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The effect of dispersal on a predator-prey model with Holling type-Ⅱ functional response
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作者 WANG Ling-shu ZHANG Mei +1 位作者 ZHANG Ya-nan WANG Yan 《Applied Mathematics(A Journal of Chinese Universities)》 2025年第3期602-616,共15页
A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By... A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By analyzing the corresponding characteristic equations,the local stability of each of the nonnegative equilibria is discussed.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the positive equilibrium,the nonnegative boundary equilibrium and the trivial equilibrium of the model,respectively.Numerical simulations are carried out to illustrate the main results. 展开更多
关键词 predator-prey model dispersal Holling type-Ⅱfunctional response time delay STAGE-STRUCTURE STABILITY
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Stability Analysis of an Epidemic Predator-Prey Model with Prey Dispersal and Holling Type-Ⅱ Functional Response
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作者 Lingshu WANG Mei ZHANG Ya-nan ZHANG 《Journal of Mathematical Research with Applications》 2025年第2期179-194,共16页
This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing ... This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the coexistence equilibrium is addressed. Using Lyapunov functionals and LaSalle's invariance principle, we obtained the sufficient conditions for the global stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the coexistence equilibrium, respectively. The paper also includes numerical simulations to illustrate the analytical results. 展开更多
关键词 predator-prey model dispersal Holling type-II functional response Hopf bifurcation stability
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Bifurcation and Turing Pattern Formation in a Diffusion Modified Leslie-Gower Predator-Prey Model with Crowley-Martin Functional Response
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作者 Dong Wang Yani Ma 《Journal of Applied Mathematics and Physics》 2024年第6期2190-2211,共22页
In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term.... In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results. 展开更多
关键词 Modified Leslie-Gower Model Crowley-Martin function response Hopf Bifurcation Transcritical Bifurcation Turing Instability
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EXISTENCE OF POSITIVE SOLUTION FOR A TWO-PATCHES COMPETITION SYSTEM WITH DIFFUSION AND TIME DELAY AND FUNCTIONAL RESPONSE 被引量:12
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作者 Li Biwen Zeng Xianwu 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第1期1-8,共8页
By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t... By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t)-b_(1)(t)x_(1)(t)-c_(1)(t)y(t)1+m(t)x_(1)(t)+D_(1)(t)[x_(2)(t)-x_(1)(t)],x_(2)(t)=x_(2)(t)a_(2)(t)-b_(2)(t)x_(2)(t)-c_(2)(t)∫^(0)_(-τ)k(s)x_(2)(t+s)d s+D_(2)(t)[x_(1)(t)-x_(2)(t)],y′(t)=y(t)a_(3)(t)-b_(3)(t)y(t)-c_(3)(t)x_(1)(t)1+m(t)x_(1)(t)is established,where a i(t),b_(i)(t),c_(i)(t)(i=1,2,3),m(t)and D_(i)(t)(i=1,2)are all positive periodic continuous functions with period w>0,τis a nonnegative constant and k(s)is a continuous nonnegative function on[-τ,0]. 展开更多
关键词 periodic solutions competition diffusive system functional response continuation theorem of coincidence degree topological degree
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Mechanism of Functional Responses to Loading of Carbon Fiber Reinforced Cement-based Composites 被引量:6
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作者 JIANG Cuixiang LI Zhuoqiu +1 位作者 SONG Xianhui LU Yong 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2008年第4期571-573,共3页
Single fiber pull-out testing was conducted to study the origin of the functional responses to loading of carbon fiber reinforced cement-based composites. The variation of electrical resistance with the bonding force ... Single fiber pull-out testing was conducted to study the origin of the functional responses to loading of carbon fiber reinforced cement-based composites. The variation of electrical resistance with the bonding force on the fiber-matrix interface was measured. Single fiber electromechanical testing was also conducted by measuring the electrical resistance under static tension. Comparison of the results shows that the resistance increasing during single fiber pull-out is mainly due to the changes at the interface. The conduction mechanism of the composite can be explained by the tunneling model. The interfacial stress causes the deformation of interfacial structure and the interfacial debonding, which have influences on the tunneling effect and result in the change of resistance. 展开更多
关键词 carbon fiber functional response tunneling effect single pull-out CEMENT
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Effects of Temperature on Functional Response of Anagrus nilaparvatae Pang et Wang (Hymenoptera:Mymaridae) on the Eggs of Whitebacked Planthopper,Sogatella furcifera Horvth and Brown Planthopper,Nilaparvata lugens Stl 被引量:4
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作者 MA Ming-yong PENG Zhao-pu HE Yuan 《Journal of Integrative Agriculture》 SCIE CAS CSCD 2012年第8期1313-1320,共8页
Understanding the temperature affecting parasitic efficiency is critical to succeed in utilizing parasitoid as natural enemy in pest management. Laboratory studies were carried out to determine the effects of temperat... Understanding the temperature affecting parasitic efficiency is critical to succeed in utilizing parasitoid as natural enemy in pest management. Laboratory studies were carried out to determine the effects of temperature on parasitoid preference of female Anagrus nilaparvatae Pang et Wang (Hymenoptera:Mymaridae) to the eggs of whitebacked planthopper (WBPH), Sogatella furcifera Horváth and brown planthopper (BPH), Nilaparvata lugens Stl to build a composite model describing changes in parasitic response along a temperature gradient (18, 22, 26, 30, 34°C). The results showed that attack responses of A. nilaparvatae on WBPH and BPH were the best described by a Type II functional response. The two parameters, attack rates (a) and handling times (Th), of A. nilaparvatae to both eggs were influenced by the temperature. The maximum attack rates to WBPH (1.235) and BPH (1.049) were at 26 and 34°C, respectively, and the shortest handling times to WBPH (0.063) and BPH (0.057) were at 30 and 26°C, respectively. However, the optimal temperature for parasitic efficiency of A. nilaparvatae to WBPH and BPH eggs was both at 26°C, which showed that the present microclimate temperature of the habitat in the paddyfield was beneficial to A. nilaparvatae and indicated that parasitic efficiency of A. nilaparvatae would be impaired by global warming. 展开更多
关键词 functional response TEMPERATURE Anagrus nilaparvatae whitebacked planthopper brown planthopper
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Crack detection using a frequency response function in offshore platforms 被引量:4
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作者 ZHANG Zhao-de CHEN Shuai 《Journal of Marine Science and Application》 2007年第3期1-5,共5页
Structural cracks can change the frequency response function (FRF) of an offshore platform. Thus, FRF shifts can be used to detect cracks. When a crack at a specific location and magnitude occurs in an offshore struct... Structural cracks can change the frequency response function (FRF) of an offshore platform. Thus, FRF shifts can be used to detect cracks. When a crack at a specific location and magnitude occurs in an offshore structure, changes in the FRF can be measured. In this way, shifts in FRF can be used to detect cracks. An experimental model was constructed to verify the FRF method. The relationship between FRF and cracks was found to be non-linear. The effect of multiple cracks on FRF was analyzed, and the shift due to multiple cracks was found to be much more than the summation of FRF shifts due to each of the cracks. Then the effects of noise and changes in the mass of the jacket on FRF were evaluated. The results show that significant damage to a beam can be detected by dramatic changes in the FRF, even when 10% random noise exists. FRF can also be used to approximately locate the breakage, but it can neither be efficiently used to predict the location of breakage nor the existence of small hairline cracks. The FRF shift caused by a 7% mass change is much less than the FRF shift caused by the breakage of any beam, but is larger than that caused by any early cracks. 展开更多
关键词 offshore platform crack detection numerical simulation frequency response function
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Research on the iterative method for model updating based on the frequency response function 被引量:3
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作者 Wei-Ming Li Jia-Zhen Hong 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第2期450-457,共8页
Model reduction technique is usually employed in model updating process. In this paper, a new model updat- ing method named as cross-model cross-frequency response function (CMCF) method is proposed and a new iterat... Model reduction technique is usually employed in model updating process. In this paper, a new model updat- ing method named as cross-model cross-frequency response function (CMCF) method is proposed and a new iterative method associating the model updating method with the mo- del reduction technique is investigated. The new model up- dating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency re- sponse function, which could greatly increase the number of the equations and the updating parameters. Based on the traditional iterative method, a correction term related to the errors resulting from the replacement of the reduction ma- trix of the experimental model with that of the finite element model is added in the new iterative method. Comparisons be- tween the traditional iterative method and the proposed itera- tive method are shown by model updating examples of solar panels, and both of these two iterative methods combine the CMCF method and the succession-level approximate reduc- tion technique. Results show the effectiveness of the CMCF method and the proposed iterative method . 展开更多
关键词 Model updating Model reduction Frequency response function ITERATION
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Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function 被引量:3
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作者 徐丽 易伟建 易志华 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2007年第2期183-189,共7页
Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables,... Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function (FRF). The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete flame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location. 展开更多
关键词 frequency response function UNCERTAINTY strain mode Bayesian method local damage damage detection concrete flame
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Dynamics Analysis of Active Variable Stiffness Vibration Isolator for Whole-Spacecraft Systems Based on Nonlinear Output Frequency Response Functions 被引量:3
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作者 Kefan Xu Yewei Zhang +2 位作者 Yunpeng Zhu Jian Zang Liqun Chen 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2020年第6期731-743,共13页
In order to improve the harsh dynamic environment experienced by heavy rockets during different external excitations,this study presents a novel active variable stiffness vibration isolator(AVS-VI)used as the vibratio... In order to improve the harsh dynamic environment experienced by heavy rockets during different external excitations,this study presents a novel active variable stiffness vibration isolator(AVS-VI)used as the vibration isolation device to reduce excessive vibration of the whole-spacecraft isolation system.The AVS-VI is composed of horizontal stiffness spring,positive stiffness spring,parallelogram linkage mechanism,piezoelectric actuator,acceleration sensor,viscoelastic damping,and PID active controller.Based on the AVS-VI,the generalized vibration transmissibility determined by the nonlinear output frequency response functions and the energy absorption rate is applied to analyze the isolation performance of the whole-spacecraft system with AVS-VI.The AVS-VI can conduct adaptive vibration suppression with variable stiffness to the whole-spacecraft system,and the analysis results indicate that the AVS-VI is efTective in reducing the extravagant vibration of the whole-spacecraft system,where the vibration isolation is decreased up to above 65%under different acceleration excitations.Finally,different parameters of AVS-VI are considered to optimize the whole-spacecraft system based on the generalized vibration transmissibility and the energy absorption rate. 展开更多
关键词 Vibration isolation Active variable stiffness vibration isolator Nonlinear output frequency response functions(NOFRFs) TRANSMISSIBILITY
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Existence of Equilibrium Solutions to a Size-Structured Predator-Prey System with Functional Response 被引量:1
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作者 LIU Keying LIU Weian 《Wuhan University Journal of Natural Sciences》 CAS 2009年第5期383-387,共5页
In this paper,we consider a nonlinear size-structured population model with functional response,which describes the dynamics of a predator-prey system living in a common habitat.We present a kind of functional respons... In this paper,we consider a nonlinear size-structured population model with functional response,which describes the dynamics of a predator-prey system living in a common habitat.We present a kind of functional response for the prey being a plant or algae,and explain its biological meanings.When the vital rates depend both on the individual's size and on the total population or only depend on the former,we obtain the existence of equilibrium solutions. 展开更多
关键词 equilibrium solutions functional response predator-prey system size-structured population model
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The Global Stability of Predator-Prey System of Gause-Type with Holling Ⅲ Functional Response 被引量:1
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作者 Feng Jian\|wen, Zen Xian\|wu College of Mathematics and Computer Sicence, Wuhan University, Wuhan 430072,China 《Wuhan University Journal of Natural Sciences》 CAS 2000年第3期271-277,共7页
This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac'... This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac's criterion is applied and lia punov functions are constructed to establish the global stability. 展开更多
关键词 global stability functional response predtor\|prey system limit cycle
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Protection zone in a diffusive predator-prey model with Ivlev-type functional response 被引量:1
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作者 ZHANG Li-na XU Fei 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2020年第4期437-451,共15页
The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcati... The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcation theory.It is shown that the protection zone for prey has beneficial effects on the coexistence of the two species when the growth rate of predator is positive.Moreover,we examine the dependence of the coexistence region on the efficiency of the predator capture of the prey and the protection zone. 展开更多
关键词 Ivlev-type functional response protection zone BIFURCATION
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Uniform persistence of multispecies ecological competition predator-pray system with Holling Ⅲ type functional response 被引量:1
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作者 LI Zhan LI Ling-xiao WANG Ke 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第4期410-412,共3页
The main purpose of this paper is to study the persistence of the general multispecies competition predator-pray system with Holling Ⅲ type functional response. In this system, the competition among predator species ... The main purpose of this paper is to study the persistence of the general multispecies competition predator-pray system with Holling Ⅲ type functional response. In this system, the competition among predator species and among prey species are simultaneously considered. By using the comparison theory and qualitative analysis, the sufficient conditions for uniform strong persistence are obtained. 展开更多
关键词 competition predator-pray system Holling type functional response persistence
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Board-invited review: Sensitivity and responses of functional groups to feed processing methods on a molecular basis 被引量:2
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作者 Peiqiang Yu 《Journal of Animal Science and Biotechnology》 SCIE CAS 2013年第1期1-4,共4页
In complex feed structures, there exist main chemical functional groups which are associated with nutrient utilization and availability and functionality. Each functional group has unique molecular structure therefore... In complex feed structures, there exist main chemical functional groups which are associated with nutrient utilization and availability and functionality. Each functional group has unique molecular structure therefore produce unique molecular vibration spectral profile. Feed processing has been used to improve nutrient utilization for many years. However, to date, there was little study on processing-induced changes of feed intrinsic structure and functional groups on a molecular basis within intact tissue. This is because limited research technique is available to study inherent structure on a molecular basis. Recently bioanalytical techniques: such as Synchrotron Infrared Microspectroscopy as well as Diffuse Reflectance Infrared Fourier Transform molecular spectroscopy have been developed. These techniques enable to detect molecular structure change within intact tissues. These techniques can prevent destruction or alteration of the intrinsic protein structures during processing for analysis. However, these techniques have not been used in animal feed and nutrition research. The objective of this review was show that with the advanced technique, sensitivity and responses of functional groups to feed processing on a molecular basis could be detected in my research team. These functional groups are highly associated with nutrient utilization in animals. 展开更多
关键词 Sensitivity and responses of functional groups Molecular structures Feed processing Nutrient utilizationand availability
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On the dielectric response function and dispersion relation in strongly coupled magnetized dusty plasmas 被引量:1
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作者 M Shahmansouri N Khodabakhshi 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第10期465-470,共6页
Using the generalized viscoelastic fluid model, we derive the dielectric response function in a strongly coupled dusty magnetoplasma which reveals two different dust acoustic(DA) wave modes in the hydrodynamic and k... Using the generalized viscoelastic fluid model, we derive the dielectric response function in a strongly coupled dusty magnetoplasma which reveals two different dust acoustic(DA) wave modes in the hydrodynamic and kinetic limits. The effects of the strong interaction of dust grains and the external magnetic on these DA modes, as well as on the shear wave are examined. It is found that both the real and imaginary parts of DA waves are significantly modified in strongly coupled dusty magnetoplasmas. The implications of our results to space and laboratory dusty plasmas are briefly discussed. 展开更多
关键词 dusty plasma strongly coupled plasma MAGNETOPLASMA dielectric response function
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DiriNet:An Estimation Network for Spectral Response Function and Point Spread Function 被引量:1
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作者 Ting Hu Siyuan Cheng Chang Liu 《Journal of Beijing Institute of Technology》 EI CAS 2024年第4期287-297,共11页
Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few wo... Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few works have been payed on the estimation of the two degra-dation functions.To learn the two functions from image pairs to be fused,we propose a Dirichletnetwork,where both functions are properly constrained.Specifically,the spatial response function isconstrained with positivity,while the Dirichlet distribution along with a total variation is imposedon the point spread function.To the best of our knowledge,the neural network and the Dirichlet regularization are exclusively investigated,for the first time,to estimate the degradation functions.Both image degradation and fusion experiments demonstrate the effectiveness and superiority of theproposed Dirichlet network. 展开更多
关键词 Dirichlet network point spread function spectral response function hyper-spectralimage multi-spectral image
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A Study on Ionospheric HF Channel with Bitemporal Response and Scattering Function 被引量:1
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作者 Chong Yan-wen Xie Shu-guo +2 位作者 Zhao Zheng-yu Huang Tian-xi Yao Yong-gang 《Wuhan University Journal of Natural Sciences》 CAS 2000年第3期317-319,共3页
At first the bitemporal response method is introduced to solve the scattering function of the ionospeeric channel. We can get the scattering function, as a function, of the group path time delay and Doppler frequency.... At first the bitemporal response method is introduced to solve the scattering function of the ionospeeric channel. We can get the scattering function, as a function, of the group path time delay and Doppler frequency. Thus Doppler effect resulting from the continuous movement of the ionosphere is analyzed to study the characteristics of the various ionospheric irregularities and diturbance. many possible problems and correction are researched lastly. 展开更多
关键词 bitemporal response function scattering function the Doppler effect the movement of the ionosphere
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TLR signaling that induces weak inflammatory response and SHIP1 enhances osteogenic functions 被引量:2
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作者 Manoj Muthukuru Richard P Darveau 《Bone Research》 SCIE CAS 2014年第4期218-230,共13页
Toll-like receptor (TLR)-mediated inflammatory response could negatively affect bone metabolism. In this study, we determined how osteogenesis is regulated during inflammatory responses that are downstream of TLR si... Toll-like receptor (TLR)-mediated inflammatory response could negatively affect bone metabolism. In this study, we determined how osteogenesis is regulated during inflammatory responses that are downstream of TLR signaling. Human primary osteoblasts were cultured in collagen gels. Pam3CSK4 (P3C) and Escherichia coli lipopolysaccharide (EcLPS) were used as TLR2 and TLR4 ligand respectively. Porphyromonas gingivalis LPS having TLR2 activity with either TLR4 agonism (Pg1690) or TLR4 antagonism (Pg1449) and mutant E. coli LPS (LPxE/LPxF/WSK) were used. IL-lp, SH2-containing inositol phosphatase-1 (SHIP1) that has regulatory roles in osteogenesis, alkaline phosphatase and mineralization were analyzed. 3α-Aminocholestane (3AC) was used to inhibit SHIP1. Our results suggest that osteoblasts stimulated by P3C, poorly induced IL-1β but strongly upregulated SHIP1 and enhanced osteogenic mediators. On the contrary, EcLPS significantly induced IL-1β and osteogenic mediators were not induced. While Pg1690 downmodulated osteogenic mediators, Pg1449 enhanced osteogenic responses, suggesting that TLR4 signaling annuls osteogenesis even with TLR2 activity. Interestingly, mutant E. coli LPS that induces weak inflammation upregulated osteogenesis, but SHIP1 was not induced. Moreover, inhibiting SHIP1 significantly upregulated TLR2-mediated inflammatory response and downmodulated osteogenesis. In conclusion, these results suggest that induction of weak inflammatory response through TLR2 (with SHIP1 activity) and mutant TLR4 ligands could enhance osteogenesis. 展开更多
关键词 TLR signaling that induces weak inflammatory response and SHIP1 enhances osteogenic functions SHIP FIGURE
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Nutrient Response Functions of Sorghum for Miesso District Central Rift Valley of Ethiopia 被引量:1
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作者 Israel Bekele Mesfin Hundessa Bahiru Tilahun 《Agricultural Sciences》 2022年第1期33-48,共16页
This study was executed to offer the basis for optimized profit from fertilizer use for sorghum yield and to determine robust crop nutrient response function and economic rate for the production of sorghum at Miesso C... This study was executed to offer the basis for optimized profit from fertilizer use for sorghum yield and to determine robust crop nutrient response function and economic rate for the production of sorghum at Miesso Central Rift Valley of Ethiopia. Trails were conducted at six experimental sites, sorghum yield response to N and P fertilizers application and economically optimum rates of nitrogen (EONR) and phosphorus (EOPR) were evaluated on a vertisols within the semi-arid Miesso districts west Hararge zone of Oromia region. The nutrient rates in 2014 cropping season four levels of Nitrogen (N) alone, these levels with 20 <span style="white-space:nowrap;">kg&#183;ha<sup>&#8722;1</sup></span> Phosphorus (P) and without N, 69 kg<span style="white-space:nowrap;">&#183;</span>ha<sup><span style="white-space:nowrap;">&#8722;</span>1</sup> N with three levels of P treatments including the zero control were evaluated. In 2015, cropping season similar rates of N alone, the same rate N with 20 <span style="white-space:nowrap;">kg&#183;ha<sup>&#8722;1</sup></span> P, 92 <span style="white-space:nowrap;">kg&#183;ha<sup>&#8722;1</sup></span> N with three rates of P including the zero control were evaluated. The treatments were arranged in a randomized complete block with three replications in factorial design. Nutrient responses of sorghum were determined using asymptotic quadratic plateau functions. The significantly highest nitrogen rate was 46 <span style="white-space:nowrap;">kg&#183;ha<sup>&#8722;1</sup></span> alone in 2014 season, which gave grain yield of 2.56 Mg<span style="white-space:nowrap;">&#183;ha<sup>&#8722;1</sup></span><sup> </sup>with a maximum yield advantage of 43%. P rates in both seasons and combined (sites + seasons) were not significantly influenced sorghum yield. Nitrogen agronomic and partial factor productivity peaked at 23 kg N <span style="white-space:nowrap;">ha<sup>&#8722;1</sup></span> but declined with increasing N rate. The EONR combined (sites + seasons) were 37, 45, 52 and 60 <span style="white-space:nowrap;">kg&#183;ha<sup>&#8722;1</sup></span><sup> </sup>and for the profit to cost ratio (PCR) were 2.43, 3.65, 4.86 and 5.79 at difference cost to grain price ratios (CP) = 3.6, 2.3, 1.6 and 1.2 respectively at Miesso Ethiopia. Nitrogen application had economically profitable than P. The study concluded that the application of N at 37 or 60 kg N <span style="white-space:nowrap;">ha<sup>&#8722;1</sup></span> to sorghum production could be economically profitable for those economically constrained farmers or economically not constrained farmers. Validation should be farther conducted on farmers’ fields for refining the results obtained. 展开更多
关键词 SORGHUM response function Economically Optimum Rates Nutrient Use Efficiency Cost to Grain Price Ratio Ethiopia
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