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Search: All articles in the CJM digital archive with keyword convergence

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1. CJM Online first

Garcia Trillos, Nicolas; Slepcev, Dejan
On the rate of convergence of empirical measures in $\infty$-transportation distance
We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is optimal in terms of scaling with the number of sample points.

Keywords:rate, convergence
Category:01B01

2. CJM 2012 (vol 64 pp. 1415)

Selmi, Ridha
Global Well-Posedness and Convergence Results for 3D-Regularized Boussinesq System
Analytical study to the regularization of the Boussinesq system is performed in frequency space using Fourier theory. Existence and uniqueness of weak solution with minimum regularity requirement are proved. Convergence results of the unique weak solution of the regularized Boussinesq system to a weak Leray-Hopf solution of the Boussinesq system are established as the regularizing parameter $\alpha$ vanishes. The proofs are done in the frequency space and use energy methods, Arselà-Ascoli compactness theorem and a Friedrichs like approximation scheme.

Keywords:regularizing Boussinesq system, existence and uniqueness of weak solution, convergence results, compactness method in frequency space
Categories:35A05, 76D03, 35B40, 35B10, 86A05, 86A10

3. CJM 2010 (vol 62 pp. 261)

Chiang, Yik-Man; Ismail, Mourad E. H.
Erratum to: On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials
No abstract.

Keywords:Complex Oscillation theory, Exponent of convergence of zeros, zero distribution of Bessel and Confluent hypergeometric functions, Lommel transform, Bessel polynomials, Heine Problem
Categories:34M10, 33C15, 33C47

4. CJM 2007 (vol 59 pp. 85)

Foster, J. H.; Serbinowska, Monika
On the Convergence of a Class of Nearly Alternating Series
Let $C$ be the class of convex sequences of real numbers. The quadratic irrational numbers can be partitioned into two types as follows. If $\alpha$ is of the first type and $(c_k) \in C$, then $\sum (-1)^{\lfloor k\alpha \rfloor} c_k$ converges if and only if $c_k \log k \rightarrow 0$. If $\alpha$ is of the second type and $(c_k) \in C$, then $\sum (-1)^{\lfloor k\alpha \rfloor} c_k$ converges if and only if $\sum c_k/k$ converges. An example of a quadratic irrational of the first type is $\sqrt{2}$, and an example of the second type is $\sqrt{3}$. The analysis of this problem relies heavily on the representation of $ \alpha$ as a simple continued fraction and on properties of the sequences of partial sums $S(n)=\sum_{k=1}^n (-1)^{\lfloor k\alpha \rfloor}$ and double partial sums $T(n)=\sum_{k=1}^n S(k)$.

Keywords:Series, convergence, almost alternating, convex, continued fractions
Categories:40A05, 11A55, 11B83

5. CJM 2006 (vol 58 pp. 726)

Chiang, Yik-Man; Ismail, Mourad E. H.
On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials
We show that the value distribution (complex oscillation) of solutions of certain periodic second order ordinary differential equations studied by Bank, Laine and Langley is closely related to confluent hypergeometric functions, Bessel functions and Bessel polynomials. As a result, we give a complete characterization of the zero-distribution in the sense of Nevanlinna theory of the solutions for two classes of the ODEs. Our approach uses special functions and their asymptotics. New results concerning finiteness of the number of zeros (finite-zeros) problem of Bessel and Coulomb wave functions with respect to the parameters are also obtained as a consequence. We demonstrate that the problem for the remaining class of ODEs not covered by the above ``special function approach" can be described by a classical Heine problem for differential equations that admit polynomial solutions.

Keywords:Complex Oscillation theory, Exponent of convergence of zeros, zero distribution of Bessel and Confluent hypergeometric functions, Lommel transform, Bessel polynomials, Heine Proble
Categories:34M10, 33C15, 33C47

6. CJM 1999 (vol 51 pp. 250)

Combari, C.; Poliquin, R.; Thibault, L.
Convergence of Subdifferentials of Convexly Composite Functions
In this paper we establish conditions that guarantee, in the setting of a general Banach space, the Painlev\'e-Kuratowski convergence of the graphs of the subdifferentials of convexly composite functions. We also provide applications to the convergence of multipliers of families of constrained optimization problems and to the generalized second-order derivability of convexly composite functions.

Keywords:epi-convergence, Mosco convergence, Painlevé-Kuratowski convergence, primal-lower-nice functions, constraint qualification, slice convergence, graph convergence of subdifferentials, convexly composite functions
Categories:49A52, 58C06, 58C20, 90C30

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