The article's purpose is twofold. First, we wish to draw attention to the insufficiently known field of continuous-time difference equations. These equations are paradigmatic for modeling complexity and chaos. Even the simplest equation , easily leads to complex dynamics, its solutions are perfectly suited to simulate strong nonlinear phenomena such as large-to-small cascades of structures, intermixing, formation of fractals, etc. Second, in the main body of the article we present a small but very important part of the theory behind the above equation marked by . Just as the discrete-time analog of this equation induces the one-dimensional dynamical system on some interval , so the equation induces the infinite-dimensional dynamical system on the space of functions . In the latter case, not only are the long-term behaviours of solutions critically dependent on the limit behaviour of the sequence (as in the discrete case) but also on the internal structure of as . Assuming to be continuous, we consider the iterations of as the semigroup generated by on the space of continuous maps, and introduce the notion of a limit semigroup for in a wider map space in order to investigate asymptotic properties of . We construct a limit semigroup in the space of upper semicontinuous maps. This enables us to describe both of the aforementioned aspects of our interest around the iterations of.

In this paper, we will examine a rather complex case of the paradoxical nature of certain conclusions that may arise when studying the numerical convergence of a specific nonlinear recursive sequence, known in the literature as Muller’s sequence. To analyze the peculiar computational behavior of this sequence, it is necessary to employ a powerful mathematical framework in order to understand the nontrivial issues that can arise when the software implementation of this seemingly simple mathematical problem. These challenges often stem from the limitations of numerical methods and the inherent errors in computer arithmetic, which can affect the accuracy and stability of the results, particularly when dealing with iterative methods like Muller's sequence.

First, based on the many levels and their cycles in geoscience, we research the hypercycle of geoscience. This is the hypercycle as a tool of self-organization applied to geoscience. It may form from a level to other higher levels. These levels influence each other and the co-evolution. Second, we discuss some possible mathematical methods, which include graph, vector, matrix, some equations, similar theories, etc. This method can be developed and perfected. Third, we propose the nonlinear whole geoscience and its three basic laws. Fourth, we discuss thermodynamics of geoscience, and in which possible entropy decrease under some sates, such as evolution and cycles of Earth, etc. Sustainable development of society must study the mode from high entropy to low entropy. Various cycles in geoscience cannot all be entropy increases, and cannot all be originated from the external interactions.

The automated parking system is an extensive branch of smart transport systems. The smartness of such systems is determined by different parameters such as parking maneuver planning. Coding this control system includes vehicle parking and understanding the environment. A high-quality classification mask has been used on each sample to analyze the automated vehicle parking parameters. Mask region-based convolutional neural networks (R-CNN) was taught using a small computational workload titled faster R-CNN that operates in five frames per second. In this paper, the rapidly-exploring random tree (RRT) method was used for routing the parking space and a nonlinear model predictive control (NMPC) controller was added to develop this system. We add the line detection algorithm commands to the mask R-CNN algorithm. The results can be useful to design a secure automatic parking system as well as a powerful perception system.

First, we propose the nonlinear whole seismology and its three basic laws. Next, based on the nonlinear equations of fluid dynamics in Earth’s crust, we obtain a chaos equation, in which chaos corresponds to the earthquake, and shows complexity on seismology. But, combining the Carlson-Langer model and the Gutenberg-Richter relation, a simplified nonlinear solution and corresponding magnitude-period formula of earthquakes may be derived approximately. Further, we research the topological seismology. From these theories some predictions can be calculated quantitatively and are already tested. Combining the Lorenz nonlinear model, we may discuss the earthquake migration to and fro. Finally, if various modern scientific instruments, different scientific theories and some paranormal ways for earthquake are combined each other, the accuracy of multilevel prediction will be increased.