Convergence Radii for Eigenvalues of Tri--diagonal Matrices

Consider a family of infinite tri--diagonal matrices of the form $L+ zB,$ where the matrix $L$ is diagonal with entries $L_{kk}= k^2,$ and the matrix $B$ is off--diagonal, with nonzero entries $B_{k,{k+1}}=B_{{k+1},k}= k^\alpha, 0 \leq \alpha < 2.$ The spectrum of $L+ zB$ is discrete. For small $|z|$ the $n$-th eigenvalue $E_n (z), E_n (0) = n^2,$ is a well--defined analytic function. Let $R_n$ be the convergence radius of its Taylor's series about $z= 0.$ It is proved that $$ R_n \leq C(\alpha) n^{2-\alpha} \quad \text{if} 0 \leq \alpha <11/6.$

Propulsion of a plasma ring in a rotary arc device at atmospheric pressure

A new form of electromagnetic plasma propulsion has been observed in experiments with high current electric arcs interacting with a magnetic field and a solid wall of particular configuration. It is shown that the post arc plasma acceleration is likely to be due to the excessive pressure at the wall that during earlier stages of arcing counteracts the Ampere force. An attempt is made to explain formation and motion of the plasma cloud taking into account wall ablation on the basis of a self-similar Sedov’s model

On the Convexity of the KdV Hamiltonian

We prove that the nonlinear part H 17 of the KdV Hamiltonian Hkdv, when expressed in action variables I=(In)n 651, extends to a real analytic function on the positive quadrant \u21132+(N) of \u21132(N) and is strictly concave near 0. As a consequence, the differential of H 17 defines a local diffeomorphism near 0 of \u21132C(N)