Gelugpa is the most influential extant religious sect of Tibetan Buddhism,which is the spiritual prop for Tibetans,with thousands of monasteries and followers in Tibetan areas of China.Studies on the spatial diffusion...Gelugpa is the most influential extant religious sect of Tibetan Buddhism,which is the spiritual prop for Tibetans,with thousands of monasteries and followers in Tibetan areas of China.Studies on the spatial diffusion processes of Gelugpa can not only reveal its historical geographical development but also lay the foundation for anticipating its future development trend.However,existing studies on Gelugpa lack geographical perspective,making it difficult to explore the spatial characteristics.Furthermore,the prevailing macro-perspective overlooks spatiotemporal heterogeneity in diffusion processes.Therefore,taking monastery as the carrier,this study establishes a multi-level diffusion model to reconstruct the diffusion networks of Gelugpa monasteries,as well as a framework to explore the detailed features in the spatial diffusion processes of Gelugpa in Tibetan areas of China based on a geodatabase of Gelugpa monastery.The results show that the multi-level diffusion model has a considerable applicability in the reconstruction of the diffusion networks of Gelugpa monasteries.Gelugpa monasteries in the Three Tibetan Inhabited Areas present disparate spatial diffusion processes with diverse diffusion bases,speeds,stages,as well as diffusion regions and centers.A powerful single-center diffusion-centered Gandan Monastery was rapidly formed in U-Tsang.Kham experienced a slower and more varied spatial diffusion process with multiple diffusion systems far apart from each other.The spatial diffusion process of Amdo was the most complex,with the highest diffusion intensity.Amdo possessed the most influential diffusion centers,with different diffusion shapes and diffusion ranges crossing and overlapping with each other.Multiple natural and human factors may contribute to the formation of Gelugpa monasteries.This study contributes to the understanding of the geography of Gelugpa and provides reference to studies on religion diffusion.展开更多
Three high dimensional spatial standardization algorithms are used for diffusion tensor image(DTI)registration,and seven kinds of methods are used to evaluate their performances.Firstly,the template used in this paper...Three high dimensional spatial standardization algorithms are used for diffusion tensor image(DTI)registration,and seven kinds of methods are used to evaluate their performances.Firstly,the template used in this paper was obtained by spatial transformation of 16 subjects by means of tensor-based standardization.Then,high dimensional standardization algorithms for diffusion tensor images,including fractional anisotropy(FA)based diffeomorphic registration algorithm,FA based elastic registration algorithm and tensor-based registration algorithm,were performed.Finally,7 kinds of evaluation methods,including normalized standard deviation,dyadic coherence,diffusion cross-correlation,overlap of eigenvalue-eigenvector pairs,Euclidean distance of diffusion tensor,and Euclidean distance of the deviatoric tensor and deviatoric of tensors,were used to qualitatively compare and summarize the above standardization algorithms.Experimental results revealed that the high-dimensional tensor-based standardization algorithms perform well and can maintain the consistency of anatomical structures.展开更多
In this work,based on the role of pre-ionization of the non-uniform electric field and its effect of reducing the collisional ionization coefficient,a diffuse dielectric barrier discharge plasma is formed in the open ...In this work,based on the role of pre-ionization of the non-uniform electric field and its effect of reducing the collisional ionization coefficient,a diffuse dielectric barrier discharge plasma is formed in the open space outside the electrode structure at a lower voltage by constructing a three-dimensional non-uniform spatial electric field using a contact electrode structure.The air purification study is also carried out.Firstly,a contact electrode structure is constructed using a three-dimensional wire electrode.The distribution characteristics of the spatial electric field formed by this electrode structure are analyzed,and the effects of the non-uniform electric field and the different angles of the vertical wire on the generation of three-dimensional spatial diffuse discharge are investigated.Secondly,the copper foam contact electrode structure is constructed using copper foam material,and the effects of different mesh sizes on the electric field distribution are analyzed.The results show that as the mesh size of the copper foam becomes larger,a strong electric field region exists not only on the surface of the insulating layer,but also on the surface of the vertical wires inside the copper foam,i.e.,the strong electric field region shows a three-dimensional distribution.Besides,as the mesh size increases,the area of the vertical strong electric field also increases.However,the electric field strength on the surface of the insulating layer gradually decreases.Therefore,the appropriate mesh size can effectively increase the discharge area,which is conducive to improving the air purification efficiency.Finally,a highly permeable stacked electrode structure of multilayer wire-copper foam is designed.In combination with an ozone treatment catalyst,an air purification device is fabricated,and the air purification experiment is carried out.展开更多
The aim of this paper is to investigate a Volterra-Lotka competition model of quasilinear parabolic equations with large interaction. Some existence, uniqueness and convergence results for the system are given. Also i...The aim of this paper is to investigate a Volterra-Lotka competition model of quasilinear parabolic equations with large interaction. Some existence, uniqueness and convergence results for the system are given. Also investigated is its spatial segregation limit when the interspecific competition rates become large. We show that the limit problem is similar to a free boundary problem.展开更多
This paper presents a development o f the extended Cellular Automata9CA),based on relational databases(RDB),to model dynamic interactions amon g spatial objects.The integration o f Geographical Information System(GIS)...This paper presents a development o f the extended Cellular Automata9CA),based on relational databases(RDB),to model dynamic interactions amon g spatial objects.The integration o f Geographical Information System(GIS)and CA has the great advantage of simu lationg geographical processes.But standard CA has some restrictions i n cellular shape and neighbourhood and neighbour rules,which restrict the CA’s ability to simulate complex,real world environ-ments.This paper discusses a cell’s spatialrelationbasedonthe spatialobject’s geometricalandmon-geometricalc haracter-istics,and extends the cell’s neighbour definition,and considers that the cell’s neighbour lies in the forms of not on ly spa-tial adjacency but also attribute co rrelation.This paper then puts forw ard that spatial relations between t wo different cells can be divided into three types,including spatial adjacency,neighbour hood and complicated separation.Ba sed on tradition-al ideas,it is impossible to settle CA’s restrictions completely.RDB-based CA is an academic experiment,in which some fields ard desighed to describe the essential information needed to define and select a cell’s neighbour.The culture innovation diffusion system has mul tiple forms of space diffusion and in herited characteristics that the RD B-based CA is capable of simulating more effectiv ely.Finally this paper details a successful case study on the diffusion o f fashion wear trends.Compared to the original CA,the RDB-based CA is a more natural and efficient representation of human k nowl-edge over space,and is an effective t ol in simulation complex systems that have multiple forms of spatial diff usion.展开更多
Large-scale non-thermal plasmas generated by nanosecond-pulse discharges have been used in various applications, including surface treatment, biomedical treatment, flow con- trol etc. In this paper, atmospheric-pressu...Large-scale non-thermal plasmas generated by nanosecond-pulse discharges have been used in various applications, including surface treatment, biomedical treatment, flow con- trol etc. In this paper, atmospheric-pressure diffuse discharge was produced by a homemade nanosecond-pulse generator with a full width at half maximum of 100 ns and a rise time of 70 ns. In order to increase the discharge area, multi-needle electrodes with a 3~3 array were designed. The electrical characteristics of the diffuse discharge array and optical images were investigated by the voltage-current waveforms and discharge images. The experimental results showed that the intensity of diffuse discharges in the center was significantly weaker than those at the margins, resulting in an inhomogeneous spatial uniformity in the diffuse discharge array. Simulation of the electric field showed that the inhomogeneous spatial uniformity was caused by the non-uniform distribution of the electric field in the diffuse discharge array. Moreover, the spatial uniformity of the diffuse discharge array could be improved by increasing the length of the needle in the centre of the array. Finally, the experimental results confirmed the simulation results, and the spatial uniformity of the nanosecond-pulse diffuse discharge array was significantly improved.展开更多
School-age children are in a specific development stage corresponding to juvenility,when the white matter of the brain experiences ongoing maturation.Dffusion-weighted magnetic resonance imaging(DWI),especially diffus...School-age children are in a specific development stage corresponding to juvenility,when the white matter of the brain experiences ongoing maturation.Dffusion-weighted magnetic resonance imaging(DWI),especially diffusion tensor imaging(DTI),is extensively used to characterize the maturation by assessing white matter properties in vivo.In the analysis of DWI data,spatial normalization is crucial for conducting inter-subject analyses or linking the individual space with the reference space.Using tensor-based registration with an appropriate diffusion tensor template presents high accuracy regarding spatial normalization.However,there is a lack of a standardized diffusion tensor template dedicated to school-age children with ongoing brain development.Here,we established the school-age children diffusion tensor(SACT)template by optimizing tensor reorientation on high-quality DTI data from a large sample of cognitively normal participants aged 6-12 years.With an age-balanced design,the SACT template represented the entire age range well by showing high similarity to the age-specific templates.Compared with the tensor template of adults,the SACT template revealed significantly higher spatial normalization accuracy and inter-subject coherence upon evaluation of subjects in two different datasets of schoolage children.A practical application regarding the age associations with the normalized DTI-derived data was conducted to further compare the SACT template and the adult template.Although similar spatial patterns were found,the SACT template showed significant effects on the distributions of the statistical results,which may be related to the performance of spatial normalization.Looking forward,the SACT template could contribute to future studies of white matter development in both healthy and clinical populations.The SACT template is publicly available now(tp://igshare com/aricles/dataseu'SACT_.template/14071283).展开更多
Considering the antiviral drugs can act on the fusion,reverse transcription,and budding stages of HIV infected cells,in this paper,we formulate a two-periodic delay heterogeneous space diffusion HIV model with three-s...Considering the antiviral drugs can act on the fusion,reverse transcription,and budding stages of HIV infected cells,in this paper,we formulate a two-periodic delay heterogeneous space diffusion HIV model with three-stage infection process to study the effects of periodic antiviral treatment and spatial heterogeneity on HIV infection process.We first study the well-posedness of the full system and then derive the basic reproduction number R_(0),which is defined as the spectral radius of the next generation operator.We further prove that R_(0) is a threshold for the elimination and persistence of HIV infection by comparison principle and persistence theory for non-autonomous system.In the spatial homogeneous case,the explicit expression of R_(0) is derived and the global attractivity of the positive steady state is proved by using the fluctuation method.Some numerical simulations are conducted to illustrate the theoretical results and our works suggest that both spatial heterogeneity and periodic delays caused by periodic antiviral therapy have a remarkable impact on the progression of HIV infection and should not be overlooked in clinical treatment process.展开更多
This study examines an optimal contraception control problem for a nonlinear competitive vermin population model that is dependent on size structure and spatial diffusion in a polluted environment.The control variable...This study examines an optimal contraception control problem for a nonlinear competitive vermin population model that is dependent on size structure and spatial diffusion in a polluted environment.The control variables are the average number of female sterilant and the input rate of exogenous toxicant.It has a good guiding effect on curbing environmental pollution and controlling the number of vermin.These results provide a theoretical basis for controlling and preventing vermin and curbing environmental pollution.The hybrid system belongs to the class of separable models,and its solution is separable in terms of size and spatial location.Therefore,we transform the system into two subsystems and prove the existence and uniqueness of non-negative solutions via the comparison principle and fixed point theorem,respectively.The necessary conditions for the optimal contraception strategy are derived by constructing an adjoint system and using tangent-normal cones.The method of characteristics and the finite difference method approximate the non-negative solutions of the two subsystems,and some numerical examples illustrate the theoretical results.展开更多
In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution （if it exists） does not depend continuously on the data. The generalized Tikhono...In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution （if it exists） does not depend continuously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained, Numerical examples are presented to illustrate the validity and effectiveness of this method.展开更多
Under the background of collaborative innovation,innovation spillovers at urban agglomeration(UA)level is an important issue but rarely discussed.Using balanced panel data of innovation activities in China’s five UAs...Under the background of collaborative innovation,innovation spillovers at urban agglomeration(UA)level is an important issue but rarely discussed.Using balanced panel data of innovation activities in China’s five UAs from 2003 to 2016,this paper shows spatio-temporal evolution process of their technological innovation capacity with discussing polarization-diffusion patterns,and simultaneously examines driving factors of that evolution processes.We report three main findings:1)there is a high degree of concentration in technological innovation capacity distribution within all China’s five UAs,linked by economic and innovation collaboration.2)Innovation capacity increase of China’s five UAs is driven by government’s investment in science and technology(S&T)to a large extent,followed by influences of infrastructure facilities construction,human capital for S&T,as well as transformation of industrial structure,with great disparities emerged between UAs in our sample period.3)While the intra-region innovation gaps are reducing in Yangtze River Delta Urban Agglomeration(YRD)with obvious innovation diffusion,urban agglomeration in middle reaches of the Yangtze River(MYR)is still dominated by innovation polarized growth.Differences in polarization-diffusion patterns between these two UAs may be explained by opposite returns of industrial structure and internet infrastructure.Our findings contribute to more effective policy making in promoting innovation development when reducing regional inequality through innovation diffusion.展开更多
We developed a novel method for real-time monitoring of alteration of the local epithelium vessel/capillary and blood oxygenation spatial pattern in epithelium exploiting a compact fibre sensor system based on spatial...We developed a novel method for real-time monitoring of alteration of the local epithelium vessel/capillary and blood oxygenation spatial pattern in epithelium exploiting a compact fibre sensor system based on spatially and spectrally resolved diffuse reflectance.The method is based on collection of spatially resolved diffuse reflectance Re(λ)by fiber sensors.The spatial resolution is provided as a dependence of Re(λ)on a set of distancesρbetween the source and detector(attenuation curve).It is expected that the new method can reasonably extract the minor spatial deviations of oxygenation and local blood volume fraction-parameters,directly related to the local vessel density and capillary spatial patterns in the epithelium.Light scattering in visible range is naturally taken into account in the proposed method.展开更多
This compendium review focuses on the spatial distribution of sensitivity to localized absorption changes in optically diffuse media,particularly for measurements relevant to near-infrared spectroscopy.The three tempo...This compendium review focuses on the spatial distribution of sensitivity to localized absorption changes in optically diffuse media,particularly for measurements relevant to near-infrared spectroscopy.The three temporal domains,continuous wave,frequency domain,and time domain,each obtain different optical data types whose changes may be related to effective homogeneous changes in the absorption coefficient.Sensitivity is the relationship between a localized perturbation and the recovered effective homogeneous absorption change.Therefore,spatial sensitivity maps representing the perturbation location can be generated for the numerous optical data types in the three temporal domains.The review first presents a history of the past 30 years of work investigating this sensitivity in optically diffuse media.These works are experimental and theoretical,presenting one-,two-,and three-dimensional sensitivity maps for different Near-Infrared Spectroscopy methods,domains,and data types.Following this history,we present a compendium of sensitivity maps organized by temporal domain and then data type.This compendium provides a valuable tool to compare the spatial sensitivity of various measurement methods and parameters in one document.Methods for one to generate these maps are provided in Appendix A,including the code.This historical review and comprehensive sensitivity map compendium provides a single source researchers may use to visualize,investigate,compare,and generate sensitivity to localized absorption change maps.展开更多
基金supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China(Grant No.18YJAZH140).
文摘Gelugpa is the most influential extant religious sect of Tibetan Buddhism,which is the spiritual prop for Tibetans,with thousands of monasteries and followers in Tibetan areas of China.Studies on the spatial diffusion processes of Gelugpa can not only reveal its historical geographical development but also lay the foundation for anticipating its future development trend.However,existing studies on Gelugpa lack geographical perspective,making it difficult to explore the spatial characteristics.Furthermore,the prevailing macro-perspective overlooks spatiotemporal heterogeneity in diffusion processes.Therefore,taking monastery as the carrier,this study establishes a multi-level diffusion model to reconstruct the diffusion networks of Gelugpa monasteries,as well as a framework to explore the detailed features in the spatial diffusion processes of Gelugpa in Tibetan areas of China based on a geodatabase of Gelugpa monastery.The results show that the multi-level diffusion model has a considerable applicability in the reconstruction of the diffusion networks of Gelugpa monasteries.Gelugpa monasteries in the Three Tibetan Inhabited Areas present disparate spatial diffusion processes with diverse diffusion bases,speeds,stages,as well as diffusion regions and centers.A powerful single-center diffusion-centered Gandan Monastery was rapidly formed in U-Tsang.Kham experienced a slower and more varied spatial diffusion process with multiple diffusion systems far apart from each other.The spatial diffusion process of Amdo was the most complex,with the highest diffusion intensity.Amdo possessed the most influential diffusion centers,with different diffusion shapes and diffusion ranges crossing and overlapping with each other.Multiple natural and human factors may contribute to the formation of Gelugpa monasteries.This study contributes to the understanding of the geography of Gelugpa and provides reference to studies on religion diffusion.
基金Supported by the National Key Research and Development Program of China(2016YFC0100300)the National Natural Science Foundation of China(61402371,61771369)+1 种基金the Natural Science Basic Research Plan in Shaanxi Province of China(2017JM6008)the Fundamental Research Funds for the Central Universities of China(3102017zy032,3102018zy020)
文摘Three high dimensional spatial standardization algorithms are used for diffusion tensor image(DTI)registration,and seven kinds of methods are used to evaluate their performances.Firstly,the template used in this paper was obtained by spatial transformation of 16 subjects by means of tensor-based standardization.Then,high dimensional standardization algorithms for diffusion tensor images,including fractional anisotropy(FA)based diffeomorphic registration algorithm,FA based elastic registration algorithm and tensor-based registration algorithm,were performed.Finally,7 kinds of evaluation methods,including normalized standard deviation,dyadic coherence,diffusion cross-correlation,overlap of eigenvalue-eigenvector pairs,Euclidean distance of diffusion tensor,and Euclidean distance of the deviatoric tensor and deviatoric of tensors,were used to qualitatively compare and summarize the above standardization algorithms.Experimental results revealed that the high-dimensional tensor-based standardization algorithms perform well and can maintain the consistency of anatomical structures.
基金supported by the Fundamental Research Funds for the Central Universities(No.2022YJS094)。
文摘In this work,based on the role of pre-ionization of the non-uniform electric field and its effect of reducing the collisional ionization coefficient,a diffuse dielectric barrier discharge plasma is formed in the open space outside the electrode structure at a lower voltage by constructing a three-dimensional non-uniform spatial electric field using a contact electrode structure.The air purification study is also carried out.Firstly,a contact electrode structure is constructed using a three-dimensional wire electrode.The distribution characteristics of the spatial electric field formed by this electrode structure are analyzed,and the effects of the non-uniform electric field and the different angles of the vertical wire on the generation of three-dimensional spatial diffuse discharge are investigated.Secondly,the copper foam contact electrode structure is constructed using copper foam material,and the effects of different mesh sizes on the electric field distribution are analyzed.The results show that as the mesh size of the copper foam becomes larger,a strong electric field region exists not only on the surface of the insulating layer,but also on the surface of the vertical wires inside the copper foam,i.e.,the strong electric field region shows a three-dimensional distribution.Besides,as the mesh size increases,the area of the vertical strong electric field also increases.However,the electric field strength on the surface of the insulating layer gradually decreases.Therefore,the appropriate mesh size can effectively increase the discharge area,which is conducive to improving the air purification efficiency.Finally,a highly permeable stacked electrode structure of multilayer wire-copper foam is designed.In combination with an ozone treatment catalyst,an air purification device is fabricated,and the air purification experiment is carried out.
文摘The aim of this paper is to investigate a Volterra-Lotka competition model of quasilinear parabolic equations with large interaction. Some existence, uniqueness and convergence results for the system are given. Also investigated is its spatial segregation limit when the interspecific competition rates become large. We show that the limit problem is similar to a free boundary problem.
基金Under the auspices of the National Natural Science Foundation of China(No.40071071)
文摘This paper presents a development o f the extended Cellular Automata9CA),based on relational databases(RDB),to model dynamic interactions amon g spatial objects.The integration o f Geographical Information System(GIS)and CA has the great advantage of simu lationg geographical processes.But standard CA has some restrictions i n cellular shape and neighbourhood and neighbour rules,which restrict the CA’s ability to simulate complex,real world environ-ments.This paper discusses a cell’s spatialrelationbasedonthe spatialobject’s geometricalandmon-geometricalc haracter-istics,and extends the cell’s neighbour definition,and considers that the cell’s neighbour lies in the forms of not on ly spa-tial adjacency but also attribute co rrelation.This paper then puts forw ard that spatial relations between t wo different cells can be divided into three types,including spatial adjacency,neighbour hood and complicated separation.Ba sed on tradition-al ideas,it is impossible to settle CA’s restrictions completely.RDB-based CA is an academic experiment,in which some fields ard desighed to describe the essential information needed to define and select a cell’s neighbour.The culture innovation diffusion system has mul tiple forms of space diffusion and in herited characteristics that the RD B-based CA is capable of simulating more effectiv ely.Finally this paper details a successful case study on the diffusion o f fashion wear trends.Compared to the original CA,the RDB-based CA is a more natural and efficient representation of human k nowl-edge over space,and is an effective t ol in simulation complex systems that have multiple forms of spatial diff usion.
基金supported by National Natural Science Foundation of China(Nos.51222701,51477164)the National Basic Research Program of China(No.2014CB239505-3)
文摘Large-scale non-thermal plasmas generated by nanosecond-pulse discharges have been used in various applications, including surface treatment, biomedical treatment, flow con- trol etc. In this paper, atmospheric-pressure diffuse discharge was produced by a homemade nanosecond-pulse generator with a full width at half maximum of 100 ns and a rise time of 70 ns. In order to increase the discharge area, multi-needle electrodes with a 3~3 array were designed. The electrical characteristics of the diffuse discharge array and optical images were investigated by the voltage-current waveforms and discharge images. The experimental results showed that the intensity of diffuse discharges in the center was significantly weaker than those at the margins, resulting in an inhomogeneous spatial uniformity in the diffuse discharge array. Simulation of the electric field showed that the inhomogeneous spatial uniformity was caused by the non-uniform distribution of the electric field in the diffuse discharge array. Moreover, the spatial uniformity of the diffuse discharge array could be improved by increasing the length of the needle in the centre of the array. Finally, the experimental results confirmed the simulation results, and the spatial uniformity of the nanosecond-pulse diffuse discharge array was significantly improved.
基金supported by the Beijing Brain Initiative of Beijing Municipal Science&Technology Commission(Z1811001518003)the National Natural Science Foundation of China(31521063)All the authors thank the National Center for Protein Sciences at Peking University for assistance_with brain scanning.The authors thank the"2019 Helmholtz-OCPC-Program for the involvement of postdocs in bilateral collaboration projects"for financial support that enabled this important study,Allthe authors are grateful for the contribution of the participants to the CBD project and the open access to the NKI-Rockiand sample.
文摘School-age children are in a specific development stage corresponding to juvenility,when the white matter of the brain experiences ongoing maturation.Dffusion-weighted magnetic resonance imaging(DWI),especially diffusion tensor imaging(DTI),is extensively used to characterize the maturation by assessing white matter properties in vivo.In the analysis of DWI data,spatial normalization is crucial for conducting inter-subject analyses or linking the individual space with the reference space.Using tensor-based registration with an appropriate diffusion tensor template presents high accuracy regarding spatial normalization.However,there is a lack of a standardized diffusion tensor template dedicated to school-age children with ongoing brain development.Here,we established the school-age children diffusion tensor(SACT)template by optimizing tensor reorientation on high-quality DTI data from a large sample of cognitively normal participants aged 6-12 years.With an age-balanced design,the SACT template represented the entire age range well by showing high similarity to the age-specific templates.Compared with the tensor template of adults,the SACT template revealed significantly higher spatial normalization accuracy and inter-subject coherence upon evaluation of subjects in two different datasets of schoolage children.A practical application regarding the age associations with the normalized DTI-derived data was conducted to further compare the SACT template and the adult template.Although similar spatial patterns were found,the SACT template showed significant effects on the distributions of the statistical results,which may be related to the performance of spatial normalization.Looking forward,the SACT template could contribute to future studies of white matter development in both healthy and clinical populations.The SACT template is publicly available now(tp://igshare com/aricles/dataseu'SACT_.template/14071283).
基金supported by the National Natural Science Foundation of China(No.12201557)the Foundation of Zhejiang Provincial Education Department(No.Y202249921).
文摘Considering the antiviral drugs can act on the fusion,reverse transcription,and budding stages of HIV infected cells,in this paper,we formulate a two-periodic delay heterogeneous space diffusion HIV model with three-stage infection process to study the effects of periodic antiviral treatment and spatial heterogeneity on HIV infection process.We first study the well-posedness of the full system and then derive the basic reproduction number R_(0),which is defined as the spectral radius of the next generation operator.We further prove that R_(0) is a threshold for the elimination and persistence of HIV infection by comparison principle and persistence theory for non-autonomous system.In the spatial homogeneous case,the explicit expression of R_(0) is derived and the global attractivity of the positive steady state is proved by using the fluctuation method.Some numerical simulations are conducted to illustrate the theoretical results and our works suggest that both spatial heterogeneity and periodic delays caused by periodic antiviral therapy have a remarkable impact on the progression of HIV infection and should not be overlooked in clinical treatment process.
基金supported by the National Natural Science Foundation of China(No.11561041)the Young Doctor Support Foundation of Gansu Education Department(No.2023QB-077)the Start-Up Foundation of Doctoral Research of Hexi University(No.KYQD2023011).
文摘This study examines an optimal contraception control problem for a nonlinear competitive vermin population model that is dependent on size structure and spatial diffusion in a polluted environment.The control variables are the average number of female sterilant and the input rate of exogenous toxicant.It has a good guiding effect on curbing environmental pollution and controlling the number of vermin.These results provide a theoretical basis for controlling and preventing vermin and curbing environmental pollution.The hybrid system belongs to the class of separable models,and its solution is separable in terms of size and spatial location.Therefore,we transform the system into two subsystems and prove the existence and uniqueness of non-negative solutions via the comparison principle and fixed point theorem,respectively.The necessary conditions for the optimal contraception strategy are derived by constructing an adjoint system and using tangent-normal cones.The method of characteristics and the finite difference method approximate the non-negative solutions of the two subsystems,and some numerical examples illustrate the theoretical results.
基金supported by the National Natural Science Foundation of China(11171136, 11261032)the Distinguished Young Scholars Fund of Lan Zhou University of Technology (Q201015)the basic scientific research business expenses of Gansu province college
文摘In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution （if it exists） does not depend continuously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained, Numerical examples are presented to illustrate the validity and effectiveness of this method.
文摘Under the background of collaborative innovation,innovation spillovers at urban agglomeration(UA)level is an important issue but rarely discussed.Using balanced panel data of innovation activities in China’s five UAs from 2003 to 2016,this paper shows spatio-temporal evolution process of their technological innovation capacity with discussing polarization-diffusion patterns,and simultaneously examines driving factors of that evolution processes.We report three main findings:1)there is a high degree of concentration in technological innovation capacity distribution within all China’s five UAs,linked by economic and innovation collaboration.2)Innovation capacity increase of China’s five UAs is driven by government’s investment in science and technology(S&T)to a large extent,followed by influences of infrastructure facilities construction,human capital for S&T,as well as transformation of industrial structure,with great disparities emerged between UAs in our sample period.3)While the intra-region innovation gaps are reducing in Yangtze River Delta Urban Agglomeration(YRD)with obvious innovation diffusion,urban agglomeration in middle reaches of the Yangtze River(MYR)is still dominated by innovation polarized growth.Differences in polarization-diffusion patterns between these two UAs may be explained by opposite returns of industrial structure and internet infrastructure.Our findings contribute to more effective policy making in promoting innovation development when reducing regional inequality through innovation diffusion.
基金The authors gratefully acknowledge funding of the Erlangen Graduate School in Advanced Optical Technologies(SAOT)by the German National Science Foundation(DFG)in the framework of the excellence initiative for support of this study.
文摘We developed a novel method for real-time monitoring of alteration of the local epithelium vessel/capillary and blood oxygenation spatial pattern in epithelium exploiting a compact fibre sensor system based on spatially and spectrally resolved diffuse reflectance.The method is based on collection of spatially resolved diffuse reflectance Re(λ)by fiber sensors.The spatial resolution is provided as a dependence of Re(λ)on a set of distancesρbetween the source and detector(attenuation curve).It is expected that the new method can reasonably extract the minor spatial deviations of oxygenation and local blood volume fraction-parameters,directly related to the local vessel density and capillary spatial patterns in the epithelium.Light scattering in visible range is naturally taken into account in the proposed method.
文摘This compendium review focuses on the spatial distribution of sensitivity to localized absorption changes in optically diffuse media,particularly for measurements relevant to near-infrared spectroscopy.The three temporal domains,continuous wave,frequency domain,and time domain,each obtain different optical data types whose changes may be related to effective homogeneous changes in the absorption coefficient.Sensitivity is the relationship between a localized perturbation and the recovered effective homogeneous absorption change.Therefore,spatial sensitivity maps representing the perturbation location can be generated for the numerous optical data types in the three temporal domains.The review first presents a history of the past 30 years of work investigating this sensitivity in optically diffuse media.These works are experimental and theoretical,presenting one-,two-,and three-dimensional sensitivity maps for different Near-Infrared Spectroscopy methods,domains,and data types.Following this history,we present a compendium of sensitivity maps organized by temporal domain and then data type.This compendium provides a valuable tool to compare the spatial sensitivity of various measurement methods and parameters in one document.Methods for one to generate these maps are provided in Appendix A,including the code.This historical review and comprehensive sensitivity map compendium provides a single source researchers may use to visualize,investigate,compare,and generate sensitivity to localized absorption change maps.
