viện trờng Cao Đẳng S Phạm Trung ơngMA. minor thesisField: English language teaching methodologyCode: 601014Supervisor: Nguyen Xuan Thom, PhD Hanoi, 2007 AcknowledgementsFirst of all, I’d like to express my deepest gratitude to my supervisor, Dr. Nguyen Xuan Thom who gave me valuable suggestions, insightful discussions and immeasurable support and encouragements in the development and completion of this study.I gratefully acknowledge all those whose works which are referred to in this study. In particular, I would like to thank Dr.To Thu Huong for her lectures and advice that helped shaping my thinking on this subject matter. My special thanks go to all the lecturers of the Postgraduate Department at the College of Foreign Languages, Vietnam National University, Hanoi for their useful lectures and guidance during the course.I also wish to thank all my colleagues and my dear students at the National Teachers Training College for their participation, assistance and support for this thesis. ABSTRACTThis study is intended to deal with one of the problems in teaching English for the students of library study at the National Teachers Training college (NTTC): That’s the shortage of an appropriate ESP syllabus for the students of library study when they take the ESP course. Thus, this study aims at designing an appropriate, practical, feasible and also enjoyable ESP syllabus for the students of library study to facilitate the process of teaching and learning ESP.The study consists of three main parts: Introduction, Development and Conclusion.The first part: Introduction discusses the rationale, aim and objectives, scope, methods and design of the study.The second part of the study contains three chapters. Chapter one is devoted to the theoretical background of the study. Chapter two is the investigation into some textbooks relating to library study. The next chapter deals with methodology of the study, data collection, findings and discussion and the proposed syllabus for the target students based on the previous chapters. The last part of the study is a summary of the study including the conclusion of the study, limitations of the The Second Condition for Equilibrium The Second Condition for Equilibrium Bởi: OpenStaxCollege Torque The second condition necessary to achieve equilibrium involves avoiding accelerated rotation (maintaining a constant angular velocity A rotating body or system can be in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it To understand what factors affect rotation, let us think about what happens when you open an ordinary door by rotating it on its hinges Several familiar factors determine how effective you are in opening the door See [link] First of all, the larger the force, the more effective it is in opening the door—obviously, the harder you push, the more rapidly the door opens Also, the point at which you push is crucial If you apply your force too close to the hinges, the door will open slowly, if at all Most people have been embarrassed by making this mistake and bumping up against a door when it did not open as quickly as expected Finally, the direction in which you push is also important The most effective direction is perpendicular to the door—we push in this direction almost instinctively 1/10 F ⊥ F′ The Second Condition for Equilibrium Torque is the turning or twisting effectiveness of a force, illustrated here for door rotation on its hinges (as viewed from overhead) Torque has both magnitude and direction (a) Counterclockwise torque is produced by this force, which means that the door will rotate in a counterclockwise due to Note that r is the perpendicular distance of the pivot from the line of action of the force (b) A smaller counterclockwise torque is produced by a smaller force acting at the same distance from the hinges (the pivot point) (c) The same force as in (a) produces a smaller counterclockwise torque when applied at a smaller distance from the hinges (d) The same force as in (a), but acting in the opposite direction, produces a clockwise torque (e) A smaller counterclockwise torque is produced by the same magnitude force acting at the same point but in a different direction Here, θ is less than 90º (f) Torque is zero here since the force just pulls on the hinges, producing no rotation In this case, θ = 0º The magnitude, direction, and point of application of the force are incorporated into the definition of the physical quantity called torque Torque is the rotational equivalent of a force It is a measure of the effectiveness of a force in changing or accelerating a rotation (changing the angular velocity over a period of time) In equation form, the magnitude of torque is defined to be τ = rF sin θ where τ (the Greek letter tau) is the symbol for torque, r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between the force and the vector directed from the point of application to the pivot point, as seen in [link] and [link] An alternative expression for torque is given in terms of the perpendicular lever arm r ⊥ as shown in [link] and [link], which is defined as r ⊥ = r sin θ 2/10 F The Second Condition for Equilibrium so that τ = r ⊥ F A force applied to an object can produce a torque, which depends on the location of the pivot point (a) The three factors r, F, and θ for pivot point A on a body are shown here—r is the distance from the chosen pivot point to the point where the force F is applied, and θ is the angle between and the vector directed from the point of application to the pivot point If the object can rotate around point A, it will rotate counterclockwise This means that torque is counterclockwise relative to pivot A (b) In this case, point B is the pivot point The torque from the applied force will cause a clockwise rotation around point B, and so it is a clockwise torque relative to B The perpendicular lever arm r ⊥ is the shortest distance from the pivot point to the line along which F acts; it is shown as a dashed line in [link] and [link] Note that the line segment that defines the distance r ⊥ is perpendicular to F, as its name implies It is sometimes easier to find or visualize r ⊥ than to find both r and θ In such cases, it may be more convenient to use τ = r ⊥ F rather than τ = rF sin θ for torque, but both are equally valid The SI unit of torque is newtons times meters, usually written as N · m For example, if you push perpendicular to the door with a force of 40 N at a distance of 0.800 m from the hinges, you exert a torque of 32 N·m(0.800 m×40 N×sin 90º) relative to the hinges If you reduce the force to 20 N, the torque is reduced to 16 N·m, and so on The torque is always calculated with reference to some chosen pivot point For the same applied force, a different choice for the location of the pivot will give you a different value for the torque, since both r and θ depend on the location of the pivot Any point in any object can be chosen to calculate the torque about that point The object may not actually pivot about the chosen ...VIETNAM NATIONAL UNIVERSITY- HANOICOLLEGE OF FOREIGN LANGUAGESPOST- GRADUATE DEPARTMENTGIAP THI YENAN EVALUATION OF THE MATERIAL “BASIC ENGLISH III” FOR THE SECOND YEAR NON- ENGLISH MAJOR STUDENTS AT BAC GIANG TEACHERS’ TRAINING COLLEGE(Đánh giá giáo trình “Tiếng Anh Cơ Bản III” dành cho sinh viên không chuyên năm thứ hai Trường Cao Đẳng Sư Phạm Bắc Giang)MINOR PROGRAM THESISFIELD : MOTHODOLOGYCODE : 601410 HA NOI- 2008 i VIETNAM NATIONAL UNIVERSITY- HANOICOLLEGE OF FOREIGN LANGUAGESPOST- GRADUATE DEPARTMENTGIÁP THỊ YẾNAN EVALUATION OF THE MATERIAL “BASIC ENGLISH III” FOR THE SECOND YEAR NON- ENGLISH MAJOR STUDENTS AT BAC GIANG TEACHERS’ TRAINING COLLEGE (Đánh giá giáo trình “Tiếng Anh Cơ Bản III” dành cho sinh viên không chuyên năm thứ hai Trường Cao Đẳng Sư Phạm Bắc Giang)MINOR PROGRAM THESISFIELD : METHODOLOGYCODE : 601410SUPERVISOR: ĐINH HẢI YẾN, M.A ha noi - 2008ii i CERTIFICATE OF ORIGINALITY I certify my authorship of the minor thesis submitted today entitled“An evaluation of the material Basic English III for the second year non-English major students at Bac Giang Teachers’ Training College”in terms of the statement of requirements for the thesdis and the field study reports in Masters’ programs is the result of my own work, except where otherwise acknowledged and that this minor thesis or any part of the same had not been submitted for a higher degree to any other universities or institution.SignatureDate: August 29th, 2008i ACKNOWLEDGEMENTSOn the completion of the thesis, I would like to thank the following people:I would like to express my deepest gratitude to my supervisor, Ms. Dinh Hai Yen, for her patient guidance, helpful suggestions, encouragement and constructive supervision in the course of writing this research. Without her help, this work would have been impossible.I would like to acknowledge my gratitude to Mr. Le Hung Tien, Head of the Department of Post- Graduate Studies, and all the professors and lecturers at College of Foreign Language (CFL), Vietnam National University (VNU) for their insightful lectures, invaluable assistance and useful guidance. I am also grateful for the valuable materials provided by Ms. Le Thu Ha- the librarian at the post- graduate studies library of CFL, VNU.I would like to take this opportunity to express my thankfulness to all of my English staff at Bac Giang Teachers’ Training College for their great help and kind cooperation in completing the questionnaires for the thesis. I wish to extend my thanks to all of my friends who have been most helpful and supportive to me during the completion of my research.Last but not least, my sincere thanks go to my parents whose love and encouragement have been equally important to my educational endeavors, especially my little son who has given me so much inspiration, energy, and support in accomplishing this challenging work.ii ABSTRACTIt is obvious that materials evaluation is one of the essential aspects of language teaching and learning. Within this regard, the thesis VIETNAM NATIONAL UNIVERSITY- HANOI COLLEGE OF FOREIGN LANGUAGES POST- GRADUATE DEPARTMENT GIAP THI YEN AN EVALUATION OF THE MATERIAL “BASIC ENGLISH III” FOR THE SECOND YEAR NON- ENGLISH MAJOR STUDENTS AT BAC GIANG TEACHERS’ TRAINING COLLEGE (Đánh giá giáo trình “Tiếng Anh Cơ Bản III” dành cho sinh viên không chuyên năm thứ hai Trường Cao Đẳng Sư Phạm Bắc Giang) MINOR PROGRAM THESIS FIELD : MOTHODOLOGY CODE : 601410 HA NOI- 2008 i VIETNAM NATIONAL UNIVERSITY- HANOI COLLEGE OF FOREIGN LANGUAGES POST- GRADUATE DEPARTMENT GIÁP THỊ YẾN AN EVALUATION OF THE MATERIAL “BASIC ENGLISH III” FOR THE SECOND YEAR NON- ENGLISH MAJOR STUDENTS AT BAC GIANG TEACHERS’ TRAINING COLLEGE (Đánh giá giáo trình “Tiếng Anh Cơ Bản III” dành cho sinh viên không chuyên năm thứ hai Trường Cao Đẳng Sư Phạm Bắc Giang) MINOR PROGRAM THESIS FIELD : METHODOLOGY CODE : 601410 SUPERVISOR: ĐINH HẢI YẾN, M.A ha noi - 2008 ii i CERTIFICATE OF ORIGINALITY I certify my authorship of the minor thesis submitted today entitled “An evaluation of the material Basic English III for the second year non-English major students at Bac Giang Teachers’ Training College” in terms of the statement of requirements for the thesdis and the field study reports in Masters’ programs is the result of my own work, except where otherwise acknowledged and that this minor thesis or any part of the same had not been submitted for a higher degree to any other universities or institution. Signature Date: August 29 th , 2008 i ACKNOWLEDGEMENTS On the completion of the thesis, I would like to thank the following people: I would like to express my deepest gratitude to my supervisor, Ms. Dinh Hai Yen, for her patient guidance, helpful suggestions, encouragement and constructive supervision in the course of writing this research. Without her help, this work would have been impossible. I would like to acknowledge my gratitude to Mr. Le Hung Tien, Head of the Department of Post- Graduate Studies, and all the professors and lecturers at College of Foreign Language (CFL), Vietnam National Annals of Mathematics The Hopf condition for bilinear forms over arbitrary fields By Daniel Dugger and Daniel C. Isaksen Annals of Mathematics, 165 (2007), 943–964 The Hopf condition for bilinear forms over arbitrary fields By Daniel Dugger and Daniel C. Isaksen Abstract We settle an old question about the existence of certain ‘sums-of-squares’ formulas over a field F, related to the composition problem for quadratic forms. A classical theorem says that if such a formula exists over a field of charac- teristic 0, then certain binomial coefficients must vanish. We prove that this result also holds over fields of characteristic p > 2. 1. Introduction Fix a field F . A classical problem asks for what values of r, s, and n do there exist identities of the form  r  i=1 x 2 i  ·  s  i=1 y 2 i  = n  i=1 z 2 i (1.1) where the z i ’s are bilinear expressions in the x’s and y’s. Equation (1.1) is to be interpreted as a formula in the polynomial ring F [x 1 , . . . , x r , y 1 , . . . , y s ]; we call it a sums-of-squares formula of type [r, s, n]. The question of when such formulas exist has been extensively studied: [L] and [S1] are excellent survey articles, and [S2] is a detailed sourcebook. In this paper we prove the following result, solving Problem C of [L]: Theorem 1.2. If F is a field of characteristic not equal to 2, and a sums- of-squares formula of type [r, s, n] exists over F, then  n i  must be even for n − r < i < s. We now give a little history. It is common to let r ∗ F s denote the smallest n for which a sums-of-squares formula of type [r, s, n] exists. Many papers have studied lower bounds on r ∗ F s, but for a long time such results were known only for fields of characteristic 0: one reduces to a geometric problem over R, and then topological methods are used to obtain the bounds (see [L] for a summary). In this paper we begin the process of extending such re- sults to characteristic p, replacing the topological methods by those of motivic homotopy theory. 944 DANIEL DUGGER AND DANIEL C. ISAKSEN The most classical result along these lines is Theorem 1.2 for the particular case F = R, which leads to lower bounds for r ∗ R s. It seems to have been proven in three places, namely [B], [Ho], and [St]; but in modern times the given condition on binomial coefficients is usually called the ‘Hopf condition’. The paper [S1] gives some history, and explains how K. Y. Lam and T. Y. Lam deduced the condition for arbitrary fields of characteristic 0. Problem C of [L, p. 188] explicitly asked whether the same condition holds over fields of characteristic p > 2. Work on this question had previously been done by Adem [A1], [A2] and Yuzvinsky [Y] for special values of r, s, and n. In [SS] a weaker version of the condition was proved for arbitrary fields and arbitrary values of r, s, and n. Stiefel’s proof of the condition for F = R used Stiefel-Whitney classes; Behrend’s (which worked over any formally real field) used some basic inter- section theory; and Hopf deduced it using singular cohomology. Our proof of the general theorem uses a variation of Hopf’s method and motivic cohomol- ogy. It can be regarded as purely algebraic—at least, as ‘algebraic’ as things like group cohomology and algebraic K-theory. These days it is perhaps not so clear that there exists a point where topology ends and algebra begins. We now explain Hopf’s proof, and our generalization, in more detail. Given a sums-of-squares formula of type [r, s, n], one has in particular a bi- linear map φ: F r × F s → F n given by (x 1 , . . . , x r ; y 1 , . . . y s ) → (z 1 , . Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009, Article ID 798319, 20 pages doi:10.1155/2009/798319 Research Article On Strong Convergence by the Hybrid Method for Equilibrium and Fixed Point Problems for an Inifnite Family of Asymptotically Nonexpansive Mappings Gang Cai and Chang song Hu Department of Mathematics, Hubei Normal University, Huangshi 435002, China Correspondence should be addressed to Gang Cai, caigang-aaaa@163.com and Chang song Hu, huchang1004@yahoo.com.cn Received 17 April 2009; Accepted 9 July 2009 Recommended by Tomonari Suzuki We introduce two modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space. Then, we prove that such two sequences converge strongly to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of asymptotically nonexpansive mappings. Our results improve and extend the results announced by many others. Copyright q 2009 G. Cai and C. S. Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Let C be a nonempty closed convex subset of a Hilbert space H. A mapping T : C → C is said to be nonexpansive if for all x, y ∈ C we have Tx−Ty≤x−y. It is said to be asymptotically nonexpansive 1 if there exists a sequence {k n } with k n ≥ 1 and lim n →∞ k n  1 such that T n x − T n y≤k n x − y for all integers n ≥ 1andforallx, y ∈ C. The set of fixed points of T is denoted by FT. Let φ : C × C → R be a bifunction, where R is the set of real number. The equilibrium problem for the function φ is to find a point x ∈ C such that φ  x, y  ≥ 0 ∀y ∈ C. 1.1 The set of solutions of 1.1 is denoted by EPφ. In 2005, Combettes and Hirstoaga 2 introduced an iterative scheme of finding the best approximation to the initial data when EPφ is nonempty, and they also proved a strong convergence theorem. 2 Fixed Point Theory and Applications For a bifunction φ : C × C → R and a nonlinear mapping A : C → H, we consider the following equilibrium problem: Find z ∈ C such that φ  z, y    Az, y − z  ≥ 0, ∀y ∈ C. 1.2 The set of such that z ∈ C is denoted by EP,thatis, EP   z ∈ C : φ  z, y    Az, y − z  ≥ 0, ∀y ∈ C  . 1.3 In the case of A  0, EP  EPφ. In the case of φ ≡ 0, EP is denoted by VIC, A. The problem 1.2  is very general i n the sense that it includes, as special cases, some optimization problems, variational inequalities, minimax problems, the Nash equilibrium problem in noncooperative games, and others see, e.g., 3, 4. Recall that a mapping A : C → H is called monotone if  Au − Av, u − v  ≥ 0, ∀u, v ∈ C. 1.4 A mapping A of C into H is called α-inverse strongly monotone, see 5–7, if there exists a positive real number α such that  x − y, Ax − Ay  ≥ α   Ax − Ay   2 1.5 for all x, y ∈ C. It is obvious that any ... on the hinges of a door will not cause it to rotate Now, the 5/10 The Second Condition for Equilibrium second condition for equilibrium is that the sum of the torques on both children is zero Therefore... from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between F and the vector directed from the point where the force acts to the pivot... to that pivot point The second condition for equilibrium holds for any choice of pivot point, and so we choose the pivot point to simplify the solution of the problem Second, the acceleration due