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In this paper, we disprove a remaining conjecture about Bohemian matrices, in which the numbers of distinct determinants of a normalized Bohemian upper-Hessenberg matrix were conjectured.

Freeze-thaw resistance ability of concrete is an important issue when evaluating its durability. In this research, the objective was to predict concrete resistance to such cycles by analyzing water absorption based on the critical water saturation theory. In order to achieve this goal, detailed experiments were conducted, including water absorption, pore structure scanning, and mercury intrusion porosimetry of concrete with air-entraining admixture and different fiber content to obtain critical indicators, such as water absorption, porosity, and air void spacing factor, which formed the basis for predicting the service life of concrete. To predict the service life of concrete under freeze-thaw cycles, the critical saturation theory was utilized, taking into account environmental parameters and experimental indexes. The service life of concrete against freeze-thaw using air-entraining admixture and fibers had been calculated quantitatively in this paper. The results show that the predicted service life of concrete with air-entraining admixture was increased by more than 50 times, and using both air-entraining admixture and fiber could increase the service life by more than 80 times, even reaching 249 years. [ABSTRACT FROM AUTHOR]

Connected Autonomous Vehicles (CAVs) have the potential to revolutionize traffic systems by autonomously handling complex maneuvers such as freeway ramp merging. However, the unpredictability of manual-driven vehicles (MDVs) poses a significant challenge. This study introduces a novel decision-making approach that incorporates the uncertainty of MDVs' driving styles, aiming to enhance merging efficiency and safety. By framing the CAV-MDV interaction as an incomplete information static game, we categorize MDVs' behaviors using a Gaussian Mixture Model–Support Vector Machine (GMM-SVM) method. The identified driving styles are then integrated into the flexible merging decision process, leveraging the concept of pure-strategy Nash equilibrium to determine optimal merging points and timing. A deep reinforcement learning algorithm is employed to refine CAVs' control decisions, ensuring efficient right-of-way acquisition. Simulations at both micro and macro levels validate the method's effectiveness, demonstrating improved merging success rates and overall traffic efficiency without compromising safety. The research contributes to the field by offering a sophisticated merging strategy that respects real-world driving behavior complexity, with potential for practical applications in urban traffic scenarios. [ABSTRACT FROM AUTHOR]

Let A be a real symmetric matrix. If after we delete a row and a column of the same index, the nullity increases by one, we call that index a P-vertex of A. When A is an n × n singular acyclic matrix, it is known that the maximum number of P-vertices is n − 2. If T is the underlying tree of A, we will show that for any integer number k ∈ {0, 1, . . . , n − 2}, there is a (singular) matrix whose graph is T and with k P-vertices. We will provide illustrative examples.

In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.

According to the “theoretical admittance " and the "observation admittance" of the actual data, the theoretical value of effective elastic thickness in the study area was 10km. Combining the gravity anomalies and vertical gravity gradient anomalies, the admittance function is used to construct the 1'×1' bathymetry model over the Philippine Sea by using the adaptive weighting technique. It is found that the accuracy of the bathymetry model constructed is the highest when the ratio of inversion result of vertical gravity gradient anomalies and inversion result of gravity anomalies is 2∶3. At the same time, using multi-source gravity data to predict bathymetry could synthesize the superiority of gravity anomalies and vertical gravity gradient anomalies on the different seafloor topography, and the accuracy is better than bathymetry model that only used gravity anomalies or vertical gravity gradient anomalies. Taking the ship test data as the checking condition, the accuracy of predicting model is slightly lower than that of V18.1 model and improved by 27.17% and 39.02% respectively compared with the ETOPO1 model and the DTU10 model. Check points which the absolute value of the relative error of the predicting model is in the range of 5% accounted for 94.25% of the total.

As an indispensable part of the power transmission system, insulators are of great importance to the safe and stable operation of power grids in terms of their healthy and reliable operation. To realize real-time monitoring of insulator defects under a complex environment, this paper proposes an insulator defect detection method based on the You Only Look Once version 7-tiny (YOLOv7- tiny) algorithm. Then an edge device-unmanned aerial vehicle (UAV) inspection system is developed to verify the real-time performance of the algorithm. By introducing the structure intersection over union (SIoU) loss function to the YOLOv7-tiny model, the regression speed of the anchor frame can be effectively accelerated on the basis of the miniature model, to accelerate the model operation. Thereafter, a smooth sigmoid linear unit (SiLU) activation function is used in the network neck to improve the nonlinear representation ability; After that, an edge computing device based on NVIDIA Jetson Xavier NX is established to verify the real-time performance of the method. Experimental results reveal mean average precision (mAP) of insulators and their missing series defects is as high as 98.31%. Besides, the detection speed of the designed model deployed to mobile edge devices can reach 35 frames per second (FPS), with real-time and accurate detection performance of insulators and their missing series defects. [ABSTRACT FROM AUTHOR]