Under the background of the current energy crisis and environmental pollution,the development of green and sustainable materials has become particularly urgent.As one of the most abundant natural polymers on earth,cel...Under the background of the current energy crisis and environmental pollution,the development of green and sustainable materials has become particularly urgent.As one of the most abundant natural polymers on earth,cellulose has attracted wide attention due to its green recycling,sustainable development,degradability,and low cost.Therefore,cellulose and its derivatives were used as the starting point for comprehensive analysis.First,the basic structural properties of cellulose were discussed,and then the extraction and utilization methods of cellulose were reviewed,including Sodium Hydroxide based solvent system,N,N-Dimethylacetamide/Lithium Chloride System,N-Methylmorpholine-N-Oxide(NMMO)system,ionic liquids(ILs)system,and deep eutectic solvent(DES)system.Then,the functional modification techniques of cellulose are introduced,including nano-modification,small molecule modification,and macromolecular modification.Finally,the potential applications of cellulose in the fields of reinforcement materials,self-healing materials,radioactive cooling,nanogenerators,and biomedicine were discussed.At the end of this paper,the challenges and future development direction of cellulose materials are prospectively analyzed,aiming at providing guidance and inspiration for the research and application in related fields.展开更多
We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan d...We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.展开更多
This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional ...This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.展开更多
In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theo...In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theorem,fractional calculus and resolvent operator functions,we prove the approximate controllability of the considered system.展开更多
Amino acids have emerged as promising green alternatives to replace toxic inhibitors in corrosion protection applications.In this study,we present a one-step synthetic approach to get 4-(tert-butyl)benzoyl)methionine(...Amino acids have emerged as promising green alternatives to replace toxic inhibitors in corrosion protection applications.In this study,we present a one-step synthetic approach to get 4-(tert-butyl)benzoyl)methionine(P-Meth)and 4-(tert-butyl)benzoyl)cysteine(P-Cys)through the acylation reactions between methionine or cysteine and p-tert-butylbenzoic acid,respectively,which exhibit a super protective performance toward metals against corrosion.The corrosion rates of Q235 steel in 1 M HCl were reduced from 4.542 to 0.202and 0.312 mg·h^(-1)·cm^(-2)in the presence of 100 mg·L^(-1)P-Meth and P-Cys,respectively.The surface structures of Q235 steel remained unbroken after 12 h in 1 M HCl medium.The charge transfer resistances of corrosion reactions were enhanced by 12 and 9 times in the presence of P-Meth and P-Cys,respectively.P-Meth and P-Cys were adsorbed onto the Q235 steel via chemical actions,which were accompanied by minimal physical action.Molecular dynamic simulations demonstrate the higher binding energy of P-Meth onto Q235 steel than P-Cys.The study contributes to the corrosion protection of metals with green and environmentally friendly methods.展开更多
A method for determining the extrema of a real-valued and differentiable function for which its dependent variables are subject to constraints and that avoided the use of Lagrange multipliers was previously presented ...A method for determining the extrema of a real-valued and differentiable function for which its dependent variables are subject to constraints and that avoided the use of Lagrange multipliers was previously presented (Corti and Fariello, Op. Res. Forum 2 (2021) 59). The method made use of projection matrices, and a corresponding Gram-Schmidt orthogonalization process, to identify the constrained extrema. Furthermore, information about the second-derivatives of the given function with constraints was generated, from which the nature of the constrained extrema could be determined, again without knowledge of the Lagrange multipliers. Here, the method is extended to the case of functional derivatives with constraints. In addition, constrained first-order and second-order derivatives of the function are generated, in which the derivatives with respect to a given variable are obtained and, concomitantly, the effect of the variations of the remaining chosen set of dependent variables are strictly accounted for. These constrained derivatives are valid not only at the extrema points, and also provide another equivalent route for the determination of the constrained extrema and their nature.展开更多
Graphene/acridine （G-Acr） hybrid structures were synthesized through covalent functionalization of graphene oxide with 9-（4- aminophenyl）acridine （APA） and its derivatives. The G-Act hybrids were characterized b...Graphene/acridine （G-Acr） hybrid structures were synthesized through covalent functionalization of graphene oxide with 9-（4- aminophenyl）acridine （APA） and its derivatives. The G-Act hybrids were characterized by Fourier transform infrared spectroscopy, ultraviolet-visible spectrophotometry, thermal gravimetric analysis and Raman spectroscopy. X-ray photoelectron spectroscopy confirms that the binding energies of APA and its derivatives shifted to higher values, revealing pronounced charge transfer at the interface of graphene and organic molecules.展开更多
In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.
In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation ...The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.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
In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are ap...In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are applied for non-smooth functions which by solving these problems we obtain a kind of generalized first derivatives. For this purpose, a linear programming problem corresponding functional optimization problem is obtained which their optimal solutions give the approximate generalized first derivative. We show the efficiency of our approach by obtaining derivative and generalized derivative of some smooth and nonsmooth functions respectively in some illustrative examples.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.
By using the Cauchy integral formula of bianalytic functions, the formula of higher derivatives of bianalytic functions and Weierstrass Theorem are obtained.
In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their...In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.展开更多
This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of...This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).展开更多
The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen-...The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral.展开更多
This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which adm...This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.展开更多
The present paper generalizes the method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen （2004） to a subclass of nonsymmetric tensor functions satisfying the commu...The present paper generalizes the method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen （2004） to a subclass of nonsymmetric tensor functions satisfying the commutative condition. This subclass of tensor functions is more general than those investigated by the existing methods. In the case of three distinct eigenvalues, the commutativity makes it possible to introduce two scalar functions, which will be used to construct the general nonsymmetric tensor functions and their derivatives. In the cases of repeated eigenvalues, the results are acquired by taking limits.展开更多
基金supported by Research Fund for the Doctoral Program of Higher Education of China(20134420120009)Science and Technology Planning Project of Guangdong(2014A010105047)Science and Technology Planning Project of Guangzhou City(201707010367).
文摘Under the background of the current energy crisis and environmental pollution,the development of green and sustainable materials has become particularly urgent.As one of the most abundant natural polymers on earth,cellulose has attracted wide attention due to its green recycling,sustainable development,degradability,and low cost.Therefore,cellulose and its derivatives were used as the starting point for comprehensive analysis.First,the basic structural properties of cellulose were discussed,and then the extraction and utilization methods of cellulose were reviewed,including Sodium Hydroxide based solvent system,N,N-Dimethylacetamide/Lithium Chloride System,N-Methylmorpholine-N-Oxide(NMMO)system,ionic liquids(ILs)system,and deep eutectic solvent(DES)system.Then,the functional modification techniques of cellulose are introduced,including nano-modification,small molecule modification,and macromolecular modification.Finally,the potential applications of cellulose in the fields of reinforcement materials,self-healing materials,radioactive cooling,nanogenerators,and biomedicine were discussed.At the end of this paper,the challenges and future development direction of cellulose materials are prospectively analyzed,aiming at providing guidance and inspiration for the research and application in related fields.
文摘We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.
基金funded by the Research,Development,and Innovation Authority(RDIA)-Kingdom of Saudi Arabia-with grant number 12803-baha-2023-BU-R-3-1-EI.
文摘This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.
基金Supported by Shandong University of Finance and Economics 2023 International Collaborative Projectsthe National Natural Science Foundation of China(Grant No.62073190)。
文摘In this article,we study the approximate controllability of neutral partial differential equations with Hilfer fractional derivative and not instantaneous impulses effects.By using the Sadovskii's fixed point theorem,fractional calculus and resolvent operator functions,we prove the approximate controllability of the considered system.
基金supported by the Shenzhen Science and Technology Research Fund(Nos.JSGG20201103153807021,GXWD20220811173736002,and KCXFZ20230731094904009)We are also grateful to the Natural Science Foundation of Guangdong Province,China(No.2021 A1515110366)+1 种基金the National Natural Science Foundation of China(Nos.22302048,82204231,and 22004024)the Shenzhen High Tech Zone Development Special Plan Innovation Platform Construction Project,China(No.29853MKCJ-2023-002-11)。
文摘Amino acids have emerged as promising green alternatives to replace toxic inhibitors in corrosion protection applications.In this study,we present a one-step synthetic approach to get 4-(tert-butyl)benzoyl)methionine(P-Meth)and 4-(tert-butyl)benzoyl)cysteine(P-Cys)through the acylation reactions between methionine or cysteine and p-tert-butylbenzoic acid,respectively,which exhibit a super protective performance toward metals against corrosion.The corrosion rates of Q235 steel in 1 M HCl were reduced from 4.542 to 0.202and 0.312 mg·h^(-1)·cm^(-2)in the presence of 100 mg·L^(-1)P-Meth and P-Cys,respectively.The surface structures of Q235 steel remained unbroken after 12 h in 1 M HCl medium.The charge transfer resistances of corrosion reactions were enhanced by 12 and 9 times in the presence of P-Meth and P-Cys,respectively.P-Meth and P-Cys were adsorbed onto the Q235 steel via chemical actions,which were accompanied by minimal physical action.Molecular dynamic simulations demonstrate the higher binding energy of P-Meth onto Q235 steel than P-Cys.The study contributes to the corrosion protection of metals with green and environmentally friendly methods.
文摘A method for determining the extrema of a real-valued and differentiable function for which its dependent variables are subject to constraints and that avoided the use of Lagrange multipliers was previously presented (Corti and Fariello, Op. Res. Forum 2 (2021) 59). The method made use of projection matrices, and a corresponding Gram-Schmidt orthogonalization process, to identify the constrained extrema. Furthermore, information about the second-derivatives of the given function with constraints was generated, from which the nature of the constrained extrema could be determined, again without knowledge of the Lagrange multipliers. Here, the method is extended to the case of functional derivatives with constraints. In addition, constrained first-order and second-order derivatives of the function are generated, in which the derivatives with respect to a given variable are obtained and, concomitantly, the effect of the variations of the remaining chosen set of dependent variables are strictly accounted for. These constrained derivatives are valid not only at the extrema points, and also provide another equivalent route for the determination of the constrained extrema and their nature.
基金the financial support from the National Natural Science Foundation of China(Nos.21072040,21071040, 21101051 and 21272050)the Program for New Century Excellent Talents in University of the Chinese Ministry of Education(No.NCET-11-0627)
文摘Graphene/acridine （G-Acr） hybrid structures were synthesized through covalent functionalization of graphene oxide with 9-（4- aminophenyl）acridine （APA） and its derivatives. The G-Act hybrids were characterized by Fourier transform infrared spectroscopy, ultraviolet-visible spectrophotometry, thermal gravimetric analysis and Raman spectroscopy. X-ray photoelectron spectroscopy confirms that the binding energies of APA and its derivatives shifted to higher values, revealing pronounced charge transfer at the interface of graphene and organic molecules.
基金The research is supported by NNSF of China(19771082)
文摘In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.
文摘In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
文摘The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.
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.
文摘In this paper, we define a functional optimization problem corresponding to smooth functions which its optimal solution is first derivative of these functions in a domain. These functional optimization problems are applied for non-smooth functions which by solving these problems we obtain a kind of generalized first derivatives. For this purpose, a linear programming problem corresponding functional optimization problem is obtained which their optimal solutions give the approximate generalized first derivative. We show the efficiency of our approach by obtaining derivative and generalized derivative of some smooth and nonsmooth functions respectively in some illustrative examples.
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.
文摘By using the Cauchy integral formula of bianalytic functions, the formula of higher derivatives of bianalytic functions and Weierstrass Theorem are obtained.
文摘In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.
基金The second named author was supported in part by an NSERC Postdoctoral Fellowship,Canada and a CR F Grant,University of Alberta
文摘This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).
文摘The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10371098, 10447007 and 10475055）, the Natural Science Foundation of Shaanxi Province of China （Grant No 2005A13）.
文摘This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.
基金the National Natural Science Foundation of China(No.50539030)
文摘The present paper generalizes the method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen （2004） to a subclass of nonsymmetric tensor functions satisfying the commutative condition. This subclass of tensor functions is more general than those investigated by the existing methods. In the case of three distinct eigenvalues, the commutativity makes it possible to introduce two scalar functions, which will be used to construct the general nonsymmetric tensor functions and their derivatives. In the cases of repeated eigenvalues, the results are acquired by taking limits.
