Rémi Vaillancourt

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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)
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)
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)
a School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia e-mail: mawardibahri@gmail.com 1 Department of Mathematics, Hasanuddin University, KM 10 Tamalanrea Makassar, Indonesia b Department of Applied Physics, University of Fukui, 910-8507 Fukui, Japan e-mail: hitzer@mech.u-fukui.ac.jp c Division of Mathematical Sciences, Osaka(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(t0) = y0, where f : R× R → R, describes the phenomenon of problem stiffness, and reviews explicit Runge–Kutta methods, and explicit and implicit linear multistep methods. It(More)
[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)