Noncommutative Stein's maximal spherical means

Based on a proper hypothesis on the noncommutative Fourier integral operators, we establish in this paper the strong-type $(p,p)$ (with $2\leq p\leq \infty$) estimates for the operator-valued Stein's maximal spherical means

Experimental and simulation study on nonlinear pitch control of Seagull underwater glider

1008-1015The Seagull underwater glider, developed by the Shanghai Jiao Tong University, is designed as a test-bed glider for the development and validation of various algorithms to enhance the glider’s long-term autonomy. In this paper, an adaptive backstepping control (ABC) method is proposed for the nonlinear pitch control of the underwater glider gliding in the vertical plane. The linear quadratic regulator (LQR) control and proportional-integral-derivative (PID) control are applied and evaluated with the ABC method to control a glider in saw-tooth motion. Simulation results demonstrate inherent effectiveness and superiority of the LQR or PID based method. According to Lyapunov stability theory, the ABC control scheme is derived to ensure the tracking errors asymptotically converge to zero. The ABC controller has been implemented on Seagull underwater glider, and verified in field experiments in the Qiandao Lake, Zhejiang

Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic-Vafa [arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in the total space of the canonical line bundle of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]), and (iii) an outer brane at zero framing in the total space of the canonical line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure