We propose an algorithm for solving two polynomial equations in two variables. Our algorithm is based on the Macaulay resultant approach, combined with new techniques including randomization to make the algorithm accurate in the presence of roundoff error. The ultimate computation is the solution of a generalized eigenvalue problem via the QZ method. We analyze the error due to roundoff of the ...

It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...

Some new complexes of thiacetazone (Thz) and quinalizarin (Qz) with Mn(II), Fe(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Pb(II) were prepared. The ligands and their metal complexes were characterized by phisco-chemical spectroscopic techniques. The spectral data suggested that the thiacetazone as a neutral bidentate ligand is coordinated with the metal ions through the N and S atoms. The ...

New unstable temperature gradient driven modes in an inhomogeneous plasma are identified. These modes represent transient ω ≃ k‖v (e,i) th sound oscillations in magnetized plasma that are kinetically destabilized via Landau interactions. Electron and ion sound branches are unstable for large values of the Larmor radius parameter k⊥ρe,i ≫ 1, respectively. The instability occurs due to a specific...

A computational scheme based on the singular value ecomposition (SVD) for a deterministic, data domain pproach to the adaptive processing problem is presented. n the direct data domain approach, a single snapshot is onsidered for an assumed direction of arrival with unnown amplitude. This unknown signal strength is estiated on a snapshot by snapshot basis. The new SVD ased method is compared wi...

The impact of applied 3D magnetic fields on the bounce-averaged precessional drifts in a tokamak plasma are calculated. Local 3D MHD equilibrium theory is used to construct solutions to the equilibrium equations in the vicinity of a magnetic surface for a large aspect ratio circular tokamak perturbed by applied 3D fields. Due to modulations of the local shear caused by near-resonant Pfirsch-Sch...

In 1961, Baker, Gammel and Wills conjectured that for functions f meromorphic in the unit ball, a subsequence of its diagonal Padé approximants converges uniformly in compact subsets of the ball omitting poles of f . There is also apparently a cruder version of the conjecture due to Padé himself, going back to the early twentieth century. We show here that for carefully chosen q on the unit cir...

Two numerically reliable algorithms to compute the periodic nonnegative definite stabilizing solution of discrete-time periodic Riccati equations are proposed. The first method represents an extension of the periodic QZ algorithm to non-square periodic pairs, while the second method represents an extension of a quotient-product swapping and collapsing ”fast” algorithm. Both approaches are compl...

We consider the families of finite Abelian groups Z/pZ × Z/pZ, Z/pZ and Z/pZ×Z/qZ for p, q two distinct prime numbers. For the two first families we give a simple characterization of all functions whose support has cardinality k while the size of the spectrum satisfies a minimality condition. We do it for a large number of values of k in the third case. Such equality cases were previously known...