We propose a conic transformation method to solve the Perspective-Three-Point (P3P) problem. In contrast to the current state-of-the-art solvers, which formulate the P3P problem by intersecting two conics and constructing a de-generate conic to find the intersection, our approach builds upon a new formulation based on a transformation that maps the two conics to a new coordinate system, where one of the conics becomes a standard parabola in a canonical form. This enables expressing one variable in terms of the other variable, and as a consequence, substantially simpli-fies the problem of finding the conic intersection. Moreover, the polynomial coefficients are fast to compute, and we only need to determine the real-valued intersection points, which avoids the requirement of using computationally expensive complex arithmetic. While the current state-of-the-art methods reduce the conic intersection problem to solving a univariate cubic equation, our approach, despite resulting in a quartic equation, is still faster thanks to this new simplified formulation. Extensive evaluations demonstrate that our method achieves higher speed while maintaining robustness and stability comparable to state-of-the-art methods.

The tire-road friction coefficient (TRFC) plays a crucial role as a control signal in governing vehicle motion, particularly in electric vehicles equipped with low roll resistance tires. Research on TRFC estimation, considering slip angle, has gained significant popularity. However, the influence of camber angle is rarely taken into account. In this paper, the influence of camber on TRFC of sideslip situation is studied. Employing both finite element analysis and theoretical analysis methods, we propose an estimator for the TRFC in combined situation of sideslip and camber. The foundational elements include pure sideslip, pure camber, and tire lateral translational stiffness. The developed estimator is validated by comparing it with the test results. The results of the validation indicate that the suggested estimator can accurately obtain the TRFC in combined situation involving sideslip and camber.

Evaluating typical rural characteristics reveals certain advantages of rural revitalization and is crucial for understanding rural disparities and promoting development. Field research and statistical data can reflect the spatial distribution of local resources and development models. However, due to cost limitations and statistical constraints, it is impossible to effectively compare and evaluate the characteristics of rural development at the long time series, large scale and fine granularity required for sustainable regeneration. This study proposes a web-based method for the extraction and evaluation of rural revitalization characteristics (WERRC). The BERT-BiLSTM-Attention model categorizes rural web texts according to five themes: industrial prosperity, ecological livability, rural civilization, effective governance, and prosperous life. The Term Frequency-Inverse Document Frequency (TF-IDF) algorithm extracts rural characteristics, and the relative advantages of these features are compared among 100 Chinese villages. WERRC extracts the typical characteristics, obtains the spatial distribution and relative advantage, and then ranks them according to the five themes. The relationship between national policy guidance and rural development is explored. The results support further exploration of differentiated, high-quality development modes that incorporate rural advantages into policy, adjust industrial structure, and optimise revitalization strategies at the rural scale.

Abstract. In 1966, Gallai asked whether there is a vertex which passes through all longest paths of a connected graph. Although this has been verified for some special classes of graphs such as outerplanar graphs, circular arc graphs, and series-parallel graphs, the answer is negative for general graphs. In this paper, we prove among other results that if we replace the vertex by a bond, then the answer is affirmative. A bond of a graph is a minimal nonempty edge-cut. In particular, in any 2-connected graph, the set of all edges incident to a vertex is a bond, called a vertex-bond. Clearly, for a 2-connected graph, a path passes through a vertex [Formula: see text] if and only if it meets the vertex-bond with respect to [Formula: see text]. Therefore, a very natural approach to Gallai’s question is to study whether there is a bond meeting all longest paths. Let [Formula: see text] denote the length of a longest path of connected graphs. We show that there is a bond meeting all paths of length at least [Formula: see text] and [Formula: see text] for any 2- and 3-connected graph, respectively. For any [Formula: see text]-connected graph [Formula: see text], we show that there is a bond meeting all paths of length at least [Formula: see text], where [Formula: see text] if [Formula: see text] is even and [Formula: see text] if [Formula: see text] is odd. Our results also provide analogs of the results on bonds meeting long cycles given in [P.-L. Wu, Combin. Probab. Comput., 6 (1997), pp. 107–113; and S. McGuinness, Combinatorica, 25 (2005), pp. 439–450].

Adaptive antenna arrays have been widely studied to reduce multiuser interference by spatial suppression. The lattice algorithm, based on least square estimation, is investigated to realize adaptive antenna beamforming. Both analytical and simulation results show that this algorithm not only has fast convergence, but also good multiuser interference suppression performance. Furthermore, the antenna weights iteration processes are discussed in different multiuser interference conditions.