Hessian sufficiency for bordered Hessian

We show that the second–order condition for strict local extrema in both constrained and unconstrained optimization problems can be expressed solely in terms of principal minors of the (Lagrengean) [sic] Hessian. This approach unifies the determinantal tests in the sense that the second-order condition can be always given solely in terms of Hessian matrix

Discontinuous Extraction of a Nonrenewable Resource

This paper examines the sequence of optimal extraction of nonrenewable resources in the presence of multiple demands. We provide conditions under which extraction of a nonrenewable resource may be discontinuous over the course of its depletion.backstop technology, dynamic optimization, energy resources, Herfindahl principle, multiple demands

Narrower eigenbounds for Hadamard products

AbstractThe Schur theorem, established in 1911, defines the global bounds for all eigenvalues of Hadamard products of positive semidefinite matrices. We establish narrower, specific bounds for each eigenvalue

A Homogeneous Class of Linear Estimators and Stronger Aitken Estimator

We define a new class of linear estimators which includes as a subset all linear unbiased estimators. Subsequently, we establish Aitken estimator, the best linear unbiased estimator, further as the best in this larger class of linear estimators.

Spin-orbit torque induced dipole skyrmion motion at room temperature

We demonstrate deterministic control of dipole-field-stabilized skyrmions by means of spin-orbit torques arising from heavy transition-metal seed layers. Experiments are performed on amorphous Fe/Gd multilayers that are patterned into wires and exhibit stripe domains and dipole skyrmions at room temperature. We show that while the domain walls and skyrmions are achiral on average due to lack of Dzyaloshinskii-Moriya interactions, the N\'eel-like closure domain walls at each surface are chiral and can couple to spin-orbit torques. The current-induced domain evolutions are reported for different magnetic phases, including disordered stripe domains, coexisting stripes and dipole skyrmions and a closed packed dipole skyrmion lattice. The magnetic textures exhibit motion under current excitations with a current density ~10^8 A/m2. By comparing the motion resulting from magnetic spin textures in Fe/Gd films with different heavy transition-metal interfaces, we confirm spin currents can be used to manipulate achiral dipole skyrmions via spin-orbit torques.Comment: 23 pages, 8 figure

Stationarity Condition for AR Index Process

The stationarity conditions for an autoregressive (AR) process in general are reduced to a remarkably simple inequality if the lag coefficients are restricted to be identical. The condition is not only analytically elegant but also applicable in checking the validity of the stationarity conditions for such a restricted AR process of any order