New implicitly solvable potential produced by second order shape invariance

New exactly solvable Hamiltonians: Shape invariance and self-similarity.

Modulation masking produced by second-order modulators.

Recent studies suggest that an auditory nonlinearity converts second-order sinusoidal amplitude modulation (SAM) (i.e., modulation of SAM depth) into a first-order SAM component, which contributes to the perception of second-order SAM. However, conversion may also occur in other ways such as cochlear filtering. The present experiments explored the source of the first-order SAM component by inve...

Shape-invariance and Exactly Solvable Problems in Quantum Mechanics

Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent two-level systems are examined. These generalize the Jaynes-Cummings Hamiltonian. Coherent states associated with shape-invariant systems are discussed. For ...

Second order sensitivity analysis for shape optimization of continuum structures

This study focuses on the optimization of the plane structure. Sequential quadratic programming (SQP) will be utilized, which is one of the most efficient methods for solving nonlinearly constrained optimization problems. A new formulation for the second order sensitivity analysis of the two-dimensional finite element will be developed. All the second order required derivatives will be calculat...

Solvable Product-type System of Difference Equations of Second Order

We show that the system of difference equations zn+1 = wa n zb n−1 , wn+1 = zc n wd n−1 , n ∈ N0, where a, b, c, d ∈ Z, and initial values z−1, z0, w−1, w0 ∈ C, is solvable in closed form, and present a method for finding its solutions.