... n−1 n ¯ 2 E xj − E [xj x] + E x j=1 n µ + σ − E xj n j=1 n j=1 n j=1 n j=1 n x k + 2 + 22 + + n 22 + + n = k=1 2 − 2 E xj − n n 2 n = E [xj xk ] j=k 2 n−1 2 − µ µ + 2 − n n n−1 22 σ − µ ... growing for the standard approach while the performance of the robust method stays the same even for 25 % occlusion 25 std approach robust approach reconstruction error 20 15 10 0 10 15 20 25 30 ... and Kernel NMF [138] More detailed discussions on kernel methods can be found in [23 , 111, 114] 4.7 .2 2D Subspace MethodsFor subspace methods usually the input images are vectorized and saved...
... perceptual system of the brain for the purpose of sensor EURASIP Journal on Embedded Systems [6] [7] [8] [9] [10] [11] [ 12] [13] [14] [15] [16] [17] [18] [19] [20 ] [21 ] [22 ] [23 ] [24 ] fusion,” in Human-Computer ... York, NY, USA, 20 02 [26 ] C Roesener, Adaptive behavior arbitration for mobile service robots in building automation, Ph.D thesis, Vienna University of Technology, Vienna, Austria, 20 07 [27 ] B Palensky, ... D Care (a) Internal States of Agent A that lead to the Formulation of a Request 100 100 100 100 75 75 75 75 50 50 50 50 25 25 25 25 A B C D Basic emotions a b c A B C D a b c Complex emotions...
... Expected reproductive success 120 30 Size (cm) 25 20 15 10 0 10 15 Age (yr) 20 25 30 100 80 60 40 20 0 10 15 Age (yr) 20 25 Figure 2.2 (a) von Bertalanffy growth for an organism with asymptotic ... dL ¼ 3L2 dt dt (2: 10) and if we use this equation in Eq (2. 9), we see that 3L2 dL ¼ L2 À cL3 dt (2: 11) so that now if we divide through by 3L2, we obtain dL c ¼ À L dt 3 3 (2: 12) and we ... 120 N(500) 100 80 60 40 20 1 .2 1.4 1.6 1.8 r 2.22. 4 2. 6 2. 8 How we understand what is happening? To begin we rewrite Eq (2. 29) as N ðt þ 1Þ ¼ ð1 þ rÞNðtÞ À rN ðt 2 K and investigate this as a...
... = (nπ)1 /2 , n ∈ Z± z2 2z = lim 2) z→0 sin (z z→0 2z cos (z ) lim = lim z→0 cos (z ) =1 379 − 4z sin (z ) lim z→(nπ)1 /2 z − (nπ)1 /2 = lim 2) 1 /2 2z cos (z ) sin (z z→(nπ) = 1 /2 (−1)n 2( nπ) Example ... are ux = vy and uy = −vx −(x − 1) + y −(x − 1 )2 + y 2( x − 1)y 2( x − 1)y = and = ((x − 1 )2 + y )2 ((x − 1 )2 + y )2 ((x − 1 )2 + y )2 ((x − 1 )2 + y )2 2 The Cauchy-Riemann equations are each identities ... x cosh y − ı cos x sinh y x2 − y + x + ı(2xy − y) Hint, Solution Exercise 8.5 f (z) is analytic for all z, (|z| < ∞) f (z1 + z2 ) = f (z1 ) f (z2 ) for all z1 and z2 (This is known as a functional...
... function Recall that for analytic functions f , f = fx = −ıfy So that fx + ıfy = 22 + = ∂u2 ∂v dw dz −1 dw dz 22 dw + = 2 ∂u ∂v dz −1 222 + ∂x2 ∂y 22 + ∂x2 ∂y Solution 8.16 ... analytic 423 We calculate the first partial derivatives of u and v u x = ex −y uy = 2 e (x cos(2xy) − y sin(2xy)) x2 −y (y cos(2xy) + x sin(2xy)) vx = e x2 −y (y cos(2xy) + x sin(2xy)) vy = e x2 −y ... f (z) = ux Note that d 2u(z /2, −ız /2) dz z z z z , −ı − ıuy , −ı 22 = ux (z /2, −ız /2) − ıuy (z /2, −ız /2) We integrate the equation to obtain: f (z) = 2u z z + c , −ı 2 We know that the real...
... , C2 and C2 C z dz = z3 − C1 z− + √ C2 z− C3 z− + = 2 + 2 + 2 z− √ √ √ z− z− z √ dz e 2 /3 z − e− 2 /3 z √ √ dz 2 /3 z − 9e z − e− 2 /3 z √ √ dz z − e 2 /3 z − e− 2 /3 z− 9 √ z e 2 /3 ... Integral Formula ezt dz 2 C z (z + a ) ezt ı ezt ı ezt ω= + − 2 C a2 z 2a (z − ıa) 2a (z + ıa) d ezt ı eıat ı e−ıat ω= − + dz a2 z=0 2a3 2a3 sin(at) t ω= 2 a a3 at − sin(at) ω= a3 ω= 2 dz Solution ... fractions z2 a= z z+ı z a b = + +1 z−ı z+ı z=ı = , b= z z−ı = z=−ı Now we can the integral with Cauchy’s formula C z2 z dz = +1 1 /2 dz + C z −ı 1 = 2 + 22 = 2 C 1 /2 dz z+ı C z2 + dz = z...
... = = for x = 2 k for x = 2 k 1−eınx 1−eıx for x = 2 k e−ıx /2 − eı(N −1 /2) x e−ıx /2 − eıx /2 for x = 2 k e−ıx /2 − eı(N −1 /2) x − 2 sin(x /2) = N −1 sin(nx) = n=1 for x = 2 k for x = 2 k for x = 2 k ... function Hint 12. 22 cos z = − cos(z − π) sin z = − sin(z − π) Hint 12. 23 CONTINUE Hint 12. 24 CONTINUE Hint 12. 25 Hint 12. 26 Hint 12. 27 Hint 12. 28 Hint 12. 29 Hint 12. 30 CONTINUE 581 12. 9 Solutions ... Solution 12. 4 ∞ n=1 (−1)n+1 = n ∞ n=1 ∞ = n=1 ∞ < 1 − 2n − 2n (2n − 1)(2n) (2n − 1 )2 n=1 ∞ < = n=1 π 12 Thus the series is convergent 587 n2 Solution 12. 5 Since 2n−1 |S2n − Sn | = j=n 2n−1 ≥ j=n j 2n...
... 1)(−1)n 2 n z n , n=0 ∞ n=0 − ı /2 − ı /2 = (z − 2) z2 − ı /2 = z2 2 n n+1 n z , 2n 1− z ∞ 2 n n=0 ∞ for |z| < for |z| < 2 − z n , for |2/ z| < (−1)n (n + 1)(−1)n 2n z −n 2 , = (2 − ı /2) for |z| ... z 2 − 2/ z =− z ∞ n=0 ∞ z n , 2n z −n−1 , =− for |2/ z| < for |z| > n=0 −1 2 n−1 z n , =− n=−∞ 620 for |z| > 2 − ı /2 = (2 − ı /2) (1 − z /2) 2 (z − 2) 4−ı = = = 4−ı 4−ı ∞ n=0 ∞ − z n , for |z /2| < ... − ı /2 z − (z − 2) 2 |z|=3 (z − ı /2) + ı /2 (z − 2) + c(z − 2) + 2c − + dz = z − ı /2 z 2 (z − 2) 2 ı 2 2+ c =0 ı c =2 z |z|=3 Thus we see that the function is f (z) = 1 − ı /2 − + + d, z − ı /2 z...
... (z + ı5) z =2 ı (z + (ı7 − 2) z − − ı 12) eız e 2 + −ı = 2 (z + ı5 )2 (z − 2) 58 116 z=0 ı e 2 = 2 − + + −ı 25 20 58 116 π 6π = − + π cos − π sin + ı − + π cos + π sin 10 58 29 25 29 58 687 We ... cosh y − ı sin x sinh y sin x cosh y + ı cos x sinh y = cos2 x cosh2 y + sin2 x sinh2 y sin2 x cosh2 y + cos2 x sinh2 y ≤ cosh2 y sinh2 y = | coth(y)| The hyperbolic cotangent, coth(y), has a ... 1/(ız) dz = + a(z − z −1 )/ (2 ) C z2 2/ a dz + ( 2/ a)z − We factor the denominator of the integrand z1 = ı 2/ a dz f (a) = C (z − z1 )(z − z2 ) √ √ −1 + − a2 −1 − − a2 , z2 = ı a a Because |a| < 1,...