A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global ...A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global dynamics is completely determined bythe basic reproductive number R（ψ）（ψ denotes per capita vaccination rate）. If R（0） 〈 1,the disease-free equilibrium is a global attractor; If R（ψ） 〈： 1, the disease-free equilibriumis locally asymptotically stable; If R（ψ） ：〉 1, an unique endemic equilibrium exists and islocally asymptotically stable under certain condition.展开更多
In this paper,we develop Gaussian quadrature formulas for the Hadamard fi- nite part integrals.In our formulas,the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate th...In this paper,we develop Gaussian quadrature formulas for the Hadamard fi- nite part integrals.In our formulas,the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate the density function f(x)so that the Gaussian quadrature formulas have degree n-1.The error estimates of the formulas are obtained.It is found from the numerical examples that the convergence rate and the accu- racy of the approximation results are satisfactory.Moreover,the rate and the accuracy can be improved by choosing appropriate weight functions.展开更多
A new subclass A(β1 , β2 , ··· , βk ; λ) of analytic functions f(z) in the open unit disk U is introduced and studied. We provide coefficient inequalities, distortion theorems, extreme points and ra...A new subclass A(β1 , β2 , ··· , βk ; λ) of analytic functions f(z) in the open unit disk U is introduced and studied. We provide coefficient inequalities, distortion theorems, extreme points and radius of close-to-convexity, starlikeness and convexity of this class.展开更多
Recent work has established that digital images of a human face, when collected with a fixed pose but under a variety of illumination conditions, possess discriminatory information that can be used in classification. ...Recent work has established that digital images of a human face, when collected with a fixed pose but under a variety of illumination conditions, possess discriminatory information that can be used in classification. In this paper we perform classification on Grassmannians to demonstrate that sufficient discriminatory information persists in feature patch (e.g., nose or eye patch) illumination spaces. We further employ the use of Karcher mean on the Grassmannians to demonstrate that this compressed representation can accelerate computations with relatively minor sacrifice on performance. The combination of these two ideas introduces a novel perspective in performing face recognition.展开更多
How to find efficient and secure member- ship revocation algorithms is one of the most important issues standing in the way of real-world applications of group signatures. In this paper, the proof of knowledge of divi...How to find efficient and secure member- ship revocation algorithms is one of the most important issues standing in the way of real-world applications of group signatures. In this paper, the proof of knowledge of divisibility is given and a novel membership revocation method in ACJT group signature scheme is proposed： the group manager issues the product E of the public keys of current members in the group, when a group member wants to sign, he should not only proves that he has a membership certificate, but also proves that the public key in his certificate divides exactly the public key product E with zero knowledge. The proposed method is efficient since the group manager only needs one division and one exponentiation when a group member is deleted, while the signing and verifying procedure are independent of the number of current group members and excluded members, as well as the original group public key and membership certificates needn＇t be changed.展开更多
In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonp...In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.展开更多
On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌...On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌H if G satisfies one of the following conditions. 1） G is a finite Abelian group. 2） The order of G is p^3. 3 ） The order of G is p^n＋1 and G has a cyclic normal subgroup N = 〈a〉 of order p^n. 4） G is a nilpotent group and if p^││G│, then for any P ∈ Sylp （G）, P has a cyclic maximal subgroup, where p is a prime; 5） G is a maximal class group of order p4（p〉3）.展开更多
The aim of this study was to evaluate the effects of silver nitrate in the in vitro development and conservation of passion fruit plants. Experiments were carried out at the Laboratory of Culture and Tissues, in the N...The aim of this study was to evaluate the effects of silver nitrate in the in vitro development and conservation of passion fruit plants. Experiments were carried out at the Laboratory of Culture and Tissues, in the National Cassava and Fruits Research Center (EMBRAPA), using microcuttings of Passiflora gibertii N. E. Br., previously cultivated in vitro. The microcuttings were placed in MS media supplemented with silver nitrate at concentrations of 0, 1, 2, 4 and 8 mg·L-1, and, during 30, 60 and 90 days, the following variables were identified: Shooting length (cm), number of roots, number and coloration of leaves. A completely randomized design with 30 replications in a split-plot scheme was employed. Polynomial regression equations were adjusted in analysis of variance to compare averages of treatments. The obtained results support the assumption of high sensitivity of passion fruit tissues to ethylene, which reflects in the lost of vigor and in the induction of culture senescence by its accumulation. Based on obtained results, and in order to mitigate this problem, it is possible to indicate an addition of 2 mg·L-1?of silver nitrate in culture media, for the micropropagation of passion fruit plant, allowing the controlling of the atmosphere inside the culture test tubes, during the establishment of explants and other steps of the process.展开更多
Antimicrobial resistance is a growing concern in the field of microbiology.In a microbial community,the Susceptible Subpopulations(SSs)and the Non-genetically Resistant Subpopulations(NRSs)can switch between each othe...Antimicrobial resistance is a growing concern in the field of microbiology.In a microbial community,the Susceptible Subpopulations(SSs)and the Non-genetically Resistant Subpopulations(NRSs)can switch between each other,and NRSs can mutate to Genetically Resistant Subpopulations(GRSs).In order to quantitatively describe the relationship between noise and signal amplification in the subpopulations,a mathematical model for three subpopulations is proposed in this paper.The gain fluctuation relation is obtained by linear noise approximation of the master equation.Then,through the simulation of these theoretical results,the following conclusions are found.First,the indirect effects of the interaction between subpopulations are much greater than the direct effects,which may be one of the reasons that the infection is dificult to cure.This is consistent with the findings of Zhou et al.and indicates the reliability of our new model.Second,the intrinsic net growth rate of SSs can be chosen as the adjustment parameter,which can effectively exploit or avoid the strong correlation between SSs and the two resistant subpopulations,including NRSs and GRSs.Third,unlike unidirectional cascades,additional intrinsic noise in GRSs can propagate to NRSs.Similarly,although there is no direct interaction between SSs and GRSs,additional intrinsic noise in GRSs can propagate to SSs,and vice versa.Finally,both total noise and adjusted noise exhibit similar amplification properties in this population.It is worth noting that the noise is consistently amplified from NRSs to GRSs.These findings may provide new insights into antimicrobial therapy.展开更多
In this paper, fractional order derivative, fractal dimension and spectral dimension are introduced into the seepage flow mechanics to establish the flow models of fluids in fractal reservoirs with the fractional deri...In this paper, fractional order derivative, fractal dimension and spectral dimension are introduced into the seepage flow mechanics to establish the flow models of fluids in fractal reservoirs with the fractional derivative. The flow characteristics of fluids through a fractal reservoir with the fractional order derivative are studied by using the finite integral transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions are obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation are also obtained. The pressure transient behavior of fluids flow through an infinite fractal reservoir is studied by using the Stehfest＇s inversion method of the numerical Laplace transform. It shows that the order of the fractional derivative affect the whole pressure behavior, particularly, the effect of pressure behavior of the early-time stage is larger The new type flow model of fluid in fractal reservoir with fractional derivative is provided a new mathematical model for studying the seepage mechanics of fluid in fractal porous media.展开更多
A formula on the complexity of the normal bases generated by prime Gauss period overfinite fields is presented in terms of cyclotomic numbers.Then,the authors determine explicitly thecomplexity of such normal bases an...A formula on the complexity of the normal bases generated by prime Gauss period overfinite fields is presented in terms of cyclotomic numbers.Then,the authors determine explicitly thecomplexity of such normal bases and their dual bases in several cases where the related cyclotomicnumbers have been calculated.Particularly,the authors find several series of such normal bases withlow complexity.展开更多
The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole.Here,we have extended the prior...The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole.Here,we have extended the prior work of Chen and Jing(S.Chen and J.Jing,JCAP,10:002(2015))for a Schwarzschild black hole to a Kiselev black hole.For this purpose,the equation of motion for the photons coupled to the Weyl tensor,null geodesic,and equation of photon sphere in a Kiselev black hole spacetime have been formulated.It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor,but also on the polarization direction of the photons.There is a critical value of the coupling parameter,α,for the existence of the marginally circular photon orbit outside the event horizon,which depends on the parameters of the black hole and the polarization direction of the photons.Further,the polarization directions of the coupled photons and the coupling parameter,α;both modify the features of the photon sphere,angle of deflection,and functions(^ˉa and^ˉb)owing to the strong gravitational lensing in the Kiselev black hole spacetime.In addition to this,the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.展开更多
This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characteri...This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characterization of the solutions involving some kind of Lagrange multipliers. The full discretization is achieved by combining the above operator-splitting methods with finite element approximations, the advection being treated by a wave-like equation 'equivalent' formulation easier to implement than the method of characteristics or high order upwinding methods. The authors illustrate the methodology discussed in this article with the results of numerical experiments concerning the simulation of wall driven cavity Bingham flow in two dimensions.展开更多
Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting ...Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting animals found inside the aquatic bodies.For stable aquatic ecosystem,the growth of both Zooplankton and Phytoplankton should be in steady state but in previous eras,there has been a universal explosion in destructive Plankton or algal blooms.Many investigators used various mathematical methodologies to try to explain the bloom phenomenon.So,in this paper,a discretized two-dimensional Phytoplankton-Zooplankton model is investigated.The results for the existence and uniqueness,and conditions for local stability with topological classifications of the equilibrium solutions are determined.It is also exhibited that at trivial and semitrivial equilibrium solutions,discrete model does not undergo fip bifurcation,but it undergoes Neimark-Sacker bifurcation at interior equilibrium solution under certain conditions.Further,state feedback method is deployed to control the chaos in the under consideration system.The extensive numerical simulations are provided to demonstrate theoretical results.展开更多
In this paper,the Caputo fractional derivative is assumed to be the prey-predator model.In order to create Caputo fractional differential equations for the prey-predator model,a discretization process is first used.Th...In this paper,the Caputo fractional derivative is assumed to be the prey-predator model.In order to create Caputo fractional differential equations for the prey-predator model,a discretization process is first used.The fixed points of the model are categorized topologically.We identify requirements for the fixed points of the suggested prey-predator model's local asymptotic stability.We demonstrate analytically that,under specific parametric conditions,a fractional order prey-predator model supports both a Neimark-Sacker(NS)bifurcation and a Flip bifurcation.We present evidence for NS and Flip bifurcations using central manifold and bifurcation theory.The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order prey-predator model.As the bifurcation parameter is increased,the system displays chaotic behavior.Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations,phase portraits,invariant closed cycles,and attractive chaotic sets in addition to validating analytical conclusions.The suggested prey-predator dynamical system's chaotic behavior will be controlled by the OGY and hybrid control methodology,which will also visualize the chaotic state for various biological parameters.展开更多
The aim of this research paper is to model the effects of misidentification in the transmissiondynamics of the super yeast, Candida auris (or C. auris), among patients receivingtreatment in the Intensive Care Units (I...The aim of this research paper is to model the effects of misidentification in the transmissiondynamics of the super yeast, Candida auris (or C. auris), among patients receivingtreatment in the Intensive Care Units (ICUs). The mathematical analysis is carried outby obtaining the reproduction number of the C. auris model using the next generationmatrix and utilizing it as a threshold value to establish the local and global stabilityproperties at the points of equilibria. The numerical investigations carried out in thispaper establish the outcomes of the effect of variations in the values of important parameterson the dynamics of C. auris colonization and infections in the health care settings.The corresponding results from the numerical simulations are illustrated graphically.展开更多
We show that the second power of the cover ideal of a path graph has linear quotients.To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients.Our const...We show that the second power of the cover ideal of a path graph has linear quotients.To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients.Our construction has a natural generalization to the larger class of chordal graphs.This generalization allows us to raise some questions that are related to some open problems about powers of cover ideals of chordal graphs.展开更多
In this paper, the authors give a survey about λ-hypersurfaces in Euclidean spaces. Especially, they focus on examples and rigidity of λ-hypersurfaces in Euclidean spaces.
基金Supported by the NSF of China（10371105） Supported by the Youth Science Foundation of Xinyang Normal University（20060202）
文摘A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global dynamics is completely determined bythe basic reproductive number R（ψ）（ψ denotes per capita vaccination rate）. If R（0） 〈 1,the disease-free equilibrium is a global attractor; If R（ψ） 〈： 1, the disease-free equilibriumis locally asymptotically stable; If R（ψ） ：〉 1, an unique endemic equilibrium exists and islocally asymptotically stable under certain condition.
基金This research is supported in part by China NSF under grant 10071096NSF of Guangdong under grant 990228+1 种基金NSF of Hainan under grant 80525the One Hundred Distinguished Young Chinese Scientists Program of the Chinese Academy of Sciences from Yuesheng Xu.
文摘In this paper,we develop Gaussian quadrature formulas for the Hadamard fi- nite part integrals.In our formulas,the classical orthogonal polynomials such as Legendre and Chebyshev polynomials are used to approximate the density function f(x)so that the Gaussian quadrature formulas have degree n-1.The error estimates of the formulas are obtained.It is found from the numerical examples that the convergence rate and the accu- racy of the approximation results are satisfactory.Moreover,the rate and the accuracy can be improved by choosing appropriate weight functions.
基金Supported by the Natural Science Foundation of China（l1271045） Supported by the Higher School Doctoral Foundation of China（20100003110004） Supported by the Natural Science Foundation of hmer Mongolia（2010MS0117）
文摘A new subclass A(β1 , β2 , ··· , βk ; λ) of analytic functions f(z) in the open unit disk U is introduced and studied. We provide coefficient inequalities, distortion theorems, extreme points and radius of close-to-convexity, starlikeness and convexity of this class.
文摘Recent work has established that digital images of a human face, when collected with a fixed pose but under a variety of illumination conditions, possess discriminatory information that can be used in classification. In this paper we perform classification on Grassmannians to demonstrate that sufficient discriminatory information persists in feature patch (e.g., nose or eye patch) illumination spaces. We further employ the use of Karcher mean on the Grassmannians to demonstrate that this compressed representation can accelerate computations with relatively minor sacrifice on performance. The combination of these two ideas introduces a novel perspective in performing face recognition.
基金supported in part by the National Nature Science Foundation of China under Grant No. 60473027
文摘How to find efficient and secure member- ship revocation algorithms is one of the most important issues standing in the way of real-world applications of group signatures. In this paper, the proof of knowledge of divisibility is given and a novel membership revocation method in ACJT group signature scheme is proposed： the group manager issues the product E of the public keys of current members in the group, when a group member wants to sign, he should not only proves that he has a membership certificate, but also proves that the public key in his certificate divides exactly the public key product E with zero knowledge. The proposed method is efficient since the group manager only needs one division and one exponentiation when a group member is deleted, while the signing and verifying procedure are independent of the number of current group members and excluded members, as well as the original group public key and membership certificates needn＇t be changed.
基金Supported by the National Natural Science Foundation of China(10571008)Supported by the Natural Science Foundation of Henan(0511013300)Supported by the National Science Foundation of Henan Education Department(2006110012)
文摘In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.
文摘On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌H if G satisfies one of the following conditions. 1） G is a finite Abelian group. 2） The order of G is p^3. 3 ） The order of G is p^n＋1 and G has a cyclic normal subgroup N = 〈a〉 of order p^n. 4） G is a nilpotent group and if p^││G│, then for any P ∈ Sylp （G）, P has a cyclic maximal subgroup, where p is a prime; 5） G is a maximal class group of order p4（p〉3）.
基金The authors thank FAPESP for the funding of the project that allowed the creation of the Laboratory of Applied Statistics(LEA)(Process:2015/18225-4)responsible for the statistical analyzes performed in this work.
文摘The aim of this study was to evaluate the effects of silver nitrate in the in vitro development and conservation of passion fruit plants. Experiments were carried out at the Laboratory of Culture and Tissues, in the National Cassava and Fruits Research Center (EMBRAPA), using microcuttings of Passiflora gibertii N. E. Br., previously cultivated in vitro. The microcuttings were placed in MS media supplemented with silver nitrate at concentrations of 0, 1, 2, 4 and 8 mg·L-1, and, during 30, 60 and 90 days, the following variables were identified: Shooting length (cm), number of roots, number and coloration of leaves. A completely randomized design with 30 replications in a split-plot scheme was employed. Polynomial regression equations were adjusted in analysis of variance to compare averages of treatments. The obtained results support the assumption of high sensitivity of passion fruit tissues to ethylene, which reflects in the lost of vigor and in the induction of culture senescence by its accumulation. Based on obtained results, and in order to mitigate this problem, it is possible to indicate an addition of 2 mg·L-1?of silver nitrate in culture media, for the micropropagation of passion fruit plant, allowing the controlling of the atmosphere inside the culture test tubes, during the establishment of explants and other steps of the process.
基金partial support provided by the National Natural Science Foundation of China(12062027/12162032)Interdisciplinary Innovation Team of Modern Applied Mathematics and Life Sciences(202405AS350003)+1 种基金Ten Thousand Talent Plans for Young Top-notch TalentsApplied Basic Research Foundation(LS21005)of Yunnan Province.
文摘Antimicrobial resistance is a growing concern in the field of microbiology.In a microbial community,the Susceptible Subpopulations(SSs)and the Non-genetically Resistant Subpopulations(NRSs)can switch between each other,and NRSs can mutate to Genetically Resistant Subpopulations(GRSs).In order to quantitatively describe the relationship between noise and signal amplification in the subpopulations,a mathematical model for three subpopulations is proposed in this paper.The gain fluctuation relation is obtained by linear noise approximation of the master equation.Then,through the simulation of these theoretical results,the following conclusions are found.First,the indirect effects of the interaction between subpopulations are much greater than the direct effects,which may be one of the reasons that the infection is dificult to cure.This is consistent with the findings of Zhou et al.and indicates the reliability of our new model.Second,the intrinsic net growth rate of SSs can be chosen as the adjustment parameter,which can effectively exploit or avoid the strong correlation between SSs and the two resistant subpopulations,including NRSs and GRSs.Third,unlike unidirectional cascades,additional intrinsic noise in GRSs can propagate to NRSs.Similarly,although there is no direct interaction between SSs and GRSs,additional intrinsic noise in GRSs can propagate to SSs,and vice versa.Finally,both total noise and adjusted noise exhibit similar amplification properties in this population.It is worth noting that the noise is consistently amplified from NRSs to GRSs.These findings may provide new insights into antimicrobial therapy.
基金Project supported by the China National 973 Program (Grant No: 2002CB211708) and the Natural Science Foundation of Shandong Province (Grant No: Y2003F01)
文摘In this paper, fractional order derivative, fractal dimension and spectral dimension are introduced into the seepage flow mechanics to establish the flow models of fluids in fractal reservoirs with the fractional derivative. The flow characteristics of fluids through a fractal reservoir with the fractional order derivative are studied by using the finite integral transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions are obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation are also obtained. The pressure transient behavior of fluids flow through an infinite fractal reservoir is studied by using the Stehfest＇s inversion method of the numerical Laplace transform. It shows that the order of the fractional derivative affect the whole pressure behavior, particularly, the effect of pressure behavior of the early-time stage is larger The new type flow model of fluid in fractal reservoir with fractional derivative is provided a new mathematical model for studying the seepage mechanics of fluid in fractal porous media.
基金supported by the National Fundamental Science Research Program 973 of China under Grant No. 2004 CB3180000the State Key Lab. (Information Security) of China
文摘A formula on the complexity of the normal bases generated by prime Gauss period overfinite fields is presented in terms of cyclotomic numbers.Then,the authors determine explicitly thecomplexity of such normal bases and their dual bases in several cases where the related cyclotomicnumbers have been calculated.Particularly,the authors find several series of such normal bases withlow complexity.
文摘The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole.Here,we have extended the prior work of Chen and Jing(S.Chen and J.Jing,JCAP,10:002(2015))for a Schwarzschild black hole to a Kiselev black hole.For this purpose,the equation of motion for the photons coupled to the Weyl tensor,null geodesic,and equation of photon sphere in a Kiselev black hole spacetime have been formulated.It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor,but also on the polarization direction of the photons.There is a critical value of the coupling parameter,α,for the existence of the marginally circular photon orbit outside the event horizon,which depends on the parameters of the black hole and the polarization direction of the photons.Further,the polarization directions of the coupled photons and the coupling parameter,α;both modify the features of the photon sphere,angle of deflection,and functions(^ˉa and^ˉb)owing to the strong gravitational lensing in the Kiselev black hole spacetime.In addition to this,the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.
文摘This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characterization of the solutions involving some kind of Lagrange multipliers. The full discretization is achieved by combining the above operator-splitting methods with finite element approximations, the advection being treated by a wave-like equation 'equivalent' formulation easier to implement than the method of characteristics or high order upwinding methods. The authors illustrate the methodology discussed in this article with the results of numerical experiments concerning the simulation of wall driven cavity Bingham flow in two dimensions.
基金The research of A.Q.Khan and F.Nazir is partially supported by the Higher Education Commission of Pakistan.
文摘Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting animals found inside the aquatic bodies.For stable aquatic ecosystem,the growth of both Zooplankton and Phytoplankton should be in steady state but in previous eras,there has been a universal explosion in destructive Plankton or algal blooms.Many investigators used various mathematical methodologies to try to explain the bloom phenomenon.So,in this paper,a discretized two-dimensional Phytoplankton-Zooplankton model is investigated.The results for the existence and uniqueness,and conditions for local stability with topological classifications of the equilibrium solutions are determined.It is also exhibited that at trivial and semitrivial equilibrium solutions,discrete model does not undergo fip bifurcation,but it undergoes Neimark-Sacker bifurcation at interior equilibrium solution under certain conditions.Further,state feedback method is deployed to control the chaos in the under consideration system.The extensive numerical simulations are provided to demonstrate theoretical results.
文摘In this paper,the Caputo fractional derivative is assumed to be the prey-predator model.In order to create Caputo fractional differential equations for the prey-predator model,a discretization process is first used.The fixed points of the model are categorized topologically.We identify requirements for the fixed points of the suggested prey-predator model's local asymptotic stability.We demonstrate analytically that,under specific parametric conditions,a fractional order prey-predator model supports both a Neimark-Sacker(NS)bifurcation and a Flip bifurcation.We present evidence for NS and Flip bifurcations using central manifold and bifurcation theory.The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order prey-predator model.As the bifurcation parameter is increased,the system displays chaotic behavior.Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations,phase portraits,invariant closed cycles,and attractive chaotic sets in addition to validating analytical conclusions.The suggested prey-predator dynamical system's chaotic behavior will be controlled by the OGY and hybrid control methodology,which will also visualize the chaotic state for various biological parameters.
文摘The aim of this research paper is to model the effects of misidentification in the transmissiondynamics of the super yeast, Candida auris (or C. auris), among patients receivingtreatment in the Intensive Care Units (ICUs). The mathematical analysis is carried outby obtaining the reproduction number of the C. auris model using the next generationmatrix and utilizing it as a threshold value to establish the local and global stabilityproperties at the points of equilibria. The numerical investigations carried out in thispaper establish the outcomes of the effect of variations in the values of important parameterson the dynamics of C. auris colonization and infections in the health care settings.The corresponding results from the numerical simulations are illustrated graphically.
文摘We show that the second power of the cover ideal of a path graph has linear quotients.To prove our result we construct a recursively defined order on the generators of the ideal which yields linear quotients.Our construction has a natural generalization to the larger class of chordal graphs.This generalization allows us to raise some questions that are related to some open problems about powers of cover ideals of chordal graphs.
基金supported by JSPS Grant-in-Aid for Scientific Research(B)(No.16H03937)the fund of Fukuoka University(No.225001)+2 种基金the National Natural Science Foundation of China(No.12171164)the Natural Science Foundation of Guangdong Province(No.2019A1515011451)GDUPS(2018)。
文摘In this paper, the authors give a survey about λ-hypersurfaces in Euclidean spaces. Especially, they focus on examples and rigidity of λ-hypersurfaces in Euclidean spaces.
