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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)
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].
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: firstname.lastname@example.org 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: email@example.com 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)
A 3-stage 6-step variable step Hermite-Birkhoff-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(x0) = y0. Its formula uses y and y as in Obrechkoff method. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the… (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)
The eigenvalue and condition number distributions of complexWishart matrices are investigated and applied to open problems in information theory.
In this paper, complex singular Wishart matrices and their applications are investigated. In particular, a volume element on the space of positive semidefinite m×m complex matrices of rank n < m is introduced and some transformation properties are established. The Jacobian for the change of variables in the singular value decomposition of general m × n… (More)