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Additional file 1: Figure S1. H&E staining of ovaries in PND-25, 35 and 45. The solid circular substances indicate corpus luteum. ���*��� and ���**��� represent the p-value less than 0.05 and 0.01 adjusted by Student���s t-test. Figure S2. Quality control of spatial transcriptomics sequencing. Figure S3. Top 10 highly-expressed genes in 14 clusters shown by violin plots. Refer to Fig. 2 for the name of 14 clusters. Figure S4. Different cell types shown by feature plots across PND-25, 35 and 45. Figure S5. Expression of Kiss1, Tac3, Pdyn and Slc18a3 shown by feature plots across PND-25, 35 and 45. Figure S6. The top 10 highly-expressed gene of Cluster 9 shown by violin plots in all 14 clusters. Figure S7. The tSNE plot showing the cells are classified into 4 subclusters based on the transcriptomes of overall gene expression relationship among the 1,787 spots of VMH (left). Feature plots showing the distribution of clusters in PND-25, 35 and 45 (right). Different cell clusters are color-coded. Figure S8. The dynamics of spots based on the gene expression profiles along the pseudo-timeline shown by feature plots. Figure S9. The proportion of different cell types in ARC of PND-25, 35 and 45 shown by feature plots.

The interactions of multiple flames are often encountered in real-world fire and industrial burners. The distance between two jets has a strong influence on the instability mode, oscillation frequency, and mean height of flickering diffusion flames, which is experimentally studied and analyzed in this paper. Five different types of instability modes are identified as the separation distance between two nozzles is increased. When the nozzle separation distance is smaller, the flame mode is similar to that of a single-nozzle flame. In this case, the flame can switch between the merged sinuous mode and the merged varicose mode due to external disturbances on the flame. As the nozzle separation distance increases, the probability of mode switching from merged varicose to merged sinuous decreases. As the nozzle separation distance increases further, the flame mode translates into symmetric sinuous mode, alternated sinuous or independent mode. In addition, the flame height and oscillation frequency of a dual-nozzle flame have their own characteristics, which are different from that of the single-nozzle flame. The increase of the nozzle separation distance, leads to a decrease and then an increase of the flame mean height. It is interesting that the flame mean height of the alternated sinuous flame is the lowest, even lower than that of the single-nozzle flame. The oscillation frequency of the symmetrical sinuous flame is lower than that of the single-nozzle flame, and the frequency of alternated sinuous flame is higher than that of the single-nozzle flame.

Buoyancy causes a horizontal jet flame to bend upward when it loses sufficient initial momentum. Therefore, the variation in flame trajectory must be considered to accurately predict the thermal radiant flux of a horizontal jet flame governed by buoyancy and momentum. We introduce the flame trajectory equation into the linear source equation of radiation to establish a new model. The flame length ratio is calculated by flame trajectory length, horizontal projected flame length, and vertical projected flame height in the new model. This paper also presents a formula for flame lift-off distance and flame radiant fraction. We further list the geometric parameters of the horizontal-kite shape, tile-kite shape, and flame trajectory models. Comparing the experimental data and model predictions shows that the flame trajectory model is more accurate than the horizontal-kite and tile-kite models, especially when the Froude number is low. We also study the effects of flame lift-off distance and flame length ratio on predictive accuracy. The flame trajectory model computes quickly, and a normal laptop computer needs only 1.08 s to get a picture with 24,000 data points.

In this paper, we study almost regular Landsberg general $(��,��)$-metrics in Finsler geometry. The corresponding equivalent equations are given. By solving the equations, we give the classification of Landsberg general $(��,��)$-metrics under the conditon that $��$ is closed and conformal to $��$. Under this condition, we prove that regular Landsberg general $(��,��)$-metrics must be Berwaldian when the dimension is greater than two. For the almost regular case, the classification also is given and some new non-Berwaldian Landsberg metrics are found., Any comment is welcome to libenling@nbu.edu.cn

The snake-like robot is composed of nine joints and the robot is proposed in this study. The serpentine locomotion mechanism of snake-like robot is studied and its moving model is established in the multi body system dynamics simulation the Software Recurdyn. The joint angle functions of serpentine locomotion are set up. We add some restrictions for model in Recurdyn and set moving functions. The simulation introduced the input of the joint angle function's influence on the winding movement of the snake-like robot. The simulation results show that the snake-like robot can complete the serpentine locomotion set before.

Using the orthogonal experimental method, we can get the linear regression model of about parallel mechanism stiffness. Selecting four factors three levels of orthogonal experiment method, in ANSYS-workbench to space in third rotation 3-SPS/S parallel mechanism for static stiffness analysis, we have won nine of the data of the experiments, the application of the MATLAB software to experimental data is linear regression, which can get the static stiffness linear regression of parallel mechanism, under the influence of the stiffness, the regression function can be predicted in the different factors of parallel mechanism, we provide a new basis and reference for the following static stiffness analysis.

This paper presents a novel 2-RPU/SPR 2R1T parallel mechanism, which has one translational degree of freedom (DOF) and two rotational DOFs. The properties of the rotational axes of the mechanism are analyzed by using screw theory, and the results show that the 2-RPU/SPR mechanism has two rotational continuous axes. The position analysis of the 2-RPU/SPR mechanism is also carried out. The proposed 2R1T mechanism has very simple kinematic model, which reduces difficulties in calibrating kinematic parameters.