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- Tharmalingam Ratnarajah, Rémi Vaillancourt, M. Alvo
- SIAM J. Matrix Analysis Applications
- 2004

In this paper, the distributions of the largest and smallest eigenvalues of complex Wishart matrices and the condition number of complex Gaussian random matrices are derived. These distributions are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. Several results are derived… (More)

- A P Calderón, R Vaillancourt
- Proceedings of the National Academy of Sciences…
- 1972

Pseudo-differential operators of order -M and type rho, delta(1), delta(2) are shown to be bounded in L(2) provided that 0 </= rho </= delta(1) < 1, 0 </= rho </= delta(2) < 1, and [Formula: see text].

- Tharmalingam Ratnarajah, Rémi Vaillancourt, M. Alvo
- Probl. Inf. Transm.
- 2005

The eigenvalue densities of complex noncentral Wishart matrices are investigated to study an open problem in information theory. Specifically, the largest, smallest and joint eigenvalue densities of complex noncentral Wishart matrices are derived. These densities are expressed in terms of complex zonal polynomials and invariant polynomials. The connection… (More)

- S. Y. C. Yong, C. Y. Choong, +8 authors R. Wickneswari
- Tree Genetics & Genomes
- 2010

The majority of plant expressed sequence tags (ESTs) available in the public databases are from non-woody species such as Arabidopsis, maize, soybean, and rice, with the exception of the model tree species, Populus. In this study, we report the first EST database constructed from the commercially important tree species Acacia. ESTs were generated from… (More)

- K B Seamon, R Vaillancourt, M Edwards, J W Daly
- Proceedings of the National Academy of Sciences…
- 1984

[12-3H]Forskolin (27 Ci/mmol) has been used to study binding sites in rat brain tissue by using both centrifugation and filtration assays. The binding isotherm measured in the presence of 5 mM MgCl2 by using the centrifugation assay is described best by a two-site model: Kd1 = 15 nM, Bmax1 (maximal binding) = 270 fmol/mg of protein; Kd2 = 1.1 microM; Bmax2… (More)

- Tharmalingam Ratnarajah, Rémi Vaillancourt
- IEEE Transactions on Information Theory
- 2005

In this correspondence, the densities of quadratic forms on complex random matrices and their joint eigenvalue densities are derived for applications to information theory. These densities are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. The derived densities are used to… (More)

The paper explains the concepts of order and absolute stability of numerical methods for solving systems of first-order ordinary differential equations (ODE) of the form y = f (t, y), y(t 0) = y 0 , where f : R × R n → R n , describes the phenomenon of problem stiffness, and reviews explicit Runge–Kutta methods, and explicit and implicit linear multistep… (More)

A 3-stage 6-step variable step Hermite-Birk-hoff-Obrechkoff method of order 14, denoted by HBO14(3,6), is constructed for solving non-stiff systems of first-order differential equations of the form y = f (x, y), y(x 0) = y 0. Its formula uses y and y as in Obrechkoff method. Forcing a Taylor expansion of the numerical solution to agree with an expansion of… (More)

Variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff methods of order 4 to 14, denoted by HBO(4-14)3, are constructed for solving non-stiff systems of first-order differential equations of the form y = f (x, y), y(x 0) = y 0. These methods use y and y as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an… (More)