discrete math if and only if symbol

... chỉ điều kiện. Ex: If I were to ask him nicely, he would help 4- WISH : a- Ước ở hiện tại: S + Wish + S + V.ed + (If only) were could + V Ex: I wish I were on the beach now. If only I were on ... wet if you (wear) a raincoat. 15- If they (know) your address, they would visit you 16- If it rains tomorrow, we (not go) on a picnic. 17- She would pass the exam if she (study) harder. 18- If ... would Lan do if she ………… the Miss world. a. would be b. were c. will be d. is. 24- If I were in your place, I …… ….a trip to England. a. will make b. had made c. made. d. would make. 25- If I …………...

... huống như vậy, bạn dùng cấu trúc if+ thì quá khứ (if I knew /if you were /if we didn’t…) nhưng nghĩa của câu là hiện tại không phải quá khứ. Tom would read more if he had more time. (but he doesn’t ... be able to go out) If I were you, I wouldn’t buy that coat hoặc If I was you… Nếu tôi là anh tôi sẽ không mua cái áo khoác đó. I’d go out if it weren’t raining hoặc if it wasn’t raining… ... dùng would ở mệnh đề if: I’d be very frightened if somebody pointed a gun at me. (không nói if somebody would point”) Tôi sẽ rất sợ nếu có ai đó chĩa súng vào tôi. If I didn’t go to their...

... Libraries Symbols and Linkage Static vs. Dynamic Linkage Linking External Libraries Symbol Resolution Issues Creating Libraries Data Structures B-trees Priority Queues 5 Functions and variables ... Addresses for static (allocated at compile time) symbols ã Symbol puts located in shared library GLIBC_2.2.5 (GNU C standard library) ã Shared symbol puts not assigned memory until run time ... added to resulting executable 15 Symbol resolution issues ã How about if we dene puts() in a shared library and attempt to use it within our programs? ã Symbols resolved in order they are...

... Lynette. Wacky word problems : games and activities that make math easy and fun / Lynette Long. p. cm. —(Magical math) Includes index. ISBN 0-471-21061-7 (pbk. : alk. paper) 1. Mathematical recreations. ... 10/25/04 10:07 AM Page 31 WACKY W ORD P ROBLEMS Games and Activities That Make Math Easy and Fun Lynette Long John Wiley & Sons, Inc. Magical Math ffirs.qxd 10/25/04 9:55 AM Page iii 15 III M ... 10/25/04 10:07 AM Page 22 WACKY W ORD P ROBLEMS Games and Activities That Make Math Easy and Fun Lynette Long John Wiley & Sons, Inc. Magical Math ffirs.qxd 10/25/04 9:55 AM Page iii 2 For example,...

... S 2 ∪ S 3 and S 2 and S 3 are disjoint, and so, by the sum principle, Equation 1.7 must hold. We now give a proof for general n and k. Theorem 1.3 If n and k are integers with n>0 and 0 <k<n, ... D precede C and E. Since there are 3! ways to arrange A, B, and D, and 2! ways to arrange C and E,bythe product principal, there are 3!2! = 12 lists in which A, B, and D precede C and E.Foreach ... as defined in the footnote). cParts b and c of this problem prove that a relationship is an equivalence relation if and only if it is symmetric, reflexive, and transitive. Explain why. (A short...

... commercial and public versions. The language is easy to learn and use because its syntax and semantics are similar to that of mathematics and logic. So the learning curve is steep and no prior ... assumption that X stands for b. This is an example of “unification” and it is a basic ingredient in the matching process used for computation in logic programming. Unification Unification is the ... block b if they are both on top. To accomplish this we’ll need to test whether the two blocks are on top and, if so, to retract one clause and to assert another clause. We’ll modify the program...

... harness math and technology and apply it to his art. Lang's complex origami is often referred to as computational origami because of his use of mathematics and the computer. Without the mathematic ... Likens 1 Without the mathematic, scientific, and technological advances of the 20th century, the contemporary sculptures of Theo Jansen, Robert Lang and Julian Voss-Andreae would not be possible. ... roots, move to Portland, Oregon and complete a BFA in Sculpture at Pacific Northwest College of Art. Julian Voss-Andreae now spends his energy interpreting, visualizing, and sculpting science...

... Just and Only Ví dụ: Nếu nói “He was just here”, có nghĩa là nói “Anh ta vừa mới vừa ở đây vài phút trước thôi”/ "Anh ta vừa mới ở đây mà". Cơ bản là mỗi khi sử dụng only , ... cả. Nó làm cho câu nói của chúng ta nghe có vẻ lịch sự và nhẹ nhàng hơn. Câu thứ hai dùng only có nghĩa là tôi muốn cám ơn nhưng lại không muốn nói gì nữa sau đó. Nhiều trường hợp, ... lệnh hơn nhỉ?] Có những trường hợp chúng ta có thể sử dụng “just” nhưng không thể thay thế bằng only . ...

... exciting and promising application of the puzzles would be in a math club where the students can compete and play games that challenge the mind and the creative spirit. Teaching and learning mathematics ... dimension: a conceptual understanding and framework. To expand the potential power of mathematics, they must enter a third dimension: the intuitive and mind-expanding creative viii Foreword flast.indd ... relatively easy word puzzles to more difficult math brainteasers and requiring math skills from addition and subtraction to determining probability and algebraic thinking. Here are the types...

... z  as x and and the value of x  − qz  as z. Finally, if we exchanged k and n to begin our process, we exchange the x and z values that were returned, and we have our greatest common divisor and ... = yz and t(x, y)tobethe statement x<y? 7. Which of the following statements (in which Z + stands for the positive integers and Z stands for all integers) is true and which is false, and why? a. ... 2.2.3 If k, q, n, and r are positive integers such that k = nq + r then gcd(k, n)= gcd(n, r). Proof: If d is a factor of k and n, then there are integers i 1 and i 2 so that k = i 1 d and n =...

... (5.5) where and are the magnitudes of and , respectively, and is the angle between and . The dot product is commuta- tive: (5.6) It also satisfies the inner product positivity rule if if and only if ... exact differentials can be given by using different notation where the symbols and are used instead of and . Similarly, the symbols and can be used to denote the functions instead of and . ... step backward. Specifically, if , then and if , then and if , then and (3.111) Finally, for matrices, cofactor components may be expressed in terms of the permutation symbol as follows ,...

... N, N > 0, p E(0,1) . N: the number of states in amodel; The functions Fq and symbol are given by (5) M the total number of observation symbols; The functions andsym lak A (a, )NN : the state transition probability matrix. and (6) respectively. and (6) respectively. ~~B=(b )Am : the observation symbol probability For Krawtchouk polynomials, the weight B m (ti sl function c(x) and squared norm p(n) are given by matrix in each state ... ;T = (;Ti )N the initial state probability matrix. NNx c(x; p, N) = K x (1 - p)Nx- (14) 3.2 System Overview n n p(n; p, N) = (_P)n rl , 0 < n < N -1 . (15) At the top level, a traditional DHMMs-based character (-N)n K P ) recognition system can be divided into two basic functional components: training and recognition. Both Same to the Tchebichef polynomials, instability also training and recognition share a common pre-processing, exists among Krawtchouk polynomials. The definition of frames generation and feature extraction stage. weighted Krawtchouk polynomial {Kn(x;p,N)} is In the training phase, after applying pre-processing steps including binarization, noise removal, boundary Kn (x; ~, N) x; p, N) (16) obtainment, and size normalization, an image p(n; p, N) I(x, y) (0 < x, y < L) is segmented into T frames The Krawtchouk moments of order (n ± m) in term of frame(i) (1 < i < T) using sliding window technique to suit for DHMMs recognition engine. The feature weighted Krawtchouk polynomials for an image with extraction module then transforms a frame intensity function I(x, y) and N x M pixels are defined as image frame(i) into a feature vector fv(i), which is then Krn m =E Kn(x; p1 ,N - )Krn (y; p2 ,M - )I(x,y) (17) translated into a symbol O(i)(l .<i<.T) by clustering x=O y=o algorithm (VQ). The codebook with M code words output by VQ is kept for further use to quantized feature 790 COMBINING DISCRETE ORTHOGONAL MOMENTS AND DHMMS FOR OFF-LINE HANDWRITTEN CHINESE CHARACTER RECOGNITION Xianmei Wang, Yang Yang, and Kang Huang School of Information and Engineering University of Science and Technology Beijing No. 30, Xueyuan Road, Beijing, China, 100083 plum-wanggtom.com Abstract moments requires a coordinate transformation which may Discrete orthogonal moment set is one of the novel also cause precision loss. feature moment-based descriptors for image analysis. Some researchers such as MuKundan et al. have The Tchebichef moments and Krawtchouk moments are suggested the use of discrete orthogonal moments to the two representatives in this class. This paper studies overcome the problems associated with the continuous the performance of the two discrete orthogonal moments orthogonal moments. In the past few years, some in the recognition of off-line handwritten Chinese amount different discrete orthogonal moments are proposed such in words under Discrete- time Hidden Markov Models as Tchebichef moments [5-7] and Krawtchouk moments (DHMMs) framework. The lower order moments are [8] [9]. These discrete orthogonal moments are directly employed asfeatures. A serial of experiments are carried defined in the image coordinate space [(O, 0), (N-1, M- out to compare their performance with that of the 1)]. The implementation of the discrete orthogonal continuous orthogonal movements such as Zernike and moments doesn't involve any numerical approximation Legendre. Experimental results suggest that the and coordinate transformation. These properties make recognition performance of two discrete orthogonal discrete orthogonal moments much more suitable for 2-D moments is higher than that of the continuous discrete images as pattern features. It has been shown that these moments. In additional, different values of the number of discrete orthogonal moments have better performance zones, observation symbols and states are also used to than the conventional continuous orthogonal moments find the better model structure for the new approach. for image reconstruction [5] [8] [9]. As we know, for off-line handwritten character Keywords: Discrete orthogonal moments; DHMMs; Off recognition, most of obstacles remain in the strong line handwritten character recognition. variability of the handwriting styles. Hidden Markov models (HMMs) are stochastic models which can deal with dynamic properties and variations among human 1. INTRODUCTION handwriting. Since the last decade, HMMs have been widely used for off-line handwritten character Moments with orthogonal basis functions, introduced recognition. There are basically two classes of HMMs by Teague [1], have minimal information redundancy in depending of the type of observation sequence, i.e. a moment set. In this class, the two most important discrete- time HMMs (DHMMs) and continuous-time orthogonal moments which have been extensively HMMs (CHMMs). Both of them have been successfully researched in pattern recognition field are Zernike applied to the recognition of off-line handwritten moments and Legendre moments [2-4]. Now they have character. However, DHMMs are more attractive because been widely used as fundamental features for character of their low computational cost. recognition. But both Zemike and Legendre moments In this paper, we proposed a method by extracting belong to the class of continuous moments. For digital discrete orthogonal moments feature for DHMMs-based images, their computation requires numerical character recognition. Then we study and compare the approximation of continuous integral. This process can discrete orthogonal moments for unconstrained off-line cause error, especially when the order of the moments handwritten Chinese amount in words recognition with increases. Additionally, the use of Zernike and Legendre 12 Chinese words. In the literature of image processing, ' ~~~~~~~~~it is well established that the important and perceptually Proc. 5th IEEE Int. Conf. on Cognitive Informatics (ICCI'06) Y.Y. Yao, Z.Z. Shi, Y. Wang, and W. Kinsner (Eds.)78 1 -4244-0475-4/06/$20.OO @2006 IEEE78 ... no matter the number Our work detailed in this paper deals with the of states is set to 6, 9 or 12. It also can be seen that the recognition of the isolated unconstrained off-line highest recognition accuracy can be achieved by setting handwritten Chinese amount in words including Chinese N to 9. However, the differences in accuracy rate for the characters from V to X and JU. All the handwritten values of N with 9 and 12 are small. Additionally, Table character samples used in the following experiments 1 also indicates that the recognition accuracy of Legendre were collected by our laboratory. They are written by moments is the lowest. numerous writers and in various writing styles. There are totally 11,966 binary digital images. We used 8,366 Table 2. Recognition speed of using different images for training and 3,600 images for testing. orthogonal moments with M=64, Z=4 All experiments were performed on a COMPAQ Evo tate Number N610C notebook PC with 768M memory and 1.8GHz M oen 6 9 12 CPU. All programs are written with Matlab 6.0 language. E Because of its simplest form, (11) was selected for the Tchebichef 513 477 442 function 8'(n, N) to maintain the equal weight of Krawtchouk 515 478 450 different Tchebichef moments. In (17), the condition of Zernike 239...

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... creates a decimal, and subtracts the result from 0.99. 5. Player 1 rolls two dice and subtracts the rolled decimal from the former difference. Example: If player 1 rolls a 6 and a 6, the created ... Time 103 VII. Wrap It Up! 105 37 Math Review Game 107 38 Problem Generator 110 39 Number Cross Puzzle 11 2 40 Math Libs 11 5 Decimals and Percents Master Certificate 117 Index 119 Subtracting ... tenths and one to represent hundredths). Player 1 subtracts the number rolled from 0.99. Example: If a player rolls a 3 and 2, the decimal created could be 0.32 or 0.23. Player 1 chooses 0.23 and...