... intimatelyrelated to eigenvalue decomposition in that the singular vectors, U and V , of the data matrix,A, are simply the eigenvectors of A ∗ ATandAT∗ A, r espectively, and the singular values, Σ, are ... the space of second words.The singularvaluedecompositionof a rect-angular data matrix, A, can be presented as;A = UΣVT(1)where U an d V are matrices of orthogonal leftand right singular ... diagonal matrix of the cor-responding singular values. The U and V ma-trices can be seen as a matched set of orthogo-nal basis vectors in their corresponding spaces,while the singularvalues specify...
... boundary value problems of Duffing equation with mixed nonlinear forcing terms. Boundary Value Problems 2011 2011:47.Alsaedi and Aqlan Boundary Value Problems 2011, 2011:47http://www.boundaryvalueproblems.com/content/2011/1/47Page ... Boundary Value Problems 2011, 2011:47http://www.boundaryvalueproblems.com/content/2011/1/47Page 8 of 11 RESEARC H Open AccessOn nonlocal three-point boundary value problems of Duffing equation with ... and possibleonset of disease. This chaos is with the help of the Duffing equation. In fact, theAlsaedi and Aqlan Boundary Value Problems 2011, 2011:47http://www.boundaryvalueproblems.com/content/2011/1/47â...
... ,Nm−1,2.8where Cxis the transposed matrix of Cx, {eix}Nmi1are the eigenvalues of Mx and{hix}Nm−1i1are the eigenvalues of Bx. Denote byMi{x ∈ ∂Ω | eix> ... kind of boundary value condition, which is consistent with Dirichlet problem if the equations areelliptic, and coincident with Keldys-Fichera boundary value problem when the equations are of second-order.We ... the Keldys-Fichera boundary value problem, with thatthe associated problem is of well-posedness. However, for higher-order ones, the discussion of well-posed boundary value problem has not been...
... equations.In this paper, by applying Medve˘d’s method of desingularization of weakly singular inequalities we establish some new singular version of the Wendroff inequality see 1, 12for functions ... CorporationJournal of Inequalities and ApplicationsVolume 2008, Article ID 909156, 13 pagesdoi:10.1155/2008/909156Research ArticleSome New Nonlinear Weakly Singular IntegralInequalities of Wendroff Type with ... for stabilization of semilinear parabolic distributed systems bymaking use of a modification of Henry-type inequalities; Ye et al. 9 proved a generalization of this type of inequalities and...
... below.3.2.1. Singularvaluedecomposition Singular valuedecomposition is used because it captures theessential information of a matrix, somewhat similarly as theeigenvalues do. A singularvalue and ... MulgrewAs we know, singularvaluedecomposition (SVD) is designed for computing singularvalues (SVs) of a matrix. Then, if it is usedfor finding SVs of an m-by-1 or 1-by-m array with elements representing ... kind of input sig-nal x[n], because the dimension of Mt matrix is 22.(7) Find singularvalues (SVs) of matrix Mf:SVD(Mf);this will return another two SVs for any kind of spec-trum (y[m]) of...
... the same valuesof theinjury severity scores: AIS head, AIS chest, AISlumbar spine and AIS cervical spine. Patients with missing GCS scores will then have their missing values replaced with observed ... subset of patients who are “similar” to the patient with the missing GCS score. In order to impute a particular GCS score,this method sorts patients both with observed values and those withmissing ... imputation [9] involves substituting individual values drawn from patients with observed data who are “similar” to the patient with the missing value. In terms of the GCSscores, this would involve imputing...
... beginning of a sentencewill be 1, and will keep decreasing at each wordbreak since it is a product of conditional probabil-ities.We tested the predictability of the model onempirical reading data ... pair of sentences. Compar-atively faster drop of probability is expected to bea good indicator of comparative processing diffi-culty. Probability re-ranking, which is a simpli-fied model of the ... adequate account of recur-sive syntactic structure is an essential component of any model of the behaviour. In this study, wetested a bigram POS tagger on different types of structural ambiguities...
... r-mixing with Eeij=0for each i(1 ≤ i ≤ n), then (3.16) holds.Proof By Corollary 3.1, with arguments similar to the proof of Lemma 3 .5, we have(3.16).4 Proof of TheoremsProof of Theorem ... n=5000.040.060.080.10.120.140.16RMSEg(t)=cos(3πt/2)(b)Figure 3 The boxplots of RMSE(b)n(b =1,2, , B) values in the estimators of g(·).Zhou and Lin Journal of Inequalities and Applications 2011, 2011:112http://www.journalofinequalitiesandapplications.com/content/2011/1/112Page ... D3n.(4:1)Zhou and Lin Journal of Inequalities and Applications 2011, 2011:112http://www.journalofinequalitiesandapplications.com/content/2011/1/112Page 12 of 18 Proof From the proof of Lemm a 3.4, it...
... solutions of nonlinear singular third-order two-point boundary value problem,”Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 413–425, 2006.12 Y. Sun, “Positive solutions of ... maxt∈ITnut≤Mntnn!uc, 3.39 10 Boundary Value Problems13 Z. Du, W. Ge, and X. Lin, “Existence of solutions for a class of third-order nonlinear boundary value problems,” Journal of Mathematical Analysis ... “Positive solutions ofsingular third-order three-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 306, no. 2, pp. 589–603, 2005. 8 Boundary Value ProblemsIf...
... proof for one-dimension case of Lemma 2.2 can be found in Pan and Lin’s work13, and the proof for n-dimension case is totally similar to one-dimension case; actually theidea of the proof ... satisfy conditions (i)and (iii) of Lemma 2.3.4. Solution of Riemann Initial-Boundary Value ProblemNow we restrict the weak entropy solutions of the Riemann initial value problem 3.1constructed ... verified. Boundary Value Problems 53. Solution of Riemann Initial Value ProblemFirst, we study the Riemann initial value problem corresponding to the Riemann initial-boundary value problem 1.1...
... α2m32∼e−√−z3−z,13 The asymptpotics of eigenvalues andtrace formula of operator associated with one singular problemNigar M AslanovaInstitute of Mathematics and Mechanics of NAS of Azerbaijan,Baku, AzerbaijanMathematics ... Levitan, BM: About sum of differences of two singular Sturm–Liouville operators. Dokl. AN SSSR 151(5), 1014–1017 (1953)[3] Rybak, MA: About asymptotic of eigenvalues of some boundary value problems for ... versions will be made available soon.The asymptotics of eigenvalues and trace formula of operator associated with one singular problemBoundary Value Problems 2012, 2012:8 doi:10.1186/1687-2770-2012-8Nigar...
... the sum of eigenvalue differences of two singular Sturm–Liouvilleoperators is studied.The asymptotics of eigenvalues and trace formulas for operators generatedby differential expressions with operator ... Levitan, BM: About sum of differences of two singular Sturm–Liouville operators. Dokl. AN SSSR 151(5), 1014–1017 (1953)[3] Rybak, MA: About asymptotic of eigenvalues of some boundary value problems for ... versions will be made available soon.The asymptotics of eigenvalues and trace formula of operator associated with one singular problemBoundary Value Problems 2012, 2012:8 doi:10.1186/1687-2770-2012-8Nigar...
... commutes with A and ispossessed of real eigenvalues λ1t, u ≤ λ2t, u ≤ ··· ≤ λnt, u . In the light of Lemma 2.2,A Bt, u is a diagonalization n ì n matrix with real eigenvalues μ1 ... self-adjointness of Bu can beremoved and Bu is not necessarily commuting with the operator A.In this note, we consider a two-point boundary value problem of a class of Duffing-type systems with non-C1perturbation ... CorporationBoundary Value ProblemsVolume 2009, Article ID 287834, 12 pagesdoi:10.1155/2009/287834Research ArticleThe Solution of Two-Point Boundary Value Problem of a Class of Duffing-Type Systems with Non-C1Perturbation...
... boundary value problem of second-order FDE,” Computers & Mathematics with Applications, vol. 37, no. 10, pp. 1–9, 1999.[5] P. X. Weng and Y. Tian, “Existence of positive solution for singular ... boundary value problem with delay,” Far East Journal of Mathematical Sciences, vol. 1, no. 3, pp. 367–382,1999.[6] F H. Wong, “Existence of positive solutions for m-Laplacian boundary value problems,” ... CorporationBoundary Value ProblemsVolume 2007, Article ID 38230, 12 pagesdoi:10.1155/2007/38230Research ArticleExistence of Positive Solutions for Boundary Value Problems of Nonlinear Functional...