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Let L n (x) denote the largest digit of the first n terms in the Lüroth expansion of x ∈ (0 , 1 ]. Shen, Yu and Zhou, A note on the largest digits in Luroth expansion, Int. J. Number Theory 10 (2014) 1015–1023 considered the level sets E (γ) = x ∈ (0 , 1 ] : lim n → ∞ log L n (x) log n = γ , γ ≥ 0 , and proved that each E (γ) has full Hausdorff dimension. In this paper, we investigate the Hausdorff dimension of the following refined exceptional set: E (α , β) = x ∈ (0 , 1 ] : liminf n → ∞ log L n (x) log n = α , limsup n → ∞ log L n (x) log n = β and show that E (α , β) has full Hausdorff dimension for each pair (α , β) with 0 ≤ α < β ≤ + ∞. Combining the two results, (0 , 1 ] can be decomposed into the disjoint union of uncountably many sets with full Hausdorff dimension. [ABSTRACT FROM AUTHOR]

An excellent catalyst with a large number of weak acid centers and highly dispersed copper nanoparticles embedded in mesoporous SBA-15 carrier was successfully constructed for the purpose of efficient conversion of aniline with biomass-derived glycerin to the high value-added 3-methylindole, in which the catalyst of Cu/SBA-15 was modified with Al2O3, La2O3 and CoO in sequence. The modified carrier and the copper-based catalysts were studied by scanning electron microscopy and energy-dispersive X-ray (SEM–EDX) spectroscopy, nitrogen physical adsorption, ammonia temperature programmed desorption (NH3-TPD), hydrogen temperature programmed reduction (H2-TPR), powder X-ray diffraction (XRD), transmission electron microscopy (TEM), thermogravimetric and differential thermal analysis (TG–DTA) and inductively coupled plasma (ICP) emission spectroscopy. The research found that the Cu/CoO/La2O3/Al2O3/SBA-15 catalyst exhibited a very good catalytic performance with 3-methylindole yield up to 73.3% and selectivity reaching 86.4%. Besides, only a 3.9% yield decreased after the catalyst was circulated seven times. The characterizations revealed that Al2O3 could enhance the polarity of the carrier, thereby the interaction between the active component and the composite carrier was strengthened and the dispersion of copper was increased significantly. Adding La2O3 to Cu/SBA-15-Al2O3 could weaken the acidity and inhibit the formation of carbon deposits. CoO promoter could increase the number of weak acid centers, which was conducive to a good dispersion of active component and the high selectivity of 3-methylindole. Furthermore, the reaction pathway of gas-phase synthesis of 3-methylindole from glycerin and aniline on Cu/CoO/La2O3/Al2O3/SBA-15 was explored. [ABSTRACT FROM AUTHOR]

Considering that pressure-induced formation of short, strong covalent bonds in light-element compounds can produce superhard materials, we employ structure searching and first-principles calculations to predict a new class of boron nitrides with a stoichiometry of BN2, which are stable relative to alpha-B and alpha-N2 at ambient pressure. At ambient pressure, the most stable phase has a layered structure (h-BN2) containing hexagonal BN layers between which there are intercalated N2 molecules. At 25 GPa, a three-dimensional P42/mmc structure with single N–N bonds becomes the most stable. Dynamical, thermal, and mechanical stability calculations reveal that this structure can be recovered under ambient conditions. Its calculated stress-strain relations demonstrate an intrinsic superhard nature with an estimated Vickers hardness of ∼43 GPa. This structure has a potentially high energy density of ∼4.19 kJ/g. [ABSTRACT FROM AUTHOR]

This paper presents an output feedback indirect dynamic inversion (IDI) approach for a class of uncertain nonaffine systems with input unmodelled dynamics. Compared with previous approaches to achieve performance recovery, the proposed method aims at dealing with a broader class of nonaffine-in-control systems with triangular structure. An IDI state feedback law is designed first, in which less knowledge of the model plant is needed compared to earlier approximate dynamic inversion methods, thus yielding more robust performance. After that, an extended high-gain observer is designed to accomplish the task with output feedback. Finally, we prove that the designed IDI controller is equivalent to an adaptive proportional-integral (PI) controller, with respect to both time response equivalence and robustness equivalence. The conclusion implies that for the studied strict-feedback non-affine systems with unmodelled dynamics, there always exits a PI controller to stabilise the systems. The effectiveness and benefits of the designed approach are verified by three examples. [ABSTRACT FROM PUBLISHER]

This paper proposes a position estimation strategy for the sensorless control of permanent-magnet synchronous motors (PMSMs) based on an improved sliding-mode observer (SMO) and a tangent function-based phase-locked loop (PLL) structure. The improved SMO adopts a rotor speed-related adaptive feedback gain, and is able to derive a flux model-based estimator that contains rotor position and speed direction information. To extract accurate rotor position from the proposed SMO and reduce position estimation errors in both forward and reverse rotation of the PMSM, a tangent function-based PLL structure is established. The proposed SMO together with the PLL structure realises a solution to position and speed estimation for sensorless PMSM drives. Compared with the conventional back electromotive force (EMF)-based position estimator, the proposed position estimation strategy has advantages of simple design and robust estimation performance at a wider speed range. Effectiveness of the proposed method has been validated with simulations on virtual platform. [ABSTRACT FROM AUTHOR]

This study presents a new observer‐based electronic line‐shafting (ELS) control scheme as motion synchronisation solution for motor drives in the industrial manufacturing process. To achieve better speed control performance for each ac motor drive, a sliding mode controller is proposed. This controller is designed based on a non‐linear reaching law, which helps to settle the reaching time/chattering dilemma in the conventional sliding mode control (SMC) approach. In addition, a sliding mode observer is proposed to estimate lumped disturbances for the motor drives. Disturbance estimation results are fed forward as compensation parts for the SMC controller; in the meantime, they are transmitted to the virtual line‐shafting drive to accurately reflect total system disturbances, thus to achieve high motor speed synchronisation precision. Effectiveness of the proposed ELS control scheme is verified by simulation results. [ABSTRACT FROM AUTHOR]

In this paper, a new adaptive control method is presented for a class of induction motors. The dynamics of the system are assumed to be unknown and also are perturbed by some disturbances such as variation of load torque and rotor resistance. A type-2 fuzzy system based on rough neural network (T2FRNN) is proposed to estimate uncertainties. The parameters of T2FRNN are adjusted based on the adaptation laws which are obtained from Lyaponuv stability analysis. The effects of the uncertainties and the approximation errors are compensated by the proposed control method. Simulation results verify the good performance of the proposed control method. Also a numerical comparison is provided to show the effectiveness of the proposed fuzzy system. [ABSTRACT FROM AUTHOR]

In this study, a new adaptive controller is introduced for the induction motors (IMs) based on immersion and invariance (I&I) technique. The dynamics of the IM system are perturbed by some disturbances such as time‐varying rotor resistance and load torque. Accordingly, an adaptive controller is designed and the uncertain parameters are online estimated. The adaptation laws are obtained from the stability analysis based on I&I method. The simulation results verified the effectiveness of the proposed control method. It is revealed that the outputs of the IM could track the desired signals in the presence of the mentioned disturbances. Also, the results are compared with the conventional control methods and it is concluded that the proposed control approach resulted in better performance. [ABSTRACT FROM AUTHOR]

Abstract This research explores the eudaimonic environmental pursuit of Generation Zers. Although how they can contribute to the environment has gained traction, extant tourism research in this regard largely lags behind. Drawing on self-determination and self-efficacy theories, this inquiry fills this void by proposing a model that delineates a motivation–behavior–goal mechanism to illuminate how pursuits for environmental sustainability can develop into self-actualization. Using an explanatory sequential design, we first undertook a survey-based investigation with data acquired through purposive sampling to sample Generation Zers who had attended a minimum of one green volunteer trip in the prior year. Results first unravel how eudaimonic environmental motivation can induce green travel involvement, leading to environmental citizenship. Exhibiting environmental citizenship presents an avenue to foster environmental goal attainment and subsequent self-actualization, synthesizing a path that depicts behavior-goal-actualization of oneself. The moderating effect of environmental self-efficacy is also warranted. A post-hoc study was followed using semistructured interviews to explore Generation Zers’ eudaimonic environment pursuits and goal attainment. Our findings pave the way for a better understanding of behavioral engagement and pursuits of this rising cohort towards a greener tomorrow. It lays the groundwork to bring personal growth needs for environmental goal attainment to light. [ABSTRACT FROM AUTHOR]

[Display omitted] • Ag/SBA-15 modified with ZnO and CeO 2 exhibited a good activity with the 3-methylindole yield of 62%. • ZnO could increase the dispersion of silver and inhibit the sintering of Ag particles effectively. • CeO 2 could promote the reduction of Ag 2 O and suppress the formation of carbon deposition. • The yield of 3-methylindole sill reached 59% when Ag/SBA-15–ZnO–CeO 2 was circulated five times. • The reaction pathway was investigated in deeply and a probable route was proposed. An efficient mesoporous catalyst of Ag/SBA-15 modified with ZnO and CeO 2 was successfully constructed with the purpose of efficiently synthesizing 3-methylindole by biomass-derived glycerol and aniline, which up to 62% yield and 75% selectivity for 3-methylindole were achieved when Ag loading was 1.00 mmol/g−1, ZnO or CeO 2 content was 1.00 or 0.05 mmol/g−1, respectively. And only 3% yield decreased when the catalyst was circulated five times. The characterizations researches on N 2 physical adsorption, Fourier transform infrared (FT-IR), scanning electron microscopy and energy-dispersive X-ray spectroscopy (SEM-EDX), temperature programmed reduction of hydrogen (H 2 -TPR), X-ray diffraction (XRD), transmission electron microscopy (TEM), temperature programmed desorption (TPD) of NH 3 and CO 2 , thermogravimetric and differential thermal analysis (TG-DTA) indicated that adding the promoter of ZnO to Ag/SBA-15 increased the dispersion of the silver particles significantly and controlled the aggregation of Ag nanoparticles during the reaction remarkably because doping ZnO greatly increased the polarity of the composite carrier SBA–15–ZnO and brought about the interaction between Ag and carrier enhanced. CeO 2 could promote the reduction of Ag 2 O and suppress the formation of carbon deposition effectively. In addition, doping ZnO and CeO 2 increased the number of the weak-acid centers of the SBA-15 supported Ag-based catalyst observably, thereby the catalyst of Ag/SBA-15-ZnO-–ZnO–CeO 2 acquired a good selectivity. Moreover, the reaction pathway for 3-methylindole synthesis by biomass-derived glycerol and aniline was probed in depth and a reasonable route was proposed. [ABSTRACT FROM AUTHOR]

This paper presents the circuit design and magnetic integration of push–pull class-E inverters for wireless power transfer (WPT) up to megahertz. The design criterion for achieving zero-voltage switching (ZVS) of a class-E inverter with coupled windings is derived mathematically. The approaches of magnetic integration for push–pull class-E inverters are analyzed and compared. Then, a new magnetic structure with hybrid magnetic materials is proposed to build the integrated inductors with either coupled windings or uncoupled windings. A 3-MHz WPT system is built to verify the analysis. The detailed comparison of the class-E inverters with magnetic integration is presented in terms of switch voltage, efficiency, harmonic currents, and thermal distribution. In the optimized design example, the switches keep ZVS over the entire load range without using any closed-loop control. The system efficiency reaches 87.1% at 350-W output power. [ABSTRACT FROM AUTHOR]