Precise neural electrical stimulation, which is a means of promoting neuronal regeneration, is a promising solution for patients with neurotrauma and neurodegenerative diseases. In this study, wirelessly controllable targeted motion and precise stimulation at the single‐cell level using S.platensis@Fe3O4@tBaTiO3 micromotors are successfully demonstrated for the first time. A highly versatile and multifunctional biohybrid soft micromotor is fabricated via the integration of S.platensis with magnetic Fe3O4 nanoparticles and piezoelectric BaTiO3 nanoparticles. The results show that this micromotor system can achieve navigation in a highly controllable manner under a low‐strength rotating magnetic field. The as‐developed system can achieve single‐cell targeted motion and then precisely induce the differentiation of the targeted neural stem‐like cell by converting ultrasonic energy to an electrical signal in situ owing to the piezoelectric effect. This new approach toward the high‐precision stimulation of neural stem‐like cells opens up new applications for micromotors and has excellent potential for precise neuronal regenerative therapies.

In this paper, we present an eigenvalue method for testing positive definiteness of a multivariate form. This problem plays an important role in the stability study of nonlinear autonomous systems via Lyapunov's direct method in automatic control. At first we apply the D'Andrea-Dickenstein version of the classical Macaulay formulas of the resultant to compute the symmetric hyperdeterminant of an even order supersymmetric tensor. By using the supersymmetry property, we give detailed computation procedures for the Bezoutians and specified ordering of monomials in this approach. We then use these formulas to calculate the characteristic polynomial of a fourth order three dimensional supersymmetric tensor and give an eigenvalue method for testing positive definiteness of a quartic form of three variables. Some numerical results of this method are reported.

Abstract. In this paper we propose a subspace limited memory quasi-Newton method for solving large-scale optimization with simple bounds on the variables. The limited memory quasi-Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. The search direction consists of three parts: a subspace quasi-Newton direction, and two subspace gradient and modified gradient directions. Our algorithm can be applied to large-scale problems as there is no need to solve any subproblems. The global convergence of the method is proved and some numerical results are also given.

In this paper we propose a quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map where the Newton method is used to solve an equivalent system of nonlinear equations. The semi-symmetric tensor is introduced to reveal the relation between homogeneous polynomial map and its associated semi-symmetric tensor. Based on this relation a globally and quadratically convergent algorithm is established where the line search is inserted. Some numerical results of this method are reported.