spline approximation for cauchy principal value integrals

... Corporation Boundary Value Problems Volume 2009, Article ID 103867, 34 pages doi:10.1155/2009/103867 Research Article An Approximation Approach to Eigenvalue Intervals for Singular Boundary Value Problems with ... λ  1 0 G  t, s  h 2  s, ω n  v  ds for v ∈ C  0, 1  ,t∈  0, 1  . 2.132 Boundary Value Problems 5 Then the eigenvalues are τ m   mπ  2 for m  1, 2, , 2.2 and the corresponding ... ωtlim n →∞ ω n t for t ∈ 0, 1, then ω ∈ C  0, 1  ,ω  t  > 0 for t ∈  0, 1  , −ω   t   ψ  t, ω  t  for t ∈  0, 1  , ω  0   ω  1   0. 2.15 Boundary Value Problems 23 Let...

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Ngày tải lên: 05/09/2013, 14:58

... ordered in quantity for bulk purchases or special sales. For more information, please contact U.S. Corporate and Government Sales, 1-800-382-3419, corpsales@pearsontechgroup.com. For sales outside ... impli- cations for professionals in the relevant fields, for corporate leaders, and, in due course, for policymakers, regulators, and the educated general public. The book will have particular import for ... an informative, comprehensive look at many foundational issues for the emerging field of sustainable business management.” —Carol Singer Neuvelt, Executive Director, National Association for...

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... singular value. Recall that in (Weng et al., 2003) the eigenvalue is calcula- ble as the average magnitude of the training update c. In our formulation, according to 17 and 18, the singular value ... never cover all the things that might reasonably be said. Language is often too rich for the task being performed; for example it can be difficult to establish that two documents are d iscussing the ... creat- ing a need for techniques which compensate for this. Imagine we have a set of data stored as a matrix. Techniques based on eigen decomposi- tion allow such a matrix to be transformed into a...

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... exactly the same structure of informa- tion states; but an implementor of a feature- based NLP system, for example, could secretly perform all of the work for those grammars in N, and no ... metric type into a non-parametric sub-hierarchy that suffices for a fixed grammar (e.g. Figure 2). The former does not suffice even for fixed gram- el~t_phon list_syn~~~elist list Figure 2: ... indicate feature names; p, q, and r for names of parametric types; and g to indicate ground instances of parametric types, 1028 Parametric Types for Typed Attribute -Value Logic Gerald Penn Universit~t...

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... curve. Maximal F 1 on the curve is .43 for Exact-graph, .41 for TNF, and .34 for No-trans. AUC in the recall range 0-0.5 is .32 for Exact-graph, .31 for TNF, and .26 for No-trans. Run-time of LP-relax ... this section we present Tree-Node-Fix, an efficient approximation algorithm for Max-Trans-Forest, as well as Graph-Node-Fix, an approximation for Max- Trans-Graph. 4.1 Tree-Node-Fix The scheme ... exactly solving Max-Trans-Graph and Max-Trans-Forest (with an ILP solver) results in nearly identical performance. An ILP formulation for Max-Trans-Forest is sim- ple – a transitive graph is an...

Ngày tải lên: 16/03/2014, 19:20

... (1995) for a rigorous definition of the effective number of parameters. 13 tool for determining the appropriate range for the level of the roughness penalty, but it can produce extreme values for ... smoothness of a cubic spline. McCulloch used regression splines for this purpose, and Fisher, Nychka, and Zervos used smoothed splines. We propose using a modification of the smoothed spline. 2 See ... techniques for using this model to obtain estimates of interest rate curves. Section 3: Curve Extraction and Cubic Splines All of our extraction methods use cubic splines as the functional form for...

Ngày tải lên: 22/03/2014, 17:20

... (A1)-(A4), where (A1) f(x, x)= 0for all x ẻ C; (A2) f is monotone, i.e. f(x, y)+f(y, x) ≤ 0 for all x, y ẻ C; (A3) for all y ẻ C, f(., y) is weakly upper semicontinuous; (A4) for all x ẻ C, f(x,.) is ... to be strictly convex if for any x, y ẻ U, x = y implies |x + y || < 2 . It is also said to be uniformly convex if for each ẻ (0, 2], there exists >0such that for any x, y ẻ U, ||x y|| ... smooth, then J is single-valued and if E is uniformly smooth, then J is uniformly norm-to-norm con- tinuous on bounded subsets of E. We s hall still denote by J the single-valued duality mapping....

Ngày tải lên: 21/06/2014, 02:20

... which discussions were for boundary value problems of ordinary differential equation. This paper studies the existence of solutions for the nonlinear two-point dynamic boundary value problem on time ... boundary value problems on time scales,” Applied Mathematics Letters, vol. 13, no. 4, pp. 7–11, 2000. 7 F. M. Atici and G. S. Guseinov, “On Green’s functions and positive solutions for boundary value problems ... on time scales,” Boundary Value Problems, vol. 2011, Article ID 198598, 15 pages, 2011. 12 J. Henderson, “Multiple solutions for 2m order Sturm-Liouville boundary value problems on a measure...

Ngày tải lên: 21/06/2014, 05:20

... positive solutions for two above cases received wide attention see 3–10. For example, Ji and Ge 4 studied the multiplicity of positive solutions for the multipoint boundary value problem  φ p  u   t     ... uniformly bounded and equicontinuous. So we have that TD is compact on C0, 1.From2.13,weknowfor∀ε>0, ∃κ>0, such that when |t 1 − t 2 | <κ, we have Boundary Value Problems 9 Next, for ... Boundary Value Problems 7 a nonnegative continuous functional on K satisfying ψλu ≤ λψu for 0 ≤ λ ≤ 1, such that for positive number M and d, α  u  ≤ ψ  u  , u≤Mγ  u  2.19 for all...

Ngày tải lên: 21/06/2014, 05:20

... fixed point theorems for single-valued nonexpansive mappings have already been extended to multivalued mappings. In 1968, Markin 1 firstly established the nonexpansive multivalued convergence results ... of a uniformly convex Banach space E and T : K → CE a multivalued nonexpansive mapping. Then T has a fixed point. In 1990, Kirk and Massa 4 obtained another important result for multivalued nonexpansive ... Jr., “Multi-valued contraction mappings,” Pacific Journal of Mathematics, vol. 30, pp. 475– 488, 1969. 3 T. C. Lim, “A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach...

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... epidemic models 2–6, and so forth. At the same time, motivated by the wide application of boundary value problems in physical and applied mathematics, boundary value problems for dynamic equations ... “Positive solutions for second-order m-point boundary value problems on time scales,” Acta Mathematica Sinica, vol. 22, no. 6, pp. 1797–1804, 2006. 11 H. R. Sun, Boundary value problems for dynamic ... boundary value problems for p-Laplacian dynamic equations on time scales,” Advances in Difference Equations, vol. 2008, Article ID 496078, 9 pages, 2008. 16 C. Song, “Eigenvalue problems for p-Laplacian...

Ngày tải lên: 21/06/2014, 20:20

... 2.2. Define the forward backward jump operator σt at t for t<sup Tρt at t for t>inf T by σ  t   inf { τ>t: τ ∈ T }  ρ  t   sup { τ<t: τ ∈ T }  2.1 for all t ∈ T. ... Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales Meiqiang Feng, 1 Xuemei Zhang, 2, 3 Xianggui Li, 1 and Weigao Ge 3 1 School of Science, Beijing Information ... C reative Platform Foundation of Beijing Municipal Commission of Education PXM2008-014224-067420. References 1 D. R. Anderson, “Eigenvalue intervals for a two-point boundary value problem...

Ngày tải lên: 21/06/2014, 20:20

... (0) = 0, f  (0) = 1}. Therefore, if f ∈ A(D), we have f (z) = z +  ∞ k=2 a k z k ,forallz ∈ D. For f ∈ A(D)andξ ∈ R, ξ>0, let us consider the complex singular integrals P ξ ( f )(z) = 1 2ξ  +∞ −∞ f  ze iu  e −|u|/ξ du, ... univalent in {|z| < 2/eM},forallξ ∈ (0,1]. 4. Complex Gauss-Weierstrass integrals In this section, we study the complex integrals W ξ ( f )(z)andW ∗ ξ ( f )(z). Concerning the approximation properties, ... similar properties for the above-defined complex singular integrals. 2. Complex Picard integrals In this section, we study the properties of P ξ ( f )(z). Firstly, we present the approximation properties. Theorem...

Ngày tải lên: 22/06/2014, 21:20

... 7–22. [3]I.BegandM.Abbas,Fixed points and best approximation in Manger convex metric spaces, Archivum Mathematicum 41 (2005), 389–397. [4] , Fixed-point theorems for weakly inward multivalued maps on a convex metric ... point and invariant approximation for all x ∈ X.Defineφ :[0,∞) → [0,∞)as φ(x) = 1 c x. (2.8) As d( fx, fy) − φ  d( fx, fy)  = (c − 1)|x − y| ≥ a|x − y|=d(Tx,Ty), (2.9) therefore T is a weakly ... f  x n+N+1  ≤ d  f  x n  , f  x n+1  − Nφ(l), (2.3) which is a contradiction for N large enough. Therefore, lim n→∞ d( f (x n ), f (x n+1 )) = 0. Furthermore, for m>n d  f  x n  , f  x m  ≤ d  f  x n  ,...

Ngày tải lên: 22/06/2014, 22:20

... solutions. This study has been continued in [5]fornth-order periodic boundary value problems, in [11] for antiperiodic dynamic equations, and in [ 1] for second-order dynamic equations with dependence ... results for nth order periodic boundary value difference equations, Journal of Mathematical Analysis and Applications 247 (2000), no. 1, 67– 86. [8] , Existence and comparison results for difference ... sequence  τ n +  t a f  s, p  σ(s),u σ n (s)  Δs  (2.27) is uniform on T. Now, by using the uniform continuity of φ −1 on compact intervals, we conclude that Tu n −→ Tu uniformly on T. (2.28) Now we are going to prove...

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