MORE ON POLYNOMIAL BEZOUTIANS WITH RESPECT TO A GENERAL BASIS ∗

Abstract. We use unified algebraic methods to investigate the properties of polynomial Bezoutians with respect to a general basis. Not only can three known results be easily verified, but also some new properties of polynomial Bezoutians are obtained. Nonsymmetric Lyapunov-type equations of polynomial Bezoutians are also discussed. It turns out that most properties of classical Bezoutians can be analogously generalized to the case of polynomial Bezoutians in the framework of algebraic methods

An Improved Vibe Algorithm Based on Adaptive Thresholding and the Deep Learning-Driven Frame Difference Method

Foreground detection is the main way to identify regions of interest. The detection effectiveness determines the accuracy of subsequent behavior analysis. In order to enhance the detection effect and optimize the problems of low accuracy, this paper proposes an improved Vibe algorithm combining the frame difference method and adaptive thresholding. First, we adopt a shallow convolutional layer of VGG16 to extract the lower-level features of the image. Features images with high correlation are fused into a new image. Second, adaptive factors based on the spatio-temporal domain are introduced to divide the foreground and background. Finally, we construct an inter-frame average speed value to measure the moving speed of the foreground, which solves the mismatch problem between background change rate and model update rate. Experimental results show that our algorithm can effectively solve the drawback of the traditional method and prevent the background model from being contaminated. It suppresses the generation of ghosting, significantly improves detection accuracy, and reduces the false detection rate

Study on Strain Field Evolution of Uniaxial Compression Sandstone Based on Digital Image Correlation Technology

The stress–strain characteristics of compressed sandstone are affected by many different factors. The study on the evolution law of the strain field of compressed sandstone is of great significance for disaster prediction and warning during the construction process of geotechnical engineering. In this paper, uniaxial compression tests of red sandstone of 100 mm height and 50 mm length and width were carried out under the conditions of (1) different loading rates, (2) different particle sizes and (3) different inclination angles of prefabricated fractures. Stress–strain curves corresponding to different conditions were presented, the evolution of strain field on the sample surfaces was analyzed with the help of Digital Image Correlation technology and the relationship between the stress–strain curves and the strain field was preliminarily given. This study may be helpful for obtaining a deeper understanding of the deformation and failure mechanism of sandstone under uniaxial compression

Preparation of Iron Carbides Formed by Iron Oxalate Carburization for Fischer–Tropsch Synthesis

Different iron carbides were synthesized from the iron oxalate precursor by varying the CO carburization temperature between 320 and 450 °C. These iron carbides were applied to the high-temperature Fischer–Tropsch synthesis (FTS) without in situ activation treatment directly. The iron oxalate as a precursor was prepared using a solid-state reaction treatment at room temperature. Pure Fe5C2 was formed at a carburization temperature of 320 °C, whereas pure Fe3C was formed at 450 °C. Interestingly, at intermediate carburization temperatures (350–375 °C), these two phases coexisted at the same time although in different proportions, and 360 °C was the transition temperature at which the iron carbide phase transformed from the Fe5C2 phase to the Fe3C phase. The results showed that CO conversions and products selectivity were affected by both the iron carbide phases and the surface carbon layer. CO conversion was higher (75–96%) when Fe5C2 was the dominant iron carbide. The selectivity to C5+ products was higher when Fe3C was alone, while the light olefins selectivity was higher when the two components (Fe5C2 and Fe3C phases) co-existed, but the quantity of Fe3C was small

Ultra-Efficient Electrolytic Ocean Carbon Removal Through Capacitive Decarbon Reactors

Direct ocean capture (DOC) is a promising technique for mitigating residual anthropogenic CO2 levels. However, the existing DOC methods are energy-intensive and may have unforeseen effects on marine ecosystems due to the chemical processes involved. We introduce a capacitive decarbon (CDC) reactor that converts carbonate ions into CaCO3, a construction material, using only calcium ions (Ca2+) from seawater and renewable electricity. After optimizations of the electrode and electrolytic reactor, the CDC reactor achieves ocean carbon removal with an exceptionally low energy consumption of 16 kJ mol−1 CO2, which is one order of magnitude lower than previously reported values. This energy requirement increases to 107 kJ mol−1 CO2 when factoring in the seawater intake and pre-treatment. We then used a global integrated analysis model to evaluate the carbon mitigation potential of this approach and found that it can remove about 360 to 1,670 million tonnes of CO2 in 2050 and 2100, respectively, which corresponds to 4.55% and 14.82% of the global carbon sequestration capacity for those years. Given the high efficiency of the CDC reactor, we anticipate it may become a viable solution for sequestering oceanic carbon