... 13 14 15 15 16 19 22 24 24 25 26 29 30 32 33 36 40 45 47 48 50 53 58 58 Source terms 3. 1 Invariant domains and entropy 3. 2 Saint Venant system ... (2. 23) (2.24) Lemma 2.8 The left-hand side of (2. 23) and the right-hand side of (2.24) are nonincreasing functions of r and l respectively In particular, for (2. 23) and (2.24) to hold it is necessary ... invariant domains, see [35 ], [36 ] Finally, the Rusanov ux is obtained according to Remark 2.2 by optimizing (2.1 03) , and taking for c in (2. 93) c= sup U=Ul ,Ur sup |j (U )| j (2.104) 32 Chapter Conservative...
... If x = ak, then straightforward use of equations (3. 23) and (3. 24) or (3. 25) and (3. 26) gives XT X – x T x = (v – q)/2 > (3. 33) Using (3. 31) and (3. 22) in (3. 33) gives (3. 34) Thus, once columns ... for computers Singular values 3. 365840 731 1E+00 1.08127 630 36E+00 6.7 431 328720E-01 5 .36 27598567E-01 3. 365840 731 1E+00 1.08127 630 36E+00 6.7 431 328701E-01 5 .36 27598503E-01 Hilbert segment: Column orthogonality ... p/(v cos φ ) for q > sin φ = sgn(p)[(v – q)/(2v ) ] cos φ = p/(υ sin φ ) ½ for q < (3. 23) (3. 24) (3. 25) (3. 26) where } sgn (p) = –1 for p > for p < (3. 27) Note that having two forms for the calculation...
... and3. 38 , we have that lim yn − ρn n→∞ 3. 43 18 Journal of Inequalities and Applications Observe that yn − Syn ≤ yn − xn xn − Sρn Sρn − Syn ≤ yn − xn xn − Sρn ρn − yn 3. 44 From 3. 27 , 3. 33 , and ... yn − p 2sn ν λ2 s2 Byn − Bp n 3. 34 s2 Byn − Bp n − 2sn ν yn − p 2 Byn − Bp Observe 3. 31 that xn −p ≤ − βn ρn − p βn xn − p 2αn λ2 3. 35 Substituting 3. 34 into 3. 35 , we have xn −p ≤ xn − p 2sn ... Trn xn and yn 1 rn η − yn , yn in 3. 12 and η F yn , yn 3. 11 η − yn , yn − xn ≥ 0, rn F yn , η yn − xn Trn xn , we have F yn , η Putting η 1 F yn , yn rn − xn ≥ 0, 3. 12 ∀η ∈ C 3. 13 yn in 3. 13 , we...
... T1 T and T2 S, then Theorem 3.3 reduces to the following corollary Corollary 3. 5 Plubtieng and Ungchittrakool 22, Theorem 3. 1 Let E be a uniformly convex and uniformly smooth Banach space, and ... Kitahara and W Takahashi, “Image recovery by convex combinations of sunny nonexpansive retractions,” Topological Methods in Nonlinear Analysis, vol 2, no 2, pp 33 3 34 2, 19 93 13 W Takahashi and T ... problem: convergence of projection methods, ” Applied Mathematics and Optimization, vol 35 , no 3, pp 31 1 33 0, 1997 10 G Crombez, “Viewing parallel projection methods as sequential ones in convex...
... email: jliang@uic.edu Library of Congress Control Number: 2006929615 ISBN 10: 0 -38 7 -33 319 -3 ISBN 13: 978- 038 7 -33 319-9 Printed on acid-free paper C 2007 Springer Science+Business Media, LLC All ... six methods [three “human-expert methods —authors’ annotation, CATH, and SCOP and three “fully-automated methods —DALI (Holm and Sander 1994), DomainParser (Guo et al., 20 03) , and PDP (Alexandrov ... the forefront of the major areas of the field and bring extensive experience and insight into the central intellectual methodsand ideas in the subdomain and its difficulties, accomplishments, and...
... curves between U1 and U3 and U2 and U3 are given by n3 and n5 , respectively Thus the semiconvex hulls of this threewell problem are described by Theorem 2.2 .3 with E3 = {n1 , n3 , n5 } In view ... solutions t 13 , s 13 and t 23 , s 23 of FtT Ft = GT Gs s and T FtT Ft = Hs Hs , respectively A short calculation shows that t 13 = ξ η 4− − , η ξ s 13 = ξ η 4− − , η ξ t 23 = η ξ + −1 , η ξ s 23 = ξ η 4− ... SO(2)Ui for i = 1, with rank(X1 − X2 ) = The minors relation and the expansion λi det Xi − det F = i=1 λ1 λ2 det(X2 − X1 ) − 3 − 3 (1 − 3 ) det λ1 λ2 X1 + X2 − X3 − 3 − 3 now imply that rank X3...
... 10 3 2.4 × 10 3 MLE 35 3 5 .3 × 10 4.6 × 10 3 LSM 69 3. 84 × 10 3 4.8 × 10 3 Method MOM RESULTS AND DISCUSSION because F(D) of the mean rank method [F(D) = i/(n + 1)] may be a larger value for ... 59 .3% , followed by the LSM 69 times (27.0%) and the MLE 35 times ( 13. 7%), respectively The mean MSEs from 152 times in MOM, 69 times in LSM and 35 times in MLE are 2.7 × 1 03, 3. 84 × 1 03and 5 .3 ... stand and tree variables Tree variable (n = 15,676 trees) Stand variable (86 plots) dbh (cm) BA (m2/tree) 8.71 10.25 0.009 53 2.47 6. 13 4.06 0.00821 150 2.50 0.45 0.50 0.00196 2 ,35 4 19.50 33 .50 36 .80...
... 49 § 3. 2.5 Preliminary Results 52 § 3.3 Registration of Myocardial Perfusion MRI 55 § 3. 3.1 Initial Alignment 55 § 3. 3.2 Heart Ventricle ... boundary between the LV and the myocardium 46 3.3 Registration results for a renal perfusion sequence 53 3.4 Registration results for a myocardial perfusion ... dundant and difficult to process To simplify the processing, the diffusivity of each voxel is usually represented by a × matrix D11 D12 D 13 D = D21 D22 D 23 , D31 D32 D 33 (2.1)...
... When ν = 0, (3. 3) gives the optimal conditions for (P 1) and (D1) For a nonzero ν, (3. 3) is the optimal condition for the log-det problems, that is, adding log barriers −ν log det x and ν log det ... 1) and (D1) are (strictly) feasible if there exists (x, y, z) satisfying the linear constraints in (3. 3) and (x, z ∈ int(K)) x, z ∈ K 3. 2 An infeasible central path and its neighborhood 3. 2 33 ... neighborhood 33 3.3 An inexact infeasible interior-point algorithm 38 3. 4 Proof of Lemma 3. 7 44 Inexact primal-dual path-following methodsfor l1 -regularized...
... Experimental Design and Data Collection 83 3 .3. 1 Mental-Fatigue EEG Experiments 83 3 .3. 1.1 Hardware and software environment 84 3. 3.1.2 Subjects ... the channel Fp1-F3 represents the voltage difference between the Fp1 electrode and the F3 electrode Next, the channel F3-C3 represents the voltage difference between F3 and C3, and so on through ... 84 3. 3.1 .3 Procedure 85 Labeling of Mental-Fatigue EEG 85 3. 3.2.1 Why AWVT? 85 3. 3.2.2 Characteristics of An Ideal Objective Performance...
... Theorems 3. 6 and3. 10, we obtain the corresponding result announced in [1, Theorem 3. 3] Numerical experiment Let H = R1 be a Hilbert space with the standart inner product x, y := xy and the norm ... as in the proof of Lemma 3. 2 and Theorem 3. 6, we conclude that F, Cn , Qn are closed and convex Besides, F ⊂ Cn ∩ Qn for all n ≥ Moreover, the sequence {xn } is bounded and lim ||xn+1 − xn || = ... ≥ (3) This algorithm was extended, modified and generelized by Anh and Hieu [3] for a finite family of asymptotically quasi φ-nonexpansive mappings in Banach spaces According to algorithm (3) ,...
... freespace 72 3. 33 Disparity map 73 3 .34 3D point map 73 3 .35 2D distance map with one freespace 73 3 .36 a Left image with one freespace 73 3 .36 b Right image ... Obstacle and Freespace Detection 62 3. 3.1 Distance Perception 63 3 .3. 2 Computation of 3D Point Map 63 3 .3. 3 Computation of 2D Distance Map 67 3. 3.4 Obstacle and Freespace ... 53 3.12a Colour rectified left image 53 3.12b Colour rectified right image 53 3.13a Edge left image 54 3. 13b Edge right image 54 3. 14 Correlation of two 3x3...