In this paper, we consider the nonlinear Klein-Gordon equation \begin{align*} \partial _{tt}u-\Delta u+u=|u|^{p-1}u,\qquad t\in \mathbb {R},\ x\in \mathbb {R}^d, \end{align*} with 1<p< 1+\frac ...{4}{d}. The equation has the standing wave solutions u_\omega =e^{i\omega t}\phi _{\omega } with the frequency \omega \in (-1,1), where \phi _{\omega } is the solution of \begin{align*} -\Delta \phi +(1-\omega ^2)\phi -\phi ^p=0. \end{align*} It was proved by Shatah Comm. Math. Phys. 91 (1983), pp. 313–327, and Shatah-Strauss Comm. Math. Phys. 100 (1985), pp. 173–190 that there exists a critical frequency \omega _c\in (0,1) such that the standing waves solution u_\omega is orbitally stable when \omega _c<|\omega |<1, and orbitally unstable when |\omega |<\omega _c. Furthermore, the strong instability for the critical frequency |\omega |=\omega _c in the high dimensions d\ge 2 was proved by Ohta-Todorova SIAM J. Math. Anal. 38 (2007), pp. 1912–1931. In this paper, we settle the only remaining problem when |\omega |=\omega _c, p> 1, and d=1, in which case we prove that the standing wave solution u_\omega is orbitally unstable.
This paper establishes the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state. ...In addition, explicit large-time decay rates for various Sobolev norms of the solutions are also obtained. These results are achieved through a new approach of diagonalizing a system of coupled linearized equations. The standard method of diagonalization via the eigenvalues and eigenvectors of the matrix symbol is very difficult to implement here. This new process allows us to obtain an integral representation of the full system through explicit kernels. In addition, in order to overcome various difficulties such as the anisotropicity and criticality, we fully exploit the structure of the integral representation and employ extremely delicate Fourier analysis and associated estimates.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Driving behavior in expressway tunnels is more complicated than in common roadbed sections because of differences in illuminance, visual range, speed perception, and reaction time. To explore the ...setting method of exit advance guide signs in expressway tunnels and improve the effectiveness of drivers' recognition of them, we propose 12 layout forms based on information quantification theory. In experiments, UC-win/Road was used to build a simulation scene, and the recognition reaction time of 12 element combinations of exit advance guide signs of different subjects was collected through an E-Prime simulation experiment. The loading effectiveness of the signs was analyzed based on the subjective workload and comprehensive evaluation scores of different subjects. The results are the following. The width of the exit advance guide sign layout in the tunnel is negatively correlated with the height of Chinese characters and the distance between the characters and the edge of the sign. The larger the height of Chinese characters and the distance between them and the edge of the sign, the smaller the maximum layout width of the sign. Considering the driver's reaction time, subjective workload, sign recognition, amount of sign information, sign accuracy, and sign safety of 12 different information combinations, we suggest that exit advance guide signs in tunnels should be laid out as Chinese/English place name + distance + guide arrow.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
In this paper, we show the orbital stability of solitons arising in the cubic derivative nonlinear Schrödinger equations. We consider the zero mass case that is not covered by earlier works. As this ...case enjoys
L
2
scaling invariance, we expect orbital stability (up to scaling symmetry) in addition to spatial and phase translations. We also show a self-similar type blow up criterion of solutions with the critical mass 4
π
.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
A dual‐motor servo mechanism is a high‐order and strong‐coupling system with unknown nonlinearity, which brings challenges to controller design to realize high‐performance tracking and ...synchronization. This article proposes a finite‐time command filtered control strategy to address this problem. In tracking control design, finite‐time command filters are adopted to obtain the derivatives of virtual controllers, and the “explosion of complexity” problem in backstepping is thus solved. An improved compensation system is designed to reduce filtering errors. The tracking control is developed based on the combination of finite‐time control and command filtered approach. Moreover, to deal with unknown nonlinearities and uncertainties, fast finite‐time extended state observers are developed to observe lumped disturbances for the load and motor, respectively. In synchronization control design, two opposite control actions are developed using the speed difference to force two motors to rotate synchronously. The finite‐time convergence of the tracking and synchronization errors is proved. The efficiency of the proposed control strategy is verified via experiments conducted on a dual‐motor servo turntable.
This paper proposes a finite‐time command filtered control strategy to address both the tracking control and the synchronization control problems. The lumped disturbances are observed by extended state observers, and the finite‐time control approach achieves fast response and high precision.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
Distance learning programs in sustainability science provide a structured curriculum that covers various aspects of sustainability. Despite the growing recognition of distance learning in higher ...education, existing literature has primarily focused on specific and detailed factors, without a comprehensive summary of the global themes, especially neglecting in-depth exploration of poor engagement factors. This study bridged this gap by not only examining detailed factors but also synthesizing the overarching themes that influenced student engagement. The aim of this study was to investigate the factors that impact student engagement in distance learning within higher education institutions across different countries. By developing a theoretical framework, three key aspects of student engagement in higher education were identified. A total of 42 students and 2 educators affiliated with universities participated in semi-structured interviews. The findings of this paper indicated that sociocultural, infrastructure, and digital equity factors were the main influencing factors of student engagement. Furthermore, a student engagement assessment system was developed using machine learning algorithms to identify students with low levels of engagement and conduct further analysis that considers the three aforementioned factors. The proposed automated approach holds the potential to enhance and revolutionize digital learning methodologies.
This study aims to use design research methods to empower future female retirees in Northeastern China to refocus their lives as they approach retirement. This social group has sacrificed much of ...their time and energy to focus on the family and making a living. In other words, they have been thinking for others. They are about to retire, which means they will have abundant time to focus on self-interests, but many are uncertain of how to devote the next phase of their lives.The approach used is the co-design workshop and a newly designed toolkit to guide participants in redesigning an ideal urban park. Participants were asked what they wanted and why. One interview, one pre-test survey, and one post-test survey were also used in this study.Four workshops were conducted, two with two participants and one designer and two with one participant and one designer. The newly designed toolkit performed well, and all the participants successfully completed the park design without paper instructions; the workshop was i
This paper focuses on the global prespecifiable fixed‐time control problem of uncertain strict‐feedback nonlinear system with input quantization. In contrast to the existing fixed‐time control ...results, the signs of the control gains can be unknown in our paper. Unlike the traditional fixed‐time control schemes, some exponential functions are added into the virtual controllers to accelerate the convergence rate. Besides, some dynamic switching functions are also introduced to compensate the unknown control signs. Based on the novel regulate law, the switching functions can be regulated online to ensure the fixed‐time stability for the considered system. Furthermore, the settling time can be easily adjusted by selecting the controller parameters. Simulation results are provided to illustrate the effectiveness of the proposed control scheme.
This paper firstly addresses the prespeciable fixed‐time control problem of uncertain strict‐feedback nonlinear system with input quantization and unknown control directions. Instead of the Nussbaum function method, some switching functions are utilized to handle the unknown control signs. Besides, some exponential functions are added into the virtual controllers to accelerate the convergence speed.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
Writing artificial logic and dynamic function into complex cellular background to achieve desired phenotypes or improved outputs calls for the development of new genetic tools as well as their ...innovative use. In this study, we present a sensor-regulator and RNAi-based bifunctional dynamic control network that can provide simultaneous upregulation and downregulation of cellular metabolism for engineered biosynthesis. The promoter-regulator-mediated upregulation function and its transduced downregulation function through RNAi are systematically verified and characterized. We apply this dynamic control network to regulate the phosphoenolpyruvate metabolic node in Escherichia coli and achieve autonomous distribution of carbon flux between its native metabolism and the engineered muconic acid biosynthetic pathway. This allows muconic acid biosynthesis to reach 1.8 g L
. This study also suggests the circumstances where dynamic control approaches are likely to take effects.
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