Website: http://www.docs.vn Email : lienhe@docs.vn Tel : 0918.775.368 Hanoi open university Faculty of English ***** Graduation paper b. a degree in English A new approach to semantic and syntactic functions of English adjectives A– contrastive analysis with their Vietnamese equivalents Supervisor : hoµng TuyÕt minh, m.a student : nguyÔn thÞ nga date of birth : 13/ 08/ 1985 course : k11a (2004- 2008) Hanoi- 2008 Graduation paper Declaration Title: A new approach to semantic and syntactic functions of English adjectives A contrastive– analysis with their Vietnamese equivalents (Graduation paper submitted in partial fulfillment for B.A Degree in English) I certify that no part of the above report has been copied or reproduced by me from any other person’s work without acknowledgements and that report is originally written by me under strict guidance of my supervisor. Date submitted: May 2008 Student Supervisor NguyÔn ThÞ Nga – K 11A Graduation paper Acknowledgements First of all, I would like to express my sincere thanks to my supervisor, Mrs Hoang Tuyet Minh. She is the person who made clear my confuse initial ideas, step by step guiding me during my writing graduation paper. I could finally complete my graduation. I own her a debt of gratitude that cannot be measured. Secondly, I would like to give my thanks to Dean and Leading Board of English faculty, who gave me opportunities to study and do my graduation paper. I would also give my deepest gratitude to all lectures of English faculty at Hanoi Open University for their enthusiastic teaching during my four_ year study. They gave me not only knowledge but also the precious experience in life. Thirdly, I should also express many thanks to my dear friends who have shared with me a lot during my studies and my research work as well. Constantly, rather than final, I would like to send my great thanks to all members in my family for their support and encouragement during my study. Hanoi, May 2008 Student: Nguyen Thi Nga NguyÔn ThÞ Nga – K 11A Graduation paper TABLE OF CONTENTS Acknowledgements Abbreviations Chapter I .1 Introduction .1 Chapter II .4 An overview of English adjectives .4 References NguyÔn ThÞ Nga – K 11A Graduation paper Abbreviations Adj : adjective C : complement Co : object complement Cs : subject complement NP :noun phrase O : objective Prep. p :preposition phrase S : subject V : verb ~ :equivalent to * : wrong sentence ∅ : without verb NguyÔn ThÞ Nga – K 11A Graduation paper Chapter I Introduction 1.1 Rationale Nowadays, English is considered as one of the most popular language for everyone all over the world. There are many problems in learning English as listening, speaking, reading, writing, Grammar, lexicology, etc. Grammar plays a very important role in English, it is not easy for English learners to study. Moreover, learners are affected by their mother tongue during the Inverses and Radical Functions Inverses and Radical Functions By: OpenStax College Precalculus A mound of gravel is in the shape of a cone with the height equal to twice the radius The volume is found using a formula from elementary geometry 1/29 Inverses and Radical Functions V = πr2h = πr2(2r) = πr3 We have written the volume V in terms of the radius r However, in some cases, we may start out with the volume and want to find the radius For example: A customer purchases 100 cubic feet of gravel to construct a cone shape mound with a height twice the radius What are the radius and height of the new cone? To answer this question, we use the formula r= √ 3V 2π This function is the inverse of the formula for V in terms of r In this section, we will explore the inverses of polynomial and rational functions and in particular the radical functions we encounter in the process Finding the Inverse of a Polynomial Function Two functions f and g are inverse functions if for every coordinate pair in f, (a, b), there exists a corresponding coordinate pair in the inverse function, g, (b, a) In other words, the coordinate pairs of the inverse functions have the input and output interchanged For a function to have an inverse function the function to create a new function that is one-to-one and would have an inverse function For example, suppose a water runoff collector is built in the shape of a parabolic trough as shown in [link] We can use the information in the figure to find the surface area of the water in the trough as a function of the depth of the water 2/29 Inverses and Radical Functions Because it will be helpful to have an equation for the parabolic cross-sectional shape, we will impose a coordinate system at the cross section, with x measured horizontally and y measured vertically, with the origin at the vertex of the parabola See [link] 3/29 Inverses and Radical Functions From this we find an equation for the parabolic shape We placed the origin at the vertex of the parabola, so we know the equation will have form y(x) = ax2 Our equation will need to pass through the point (6, 18), from which we can solve for the stretch factor a 18 = a62 a= = 18 36 Our parabolic cross section has the equation y(x) = x2 We are interested in the surface area of the water, so we must determine the width at the top of the water as a function of the water depth For any depth y the width will be given by 2x, so we need to solve the equation above for x and find the inverse function However, notice that the original function is not one-to-one, and indeed, given any output there are two inputs that produce the same output, one positive and one negative To find an inverse, we can restrict our original function to a limited domain on which it is one-to-one In this case, it makes sense to restrict ourselves to positive x values On this domain, we can find an inverse by solving for the input variable: y = x2 2y = x2 x = ± √2y This is not a function as written We are limiting ourselves to positive x values, so we eliminate the negative solution, giving us the inverse function we’re looking for y= x2 , x>0 Because x is the distance from the center of the parabola to either side, the entire width of the water at the top will be 2x The trough is feet (36 inches) long, so the surface area will then be: 4/29 Inverses and Radical Functions Area = l ⋅ w = 36 ⋅ 2x = 72x = 72√2y This example illustrates two important points: When finding the inverse of a quadratic, we have to limit ourselves to a domain on which the function is one-to-one The inverse of a quadratic function is a square root function Both are toolkit functions and different types of power functions Functions involving roots are often called radical functions While it is not possible to find an inverse of most polynomial functions, some basic polynomials have inverses Such functions are called invertible functions, and we use the notation f − 1(x) Warning: f − 1(x) is not the same as the reciprocal of the function f(x) This use of “–1” is reserved to denote inverse functions To denote the reciprocal of a function f(x), we −1 would need to write (f(x)) = f(x) An important relationship between inverse functions is that they “undo” each other If f − is the inverse of a function f, then f is the inverse of the function f − In other words, whatever the function f does to x, f − undoes it—and vice-versa More formally, we write f − 1(f(x)) = x, for all x in the domain of f and f(f − 1(x)) = x, for all x in the domain of f − A General Note Verifying Two Functions Are Inverses of One Another Two functions, f and g, are inverses of one another if for all x in the domain of f and g g(f(x)) = f(g(x)) = x How To Given a polynomial function, find the inverse of the function by restricting the domain in such a way that the new function is one-to-one 5/29 Inverses and Radical Functions Replace f(x) with y Interchange x and y Solve for y, and rename the function f − 1(x) Verifying Inverse Functions ... Chapter 1 Convex sets and convex functions taking the infinity value Chapter 1. Convex sets and convex functions taking the infinity value tvnguyen (University of Science) Convex Optimization 4 / 108 Chapter 1 Convex sets and convex functions taking the infinity value Convex set Definition. A subset C of IR n is convex if ∀x, y ∈ C ∀t ∈ [0, 1] tx + (1 − t)y ∈ C Proposition. If C is convex, then its interior int C and its closure C are convex Convexity is preserved by the following operations : Let I be an arbitrary set. If C i ⊆ IR n , i ∈ I , are convex, then C = ∩ i∈I C i is convex Let C and D be two convex sets in IR n and let a and b be two real numbers. Then the following set is convex : aC + bD := {ac + bd | c ∈ C , d ∈ D} tvnguyen (University of Science) Convex Optimization 5 / 108 Chapter 1 Convex sets and convex functions taking the infinity value Illustration Y X X Y convex non convex tvnguyen (University of Science) Convex Optimization 6 / 108 Chapter 1 Convex sets and convex functions taking the infinity value Examples of convex sets The following are some examples of convex sets : (1) Hyperplane : S = {x|p T x = α}, where p is a nonzero vector in IR n , called the normal to the hyperplane, and α is a scalar. (2) Half-space : S = {x|p T x ≤ α}, where p is a nonzero vector in IR n , and α is a scalar. (3) Open half-space : S = {x|p T x < α}, where p is a nonzero vector in IR n and α is a scalar. (4) Polyhedral set : S = {x|Ax ≤ b}, where A is an m × n matrix, and b is an m vector. (Here the inequality should be interpreted elementwise.) tvnguyen (University of Science) Convex Optimization 7 / 108 Chapter 1 Convex sets and convex functions taking the infinity value Examples of convex sets (5) Polyhedral cone : S = {x|Ax ≤ 0}, where A is an m × n matrix. (6) Cone spanned by a finite number of vectors : S = {x|x = m j=1 λ j a j |λ j ≥ 0, j = 1, . . . , m}, where a 1 , . . . , a m are given vectors in IR n . (7) Neighborhood : N ε (¯x) = {x ∈ IR n |x − ¯x < ε}, where ¯x is a fixed vector in IR n and ε > 0. tvnguyen (University of Science) Convex Optimization 8 / 108 Chapter 1 Convex sets and convex functions taking the infinity value Convex cone Some of the geometric optimality conditions that we will study use convex cones. Definition. A nonempty set C in IR n is called a cone with vertex zero if x ∈ C implies that αx ∈ C for all α ≥ 0. If, in addition, C is convex, then C is called a convex cone. 0 0 xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx Convex cone Nonconvex cone tvnguyen (University of Science) Convex Optimization 9 / 108 Chapter 1 Convex sets and convex functions taking the infinity value Convex < Day Day Up > Using Local Variables and Creating Functions that Return Results The variables you've created and used so far can be accessed at any time by any script in the Flash movie. In contrast, local variables are special variables you can create and use only within the scope of a function definition. In other words, a local variable is created within the function definition, used by the function when it's called, then deleted automatically when that function has finished executing. Local variables exist only within the function where they are created. Although local variables are not absolutely required in ActionScript, it's good programming practice to use them. Applications that require many and frequent calculations create a lot of variables and will slow applications over time. By using local variables, however, you minimize memory usage and help prevent naming collisions, which occur when your project gets so big you unknowingly create and use variable names that are already in use. However, local variables in one function definition can have the same names as local variables within another function definition—even if both definitions exist on the same timeline. This is because Flash understands that a local variable has meaning only within the function definition where the variable was created. There is only one way to create a local variable manually, and you have been using this syntax for four lessons. Here's the syntax: var myName:String = "Jobe"; This variable becomes a local variable by simply being declared within a function definition, using the keyword var. To better grasp this concept, consider this example. In the previous exercise, we declared (created) the variable currentChannel on Frame 1 of the main timeline using the following syntax: var currentChannel:Number; Because the line of script that created the variable was on Frame 1 of the main timeline, and it didn't exist within a function definition, currentChannel became a variable of the main timeline. If we place this exact syntax within a function definition, currentChannel is considered a local variable (belonging to the function only); it exists only when the function is called and is deleted immediately upon the completion of the function's execution. Think of local variables as temporary variables, for use within functions. If you need to create a timeline variable from within a function, do not use the var syntax when declaring it. Declare the variable like this: name = "Jobe"; TIP It is best to create timeline variables outside of function definitions. Declaring a timeline variable outside of a function is considered good practice because you group all your timeline variables together. When coming back to your code months later or having another programmer look at your code, this variable organization will be appreciated. Multiple local variables can be declared within a function definition on a single line using this syntax: var firstName:String = "Jobe", lastName:String = "Makar", email:String = "jobe@electrotank .com"; Returning Results from a Function Call Not only do functions simply execute sets of actions; you can also use them like mini- programs within your movie, processing information sent to them and returning values. Take a look at this function definition: function buyCD(availableFunds:Number, currentDay:String):Boolean{ var myVariable:Boolean; if(currentDay != "Sunday" && availableFunds >= 20){ myVariable = true; }else{ myVariable = Attia, John Okyere. “AC Analysis and Network Functions.” Electronics and Circuit Analysis using MATLAB. Ed. John Okyere Attia Boca Raton: CRC Press LLC, 1999 © 1999 by CRC PRESS LLC CHAPTER SIX AC ANALYSIS AND NETWORK FUNCTIONS This chapter discusses sinusoidal steady state power calculations. Numerical integration is used to obtain the rms value, average power and quadrature power. Three-phase circuits are analyzed by converting the circuits into the frequency domain and by using the Kirchoff voltage and current laws. The un- known voltages and currents are solved using matrix techniques. Given a network function or transfer function, MATLAB has functions that can be used to (i) obtain the poles and zeros, (ii) perform partial fraction expan- sion, and (iii) evaluate the transfer function at specific frequencies. Further- more, the frequency response of networks can be obtained using a MATLAB function. These features of MATLAB are applied in this chapter. 6.1 STEADY STATE AC POWER Figure 6.1 shows an impedance with voltage across it given by vt () and cur- rent through it it () . v(t) i(t) Z + Figure 6.1 One-Port Network with Impedance Z The instantaneous power pt () is pt vtit () ()() = (6.1) If vt () and it () are periodic with period T , the rms or effective values of the voltage and current are © 1999 CRC Press LLC © 1999 CRC Press LLC V T vtdt rms T = ∫ 1 2 0 () (6.2) I T itdt rms T = ∫ 1 2 0 () (6.3) where V rms is the rms value of vt () I rms is the rms value of it () The average power dissipated by the one-port network is P T vtitdt T = ∫ 1 0 ()() (6.4) The power factor, pf , is given as pf P VI rms rms = (6.5) For the special case, where both the current it () and voltage vt () are both sinusoidal, that is, vt V wt mV () cos( ) =+ θ (6.6) and it I wt mI () cos( ) =+ θ (6.7) the rms value of the voltage vt () is V V rms m = 2 (6.8) and that of the current is © 1999 CRC Press LLC © 1999 CRC Press LLC I I rms m = 2 (6.9) The average power P is PVI rms rms V I =− cos( ) θθ (6.10) The power factor, pf , is pf VI =− cos( ) θθ (6.11) The reactive power Q is QVI rms rms V I =− sin( ) θθ (6.12) and the complex power, S , is SPjQ=+ (6.13) [] SVI j rms rms V I V I =−+− cos( ) sin( ) θθ θθ (6.14) Equations (6.2) to (6.4) involve the use of integration in the determination of the rms value and the average power. MATLAB has two functions, quad and quad8, for performing numerical function integration. 6.1.1 MATLAB Functions quad and quad8 The quad function uses an adaptive, recursive Simpson’s rule. The quad8 function uses an adaptive, recursive Newton Cutes 8 panel rule. The quad8 function is better than the quad at handling functions with “soft” singularities such as xdx ∫ . Suppose we want to find q given as q funct x dx a b = ∫ () The general forms of quad and quad8 functions that can be used to find q are © 1999 CRC Press LLC © 1999 CRC Press LLC quad funct a b tol trace (' ', , , , ) quad funct a b tol trace 8(' ' , , , , ) where funct is a MATLAB function name (in quotes) that returns a vector of values of fx () for a given vector of input values x . a is the lower limit of integration. b is the upper limit of integration. tol is the tolerance limit set for stopping the iteration of the numerical integration. The iteration continues until the rela- tive error is less than tol. The default value is ... 5/29 Inverses and Radical Functions Replace f(x) with y Interchange x and y Solve for y, and rename the function f − 1(x) Verifying Inverse Functions Show that f(x) = x+1 and f − 1(x) = x − are inverses, ... 14/29 Inverses and Radical Functions Try It Restrict the domain and then find the inverse of the function f(x) = √2x + f − 1(x) = x2 − , x≥0 Solving Applications of Radical Functions Radical functions. .. 1(x) = x+3 x − 2x + x−1 18/29 Inverses and Radical Functions Media Access these online resources for additional instruction and practice with inverses and radical functions • • • • • Graphing