Approximate relativistic bound state solutions of the Tietz-Hua rotating oscillator for any -state

Approximate analytic solutions of the Dirac equation with Tietz-Hua (TH) potential are obtained for arbitrary spin-orbit quantum number using the Pekeris approximation scheme to deal with the spin-orbit coupling terms In the presence of exact spin and pseudo-spin (pspin) symmetric limitation, the bound state energy eigenvalues and associated two-component wave functions of the Dirac particle moving in the field of attractive and repulsive TH potential are obtained using the parametric generalization of the Nikiforov-Uvarov (NU) method. The cases of the Morse potential, the generalized Morse potential and non-relativistic limits are studied.Comment: 19 pages; 7 figures; Few-Body Systems (2012) (at press

Machine Learning in Additive Manufacturing: A Review of Learning Techniques and Tasks

Due to recent advances, Machine Learning (ML) has gained attention in the Additive Manufacturing (AM) community as a new way to improve parts and processes. The capability of ML to produce insights from large amounts of data by solving tasks such as classification, regression, and clustering provide possibilities to impact every step of the AM process. In the design phase, ML can optimize part design with respect to geometry, material selection, and part count. Prior to printing, process simulations can offer understanding into the how the part will be printed, and energy, time, and cost estimates of a print can be made to assist with resource planning. During printing, AM can benefit from in-situ printing optimization and quality monitoring. Lastly, ML can characterize printed parts from in-situ or ex-situ data. This article describes some of the ML learning techniques and tasks commonly employed in AM and provides examples of their use in previous works.Mechanical Engineerin

Strict language inequalities and their decision problems

Abstract. Systems of language equations of the form {ϕ(X1,..., Xn) = ∅, ψ(X1,..., Xn) � = ∅} are studied, where ϕ, ψ may contain set-theoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X1,..., Xn) ⊂ L0. It is proved that the problem whether such an inequality has a solution is Σ2-complete, the problem whether it has a unique solution is in (Σ3 ∩Π3)\(Σ2 ∪Π2), the existence of a regular solution is a Σ1-complete problem, while testing whether there are finitely many solutions is Σ3-complete. The class of languages representable by their unique solutions is exactly the class of recursive sets, though a decision procedure cannot be algorithmically constructed out of an inequality, even if a proof of solution uniqueness is attached.