The unique composition of milk makes this basic foodstuff into an exceptional raw material for the production of new ingredients with desired properties and diverse applications in the food industry. The fractionation...The unique composition of milk makes this basic foodstuff into an exceptional raw material for the production of new ingredients with desired properties and diverse applications in the food industry. The fractionation of milk is the key in the development of those ingredients and products;hence continuous research and development on this field, especially various levels of fractionation and separation by filtration, have been carried out. This review focuses on the production of milk fractions as well as their particular properties, applications and processes that increase their exploitation. Whey proteins and caseins from the protein fraction are excellent emulsifiers and protein supplements. Besides, they can be chemically or enzymatically modified to obtain bioactive peptides with numerous functional and nutritional properties. In this context, valorization techniques of cheese-whey proteins, by-product of dairy industry that constitutes both economic and environmental problems, are being developed. Phospholipids from the milk fat fraction are powerful emulsifiers and also have exclusive nutraceutical properties. In addition, enzyme modification of milk phospholipids makes it possible to tailor emulsifiers with particular properties. However, several aspects remain to be overcome;those refer to a deeper understanding of the healthy, functional and nutritional properties of these new ingredients that might be barriers for its use and acceptability. Additionally, in this review, alternative applications of milk constituents in the non-food area such as in the manufacture of plastic materials and textile fibers are also introduced. The unmet needs, the cross-fertilization in between various protein domains,the carbon footprint requirements, the environmental necessities, the health and wellness new demand, etc., are dominant factors in the search for innovation approaches;these factors are also outlining the further innovation potential deriving from those “apparent” constrains obliging science and technology to take them into account.展开更多
The space-time fractional advection dispersion equations are linear partial pseudo-differential equations with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. ...The space-time fractional advection dispersion equations are linear partial pseudo-differential equations with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. The time fractional order is denoted by β∈ and ?is devoted to the space fractional order. The time fractional advection dispersion equations describe particle motion with memory in time. Space-fractional advection dispersion equations arise when velocity variations are heavy-tailed and describe particle motion that accounts for variation in the flow field over entire system. In this paper, I focus on finding the precise explicit discrete approximate solutions to these models for some values of ?with ?, ?while the Cauchy case as ?and the classical case as ?with ?are studied separately. I compare the numerical results of these models for different values of ?and ?and for some other related changes. The approximate solutions of these models are also discussed as a random walk with or without a memory depending on the value of . Then I prove that the discrete solution in the Fourierlaplace space of theses models converges in distribution to the Fourier-Laplace transform of the corresponding fractional differential equations for all the fractional values of ?and .展开更多
The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is ob...The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.展开更多
Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related gen...Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.展开更多
The dynamics of a fractionalized semi-linear scalar differential equation is considered with a Caputo fractional derivative. By using a symbolic operational method, a fractional order initial value problem is converte...The dynamics of a fractionalized semi-linear scalar differential equation is considered with a Caputo fractional derivative. By using a symbolic operational method, a fractional order initial value problem is converted into an equivalent Volterra integral equation of second kind. A brief discussion is included to show that the fractional order derivatives and integrals incorporate a fading memory (also known as long memory) and that the order of the fractional derivative can be considered to be an index of memory. A variation of constants formula is established for the fractionalized version and it is shown by using the Fourier integral theorem that this formula reduces to that of the integer order differential equation as the fractional order approaches an integer. The global existence of a unique solution and the global Mittag-Leffler stability of an equilibrium are established by exploiting the complete monotonicity of one and two parameter Mittag-Leffler functions. The method and the analysis employed in this article can be used for the study of more general systems of fractional order differential equations.展开更多
Equilibrium isotope fractionation of thallium(Tl) includes the traditional mass-dependent isotope fractionation effect and the nuclear volume effect(NVE). The NVE dominates the overall isotope fractionation, especiall...Equilibrium isotope fractionation of thallium(Tl) includes the traditional mass-dependent isotope fractionation effect and the nuclear volume effect(NVE). The NVE dominates the overall isotope fractionation, especially at high temperatures. Heavy Tl isotopes tend to be enriched in oxidized Tl^3+-bearing species. Our NVE fractionation results of oxidizing Tl^+ to Tl^3+ can explain the positive enrichments observed in ferromanganese sediments. Experimental results indicate that there could be0.2–0.3 e-unit fractionation between sulfides and silicates at 1650 ℃. It is consistent with our calculation results,which are in the range of 0.17–0.38 e-unit. Importantly,Tl’s concentration in the bulk silicate Earth(BSE) can be used to constrain the amount of materials delivered to Earth during the late veneer accretion stage. Because the Tl concentration in BSE is very low and its Tl isotope composition is similar with that of chondrites, suggesting either no Tl isotope fractionation occurred during numerous evaporation events, or the Tl in current BSE was totally delivered by late veneer. If it is the latter, the Tl-contentbased estimation could challenge the magnitude of late veneer which had been constrained by the amount of highly siderophile elements in BSE. Our results show that the lateaccreted mass is at least five-times larger than the previously suggested magnitude, i.e., 0.5 wt% of current Earth’s mass. The slightly lighter 205 Tl composition of BSE relative to chondrites is probable a sign of occurrence of Tlbearing sulfides, which probably were removed from the mantle in the last accretion stage of the Earth.展开更多
This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and extern...This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.展开更多
In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper a...In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper and lower solution, the sufficient condition for the existence of the boundary value problem is obtained, and the range of the solution is determined. Then the existence and uniqueness of the solution are proved by the proof by contradiction. Finally, a concrete example is given to illustrate the wide applicability of our main results.展开更多
Evoked potentials (EPs) have been widely used to quantify neurological system properties. Tra-ditional EP analysis methods are developed under the condition that the background noises in EP are Gaussian distributed. A...Evoked potentials (EPs) have been widely used to quantify neurological system properties. Tra-ditional EP analysis methods are developed under the condition that the background noises in EP are Gaussian distributed. Alpha stable distribution, a generalization of Gaussian, is better for modeling impulsive noises than Gaussian distribution in biomedical signal proc-essing. Conventional blind separation and es-timation method of evoked potentials is based on second order statistics or high order Statis-tics. Conventional blind separation and estima-tion method of evoked potentials is based on second order statistics (SOS). In this paper, we propose a new algorithm based on minimum dispersion criterion and fractional lower order statistics. The simulation experiments show that the proposed new algorithm is more robust than the conventional algorithm.展开更多
Flow fractional reserve(FFR) allows to evaluate the functional significance of coronary artery lesions, through the ratio of the mean coronary artery pressure after the stenosis to the mean aortic pressure duringmaxim...Flow fractional reserve(FFR) allows to evaluate the functional significance of coronary artery lesions, through the ratio of the mean coronary artery pressure after the stenosis to the mean aortic pressure duringmaximum hyperemia. The actual widely accepted cutoff value is 0.80. Below this value a coronary lesion is considered significant and therefore it requires invasive revascularization. Several studies [in particular Fractional Flow Reserve vs Angiography for Multivessel Evaluation 1(FAME-1) and FAME-2] have shown the relationship between FFR measurement and hard end-points(death, myocardial infarction, and urgent revascularization). Consequently, FFR evaluation represents the cornerstone in the decision-making in intermediate coronary lesions. Recent studies paved the way for further applications of FFR evaluation in complex and tricky clinical settings. In this paper, we perform an overview of the data regarding contemporary application of FFR. In particular, we review the use of FFR in: left main intermediate stenoses, serial stenoses, evaluation after stenting, guidance in coronary artery bypass surgery, and acute coronary syndrome. All the data presented in our overview confirm the essential role of FFR assessment in the daily clinical practice. The shift from "operator-dependent" to "FFR-dependent" evaluation in intermediate coronary artery stenosis is of paramount importance in order to improve the prognosis of our patients, through the discrimination of the functional role of every single coronary stenosis.展开更多
In this paper, fractional order PI(FOPI) control is developed for speed control of permanent magnet synchronous motor(PMSM). Designing the parameters for FOPI controller is a challenging task, especially for nonlinear...In this paper, fractional order PI(FOPI) control is developed for speed control of permanent magnet synchronous motor(PMSM). Designing the parameters for FOPI controller is a challenging task, especially for nonlinear systems like PMSM.All three PI controllers in the conventional vector controlled speed drive are replaced by FOPI controllers. Design of these FOPI controllers is based on the locally linearized model of PMSM around an operating point. This operating point changes with the load torque. The novelty of the work reported here is in use of Non Linear Disturbance Observer(NLDO) to estimate load torque to obtain this new operating point. All three FOPI controllers are then designed adaptively using this new operating point. The scheme is tested on simulation using MATLAB/SIMULINK and results are presented.展开更多
To explore the characteristics of plant calcium(Ca) fraction, we analyzed 91 plant species in the Ningxia Habahu National Nature Reserve in Yanchi County of Ningxia and 84 plant species in Zhenglan Banner of Inner Mon...To explore the characteristics of plant calcium(Ca) fraction, we analyzed 91 plant species in the Ningxia Habahu National Nature Reserve in Yanchi County of Ningxia and 84 plant species in Zhenglan Banner of Inner Mongolia. Results show that, for the two regions, there is no significant difference between Ca fraction for the same growth type, and between water soluble Ca content or between hydrochloric acid soluble Ca content for plants of the same ecosystem and between hydrochloric acid soluble Ca content for plants of the same family. In similar vegetation zones, there is a significant difference among hydrochloric acid soluble Ca content for different growth types in Yanchi County and Zhenglan Banner,which was the highest for annual herbs and the lowest for perennial herbs. There is a significant difference between acetic acid soluble Ca content and between hydrochloric acid soluble Ca content for sandy land and grassland ecosystems in Yanchi County. There is a significant difference among the same Ca fraction of different families in the same region. Thus, the characteristics of plant Ca fraction are results of long-term adaptation to the environment.展开更多
The aim of this paper is to study the existence of integrable solutions of a nonlinear functional integral equation in the space of Lebesgue integrable functions on unbounded interval, L1(R+). As an application we ded...The aim of this paper is to study the existence of integrable solutions of a nonlinear functional integral equation in the space of Lebesgue integrable functions on unbounded interval, L1(R+). As an application we deduce the existence of solution of an initial value problem of fractional order that be studied only on a bounded interval. The main tools used are Schauder fixed point theorem, measure of weak noncompactness, superposition operator and fractional calculus.展开更多
In this paper, we give various existence results concerning the existence of mild solutions for nonlocal impulsive differential inclusions with delay and of fractional order in Caputo sense in Banach space. We conside...In this paper, we give various existence results concerning the existence of mild solutions for nonlocal impulsive differential inclusions with delay and of fractional order in Caputo sense in Banach space. We consider the case when the values of the orient field are convex as well as nonconvex. Our obtained results improve and generalize many results proved in recent papers.展开更多
In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex trans...In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation method has been implemented, to find the exact solutions of these equations, in the sense of modified Riemann-Liouville derivative. For applications, the exact solutions of time-space fractional derivative Burgers’ equation and time-space fractional derivative foam drainage equation have been discussed. Moreover, it can also be concluded that the proposed method is easy, direct and concise as compared to other existing methods.展开更多
文摘The unique composition of milk makes this basic foodstuff into an exceptional raw material for the production of new ingredients with desired properties and diverse applications in the food industry. The fractionation of milk is the key in the development of those ingredients and products;hence continuous research and development on this field, especially various levels of fractionation and separation by filtration, have been carried out. This review focuses on the production of milk fractions as well as their particular properties, applications and processes that increase their exploitation. Whey proteins and caseins from the protein fraction are excellent emulsifiers and protein supplements. Besides, they can be chemically or enzymatically modified to obtain bioactive peptides with numerous functional and nutritional properties. In this context, valorization techniques of cheese-whey proteins, by-product of dairy industry that constitutes both economic and environmental problems, are being developed. Phospholipids from the milk fat fraction are powerful emulsifiers and also have exclusive nutraceutical properties. In addition, enzyme modification of milk phospholipids makes it possible to tailor emulsifiers with particular properties. However, several aspects remain to be overcome;those refer to a deeper understanding of the healthy, functional and nutritional properties of these new ingredients that might be barriers for its use and acceptability. Additionally, in this review, alternative applications of milk constituents in the non-food area such as in the manufacture of plastic materials and textile fibers are also introduced. The unmet needs, the cross-fertilization in between various protein domains,the carbon footprint requirements, the environmental necessities, the health and wellness new demand, etc., are dominant factors in the search for innovation approaches;these factors are also outlining the further innovation potential deriving from those “apparent” constrains obliging science and technology to take them into account.
文摘The space-time fractional advection dispersion equations are linear partial pseudo-differential equations with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. The time fractional order is denoted by β∈ and ?is devoted to the space fractional order. The time fractional advection dispersion equations describe particle motion with memory in time. Space-fractional advection dispersion equations arise when velocity variations are heavy-tailed and describe particle motion that accounts for variation in the flow field over entire system. In this paper, I focus on finding the precise explicit discrete approximate solutions to these models for some values of ?with ?, ?while the Cauchy case as ?and the classical case as ?with ?are studied separately. I compare the numerical results of these models for different values of ?and ?and for some other related changes. The approximate solutions of these models are also discussed as a random walk with or without a memory depending on the value of . Then I prove that the discrete solution in the Fourierlaplace space of theses models converges in distribution to the Fourier-Laplace transform of the corresponding fractional differential equations for all the fractional values of ?and .
文摘The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.
文摘Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F, α ,p ,d ,b , φ )β vector-pseudo- quasi-Type I and formulate a higher-order duality for minimax fractional type programming involving symmetric matrices, and give the weak, strong and strict converse duality theorems under the condition of higher-order (F, α ,p ,d ,b , φ )β vector-pseudoquasi-Type I.
文摘The dynamics of a fractionalized semi-linear scalar differential equation is considered with a Caputo fractional derivative. By using a symbolic operational method, a fractional order initial value problem is converted into an equivalent Volterra integral equation of second kind. A brief discussion is included to show that the fractional order derivatives and integrals incorporate a fading memory (also known as long memory) and that the order of the fractional derivative can be considered to be an index of memory. A variation of constants formula is established for the fractionalized version and it is shown by using the Fourier integral theorem that this formula reduces to that of the integer order differential equation as the fractional order approaches an integer. The global existence of a unique solution and the global Mittag-Leffler stability of an equilibrium are established by exploiting the complete monotonicity of one and two parameter Mittag-Leffler functions. The method and the analysis employed in this article can be used for the study of more general systems of fractional order differential equations.
基金the funding supports from the strategic priority research program (B) of CAS (XDB18010100)Chinese NSF projects (Nos. 41530210, 41490635)
文摘Equilibrium isotope fractionation of thallium(Tl) includes the traditional mass-dependent isotope fractionation effect and the nuclear volume effect(NVE). The NVE dominates the overall isotope fractionation, especially at high temperatures. Heavy Tl isotopes tend to be enriched in oxidized Tl^3+-bearing species. Our NVE fractionation results of oxidizing Tl^+ to Tl^3+ can explain the positive enrichments observed in ferromanganese sediments. Experimental results indicate that there could be0.2–0.3 e-unit fractionation between sulfides and silicates at 1650 ℃. It is consistent with our calculation results,which are in the range of 0.17–0.38 e-unit. Importantly,Tl’s concentration in the bulk silicate Earth(BSE) can be used to constrain the amount of materials delivered to Earth during the late veneer accretion stage. Because the Tl concentration in BSE is very low and its Tl isotope composition is similar with that of chondrites, suggesting either no Tl isotope fractionation occurred during numerous evaporation events, or the Tl in current BSE was totally delivered by late veneer. If it is the latter, the Tl-contentbased estimation could challenge the magnitude of late veneer which had been constrained by the amount of highly siderophile elements in BSE. Our results show that the lateaccreted mass is at least five-times larger than the previously suggested magnitude, i.e., 0.5 wt% of current Earth’s mass. The slightly lighter 205 Tl composition of BSE relative to chondrites is probable a sign of occurrence of Tlbearing sulfides, which probably were removed from the mantle in the last accretion stage of the Earth.
文摘This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.
文摘In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper and lower solution, the sufficient condition for the existence of the boundary value problem is obtained, and the range of the solution is determined. Then the existence and uniqueness of the solution are proved by the proof by contradiction. Finally, a concrete example is given to illustrate the wide applicability of our main results.
文摘Evoked potentials (EPs) have been widely used to quantify neurological system properties. Tra-ditional EP analysis methods are developed under the condition that the background noises in EP are Gaussian distributed. Alpha stable distribution, a generalization of Gaussian, is better for modeling impulsive noises than Gaussian distribution in biomedical signal proc-essing. Conventional blind separation and es-timation method of evoked potentials is based on second order statistics or high order Statis-tics. Conventional blind separation and estima-tion method of evoked potentials is based on second order statistics (SOS). In this paper, we propose a new algorithm based on minimum dispersion criterion and fractional lower order statistics. The simulation experiments show that the proposed new algorithm is more robust than the conventional algorithm.
文摘Flow fractional reserve(FFR) allows to evaluate the functional significance of coronary artery lesions, through the ratio of the mean coronary artery pressure after the stenosis to the mean aortic pressure duringmaximum hyperemia. The actual widely accepted cutoff value is 0.80. Below this value a coronary lesion is considered significant and therefore it requires invasive revascularization. Several studies [in particular Fractional Flow Reserve vs Angiography for Multivessel Evaluation 1(FAME-1) and FAME-2] have shown the relationship between FFR measurement and hard end-points(death, myocardial infarction, and urgent revascularization). Consequently, FFR evaluation represents the cornerstone in the decision-making in intermediate coronary lesions. Recent studies paved the way for further applications of FFR evaluation in complex and tricky clinical settings. In this paper, we perform an overview of the data regarding contemporary application of FFR. In particular, we review the use of FFR in: left main intermediate stenoses, serial stenoses, evaluation after stenting, guidance in coronary artery bypass surgery, and acute coronary syndrome. All the data presented in our overview confirm the essential role of FFR assessment in the daily clinical practice. The shift from "operator-dependent" to "FFR-dependent" evaluation in intermediate coronary artery stenosis is of paramount importance in order to improve the prognosis of our patients, through the discrimination of the functional role of every single coronary stenosis.
文摘In this paper, fractional order PI(FOPI) control is developed for speed control of permanent magnet synchronous motor(PMSM). Designing the parameters for FOPI controller is a challenging task, especially for nonlinear systems like PMSM.All three PI controllers in the conventional vector controlled speed drive are replaced by FOPI controllers. Design of these FOPI controllers is based on the locally linearized model of PMSM around an operating point. This operating point changes with the load torque. The novelty of the work reported here is in use of Non Linear Disturbance Observer(NLDO) to estimate load torque to obtain this new operating point. All three FOPI controllers are then designed adaptively using this new operating point. The scheme is tested on simulation using MATLAB/SIMULINK and results are presented.
基金supported by the National Key Research and Development Program of China (2016YFC0500706)
文摘To explore the characteristics of plant calcium(Ca) fraction, we analyzed 91 plant species in the Ningxia Habahu National Nature Reserve in Yanchi County of Ningxia and 84 plant species in Zhenglan Banner of Inner Mongolia. Results show that, for the two regions, there is no significant difference between Ca fraction for the same growth type, and between water soluble Ca content or between hydrochloric acid soluble Ca content for plants of the same ecosystem and between hydrochloric acid soluble Ca content for plants of the same family. In similar vegetation zones, there is a significant difference among hydrochloric acid soluble Ca content for different growth types in Yanchi County and Zhenglan Banner,which was the highest for annual herbs and the lowest for perennial herbs. There is a significant difference between acetic acid soluble Ca content and between hydrochloric acid soluble Ca content for sandy land and grassland ecosystems in Yanchi County. There is a significant difference among the same Ca fraction of different families in the same region. Thus, the characteristics of plant Ca fraction are results of long-term adaptation to the environment.
文摘The aim of this paper is to study the existence of integrable solutions of a nonlinear functional integral equation in the space of Lebesgue integrable functions on unbounded interval, L1(R+). As an application we deduce the existence of solution of an initial value problem of fractional order that be studied only on a bounded interval. The main tools used are Schauder fixed point theorem, measure of weak noncompactness, superposition operator and fractional calculus.
文摘In this paper, we give various existence results concerning the existence of mild solutions for nonlocal impulsive differential inclusions with delay and of fractional order in Caputo sense in Banach space. We consider the case when the values of the orient field are convex as well as nonconvex. Our obtained results improve and generalize many results proved in recent papers.
文摘In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation method has been implemented, to find the exact solutions of these equations, in the sense of modified Riemann-Liouville derivative. For applications, the exact solutions of time-space fractional derivative Burgers’ equation and time-space fractional derivative foam drainage equation have been discussed. Moreover, it can also be concluded that the proposed method is easy, direct and concise as compared to other existing methods.
