The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic fu...The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.展开更多
In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval...In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.展开更多
Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Nume...Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.展开更多
Using Hartogs’fundamental theorem for analytic functions in several complex variables and q-partial differential equations,we establish a multiple q-exponential differential formula for analytic functions in several ...Using Hartogs’fundamental theorem for analytic functions in several complex variables and q-partial differential equations,we establish a multiple q-exponential differential formula for analytic functions in several variables.With this identity,we give new proofs of a variety of important classical formulas including Bailey’s 6ψ6 series summation formula and the Atakishiyev integral.A new transformation formula for a double q-series with several interesting special cases is given.A new transformation formula for a 3ψ3 series is proved.展开更多
Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this p...Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.展开更多
Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=0.In this paper,we define a new generalized subclass of H associated with the(p,q)-Ruschewey...Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=0.In this paper,we define a new generalized subclass of H associated with the(p,q)-Ruscheweyh-type harmonic differential operator in D.We first obtain a sufficient coefficient condition that guarantees that a function f in H is sense-preserving harmonic univalent in D and belongs to the aforementioned class.Using this coefficient condition,we then examine ratios of partial sums of f in H.In all cases the results are sharp.In addition,the results so obtained generalize the related works of some authors,and many other new results are obtained.展开更多
This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic...This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic differential operator(PDDO),eliminating the need for calibration procedures.The model employs a multi-rate explicit time integration scheme to handle varying time scales in multi-physics systems.Through simulations conducted on granite and ceramic materials,this model demonstrates its effectiveness.It successfully simulates thermal damage behavior in granite arising from incompatible mineral expansion and accurately calculates thermal crack propagation in ceramic slabs during quenching.To account for material heterogeneity,the model utilizes the Shuffle algorithm andWeibull distribution,yielding results that align with numerical simulations and experimental observations.This coupled thermomechanical model shows great promise for analyzing intricate thermomechanical phenomena in brittle materials.展开更多
Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using t...Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.展开更多
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in■.We estimate the relative widths of■and its generalized class K_(p)■(P_(r)),where K_(p)H^(ω)(Pr)is defined by a self-conju...This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in■.We estimate the relative widths of■and its generalized class K_(p)■(P_(r)),where K_(p)H^(ω)(Pr)is defined by a self-conjugate differential operator P_(r)(D)induced by■Also,the modulus of continuity of the r-th derivative,or r-th self-conjugate differential,does not exceed a given modulus of continuityω.Then we obtain the asymptotic results,especially for the case p=∞,1≤q≤∞.展开更多
In this paper,a new subclass of close-to-convex harmonic functions defined by differential operators is introduced.Some properties for functions belonging to that,such as,representation theorem,sufficient conditions,i...In this paper,a new subclass of close-to-convex harmonic functions defined by differential operators is introduced.Some properties for functions belonging to that,such as,representation theorem,sufficient conditions,inclusion relations,coefficient inequalities,growth and convex combination problems are obtained.In addition,the radius of starlike,the radius of convexity and convolution properties of this class are obtained.展开更多
In this paper,the degradation of mechanical properties of engineering cementitious composites(ECCs)at elevated temperatures and the failure of fiber are considered.A failure model under coupled thermo-mechanical loads...In this paper,the degradation of mechanical properties of engineering cementitious composites(ECCs)at elevated temperatures and the failure of fiber are considered.A failure model under coupled thermo-mechanical loads for ECC is developed based on bond-based peridynamics.A semi-discrete model is constructed to describe fiber–matrix interactions and simulate thermal failure in ECC.The peridynamic differential operator(PDDO)is utilized for non-local modeling of thermal fluid flow and heat transfer.A multi-rate explicit time integration method is adopted to address thermo-mechanical coupling over different time scales.Model validation is achieved through simulating transient heat transfer in a homogeneous plate,with results aligning with analytical solutions.The damage behavior of a heated ECC plate in a borehole and under a fire scenario is analyzed,providing insights for enhancing fire resistance and high-temperature performance of ECC materials and structures.展开更多
When D:ξ→η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D<sub>1:</su...When D:ξ→η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D<sub>1:</sub>η→ξ such that Dξ = η implies D<sub>1</sub>η = 0. When D is involutive, the procedure provides successive first-order involutive operators D<sub>1</sub>,...,D<sub>n </sub>when the ground manifold has dimension n. Conversely, when D<sub>1</sub> is given, a much more difficult “inverse problem” is to look for an operator D:ξ→η having the generating CC D<sub>1</sub>η = 0. If this is possible, that is when the differential module defined by D<sub>1</sub> is “torsion-free”, that is when there does not exist any observable quantity which is a sum of derivatives of η that could be a solution of an autonomous OD or PD equation for itself, one shall say that the operator D<sub>1</sub> is parametrized by D. The parametrization is said to be “minimum” if the differential module defined by D does not contain a free differential submodule. The systematic use of the adjoint of a differential operator provides a constructive test with five steps using double differential duality. We prove and illustrate through many explicit examples the fact that a control system is controllable if and only if it can be parametrized. Accordingly, the controllability of any OD or PD control system is a “built in” property not depending on the choice of the input and output variables among the system variables. In the OD case and when D<sub>1</sub> is formally surjective, controllability just amounts to the formal injectivity of ad(D<sub>1</sub>), even in the variable coefficients case, a result still not acknowledged by the control community. Among other applications, the parametrization of the Cauchy stress operator in arbitrary dimension n has attracted many famous scientists (G. B. Airy in 1863 for n = 2, J. C. Maxwell in 1870, E. Beltrami in 1892 for n = 3, and A. Einstein in 1915 for n = 4). We prove that all these works are already explicitly using the self-adjoint Einstein operator, which cannot be parametrized and the comparison needs no comment. As a byproduct, they are all based on a confusion between the so-called div operator D<sub>2</sub> induced from the Bianchi operator and the Cauchy operator, adjoint of the Killing operator D which is parametrizing the Riemann operator D<sub>1</sub> for an arbitrary n. This purely mathematical result deeply questions the origin and existence of gravitational waves, both with the mathematical foundations of general relativity. As a matter of fact, this new framework provides a totally open domain of applications for computer algebra as the quoted test can be studied by means of Pommaret bases and related recent packages.展开更多
To fully extract and mine the multi-scale features of reservoirs and geologic structures in time/depth and space dimensions, a new 3D multi-scale volumetric curvature （MSVC） methodology is presented in this paper. W...To fully extract and mine the multi-scale features of reservoirs and geologic structures in time/depth and space dimensions, a new 3D multi-scale volumetric curvature （MSVC） methodology is presented in this paper. We also propose a fast algorithm for computing 3D volumetric curvature. In comparison to conventional volumetric curvature attributes, its main improvements and key algorithms introduce multi-frequency components expansion in time-frequency domain and the corresponding multi-scale adaptive differential operator in the wavenumber domain, into the volumetric curvature calculation. This methodology can simultaneously depict seismic multi-scale features in both time and space. Additionally, we use data fusion of volumetric curvatures at various scales to take full advantage of the geologic features and anomalies extracted by curvature measurements at different scales. The 3D MSVC can highlight geologic anomalies and reduce noise at the same time. Thus, it improves the interpretation efficiency of curvature attributes analysis. The 3D MSVC is applied to both land and marine 3D seismic data. The results demonstrate that it can indicate the spatial distribution of reservoirs, detect faults and fracture zones, and identify their multi-scale properties.展开更多
In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions bel...In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions belonging to the classes Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）are investigated. Also, we point out some new or known consequences of our main results.展开更多
Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient con...Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical ＇σ/σx＇-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic(MHD)time-dependent Maxwell fluid over an unbounded plate embedded ...The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic(MHD)time-dependent Maxwell fluid over an unbounded plate embedded in a permeable medium.Non-dimensional parameters along with Laplace transformation and inversion algorithms are used to find the solution of shear stress,energy,and velocity profile.Recently,new fractional differential operators are used to define ramped temperature and ramped velocity.The obtained analytical solutions are plotted for different values of emerging parameters.Fractional time derivatives are used to analyze the impact of fractional parameters(memory effect)on the dynamics of the fluid.While making a comparison,it is observed that the fractional-order model is best to explain the memory effect as compared to classical models.Our results suggest that the velocity profile decrease by increasing the effective Prandtl number.The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.The incremental value of the M is observed for a decrease in the velocity field,which reflects to control resistive force.Further,it is noted that the Atangana-Baleanu derivative in Caputo sense(ABC)is the best to highlight the dynamics of the fluid.The influence of pertinent parameters is analyzed graphically for velocity and energy profile.Expressions for skin friction and Nusselt number are also derived for fractional differential operators.展开更多
In the cost function of three- or four-dimensional variational dataassimilation, each term is weighted by the inverse of its associated error covariance matrix and thebackground error covariance matrix is usually much...In the cost function of three- or four-dimensional variational dataassimilation, each term is weighted by the inverse of its associated error covariance matrix and thebackground error covariance matrix is usually much larger than the other covariance matrices.Although the background error covariances are traditionally normalized and parameterized by simplesmooth homogeneous correlation functions, the covariance matrices constructed from these correlationfunctions are often too large to be inverted or even manipulated. It is thus desirable to finddirect representations of the inverses of background error correlations. This problem is studied inthis paper. In particular, it is shown that the background term can be written into ∫ dx∣Dυ(x)∣~2, that is, a squared 1/2 norm of a vector differential operator D, called theD-operator, applied to the field of analysis increment υ(x). For autoregressive correlationfunctions, the D-operators are of finite orders. For Gaussian correlation functions, the D-operatorsare of infinite order. For practical applications, the Gaussian D-operators must be truncated tofinite orders. The truncation errors are found to be small even when the Gaussian D-operators aretruncated to low orders. With a truncated D-operator, the background term can be easily constructedwith neither inversion nor direct calculation of the covariance matrix. D-operators are also derivedfor non-Gaussian correlations and transformed into non-isotropic forms.展开更多
基金Supported by Natural Science Foundation of Guangdong Province in China(2018KTSCX161)。
文摘The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.
基金Supported by NSFC (No.12361027)NSF of Inner Mongolia (No.2018MS01021)+1 种基金NSF of Shandong Province (No.ZR2020QA009)Science and Technology Innovation Program for Higher Education Institutions of Shanxi Province (No.2024L533)。
文摘In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.
基金supported by Ajman University Internal Research Grant No.(DRGS Ref.2024-IRGHBS-3).
文摘Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.
基金supported by the National Natural Science Foundation of China(11971173)the Science and Technology Commission of Shanghai Municipality(22DZ2229014).
文摘Using Hartogs’fundamental theorem for analytic functions in several complex variables and q-partial differential equations,we establish a multiple q-exponential differential formula for analytic functions in several variables.With this identity,we give new proofs of a variety of important classical formulas including Bailey’s 6ψ6 series summation formula and the Atakishiyev integral.A new transformation formula for a double q-series with several interesting special cases is given.A new transformation formula for a 3ψ3 series is proved.
文摘Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.
文摘Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=0.In this paper,we define a new generalized subclass of H associated with the(p,q)-Ruscheweyh-type harmonic differential operator in D.We first obtain a sufficient coefficient condition that guarantees that a function f in H is sense-preserving harmonic univalent in D and belongs to the aforementioned class.Using this coefficient condition,we then examine ratios of partial sums of f in H.In all cases the results are sharp.In addition,the results so obtained generalize the related works of some authors,and many other new results are obtained.
基金supported by the University Natural Science Foundation of Jiangsu Province(Grant No.23KJB130004)the National Natural Science Foundation of China(Grant Nos.11932006,U1934206,12172121,12002118).
文摘This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic differential operator(PDDO),eliminating the need for calibration procedures.The model employs a multi-rate explicit time integration scheme to handle varying time scales in multi-physics systems.Through simulations conducted on granite and ceramic materials,this model demonstrates its effectiveness.It successfully simulates thermal damage behavior in granite arising from incompatible mineral expansion and accurately calculates thermal crack propagation in ceramic slabs during quenching.To account for material heterogeneity,the model utilizes the Shuffle algorithm andWeibull distribution,yielding results that align with numerical simulations and experimental observations.This coupled thermomechanical model shows great promise for analyzing intricate thermomechanical phenomena in brittle materials.
基金This work was financially supported by the Key Science and Technology Project of Longmen Laboratory(No.LMYLKT-001)Innovation and Entrepreneurship Training Program for College Students of Henan Province(No.202310464050)。
文摘Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
基金supported by National Natural Science Foundation of China(11871006).
文摘This paper investigates the relative Kolmogorov n-widths of 2π-periodic smooth classes in■.We estimate the relative widths of■and its generalized class K_(p)■(P_(r)),where K_(p)H^(ω)(Pr)is defined by a self-conjugate differential operator P_(r)(D)induced by■Also,the modulus of continuity of the r-th derivative,or r-th self-conjugate differential,does not exceed a given modulus of continuityω.Then we obtain the asymptotic results,especially for the case p=∞,1≤q≤∞.
基金Supported by the Natural Science Foundation of Inner Mongolia(Grant Nos.2024MS01014,2022MS01004)the Higher-School Science Foundation of Inner Mongolia(Grant No.NJZZ19209)。
文摘In this paper,a new subclass of close-to-convex harmonic functions defined by differential operators is introduced.Some properties for functions belonging to that,such as,representation theorem,sufficient conditions,inclusion relations,coefficient inequalities,growth and convex combination problems are obtained.In addition,the radius of starlike,the radius of convexity and convolution properties of this class are obtained.
基金supported by National Natural Science Foundation of China(Grant Numbers 11872339,11472248).
文摘In this paper,the degradation of mechanical properties of engineering cementitious composites(ECCs)at elevated temperatures and the failure of fiber are considered.A failure model under coupled thermo-mechanical loads for ECC is developed based on bond-based peridynamics.A semi-discrete model is constructed to describe fiber–matrix interactions and simulate thermal failure in ECC.The peridynamic differential operator(PDDO)is utilized for non-local modeling of thermal fluid flow and heat transfer.A multi-rate explicit time integration method is adopted to address thermo-mechanical coupling over different time scales.Model validation is achieved through simulating transient heat transfer in a homogeneous plate,with results aligning with analytical solutions.The damage behavior of a heated ECC plate in a borehole and under a fire scenario is analyzed,providing insights for enhancing fire resistance and high-temperature performance of ECC materials and structures.
文摘When D:ξ→η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D<sub>1:</sub>η→ξ such that Dξ = η implies D<sub>1</sub>η = 0. When D is involutive, the procedure provides successive first-order involutive operators D<sub>1</sub>,...,D<sub>n </sub>when the ground manifold has dimension n. Conversely, when D<sub>1</sub> is given, a much more difficult “inverse problem” is to look for an operator D:ξ→η having the generating CC D<sub>1</sub>η = 0. If this is possible, that is when the differential module defined by D<sub>1</sub> is “torsion-free”, that is when there does not exist any observable quantity which is a sum of derivatives of η that could be a solution of an autonomous OD or PD equation for itself, one shall say that the operator D<sub>1</sub> is parametrized by D. The parametrization is said to be “minimum” if the differential module defined by D does not contain a free differential submodule. The systematic use of the adjoint of a differential operator provides a constructive test with five steps using double differential duality. We prove and illustrate through many explicit examples the fact that a control system is controllable if and only if it can be parametrized. Accordingly, the controllability of any OD or PD control system is a “built in” property not depending on the choice of the input and output variables among the system variables. In the OD case and when D<sub>1</sub> is formally surjective, controllability just amounts to the formal injectivity of ad(D<sub>1</sub>), even in the variable coefficients case, a result still not acknowledged by the control community. Among other applications, the parametrization of the Cauchy stress operator in arbitrary dimension n has attracted many famous scientists (G. B. Airy in 1863 for n = 2, J. C. Maxwell in 1870, E. Beltrami in 1892 for n = 3, and A. Einstein in 1915 for n = 4). We prove that all these works are already explicitly using the self-adjoint Einstein operator, which cannot be parametrized and the comparison needs no comment. As a byproduct, they are all based on a confusion between the so-called div operator D<sub>2</sub> induced from the Bianchi operator and the Cauchy operator, adjoint of the Killing operator D which is parametrizing the Riemann operator D<sub>1</sub> for an arbitrary n. This purely mathematical result deeply questions the origin and existence of gravitational waves, both with the mathematical foundations of general relativity. As a matter of fact, this new framework provides a totally open domain of applications for computer algebra as the quoted test can be studied by means of Pommaret bases and related recent packages.
基金supported by the National Natural Science Foundation of China (No. 41004054) Research Fund for the Doctoral Program of Higher Education of China (No. 20105122120002)Natural Science Key Project, Sichuan Provincial Department of Education (No. 092A011)
文摘To fully extract and mine the multi-scale features of reservoirs and geologic structures in time/depth and space dimensions, a new 3D multi-scale volumetric curvature （MSVC） methodology is presented in this paper. We also propose a fast algorithm for computing 3D volumetric curvature. In comparison to conventional volumetric curvature attributes, its main improvements and key algorithms introduce multi-frequency components expansion in time-frequency domain and the corresponding multi-scale adaptive differential operator in the wavenumber domain, into the volumetric curvature calculation. This methodology can simultaneously depict seismic multi-scale features in both time and space. Additionally, we use data fusion of volumetric curvatures at various scales to take full advantage of the geologic features and anomalies extracted by curvature measurements at different scales. The 3D MSVC can highlight geologic anomalies and reduce noise at the same time. Thus, it improves the interpretation efficiency of curvature attributes analysis. The 3D MSVC is applied to both land and marine 3D seismic data. The results demonstrate that it can indicate the spatial distribution of reservoirs, detect faults and fracture zones, and identify their multi-scale properties.
基金Supported by the National Natural Science Foundation of China(Grant No.11271045)the Funds of Doctoral Programme of China(Grant No.20100003110004)the Natural Science Foundation of Inner Mongolia Province(Grant No.2010MS0117)
文摘In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions belonging to the classes Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）are investigated. Also, we point out some new or known consequences of our main results.
基金Project supported by the National Natural Science Foundation of China （Grant No 10562002） and the Natural Science Foundation of Nei Mongol, China （Grant No 200508010103）.
文摘Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical ＇σ/σx＇-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
文摘The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic(MHD)time-dependent Maxwell fluid over an unbounded plate embedded in a permeable medium.Non-dimensional parameters along with Laplace transformation and inversion algorithms are used to find the solution of shear stress,energy,and velocity profile.Recently,new fractional differential operators are used to define ramped temperature and ramped velocity.The obtained analytical solutions are plotted for different values of emerging parameters.Fractional time derivatives are used to analyze the impact of fractional parameters(memory effect)on the dynamics of the fluid.While making a comparison,it is observed that the fractional-order model is best to explain the memory effect as compared to classical models.Our results suggest that the velocity profile decrease by increasing the effective Prandtl number.The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.The incremental value of the M is observed for a decrease in the velocity field,which reflects to control resistive force.Further,it is noted that the Atangana-Baleanu derivative in Caputo sense(ABC)is the best to highlight the dynamics of the fluid.The influence of pertinent parameters is analyzed graphically for velocity and energy profile.Expressions for skin friction and Nusselt number are also derived for fractional differential operators.
文摘In the cost function of three- or four-dimensional variational dataassimilation, each term is weighted by the inverse of its associated error covariance matrix and thebackground error covariance matrix is usually much larger than the other covariance matrices.Although the background error covariances are traditionally normalized and parameterized by simplesmooth homogeneous correlation functions, the covariance matrices constructed from these correlationfunctions are often too large to be inverted or even manipulated. It is thus desirable to finddirect representations of the inverses of background error correlations. This problem is studied inthis paper. In particular, it is shown that the background term can be written into ∫ dx∣Dυ(x)∣~2, that is, a squared 1/2 norm of a vector differential operator D, called theD-operator, applied to the field of analysis increment υ(x). For autoregressive correlationfunctions, the D-operators are of finite orders. For Gaussian correlation functions, the D-operatorsare of infinite order. For practical applications, the Gaussian D-operators must be truncated tofinite orders. The truncation errors are found to be small even when the Gaussian D-operators aretruncated to low orders. With a truncated D-operator, the background term can be easily constructedwith neither inversion nor direct calculation of the covariance matrix. D-operators are also derivedfor non-Gaussian correlations and transformed into non-isotropic forms.
