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In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for

Purpose. Development of a method for constructing the structure of the combined management with compensation of parametric and coordinate perturbations on the basis of two discrete time equalizers and experimental evaluation of the effectiveness of additional compensating equalizer. Methodology. The theory of transition functions of finite duration is used to set the desired dynamic properties of automatic control systems in discrete time intervals. The modified structural schemes symmetry principle provides the formation of desired dynamic characteristics of closed-loop system with limited gain factor. Findings. A method of designing a combined control structure with compensation of parametric and coordinate perturbations based on two discrete time equalizers is developed and experimentally tested. The method is one of the components of the methodology of the synthesis of automatic control systems, and provides the setting of the desired dynamic properties for the output coordinate in the graphical form or in the form of points set of the desired transient function. Originality. The technique of designing the structure of the combined control system based on two discrete time equalizers (basic and compensating) was developed for the first time. The technique differs from the known (with only one discrete time equalizer) by the introduction of a parallel correction branch with a discrete time equalizer, configured to fully compensate for the dynamic properties of the control object. This makes it possible to reduce the sensitivity of the system to coordinate and parametric perturbations. Practical value. The research results can be used for designing control algorithms for technical objects with their subsequent implementation program in the microcontroller or microprocessor control system.

Development of a synthesis method for automatic control systems with the desired dynamic properties that are specified by quantized transition functions of finite duration. The theory of transition functions of finite duration is used to set the desired dynamic properties of automatic control systems in discrete time intervals. The modified structural block-diagram symmetry principle provides the formation of accessible desired dynamic characteristics of a closed-loop system with a limited gain factor. The method for automatic control system synthesis on the base of discrete time equalizer was developed on condition of full compensation of dynamic properties of the control object and with their partial compensation due to use of modification blocks of reverse structural block-diagram transformation. The first proposed mathematical apparatus allows the use of discrete time equalizer as a discrete regulator in automatic control systems. The research on automatic control system synthesis on the base of discrete time equalizer revealed that modified principle of structural block-diagram symmetry should be used for providing the real dynamics of automatic control systems. The results of the research can be used for building the control algorithms for technical objects with their further program implementation in the microcontroller or microprocessor control system.

Any engineering system involves transitions that reduce the performance of the system and lower its comfort. In the field of automotive engineering, the combination of multiple motors and multiple power sources is a trend that is being used to enhance hybrid electric vehicle (HEV) propulsion and autonomy. However, HEV riding comfort is significantly reduced because of high peaks that occur during the transition from a single power source to a multisource powering mode or from a single motor to a multiple motor traction mode. In this study, a novel model-based soft transition algorithm (STA) is used for the suppression of large transient ripples that occur during HEV drivetrain commutations and power source switches. In contrast to classical abrupt switching, the STA detects transitions, measures their rates, generates corresponding transition periods, and uses adequate transition functions to join the actual and the targeted operating points of a given HEV system variable. As a case study, the STA was applied to minimize the transition ripples that occur in a fuel cell-supercapacitor HEV. The transitions that occurred within the HEV were handled using two proposed transition functions which were: a linear-based transition function and a stair-based transition function. The simulation results show that, in addition to its ability to improve driving comfort by minimizing transient torque ripples and DC bus voltage fluctuations, the STA helps to increase the lifetime of the motor and power sources by reducing the currents drawn during the transitions. It is worth noting that the considered HEV runs on four-wheel drive when the load torque applied on it exceeds a specified torque threshold; otherwise, it operates in rear-wheel drive.

This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes. This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.

As is well-known, transition probabilities of jump Markov processes satisfy Kolmogorov’s backward and forward equations. In the seminal 1940 paper, William Feller investigated solutions of Kolmogorov’s equations for jump Markov processes. Recently the authors solved the problem studied by Feller and showed that the minimal solution of Kolmogorov’s backward and forward equations is the transition probability of the corresponding jump Markov process if the transition rate at each state is bounded. This paper presents more general results. For Kolmogorov’s backward equation, the sufficient condition for the described property of the minimal solution is that the transition rate at each state is locally integrable, and for Kolmogorov’s forward equation the corresponding sufficient condition is that the transition rate at each state is locally bounded.

Land use function transition can change the eco-environment. To achieve an “Intensive and efficient production space, moderately livable living space, and beautiful ecological space”, the ecological effects of land use function transition in the context of ecologically fragile areas and rapidly developing areas of socio-economic importance need to be studied. In this study, from the perspective of “production-living-ecological” spaces, we calculated the index of regional eco-environment quality, positive and negative effects of eco-environment impact, and the ecological contribution rate and analyzed the driving factors. We found the following: (1) The production space was greatly compressed, living space was expanded, and ecological space was significantly squeezed. Haikou underwent a rapid transformation from an agriculture-dependent city to an industrial city. Land supply for urban and rural living was guaranteed by the Chinese land management department. However, Haikou prioritized economic development over environmental protection. (2) The regional eco-environment quality index decreased from 2009 to 2018. The expansion of pasture-based ecological spaces is important for improving the quality of the eco-environment, and the reduction of forest ecological space strongly influences the deterioration of the eco-environment. (3) Resource base, historical level of utilization, suitability of land, the ecological value potentiality, and regional policies greatly affected land use function transition and its eco-environment. (4) Refining the planning of territorial space, comprehensively improving land and resources, and reforming the rural land system greatly influenced policy guidance and technical regulation for coordinating “production-living-ecological” spaces and improving the regional eco-environment. In this study, we tested the effect of regional policy regulation on land use function transition and provided a reference for coordinating “production-living-ecological” spaces.

The main problem of RADG (Reaction Automata Directed Graph) is the fixed design of the graph. The purpose of this paper is to develop the transition function from fixed design to dynamic design, the dynamic design based on a key between sender and receiver in addition to some rules, the new design is more efficient and fairly distributed between standard states and reaction states, that design keeps the main aspect of RADG which gives more than one ciphertext to the same plaintext and adds high level of security to the wireless network.

We study planar piecewise smooth differential systems of the form z ˙ = Z ( z ) = 1 + sgn ( F ) 2 X ( z ) + 1 - sgn ( F ) 2 Y ( z ) , where F : R 2 → R is a smooth map having 0 as a regular value. We consider linear regularizations Z ε φ of Z by replacing sgn ( F ) by φ ( F / ε ) in the last equation, with ε > 0 small and φ being a transition function (not necessarily monotonic). Nonlinear regularizations of the vector field Z whose transition function is monotonic are considered too. It is a well-known fact that the regularized system is a slow-fast system. In this paper, we study typical singularities of slow-fast systems that arise from (linear or nonlinear) regularizations, namely, fold, transcritical and pitchfork singularities. Furthermore, the dependence of the slow-fast system on the graphical properties of the transition function is investigated.

The objective of this study was to enhance the tracking effectiveness of the position adjustment for the electronic throttle in electric vehicles, as well as boost fuel efficiency and the dynamic performance of the vehicles. Firstly, a mathematical model, which pertains to the electronic throttle system, is established, and subsequently, the nonlinear uncertain system is made into a linear uncertain system. Subsequently, a self-coupling PID control law is designed, and an analysis is conducted on the system’s stability and its capacity to reject disturbances. Secondly, taking into consideration that the parameters of the PID controller with self-coupling mechanism are related to the system’s response speed, disturbance rejection capability, and overshoot, a self-adjusting speed factor transition function is put forward to address the conflict between speed and overshoot. Finally, numerical simulations and experimental tests are carried out. The results verify that, compared with the conventional PID controller, ADRC (Active Disturbance Rejection Control), and fuzzy PID, the proposed controller has a faster response speed, higher control accuracy, and better robustness.