This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this n...This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.展开更多
Scalar fields should have no spin angular momentum according to conventional textbook understandings inclassical field theory.Yet,recent studies demonstrate the undoubted existence of wave spin endowed by acousticand ...Scalar fields should have no spin angular momentum according to conventional textbook understandings inclassical field theory.Yet,recent studies demonstrate the undoubted existence of wave spin endowed by acousticand elastic longitudinal waves,which are of irrotational curl-free nature without vorticity and can be describedby scalar fields.Moreover,the conventional theory cannot even answer the question of whether wave spin existsin dissipative fields,given the ubiquitous dissipation in reality.Here,to resolve the seeming paradox and answerthe challenging question,we uncover the origin of wave spin in scalar fields beyond traditional formalism byclarifying that the presence of higher-order derivatives in scalar field Lagrangians can give rise to non-vanishingwave spin.For“spinless”scalar fields of only first-order derivatives,we can make the hidden wave spin emergeby revealing a latent field that leads to the original field through a time derivative,thus giving higher-order termsin Lagrangian.Based on the standard Noether theorem approach,we exemplify the wave spin for unconventionaldrifted acoustic fields,and even for dissipative media,in scalar fields with higher-order derivative Lagrangian.The results would prompt people to build more comprehensive and fundamental understandings of structuralwave spin in classical fields.展开更多
In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators...In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.展开更多
The conformable fractional derivative method has been utilized in order to examine the logistic model with constant harvesting.Such method introduces a generalization to the classical analysis of Logistic model,and he...The conformable fractional derivative method has been utilized in order to examine the logistic model with constant harvesting.Such method introduces a generalization to the classical analysis of Logistic model,and hence the features of the Logistic model,such as subcritical and supercritical harvesting,have been investigated in a view of fractional calculus.The positive auxiliary parameter,σ,with dimension of time is implemented to maintain the dimensionality of the system.The significant information of such parameter to the population has been discussed.The population expressions,obtained by conformable description,are compared with the expressions of the classical derivative.This comparison shows that the non-integer expressions are in a parallel line with that of the classical one.展开更多
Two new methods, the generalized Levy method and the weighted iteration method, are presented for identification of non-integer order systems. The first method generalizes the Levy identification method from the integ...Two new methods, the generalized Levy method and the weighted iteration method, are presented for identification of non-integer order systems. The first method generalizes the Levy identification method from the integer order systems to the non-integer order systems. Then, the weighted iteration method is presented to overcome the shortcomings of the first method. Results show that the proposed methods have better performance compared with the integer order identification method. For the non-integer order systems, the proposed methods have the better fitting for the system frequency response. For the integer order system, if commensurate order scanning is applied, the proposed methods can also achieve the best integer order model which fits the system frequency response. At the same time, the proposed algorithms are more stable.展开更多
According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of va...According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of variations are researched, the functionals depend on single argument, arbitrary unknown functions and their derivatives of higher orders. A new view point is posed and demonstrated, i.e. when the first variation of the functional is equal to zero, all the variational terms are not independent to each other, and at least one of them is equal to zero. Some theorems and corollaries of the variational problems of the functionals are obtained.展开更多
We give general solutions(the explicit solutions) of a class of multi-term impulsive fractional differential equations involving the Riemann-Liouville fractional derivatives. This paper contributes within the domain o...We give general solutions(the explicit solutions) of a class of multi-term impulsive fractional differential equations involving the Riemann-Liouville fractional derivatives. This paper contributes within the domain of impulsive fractional differential equations. The author strongly believes that the article will highly be appreciated by the researchers working in the field of fractional calculus and on fractional differential models.展开更多
Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
A novel method for the determination of vitamin C（Vc） is proposed in this article. After the reaction with Folin-Ciocalteau reagent at ambient temperature, Vc solution was scanned at 750--1100 nm, and its first-orde...A novel method for the determination of vitamin C（Vc） is proposed in this article. After the reaction with Folin-Ciocalteau reagent at ambient temperature, Vc solution was scanned at 750--1100 nm, and its first-order derivative spectrum were obtained from the original spectrum. The values of derivative selected at 995 nm were used for determination. It was proved that Vc could quickly react with Folin-Ciocalteau reagent within 5 min and the product was quite stable for a long time. The conditions required for this method is not very complicated, its precision and accuracy are similar to those of the iodometric titration described in Chinese Pharmacopoeia, and the limit of detection is 0.312 μg/mL. The determination of the results of vitamin C tablet, pill, and injection demonstrates that this method has wide pharmaceutical applications.展开更多
In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given seco...In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other.展开更多
It was found that micro amounts of oxalate showed a very strong catalytic effect on the slow reaction between K 2Cr 2O 7 and Orange Ⅳ in a diluted sulfuric acid medium in a water bath at 70 ℃ . Orange Ⅳ exhib...It was found that micro amounts of oxalate showed a very strong catalytic effect on the slow reaction between K 2Cr 2O 7 and Orange Ⅳ in a diluted sulfuric acid medium in a water bath at 70 ℃ . Orange Ⅳ exhibited a sensitive second order derivative polarographic wave at -0 50 V( vs . SCE). This provides the basis for a sensitive and selective catalytic kinetic method for oxalate determination with second order derivative oscillopolarography. The effects of sulphuric acid, K 2Cr 2O 7, and orange Ⅳ concentrations, reaction temperature and reaction time were investigated. A calibration curve of oxalate in the range of 0 1-2 0 μg/mL was obtained by the fixed time procedure. The detection limit was 0 03 μg/ mL. The possible interference from co existing substances or ions was examined. The new method has a high sensitivity and a good selectivity compared to other existing methods for oxalic acid determination. It has been applied to the determination of micro amounts of oxalate in real urine samples with satisfactory results.展开更多
The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals ...The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established.展开更多
This paper deals with the study of fractional order system tuning method based on Factional Order Proportional Integral Derivative( FOPID) controller in allusion to the nonlinear characteristics and fractional order m...This paper deals with the study of fractional order system tuning method based on Factional Order Proportional Integral Derivative( FOPID) controller in allusion to the nonlinear characteristics and fractional order mathematical model of bioengineering systems. The main contents include the design of FOPID controller and the simulation for bioengineering systems. The simulation results show that the tuning method of fractional order system based on the FOPID controller outperforms the fractional order system based on Fractional Order Proportional Integral( FOPI) controller. As it can enhance control character and improve the robustness of the system.展开更多
The Pfaff-Birkhoff variational problem and its Noether symmetry are studied in terms of Riemann-Liouville fractional derivatives of variable order. Based on the combination of variational principle and fractional calc...The Pfaff-Birkhoff variational problem and its Noether symmetry are studied in terms of Riemann-Liouville fractional derivatives of variable order. Based on the combination of variational principle and fractional calculus of variable order,the Pfaff-Birkhoff variational principle with Riemann-Liouville fractional derivatives of variable order is proposed, and the fractional Birkhoff's equations of variable order are derived. Then,the Noether 's theorem for the fractional Birkhoffian system of variable order is given. At last,an example is expressed to illustrate the application of the results.展开更多
In this paper,we obtain the fractal dimension of the graph of the Weierstrass function, its derivative of the fractional order and the relation between the dimension and the order of the fractional derivative.
The equations of the second and third order derivative curves of time with respect to potential for a reversible process in adsorption chronopotentiometry are derived and experimentally verified.
The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear opti...The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity transparency thermal stability trade off is achieved for them.展开更多
The state of Tb3+ is investigated in liposome. When the concentration of PC is below CMC (critical micell concentration), most of Tb3+ is associated with PC, the binding constant is about 3.35×103 L/mol. When the...The state of Tb3+ is investigated in liposome. When the concentration of PC is below CMC (critical micell concentration), most of Tb3+ is associated with PC, the binding constant is about 3.35×103 L/mol. When the concentration of PC is beyond CMC, most of Tb3+ is dimerized, the dimerization constant is about 3.92×104L/mol. In PC?CH?H2O system, the binding constant of Tb3+?CH complex 2.93×104L/mol is obtained.展开更多
There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions...There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.展开更多
alculations of the nonlinear second-order optical susceptlbilities(β_(ijk))for sub- stituted tl1iophene derivative;with quinoidlike conformation are reported.These systetems possess small dipole moment;and large diff...alculations of the nonlinear second-order optical susceptlbilities(β_(ijk))for sub- stituted tl1iophene derivative;with quinoidlike conformation are reported.These systetems possess small dipole moment;and large differences between dipole mo- ments of ground and first-excited states.Geometry optimizations of the molecules investigated were carried out using AM 1 method.The calculations were performed using INDO/CI method comboned with a sum-over-states expression for β_(jik). The calculated results sbw that the second-order susceptibility is a function of the na- ture and location of substituents and is larger for disubstituted molecules than monosubstituted molecules. Bipolymeric thiophenemetmne with NH_2/NO_2 groups was calctilated to have a β_μof 79. 920 × 10￣(-30) esu. It was found that the NH_2 and NO_2 groups in above disubstituted molecules are pull-pull groups in ground states,but are usual push-pull groups in the first excited states.展开更多
文摘This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.
基金supported by the National Key R&D Program of China(Grant Nos.2022YFA1404400 and 2023YFA1406900)the Natural Science Foundation of Shanghai(Grant No.23ZR1481200)the Program of Shanghai Academic Research Leader(Grant No.23XD1423800)。
文摘Scalar fields should have no spin angular momentum according to conventional textbook understandings inclassical field theory.Yet,recent studies demonstrate the undoubted existence of wave spin endowed by acousticand elastic longitudinal waves,which are of irrotational curl-free nature without vorticity and can be describedby scalar fields.Moreover,the conventional theory cannot even answer the question of whether wave spin existsin dissipative fields,given the ubiquitous dissipation in reality.Here,to resolve the seeming paradox and answerthe challenging question,we uncover the origin of wave spin in scalar fields beyond traditional formalism byclarifying that the presence of higher-order derivatives in scalar field Lagrangians can give rise to non-vanishingwave spin.For“spinless”scalar fields of only first-order derivatives,we can make the hidden wave spin emergeby revealing a latent field that leads to the original field through a time derivative,thus giving higher-order termsin Lagrangian.Based on the standard Noether theorem approach,we exemplify the wave spin for unconventionaldrifted acoustic fields,and even for dissipative media,in scalar fields with higher-order derivative Lagrangian.The results would prompt people to build more comprehensive and fundamental understandings of structuralwave spin in classical fields.
文摘In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.
文摘The conformable fractional derivative method has been utilized in order to examine the logistic model with constant harvesting.Such method introduces a generalization to the classical analysis of Logistic model,and hence the features of the Logistic model,such as subcritical and supercritical harvesting,have been investigated in a view of fractional calculus.The positive auxiliary parameter,σ,with dimension of time is implemented to maintain the dimensionality of the system.The significant information of such parameter to the population has been discussed.The population expressions,obtained by conformable description,are compared with the expressions of the classical derivative.This comparison shows that the non-integer expressions are in a parallel line with that of the classical one.
文摘Two new methods, the generalized Levy method and the weighted iteration method, are presented for identification of non-integer order systems. The first method generalizes the Levy identification method from the integer order systems to the non-integer order systems. Then, the weighted iteration method is presented to overcome the shortcomings of the first method. Results show that the proposed methods have better performance compared with the integer order identification method. For the non-integer order systems, the proposed methods have the better fitting for the system frequency response. For the integer order system, if commensurate order scanning is applied, the proposed methods can also achieve the best integer order model which fits the system frequency response. At the same time, the proposed algorithms are more stable.
文摘According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of variations are researched, the functionals depend on single argument, arbitrary unknown functions and their derivatives of higher orders. A new view point is posed and demonstrated, i.e. when the first variation of the functional is equal to zero, all the variational terms are not independent to each other, and at least one of them is equal to zero. Some theorems and corollaries of the variational problems of the functionals are obtained.
基金Supported by the Natural Science Foundation of Guangdong Province(Grant No.S2011010001900)the Natural Science Research Project for Colleges and Universities of Guangdong Province(Grant No.2014KTSCX126)+1 种基金the Foundation for High-Level Talents in Guangdong Higher Education(Grant No.201707010425)the Foundations of Guangzhou Science and Technology(Grant No.201804010350).
文摘We give general solutions(the explicit solutions) of a class of multi-term impulsive fractional differential equations involving the Riemann-Liouville fractional derivatives. This paper contributes within the domain of impulsive fractional differential equations. The author strongly believes that the article will highly be appreciated by the researchers working in the field of fractional calculus and on fractional differential models.
文摘Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
基金Natural Science Foundation of Jilin Province, China(No.200305502)
文摘A novel method for the determination of vitamin C（Vc） is proposed in this article. After the reaction with Folin-Ciocalteau reagent at ambient temperature, Vc solution was scanned at 750--1100 nm, and its first-order derivative spectrum were obtained from the original spectrum. The values of derivative selected at 995 nm were used for determination. It was proved that Vc could quickly react with Folin-Ciocalteau reagent within 5 min and the product was quite stable for a long time. The conditions required for this method is not very complicated, its precision and accuracy are similar to those of the iodometric titration described in Chinese Pharmacopoeia, and the limit of detection is 0.312 μg/mL. The determination of the results of vitamin C tablet, pill, and injection demonstrates that this method has wide pharmaceutical applications.
基金Supported by the National Natural Science Foundation of China (10871029,11071025)the Foundation of CAEP (2010A0202010)the Foundation of National Key Laboratory of Science and Technology on Computational Physics
文摘In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order directional derivatives in three nonparallel directions, or given second-order directional derivatives and mixed directional derivatives in two nonparallel directions, the formulae for the extremum of second-order directional derivatives are derived, and the directions corresponding to maximum and minimum are perpendicular to each other.
文摘It was found that micro amounts of oxalate showed a very strong catalytic effect on the slow reaction between K 2Cr 2O 7 and Orange Ⅳ in a diluted sulfuric acid medium in a water bath at 70 ℃ . Orange Ⅳ exhibited a sensitive second order derivative polarographic wave at -0 50 V( vs . SCE). This provides the basis for a sensitive and selective catalytic kinetic method for oxalate determination with second order derivative oscillopolarography. The effects of sulphuric acid, K 2Cr 2O 7, and orange Ⅳ concentrations, reaction temperature and reaction time were investigated. A calibration curve of oxalate in the range of 0 1-2 0 μg/mL was obtained by the fixed time procedure. The detection limit was 0 03 μg/ mL. The possible interference from co existing substances or ions was examined. The new method has a high sensitivity and a good selectivity compared to other existing methods for oxalic acid determination. It has been applied to the determination of micro amounts of oxalate in real urine samples with satisfactory results.
文摘The Peano derivatives are introduced for functions along an arc in the complex plane. Singular integrals of arbitrary order with singularities at its end-points are defined so that a unified theory for such integrals and Cauchy principal value integrals is established.
文摘This paper deals with the study of fractional order system tuning method based on Factional Order Proportional Integral Derivative( FOPID) controller in allusion to the nonlinear characteristics and fractional order mathematical model of bioengineering systems. The main contents include the design of FOPID controller and the simulation for bioengineering systems. The simulation results show that the tuning method of fractional order system based on the FOPID controller outperforms the fractional order system based on Fractional Order Proportional Integral( FOPI) controller. As it can enhance control character and improve the robustness of the system.
基金National Natural Science Foundations of China(Nos.10972151,11272227,11572212)
文摘The Pfaff-Birkhoff variational problem and its Noether symmetry are studied in terms of Riemann-Liouville fractional derivatives of variable order. Based on the combination of variational principle and fractional calculus of variable order,the Pfaff-Birkhoff variational principle with Riemann-Liouville fractional derivatives of variable order is proposed, and the fractional Birkhoff's equations of variable order are derived. Then,the Noether 's theorem for the fractional Birkhoffian system of variable order is given. At last,an example is expressed to illustrate the application of the results.
基金Project supported by National Natural Science Foundation of China.
文摘In this paper,we obtain the fractal dimension of the graph of the Weierstrass function, its derivative of the fractional order and the relation between the dimension and the order of the fractional derivative.
文摘The equations of the second and third order derivative curves of time with respect to potential for a reversible process in adsorption chronopotentiometry are derived and experimentally verified.
基金Supported by the Natural Science Foundation of Hubei ProvinceChina(No.2 0 0 0 J15 6 )
文摘The design and the synthesis of two conjugated donor acceptor imidazole derivatives(1, 2) were carried out for second order nonlinear optics. The thermal properties, the transparency and second order nonlinear optical properties of the molecules were investigated. The experimental results indicate that a good nonlinearity transparency thermal stability trade off is achieved for them.
文摘The state of Tb3+ is investigated in liposome. When the concentration of PC is below CMC (critical micell concentration), most of Tb3+ is associated with PC, the binding constant is about 3.35×103 L/mol. When the concentration of PC is beyond CMC, most of Tb3+ is dimerized, the dimerization constant is about 3.92×104L/mol. In PC?CH?H2O system, the binding constant of Tb3+?CH complex 2.93×104L/mol is obtained.
基金Supported by the National Natural Science Foundation of China(11361001)Natural Science Foundation of Ningxia(NZ14101)
文摘There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.
文摘alculations of the nonlinear second-order optical susceptlbilities(β_(ijk))for sub- stituted tl1iophene derivative;with quinoidlike conformation are reported.These systetems possess small dipole moment;and large differences between dipole mo- ments of ground and first-excited states.Geometry optimizations of the molecules investigated were carried out using AM 1 method.The calculations were performed using INDO/CI method comboned with a sum-over-states expression for β_(jik). The calculated results sbw that the second-order susceptibility is a function of the na- ture and location of substituents and is larger for disubstituted molecules than monosubstituted molecules. Bipolymeric thiophenemetmne with NH_2/NO_2 groups was calctilated to have a β_μof 79. 920 × 10￣(-30) esu. It was found that the NH_2 and NO_2 groups in above disubstituted molecules are pull-pull groups in ground states,but are usual push-pull groups in the first excited states.
