Weak convergence theorems for asymptotically nonexpansive nonself-mappings

AbstractSuppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1,T2:K→E be two asymptotically nonexpansive nonself-mappings with sequences {kn},{ln}⊂[1,∞) such that ∑n=1∞(kn−1)<∞ and ∑n=1∞(ln−1)<∞, respectively and F(T1)∩F(T2)={x∈K:T1x=T2x=x}≠0̸. Suppose that {xn} is generated iteratively by {x1∈Kxn+1=P((1−αn)xn+αnT1(PT1)n−1yn)yn=P((1−βn)xn+βnT2(PT2)n−1xn),∀n≥1, where {αn} and {βn} are two real sequences in [ϵ,1−ϵ] for some ϵ>0. If E also has a Fréchet differentiable norm or its dual E∗ has the Kadec–Klee property, then weak convergence of {xn} to some q∈F(T1)∩F(T2) are obtained

Composite state variable based nonlinear backstepping design for the underactuated TORA system

A nonlinear vibration controller is proposed for the translational oscillators with rotating actuator (TORA) system with the recursive technology. A composite state variable (CSV) is defined for the TORA system to start the recursive process. The design procedure treats the some state variables as virtual control inputs to design the virtual controllers step by step until the nonlinear vibration controller is obtained. The system stability is studied via a stability theorem and simulation results show the validity of the proposed controller

Nonlinear backstepping design for the underactuated TORA system

The nonlinear feedback cascade model of the underactuated translational oscillators with rotating actuator is obtained through a collocated partial feedback linearization and a global change of coordinates. A nonlinear controller is designed with the backsteping technology, which treats the state variables as virtual control inputs to design the virtual controllers step by step. The system stability is proved with the Lyapunov stability theorem. The simulation results show the system under any initial states can be asymptotically stabilized to the origin and the controller has a good control performance

Oxidation behavior of two-phase (γ’+β) Ni-Al coatings doped with Dy and Hf

Dy/Hf co-doped two-phase (γ’+β) Ni-Al coatings were prepared by electron beam physical vapour deposition (EB-PVD). Cyclic oxidation behaviour of the coatings were investigated at 1100℃. The addition of 0.1at% Dy or 0.05at% Dy +0.3at% Hf to two-phase (γ’+β) Ni-Al coating significantly improved cyclic oxidation resistance, while addition of 0.5at% Hf to (γ’+β) Ni-Al coating no obvious effect on scale adhesion. The 0.1at% Dy doped and 0.05at% Dy +0.3at% Hf co-doped two-phase (γ’+β) Ni-Al coatings yielded mass gain of 1.24 mg/cm2 and 1.04 mg/cm2 after 100h cyclic oxidation. The Dy/Hf co-doped coating showed even further lower oxidation rate as compared to the corresponding Dy doped. In order to sufficiently exert reactive element effect (REE), extremely low solubility of the reactive element in each phase of the coatings should be guaranteed

Retrieval of phase memory in two independent atomic ensembles by Raman process

In spontaneous Raman process in atomic cell at high gain, both the Stokes field and the accompanying collective atomic excitation (atomic spin wave) are coherent. We find that, due to the spontaneous nature of the process, the phases of the Stokes field and the atomic spin wave change randomly from one realization to another but are anti-correlated. The phases of the atomic ensembles are read out via another Raman process at a later time, thus realizing phase memory in atoms. The observation of phase correlation between the Stokes field and the collective atomic excitations is an important step towards macroscopic EPR-type entanglement of continuous variables between light and atoms

UNITS: Unsupervised Intermediate Training Stage for Scene Text Detection

Recent scene text detection methods are almost based on deep learning and data-driven. Synthetic data is commonly adopted for pre-training due to expensive annotation cost. However, there are obvious domain discrepancies between synthetic data and real-world data. It may lead to sub-optimal performance to directly adopt the model initialized by synthetic data in the fine-tuning stage. In this paper, we propose a new training paradigm for scene text detection, which introduces an \textbf{UN}supervised \textbf{I}ntermediate \textbf{T}raining \textbf{S}tage (UNITS) that builds a buffer path to real-world data and can alleviate the gap between the pre-training stage and fine-tuning stage. Three training strategies are further explored to perceive information from real-world data in an unsupervised way. With UNITS, scene text detectors are improved without introducing any parameters and computations during inference. Extensive experimental results show consistent performance improvements on three public datasets.Comment: Accepted by ICME 202