Spatial Heterogeneity of Agricultural Science and Technology Parks Technology Diffusion: A Case Study of Yangling ASTP

Agricultural science and technology parks(ASTPs) represent an important growth pole in China’s agricultural modernization.Clarifying their diffusion laws can optimize the technological diffusion process and improve its efficiency. Our study uses disaggregated spatial information in its model to analyze ASTP technology diffusion in a heterogeneous space. We constructed a comprehensive index system to evaluate the diffusion environmental quality and introduced the heterogeneous diffusion equation to calculate the technological diffusion probability. We applied this framework to a real-world scenario: the apple planting technology diffusion of the Yangling ASTP in the Loess Plateau, China. The results indicated: (1)the technological diffusion environment of the Loess Plateau advantageous apple producing area showed strong spatial heterogeneity caused by climate, topography, and external transportation links.(2) Under the combined effects of distance and spatial heterogeneity, the spatial diffusion pattern of the Yangling ASTP apple technology was expansion diffusion supplemented by hierarchical diffusion and banded diffusion, and (3) ASTP technology diffusion showed a strong distance attenuation effect, and the frictional effect of distance can be decreased by improving the diffusion environmental quality. These laws can promote regional balanced ASTP-driven development.

An analytical solution of multi-dimensional space fractional diffusion equations with variable coefficients

In this paper,we have considered the multi-dimensional space fractional diffusion equations with variable coefficients.The fractional operators(derivative/integral)are used based on the Caputo definition.This study provides an analytical approach to determine the analytical solution of the considered problems with the help of the two-step Adomian decomposition method(TSADM).Moreover,new results have been obtained for the existence and uniqueness of a solution by using the Banach contraction principle and a fixed point theorem.We have extended the dimension of the space fractional diffusion equations with variable coefficients into multi-dimensions.Finally,the generalized problems with two different types of the forcing term have been included demonstrating the applicability and high efficiency of the TSADM in comparison to other existing numerical methods.The diffusion coefficients do not require to satisfy any certain conditions/restrictions for using the TSADM.There are no restrictions imposed on the problems for diffusion coefficients,and a similar procedures of the TSADM has followed to the obtained analytical solution for the multi-dimensional space fractional diffusion equations with variable coefficients.

Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

In this paper,we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations(RSFDEs)with time delay,which constitute an important class of differential equations of practical significance.We develop a novel implicit alternating direction method that can effectively and efficiently tackle the RSFDEs in both two and three dimensions.The numerical method is proved to be uniquely solvable,stable and convergent with second order accuracy in both space and time.Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.

Glymphatic function and its influencing factors in different glucose metabolism states

BACKGROUND Dysfunction of the glymphatic system in the brain in different stages of altered glucose metabolism and its influencing factors are not well characterized.AIM To investigate the function of the glymphatic system and its clinical correlates in patients with different glucose metabolism states,the present study employed diffusion tensor imaging along the perivascular space(DTI-ALPS)index.METHODS Sample size was calculated using the pwr package in R software.This crosssectional study enrolled 22 patients with normal glucose metabolism(NGM),20 patients with prediabetes,and 22 patients with type 2 diabetes mellitus(T2DM).A 3.0T magnetic resonance imaging was used to evaluate the function of the glymphatic system.The mini-mental state examination(MMSE)was used to assess general cognitive function.The DTI-ALPS index of bilateral basal ganglia and the mean DTI-ALPS index was calculated.Further,the correlation between DTI-ALPS and clinical features was assessed.RESULTS The left-side,right-side,and mean DTI-ALPS index in the T2DM group were significantly lower than that in the NGM group.The right-side DTI-ALPS and mean DTI-ALPS index in the T2DM group were significantly lower than those in the prediabetes group.DTI-ALPS index lateralization was not observed.The MMSE score in the T2DM group was significantly lower than that in the NGM and prediabetes group.After controlling for sex,the left-side DTI-ALPS and mean DTI-ALPS index in the prediabetes group were positively correlated with 2-hour postprandial blood glucose level;the left-side DTI-ALPS index was negatively correlated with total cholesterol and low-density lipoprotein level.The right-side DTI-ALPS and mean DTI-ALPS index were negatively correlated with the glycosylated hemoglobin level and waist-to-hip ratio in the prediabetes group.The left-side,right-side,and mean DTI-ALPS index in the T2DM group were positively correlated with height.The left-side and mean DTIALPS index in the T2DM group were negatively correlated with high-density lipoprotein levels.CONCLUSION Cerebral glymphatic system dysfunction may mainly occur in the T2DM stage.Various clinical variables were found to affect the DTI-ALPS index in different glucose metabolism states.This study enhances our understanding of the pathophysiology of diabetic brain damage and provides some potential biological evidence for its early diagnosis.