We study a periodic arrangement of magnetic regions in one-dimensional superconducting wire. Due to the local exchange field, each region supports Andreev bound states that hybridize forming Bloch bands subgap spectrum what we call crystal (AC). As an illustration, ACs with ferromagnetic and antiferromagnetic alignment are considered. relate spectral asymmetry index spin-resolved Hamiltonian sp...

Inversion of MT data is an inherently nonunique and unstable problem due to the ill-posedness of the electromagnetic inverse problem. A variety of models may fit the data very well. To overcome this illposed nature of the inverse problem, we use Tikhonov’s regularization in which the ill-posed problem is replaced by a family of well-posed problems. We also analyze the behavior of the Tikhonov r...

This paper presents novel algorithms for planning feasible and minimum energy paths. The algorithms rely on series expansions to characterize planning problems for polynomial control systems. The resulting inversion problem is solved through an iterative contraction or a power series inversion. While the design methodology is general, our focus is on a class of polynomial control systems for wh...

We consider the questions of inversion modulo a regular chain in dimension zero and of matrix inversion modulo such a regular chain. We show that a well-known idea, Leverrier’s algorithm, yields new results for these questions.

and Applied Analysis 3 Theorem8. Let (α ≥ 0) ∈ R.Then, for everyf(x) ∈ L 1 [a, b], Dα a Jα a f(x) = f(x). Proof. For α = 0, both operator, are the identity. For α > 0, letm ≥ ⌈α⌉; then, D α a J α a f (x) = D m a J m−α a J α a f (x) = D m a J m a f (x) = D m a J m a f(x) = f(x) . (7) Corollary 9. Letf be analytic in (a−h, a+h) for some h > 0, and let (α ≥ 0) ∈ R. Then, (I-1) Jα a f(x) = ∞

One of the most challenging problems of electromagnetic (EM) geophysical methods is developing three-dimensional (3-D) EM inversion techniques. This problem is of utmost importance in practical applications because of the 3-D nature of the geological structures. The main difficulties in 3-D inversion are related to (1) limitations of 3-D forward modeling codes available and (2) ill-posedness of...