Linear arboricity of degenerate graphs

A linear forest is a union of vertex-disjoint paths, and the linear arboricity of a graph $G$, denoted by $\operatorname{la}(G)$, is the minimum number of linear forests needed to partition the edge set of $G$. Clearly, $\operatorname{la}(G) \ge \lceil\Delta(G)/2\rceil$ for a graph $G$ with maximum degree $\Delta(G)$. On the other hand, the Linear Arboricity Conjecture due to Akiyama, Exoo, and Harary from 1981 asserts that $\operatorname{la}(G) \leq \lceil(\Delta(G)+1) / 2\rceil$ for every graph $G$. This conjecture has been verified for planar graphs and graphs whose maximum degree is at most $6$, or is equal to $8$ or $10$. Given a positive integer $k$, a graph $G$ is $k$-degenerate if it can be reduced to a trivial graph by successive removal of vertices with degree at most $k$. We prove that for any $k$-degenerate graph $G$, $\operatorname{la}(G) = \lceil\Delta(G)/2 \rceil$ provided $\Delta(G) \ge 2k^2 -k$.Comment: 15 pages, 1 figur

A Study on the Optimal Grasping Angle Algorithm for Plug Seedlings Based on Machine Vision

During the replanting operation of a seedling tray, the end-effector needs to repeatedly grab the qualified plug seedlings in the supply tray and release them to the target tray for replanting, and in the process of grasping, the end-effector may cause some mechanical damage to the plug seedlings, thus affecting their quality. Therefore, in order to be able to adjust the position of the hand claw grasping point according to the morphological characteristics of the plug seedlings and select the optimal grasping point, this paper proposes research on the optimal grasping angle algorithm for plug seedlings based on machine vision. Firstly, a rotatable three-jaw end-effector is designed, which uses a three-jaw structure for grasping the burrowing seedlings. The three claws are driven with a telescopic cylinder to carry out clamping and relaxing actions. The rotation of the three claws is controlled with the stepper motor to adjust the optimal grasping position. Secondly, based on the pre-processing of an image of the hole tray seedling, the extraction of feature points in the region of interest, and the calculation of localization, the angle between the angular bisector of the cotyledon leaf blade of the hole tray seedling and the horizontal positive direction is solved. In this paper, two methods are designed to calculate the coordinates of feature points: one is the geometric method and the other is the center-of-mass method. Finally, the optimal grasping angle is calculated by analyzing the angle between the angular bisector of the cotyledon leaf blade and the horizontal positive direction of the cavity seedlings. According to the test, the average calculation error of the proposed algorithm is 3.12 degrees, and the average calculation time is 0.512 sec/sheet, which meet the requirements of the replanting operation

In–situ modification of UiO–66(Zr) organic ligand to synthesize highly recyclable solid acid for biodiesel production

To transfer high free fatty acid oil into biodiesel in mild conditions is still facing challenge, thereinto, the key is efficient acid catalyst. In this study, 2,5–dimercaptoterephthalic acid was adopted to substitute terephthalic acid as ligand for UiO–66–(SH)2 synthesis, then the sulfydryl (–SH) was in-situ oxidized by hydrogen peroxide and acidified via sulfuric acid thus generating sulfonic catalyst UiO–66–(SO3H)2. To further reveal the relationship between physico–chemical property and catalytic activity, catalyst was characterized via thermogravimetry analysis (TG), X–ray diffraction (XRD), N2 absorption–desorption, scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), and pyridine absorption–Fourier transform infrared spectroscopy (Py–FTIR). Results indicate the in–situ modification increases the quantity of acid sites for UiO–66(Zr), where the acidity is aggrandized from 0.02 mmol/g to 2.28 mmol/g. The maximum conversion of oleic acid to biodiesel was 86.52 % with catalyst amount of 10 wt% and molar ratio of methanol/oleic acid of 15 at 90 °C within 4 h. Moreover, UiO–66–(SO3H)2 exhibited favorable reusability and water resistance, which maintained an excellent esterification conversion after four cycles and no obvious impact was detected as the water content was 10 wt%. The quality of obtained biodiesel in this study satisfied the European Union standard of EN 14214, which could be used as transport fuel

Infrared and Visible Image Fusion Based on Co-Occurrence Analysis Shearlet Transform

This study based on co-occurrence analysis shearlet transform (CAST) effectively combines the latent low rank representation (LatLRR) and the regularization of zero-crossing counting in differences to fuse the heterogeneous images. First, the source images are decomposed by CAST method into base-layer and detail-layer sub-images. Secondly, for the base-layer components with larger-scale intensity variation, the LatLRR, is a valid method to extract the salient information from image sources, and can be applied to generate saliency map to implement the weighted fusion of base-layer images adaptively. Meanwhile, the regularization term of zero crossings in differences, which is a classic method of optimization, is designed as the regularization term to construct the fusion of detail-layer images. By this method, the gradient information concealed in the source images can be extracted as much as possible, then the fusion image owns more abundant edge information. Compared with other state-of-the-art algorithms on publicly available datasets, the quantitative and qualitative analysis of experimental results demonstrate that the proposed method outperformed in enhancing the contrast and achieving close fusion result

Infrared and Visible Image Fusion Based on Co-Occurrence Analysis Shearlet Transform

This study based on co-occurrence analysis shearlet transform (CAST) effectively combines the latent low rank representation (LatLRR) and the regularization of zero-crossing counting in differences to fuse the heterogeneous images. First, the source images are decomposed by CAST method into base-layer and detail-layer sub-images. Secondly, for the base-layer components with larger-scale intensity variation, the LatLRR, is a valid method to extract the salient information from image sources, and can be applied to generate saliency map to implement the weighted fusion of base-layer images adaptively. Meanwhile, the regularization term of zero crossings in differences, which is a classic method of optimization, is designed as the regularization term to construct the fusion of detail-layer images. By this method, the gradient information concealed in the source images can be extracted as much as possible, then the fusion image owns more abundant edge information. Compared with other state-of-the-art algorithms on publicly available datasets, the quantitative and qualitative analysis of experimental results demonstrate that the proposed method outperformed in enhancing the contrast and achieving close fusion result

Surface chemistry regulation on particle-support interaction of ruthenium and Cr-Fe oxides for selective oxidation of 5-hydroxymethylfurfural

The selective oxidation of 5-hydroxymethylfurfural (HMF) into 2,5-furandicarboxylic acid (FDCA) is an essential reaction to produce a wide variety of fine chemicals and polymers. To promote the selectivity and the product yield, cost-effective catalysts are highly required. Particularly, support-type catalysts, which are generally composed of a specific noble metal particle loaded onto a suitable support, are well recognized as promising candidates. Herein, ruthenium nanoparticles loaded on the Cr-Fe-O support (Ru/Cr-Fe-O) are synthesized and used for the selective oxidation of HMF to produce FDCA. Contributed by the particle-support interaction, the resultant Ru/Cr-Fe-O catalysts deliver good low-temperature reducibility and hold abundant weak acid sites. Under the optimal reaction conditions, in which the reaction time was 16 h at an oxygen pressure of 1 MPa and a reaction temperature of 100 °C in a weak base system, a HMF conversion ratio of 100 % and a FDCA yield of 99.9 % are achieved. Further characterizations reveal that the activities are largely associated with the surface chemistry states of the Ru/Cr-Fe-O catalyst. This work offers some insights into the rational selection of support-type catalysts for selective oxidization reactions.</p