A multi-group cross-section library is fundamental for deterministic lattice physics calculations.Most existing multi-group cross-section libraries are customized for particular computer codes,as well as for particula...A multi-group cross-section library is fundamental for deterministic lattice physics calculations.Most existing multi-group cross-section libraries are customized for particular computer codes,as well as for particular types of nuclear reactors.This paper presents an HDF5-format multi-group cross-section library named XPZLIB.XPZLIB was produced using a selfdeveloped XPZR module integrated into the NJOY2016 code,and an in-house PyNjoy2022 system was developed for autoprocessing.XPZLIB contains detailed data content and well-organized data structures that are user-and developer-friendly.Three typical XPZLIBs with different numbers of energy groups,nuclides,and depletion reaction types were released via the Tsinghua cloud website.Furthermore,the applicability of the released XPZLIBs was investigated using HTGR and PWR lattice calculations,which can provide guidance for applying XPZLIB under different scenarios.展开更多
The accurate modeling of depletion,intricately tied to the solution of the neutron transport equation,is crucial for the design,analysis,and licensing of nuclear reactors and their fuel cycles.This paper introduces a ...The accurate modeling of depletion,intricately tied to the solution of the neutron transport equation,is crucial for the design,analysis,and licensing of nuclear reactors and their fuel cycles.This paper introduces a novel multi-group Monte-Carlo depletion calculation approach.Multi-group cross-sections(MGXS)are derived from both 3D whole-core model and 2D fuel subassembly model using the continuous-energy Monte-Carlo method.Core calculations employ the multi-group Monte-Carlo method,accommodating both homogeneous and specific local heterogeneous geometries.The proposed method has been validated against the MET-1000 metal-fueled fast reactors,using both the OECD/NEA benchmark and a new refueling benchmark introduced in this paper.Our findings suggest that microscopic MGXS,produced via the Monte-Carlo method,are viable for fast reactor depletion analyses.Furthermore,the locally heterogeneous model with angular-dependent MGXS offers robust predictions for core reactivity,control rod value,sodium void value,Doppler constants,power distribution,and concentration levels.展开更多
In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch in...In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].展开更多
Muon tomography is a capable imaging technique to measure the geometry of high-Z objects. However,most existed algorithms used in muon tomography have obscured the effects of angular distribution and momentum spectra ...Muon tomography is a capable imaging technique to measure the geometry of high-Z objects. However,most existed algorithms used in muon tomography have obscured the effects of angular distribution and momentum spectra of cosmic ray muons and reduced the spatial resolution. We present a modified multi-group model that takes into account these effects and calibrates the model by the material of lead. Performance tests establish that the model is capable of measuring the thickness of a Pb slab and identifying the material of an unknown slab on a reasonable exposure timescale, in both cases of complete and incomplete angular data. Results show that the modified multi-group model is helpful for improvements in image resolution in real applications.展开更多
In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR （susceptible-infected-quarantined-removed） model is proposed for computer worms by explicitly c...In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR （susceptible-infected-quarantined-removed） model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.展开更多
To overcome the default of single search tendency, the ants in the colony are divided into several sub-groups. The ants in different subgroups have different trail information and expectation coefficients. The simulat...To overcome the default of single search tendency, the ants in the colony are divided into several sub-groups. The ants in different subgroups have different trail information and expectation coefficients. The simulated annealing method is introduced to the algorithm. Through setting the temperature changing with the iterations, after each turn of tours, the solution set obtained by the ants is taken as the candidate set. The update set is obtained by adding the solutions in the candidate set to the previous update set with the probability determined by the temperature. The solutions in the candidate set are used to update the trail information. In each turn of updating, the current best solution is also used to enhance the trail information on the current best route. The trail information is reset when the algorithm is in stagnation state. The computer experiments demonstrate that the proposed algorithm has higher stability and convergence speed.展开更多
In this paper,a stochastic multi-group AIDS model with saturated incidence rate is studied.We prove that the system is persistent in the mean under some parametric restrictions.We also obtain the sufficient condition ...In this paper,a stochastic multi-group AIDS model with saturated incidence rate is studied.We prove that the system is persistent in the mean under some parametric restrictions.We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function.Our results indicate that the existence of ergodic stationary distribution does not rely on the interior equilibrium of the corresponding deterministic system,which greatly improves upon previous results.展开更多
We establish a stochastic differential equation epidemic model of multi-group SIR type based on the deterministic multi-group SIR mode. Then, we define the basic reproduction number R0^S and show that it is a sharp th...We establish a stochastic differential equation epidemic model of multi-group SIR type based on the deterministic multi-group SIR mode. Then, we define the basic reproduction number R0^S and show that it is a sharp threshold for the dynamic of the stochastic multi-group SIR model. More specially, if R0^S 〈 1, then the disease-free equilibrium will be asymptotically stable which means the disease will die out, if R0^S 〉 1, the disease-free equilibrium will unstable, and our model will positively recurrence to a positive domain which implies the persistence of our model. Numerical simulation examples are carried out to substantiate the analytical results.展开更多
In this study, based differential equations methods are used to solve equations because these methods are dependent on boundary value data more than other mathematical equations. We have calculated neutron flux, criti...In this study, based differential equations methods are used to solve equations because these methods are dependent on boundary value data more than other mathematical equations. We have calculated neutron flux, criticality and geometrical eigenvalue by using multi-group method and solving the neutron diffusion equation for finite and infinite cylindrical and spherical reactors in this study. For the calculation of the total neutron flux cross sections, we need the neutron diffusion equation. Thus, we have established the relationship between neuron flow and cross-section of neuron depending on neutron energy. Critical calculations have been made by comparing the results with MNCP (montecarlo n-partical) simulation methods. For necessary computer calculations, the programme, Wolfram-Matematica-7 has been used.展开更多
Background:Understanding the spatial pattern and driving factors of forest carbon density in mountainous terrain is of great importance for monitoring forest carbon in support of sustainable forest management for miti...Background:Understanding the spatial pattern and driving factors of forest carbon density in mountainous terrain is of great importance for monitoring forest carbon in support of sustainable forest management for mitigating climate change.Methods:We collected the forest inventory data in 2015 in Shanxi Province,eastern Loess Plateau of China,to explore the spatial pattern and driving factors of biomass carbon density(BCD)for natural and planted coniferous forests using Anselin Local Moran’s I,Local Getis-Ord G*and semivariogram analyses,and multi-group structural equation modeling,respectively.Results:The result of spatial pattern of BCDs for natural forests showed that the BCD was generally higher in the north but lower in the south of Shanxi.The spatial pattern for planted forests was substantially different from that for natural forests.The results of multi-group SEM suggested that elevation(or temperature as the alternative factor of elevation)and stand age were important driving factors of BCD for these two forest types.Compared with other factors,the effects of latitude and elevation on BCD showed much greater difference between these two forest types.The difference in indirect effect of latitude(mainly through affecting elevation and stand age)between natural and planted forests was to some extent a reflection of the difference between the spatial patterns of BCDs for natural and planted forests in Shanxi.Conclusions:The natural coniferous forests had a higher biomass carbon density,a stronger spatial dependency of biomass carbon density relative to planted coniferous forests in Shanxi.Elevation was the most important driving factor,and the effect on biomass carbon density was stronger for natural than planted coniferous forests.Besides,latitude presented only indirect effect on it for the two forest types.展开更多
BACKGROUND Early thrombolytic therapy is crucial to treat acute cerebral infarction,especially since the onset of thrombolytic therapy takes 1-6 h.Therefore,early diagnosis and evaluation of cerebral infarction is imp...BACKGROUND Early thrombolytic therapy is crucial to treat acute cerebral infarction,especially since the onset of thrombolytic therapy takes 1-6 h.Therefore,early diagnosis and evaluation of cerebral infarction is important.AIM To investigate the diagnostic value of magnetic resonance multi-delay threedimensional arterial spin labeling(3DASL)and diffusion kurtosis imaging(DKI)in evaluating the perfusion and infarct area size in patients with acute cerebral ischemia.METHODS Eighty-four patients who experienced acute cerebral ischemia from March 2019 to February 2021 were included.All patients in the acute stage underwent magnetic resonance-based examination,and the data were processed by the system’s own software.The apparent diffusion coefficient(ADC),average diffusion coefficient(MD),axial diffusion(AD),radial diffusion(RD),average kurtosis(MK),radial kurtosis(fairly RK),axial kurtosis(AK),and perfusion parameters post-labeling delays(PLD)in the focal area and its corresponding area were compared.The correlation between the lesion area of cerebral infarction under MK and MD and T2-weighted imaging(T2WI)was analyzed.RESULTS The DKI parameters of focal and control areas in the study subjects were compared.The ADC,MD,AD,and RD values in the lesion area were significantly lower than those in the control area.The MK,RK,and AK values in the lesion area were significantly higher than those in the control area.The MK/MD value in the infarct lesions was used to determine the matching situation.MK/MD<5 mm was considered matching and MK/MD≥5 mm was considered mismatching.PLD1.5s and PLD2.5s perfusion parameters in the central,peripheral,and control areas of the infarct lesions in MK/MD-matched and-unmatched patients were not significantly different.PLD1.5s and PLD2.5s perfusion parameter values in the central area of the infarct lesions in MK/MD-matched and-unmatched patients were significantly lower than those in peripheral and control areas.The MK and MD maps showed a lesion area of 20.08±5.74 cm^(2) and 22.09±5.58 cm^(2),respectively.T2WI showed a lesion area of 19.76±5.02 cm^(2).There were no significant differences in the cerebral infarction lesion areas measured using the three methods.MK,MD,and T2WI showed a good correlation.CONCLUSION DKI parameters showed significant difference between the focal and control areas in patients with acute ischemic cerebral infarction.3DASL can effectively determine the changes in perfusion levels in the lesion area.There was a high correlation between the area of the infarct lesions diagnosed by DKI and T2WI.展开更多
In this paper, we present a method for finding the solution of the linear multi-delay systems (MDS) by using the hybrid of the Block-Pulse functions and the Bernoulli polynomials. In this approach, the MDS is reduced ...In this paper, we present a method for finding the solution of the linear multi-delay systems (MDS) by using the hybrid of the Block-Pulse functions and the Bernoulli polynomials. In this approach, the MDS is reduced to a system of linear algebraic equations by expanding various time functions for the hybrid functions and using operational matrices. To demonstrate the validity and the applicability of the technique, some examples are presented.展开更多
The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons,which describes the spectrum behavior of neutron density int...The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons,which describes the spectrum behavior of neutron density into the homogenous nuclear reactors, is developed. This system is one of the most important stiff coupled nonlinear fractional differentials for nuclear reactor dynamics. The generalization of Taylor's formula that involves Caputo fractional derivatives is developed in an attempt to overcome the difficulty of the stiffness of the nonlinear fractional differential model. Moreover, the general fractional derivatives are calculated analytically throughout this work. Furthermore, the local and global estimated errors were analyzed, which suggest that the error quantification should take into account the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error(local truncation error). The neutron density response with time is analyzed for the anomalous diffusion, sub-diffusion, and super-diffusion processes.展开更多
In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the ...In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.展开更多
Consider the heterogeneity(e.g.,heterogeneous social behaviour,heterogeneity due to different geography,contrasting contact patterns and different numbers of sexual partners etc.)of host population,in this paper,the a...Consider the heterogeneity(e.g.,heterogeneous social behaviour,heterogeneity due to different geography,contrasting contact patterns and different numbers of sexual partners etc.)of host population,in this paper,the authors propose an infection age multigroup SEIR epidemic model.The model system also incorporates the feedback variables,where the infectivity of infected individuals may depend on the infection age.In the direction of mathematical analysis of model,the basic reproduction number R_0 has been computed.The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R_(0).More precisely,for R_(0)≤1,the disease-free equilibrium is globally asymptotically stable and for R_(0)>1,they establish global stability of endemic equilibrium using some graph theoretic techniques to Lyapunov function method.By considering a numerical example,they investigate the effects of infection age and feedback on the prevalence of the disease.Their result shows that feedback parameters have different and even opposite effects on different groups.However,by choosing an appropriate value of feedback parameters,the disease could be eradicated or maintained at endemic level.Besides,the infection age of infected individuals may also change the behaviour of the disease,global stable to damped oscillations or damped oscillations to global stable.展开更多
Computed tomography(CT) reconstruction with a well-registered priori magnetic resonance imaging(MRI) image can improve reconstruction results with low-dose CT, because well-registered CT and MRI images have similar st...Computed tomography(CT) reconstruction with a well-registered priori magnetic resonance imaging(MRI) image can improve reconstruction results with low-dose CT, because well-registered CT and MRI images have similar structures. However, in clinical settings, the CT image of patients does not always match the priori MRI image because of breathing and movement of patients during CT scanning. To improve the image quality in this case, multi-group datasets expansion is proposed in this paper. In our method, multi-group CT-MRI datasets are formed by expanding CT-MRI datasets. These expanded datasets can also be used by most existing CT-MRI algorithms and improve the reconstructed image quality when the CT image of a patient is not registered with the priori MRI image. In the experiments, we evaluate the performance of the algorithm by using multi-group CT-MRI datasets in several unregistered situations. Experiments show that when the CT and priori MRI images are not registered, the reconstruction results of using multi-group dataset expansion are better than those obtained without using the expansion.展开更多
In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics a...In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.展开更多
In this paper, we investigate the threshold dynamics of a multi-group SEAR alcoholism epidemic model with public health education. The multi-group model allows us to describe interactions both within-group and inter-g...In this paper, we investigate the threshold dynamics of a multi-group SEAR alcoholism epidemic model with public health education. The multi-group model allows us to describe interactions both within-group and inter-group separately. We prove that the basic reproduction number R0 plays the role of a threshold for the long-time behavior of the model. The alcohol-free equilibrium P0 of the model is globally asymptotically stable if R0≤1,while the alcohol-present equilibrium P* exists uniquely and is globally asymptotically stable if R0>1.For the proofs of main results, we use the classical method of Lyapunov functions and apply subtle grouping technique in estimating the derivatives of Lyapunov functions guided by graph theory. Our results expand the previous results which have been obtained in single-group models. Sensitivity analysis and numerical simulations are also performed to illustrate our results.展开更多
In this paper, by applying Lyapunov functional approach, we establish a sufficient condition on the global stability of a ＂delayed＂ multi-group SIRS epidemic model with cure rate and incomplete recovery rate which d...In this paper, by applying Lyapunov functional approach, we establish a sufficient condition on the global stability of a ＂delayed＂ multi-group SIRS epidemic model with cure rate and incomplete recovery rate which does not depend on the delays and is an extension of the ＂light drug model＂ studied in the recent paper [Muroya, Li and Kuniya, Complete global analysis of an SIRS epidemic model with graded cure rate and incomplete recovery rate, J. Math. Anal. Appl. 410 （2014） 719-732] to a multi-group model. Applying a Lyapunov functional on total population of each compartment, we offer new techniques for the delayed system, how to prove the permanence, the existence of the endemic equilibrium and the global stability of disease-free equilibrium for the reproduction number R0 ≤ 1 and endemic equilibrium forR0 ≥ 1.展开更多
ENDF/B-Ⅶ.0, which was released by the USA Cross Section Evaluation Working Group （CSEWG） in December 2006, was demonstrated to perform much better than previous ENDF evaluations over a broad range of benchmark expe...ENDF/B-Ⅶ.0, which was released by the USA Cross Section Evaluation Working Group （CSEWG） in December 2006, was demonstrated to perform much better than previous ENDF evaluations over a broad range of benchmark experiments. A high-energy （up to 150 MeV） multi-group library set named HEST1.0 with 253-neutron and 48-photon groups has been developed based on ENDF/B-Ⅶ.0 using the N JOY code. This paper provides a summary of the procedure to produce the library set and a detailed description of the verification of the multi-group library set by several shielding benchmark devices, in particular for high-energy neutron data. In addition, the first application of HEST1.0 to the shielding design of the China Spallation Neutron Source （CSNS） is demonstrated.展开更多
基金supported by the National Key R&D Program of China(2020YFE0202500).
文摘A multi-group cross-section library is fundamental for deterministic lattice physics calculations.Most existing multi-group cross-section libraries are customized for particular computer codes,as well as for particular types of nuclear reactors.This paper presents an HDF5-format multi-group cross-section library named XPZLIB.XPZLIB was produced using a selfdeveloped XPZR module integrated into the NJOY2016 code,and an in-house PyNjoy2022 system was developed for autoprocessing.XPZLIB contains detailed data content and well-organized data structures that are user-and developer-friendly.Three typical XPZLIBs with different numbers of energy groups,nuclides,and depletion reaction types were released via the Tsinghua cloud website.Furthermore,the applicability of the released XPZLIBs was investigated using HTGR and PWR lattice calculations,which can provide guidance for applying XPZLIB under different scenarios.
基金supported by the National Natural Science Foundation of China(Nos.12105170,12135008)Science and Technology on Reactor System Design Technology Laboratory.
文摘The accurate modeling of depletion,intricately tied to the solution of the neutron transport equation,is crucial for the design,analysis,and licensing of nuclear reactors and their fuel cycles.This paper introduces a novel multi-group Monte-Carlo depletion calculation approach.Multi-group cross-sections(MGXS)are derived from both 3D whole-core model and 2D fuel subassembly model using the continuous-energy Monte-Carlo method.Core calculations employ the multi-group Monte-Carlo method,accommodating both homogeneous and specific local heterogeneous geometries.The proposed method has been validated against the MET-1000 metal-fueled fast reactors,using both the OECD/NEA benchmark and a new refueling benchmark introduced in this paper.Our findings suggest that microscopic MGXS,produced via the Monte-Carlo method,are viable for fast reactor depletion analyses.Furthermore,the locally heterogeneous model with angular-dependent MGXS offers robust predictions for core reactivity,control rod value,sodium void value,Doppler constants,power distribution,and concentration levels.
基金supported by Japan Society for the Promotion of Science (Grant Scientific Research (c), No. 24540219 to the first author, JSPS Fellows, No.237213 to the second author, and No. 222176 to the third author)
文摘In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].
基金supported by the Science and Technology Development Foundation of CAEP(No.2015B0103014)the National Natural Science Foundation of China(No.11605163)
文摘Muon tomography is a capable imaging technique to measure the geometry of high-Z objects. However,most existed algorithms used in muon tomography have obscured the effects of angular distribution and momentum spectra of cosmic ray muons and reduced the spatial resolution. We present a modified multi-group model that takes into account these effects and calibrates the model by the material of lead. Performance tests establish that the model is capable of measuring the thickness of a Pb slab and identifying the material of an unknown slab on a reasonable exposure timescale, in both cases of complete and incomplete angular data. Results show that the modified multi-group model is helpful for improvements in image resolution in real applications.
基金Project supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2010526)the Six Projects Sponsoring Talent Summits of Jiangsu Province, China (Grant No. SJ209006)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103223110003)the Ministry of Education Research in the Humanities and Social Sciences Planning Fund of China (Grant No. 12YJAZH120)the Graduate Student Innovation Research Project of Jiangsu Province, China (Grant Nos. CXLX11 0417 and CXLX11 0404)
文摘In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR （susceptible-infected-quarantined-removed） model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.
基金Project supported by the National Natural Science Foundation of China (Grant No.50608069)
文摘To overcome the default of single search tendency, the ants in the colony are divided into several sub-groups. The ants in different subgroups have different trail information and expectation coefficients. The simulated annealing method is introduced to the algorithm. Through setting the temperature changing with the iterations, after each turn of tours, the solution set obtained by the ants is taken as the candidate set. The update set is obtained by adding the solutions in the candidate set to the previous update set with the probability determined by the temperature. The solutions in the candidate set are used to update the trail information. In each turn of updating, the current best solution is also used to enhance the trail information on the current best route. The trail information is reset when the algorithm is in stagnation state. The computer experiments demonstrate that the proposed algorithm has higher stability and convergence speed.
基金The work was supported by NSF of China(11801041,11871473)Foudation of Jilin Province Science and Technology Development(20190201130JC)+1 种基金Scientific Rsearch Foundation of Jilin Provincial Education Department(JJKH20181172KJ,JJKH20190503KJ)Natural Science Foundation of Changchun Normal University.
文摘In this paper,a stochastic multi-group AIDS model with saturated incidence rate is studied.We prove that the system is persistent in the mean under some parametric restrictions.We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function.Our results indicate that the existence of ergodic stationary distribution does not rely on the interior equilibrium of the corresponding deterministic system,which greatly improves upon previous results.
基金Acknowledgments This work was supported by the National Natural Science Foundation of China Grant 61273126, and the Natural Science Foundation of Guangdong Province Under Grants 10251064101000008 and S201210009675, the Fundamental Research Funds for the Central Universities 2012ZM0059, and Research Fund for the Doctoral Program of Higher Education of China under grant 20130172110027.
文摘We establish a stochastic differential equation epidemic model of multi-group SIR type based on the deterministic multi-group SIR mode. Then, we define the basic reproduction number R0^S and show that it is a sharp threshold for the dynamic of the stochastic multi-group SIR model. More specially, if R0^S 〈 1, then the disease-free equilibrium will be asymptotically stable which means the disease will die out, if R0^S 〉 1, the disease-free equilibrium will unstable, and our model will positively recurrence to a positive domain which implies the persistence of our model. Numerical simulation examples are carried out to substantiate the analytical results.
文摘In this study, based differential equations methods are used to solve equations because these methods are dependent on boundary value data more than other mathematical equations. We have calculated neutron flux, criticality and geometrical eigenvalue by using multi-group method and solving the neutron diffusion equation for finite and infinite cylindrical and spherical reactors in this study. For the calculation of the total neutron flux cross sections, we need the neutron diffusion equation. Thus, we have established the relationship between neuron flow and cross-section of neuron depending on neutron energy. Critical calculations have been made by comparing the results with MNCP (montecarlo n-partical) simulation methods. For necessary computer calculations, the programme, Wolfram-Matematica-7 has been used.
基金the Shanxi Province Science and Technology Project(Grant number:2014091003-0106).
文摘Background:Understanding the spatial pattern and driving factors of forest carbon density in mountainous terrain is of great importance for monitoring forest carbon in support of sustainable forest management for mitigating climate change.Methods:We collected the forest inventory data in 2015 in Shanxi Province,eastern Loess Plateau of China,to explore the spatial pattern and driving factors of biomass carbon density(BCD)for natural and planted coniferous forests using Anselin Local Moran’s I,Local Getis-Ord G*and semivariogram analyses,and multi-group structural equation modeling,respectively.Results:The result of spatial pattern of BCDs for natural forests showed that the BCD was generally higher in the north but lower in the south of Shanxi.The spatial pattern for planted forests was substantially different from that for natural forests.The results of multi-group SEM suggested that elevation(or temperature as the alternative factor of elevation)and stand age were important driving factors of BCD for these two forest types.Compared with other factors,the effects of latitude and elevation on BCD showed much greater difference between these two forest types.The difference in indirect effect of latitude(mainly through affecting elevation and stand age)between natural and planted forests was to some extent a reflection of the difference between the spatial patterns of BCDs for natural and planted forests in Shanxi.Conclusions:The natural coniferous forests had a higher biomass carbon density,a stronger spatial dependency of biomass carbon density relative to planted coniferous forests in Shanxi.Elevation was the most important driving factor,and the effect on biomass carbon density was stronger for natural than planted coniferous forests.Besides,latitude presented only indirect effect on it for the two forest types.
文摘BACKGROUND Early thrombolytic therapy is crucial to treat acute cerebral infarction,especially since the onset of thrombolytic therapy takes 1-6 h.Therefore,early diagnosis and evaluation of cerebral infarction is important.AIM To investigate the diagnostic value of magnetic resonance multi-delay threedimensional arterial spin labeling(3DASL)and diffusion kurtosis imaging(DKI)in evaluating the perfusion and infarct area size in patients with acute cerebral ischemia.METHODS Eighty-four patients who experienced acute cerebral ischemia from March 2019 to February 2021 were included.All patients in the acute stage underwent magnetic resonance-based examination,and the data were processed by the system’s own software.The apparent diffusion coefficient(ADC),average diffusion coefficient(MD),axial diffusion(AD),radial diffusion(RD),average kurtosis(MK),radial kurtosis(fairly RK),axial kurtosis(AK),and perfusion parameters post-labeling delays(PLD)in the focal area and its corresponding area were compared.The correlation between the lesion area of cerebral infarction under MK and MD and T2-weighted imaging(T2WI)was analyzed.RESULTS The DKI parameters of focal and control areas in the study subjects were compared.The ADC,MD,AD,and RD values in the lesion area were significantly lower than those in the control area.The MK,RK,and AK values in the lesion area were significantly higher than those in the control area.The MK/MD value in the infarct lesions was used to determine the matching situation.MK/MD<5 mm was considered matching and MK/MD≥5 mm was considered mismatching.PLD1.5s and PLD2.5s perfusion parameters in the central,peripheral,and control areas of the infarct lesions in MK/MD-matched and-unmatched patients were not significantly different.PLD1.5s and PLD2.5s perfusion parameter values in the central area of the infarct lesions in MK/MD-matched and-unmatched patients were significantly lower than those in peripheral and control areas.The MK and MD maps showed a lesion area of 20.08±5.74 cm^(2) and 22.09±5.58 cm^(2),respectively.T2WI showed a lesion area of 19.76±5.02 cm^(2).There were no significant differences in the cerebral infarction lesion areas measured using the three methods.MK,MD,and T2WI showed a good correlation.CONCLUSION DKI parameters showed significant difference between the focal and control areas in patients with acute ischemic cerebral infarction.3DASL can effectively determine the changes in perfusion levels in the lesion area.There was a high correlation between the area of the infarct lesions diagnosed by DKI and T2WI.
文摘In this paper, we present a method for finding the solution of the linear multi-delay systems (MDS) by using the hybrid of the Block-Pulse functions and the Bernoulli polynomials. In this approach, the MDS is reduced to a system of linear algebraic equations by expanding various time functions for the hybrid functions and using operational matrices. To demonstrate the validity and the applicability of the technique, some examples are presented.
文摘The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons,which describes the spectrum behavior of neutron density into the homogenous nuclear reactors, is developed. This system is one of the most important stiff coupled nonlinear fractional differentials for nuclear reactor dynamics. The generalization of Taylor's formula that involves Caputo fractional derivatives is developed in an attempt to overcome the difficulty of the stiffness of the nonlinear fractional differential model. Moreover, the general fractional derivatives are calculated analytically throughout this work. Furthermore, the local and global estimated errors were analyzed, which suggest that the error quantification should take into account the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error(local truncation error). The neutron density response with time is analyzed for the anomalous diffusion, sub-diffusion, and super-diffusion processes.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60604007 and 50775226)
文摘In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.
基金supported by the National Natural Science Foundation of China(No.12022113)Henry Fok Foundation for Young Teachers,China(No.171002)+2 种基金Outstanding Young Talents Support Plan of Shanxi Province,Science and Engineering Research Board(SERB for short),India(No.ECR/2017/002786)UGC-BSR Research Start-Up-Grant,India(No.F.30-356/2017(BSR))Senior Research Fellowship from the Council of Scientific and Industrial Research(CSIR for short),India(No.09/1131(0006)/2017-EMR-I)。
文摘Consider the heterogeneity(e.g.,heterogeneous social behaviour,heterogeneity due to different geography,contrasting contact patterns and different numbers of sexual partners etc.)of host population,in this paper,the authors propose an infection age multigroup SEIR epidemic model.The model system also incorporates the feedback variables,where the infectivity of infected individuals may depend on the infection age.In the direction of mathematical analysis of model,the basic reproduction number R_0 has been computed.The global stability of disease-free equilibrium and endemic equilibrium have been established in the term of R_(0).More precisely,for R_(0)≤1,the disease-free equilibrium is globally asymptotically stable and for R_(0)>1,they establish global stability of endemic equilibrium using some graph theoretic techniques to Lyapunov function method.By considering a numerical example,they investigate the effects of infection age and feedback on the prevalence of the disease.Their result shows that feedback parameters have different and even opposite effects on different groups.However,by choosing an appropriate value of feedback parameters,the disease could be eradicated or maintained at endemic level.Besides,the infection age of infected individuals may also change the behaviour of the disease,global stable to damped oscillations or damped oscillations to global stable.
基金the National Natural Science Foundation of China(No.813716234)the National Basic Research Program(973)of China(No.2010CB834302)Shanghai Jiao Tong University Medical Engineering Cross Research Funds(Nos.YG2013MS30 and YG2014ZD05)
文摘Computed tomography(CT) reconstruction with a well-registered priori magnetic resonance imaging(MRI) image can improve reconstruction results with low-dose CT, because well-registered CT and MRI images have similar structures. However, in clinical settings, the CT image of patients does not always match the priori MRI image because of breathing and movement of patients during CT scanning. To improve the image quality in this case, multi-group datasets expansion is proposed in this paper. In our method, multi-group CT-MRI datasets are formed by expanding CT-MRI datasets. These expanded datasets can also be used by most existing CT-MRI algorithms and improve the reconstructed image quality when the CT image of a patient is not registered with the priori MRI image. In the experiments, we evaluate the performance of the algorithm by using multi-group CT-MRI datasets in several unregistered situations. Experiments show that when the CT and priori MRI images are not registered, the reconstruction results of using multi-group dataset expansion are better than those obtained without using the expansion.
文摘In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.
文摘In this paper, we investigate the threshold dynamics of a multi-group SEAR alcoholism epidemic model with public health education. The multi-group model allows us to describe interactions both within-group and inter-group separately. We prove that the basic reproduction number R0 plays the role of a threshold for the long-time behavior of the model. The alcohol-free equilibrium P0 of the model is globally asymptotically stable if R0≤1,while the alcohol-present equilibrium P* exists uniquely and is globally asymptotically stable if R0>1.For the proofs of main results, we use the classical method of Lyapunov functions and apply subtle grouping technique in estimating the derivatives of Lyapunov functions guided by graph theory. Our results expand the previous results which have been obtained in single-group models. Sensitivity analysis and numerical simulations are also performed to illustrate our results.
文摘In this paper, by applying Lyapunov functional approach, we establish a sufficient condition on the global stability of a ＂delayed＂ multi-group SIRS epidemic model with cure rate and incomplete recovery rate which does not depend on the delays and is an extension of the ＂light drug model＂ studied in the recent paper [Muroya, Li and Kuniya, Complete global analysis of an SIRS epidemic model with graded cure rate and incomplete recovery rate, J. Math. Anal. Appl. 410 （2014） 719-732] to a multi-group model. Applying a Lyapunov functional on total population of each compartment, we offer new techniques for the delayed system, how to prove the permanence, the existence of the endemic equilibrium and the global stability of disease-free equilibrium for the reproduction number R0 ≤ 1 and endemic equilibrium forR0 ≥ 1.
基金Supported by National Natural Science Foundation of China (10875042)Fundamental Research Funds for The Central Universities (10ZG08)Program for New Century Excellent Talents in University
文摘ENDF/B-Ⅶ.0, which was released by the USA Cross Section Evaluation Working Group （CSEWG） in December 2006, was demonstrated to perform much better than previous ENDF evaluations over a broad range of benchmark experiments. A high-energy （up to 150 MeV） multi-group library set named HEST1.0 with 253-neutron and 48-photon groups has been developed based on ENDF/B-Ⅶ.0 using the N JOY code. This paper provides a summary of the procedure to produce the library set and a detailed description of the verification of the multi-group library set by several shielding benchmark devices, in particular for high-energy neutron data. In addition, the first application of HEST1.0 to the shielding design of the China Spallation Neutron Source （CSNS） is demonstrated.
