In order to study the temporal and spatial variation characteristics of the regional ionosphere and the modeling accuracy,the experiment is based on the spherical harmonic function model,using the GPS,Glonass,and Gali...In order to study the temporal and spatial variation characteristics of the regional ionosphere and the modeling accuracy,the experiment is based on the spherical harmonic function model,using the GPS,Glonass,and Galileo dual-frequency observation data from the 305th-334th day of the European CORS network in 2019 to establish a global ionospheric model.By analyzing and evaluating the accuracy of the global ionospheric puncture points,VTEC,and comparing code products,the test results showed that the GPS system has the most dense puncture electricity distribution,the Glonass system is the second,and the Galileo system is the weakest.The values of ionospheric VTEC calculated by GPS,Glonass and Galileo are slightly different,but in terms of trends,they are the same as those of ESA,JPL and UPC.GPS data has the highest accuracy in global ionospheric modeling.GPS,Glonass and Galileo have the same trend,but Glonass data is unstable and fluctuates greatly.展开更多
Spherical harmonic analysis(SHA)and synthesis(SHS)are widely used by researchers in various fields.Both numerical integration and least-squares methods can be employed for analysis and synthesis.However,these approach...Spherical harmonic analysis(SHA)and synthesis(SHS)are widely used by researchers in various fields.Both numerical integration and least-squares methods can be employed for analysis and synthesis.However,these approaches,when calculated via summation,are computationally intensive.Although the Fast Fourier Transform(FFT)algorithm is efficient,it is traditionally limited to processing global grid points starting from zero longitude.In this paper,we derive an improved FFT algorithm for spherical harmonic analysis and synthesis.The proposed algorithm eliminates the need for grid points to start at zero longitude,thereby expanding the applicability of FFT-based methods.Numerical experiments demonstrate that the new algorithm retains the computational efficiency of conventional FFT while achieving accuracy comparable to the summation method.Consequently,it enables direct harmonic coefficient calculation from global grid data without requiring interpolation to align with zero longitude.Additionally,the algrithm can generate grid points with equi-angular spacing using the improved FFT algorithm,starting from non-zero longitudes.To address the loss of orthogonality in latitude due to discrete spherical grids,a quadrature weight factor-dependent on grid type(e.g.,regular or Gauss grid)-is incorporated,as summarized in this study.展开更多
The global gravitational model can be expressed as a series of spherical harmonic coefficients computed up to a certain degree and order.The main ordering characteristic can depend on the degree,order,or type of coeff...The global gravitational model can be expressed as a series of spherical harmonic coefficients computed up to a certain degree and order.The main ordering characteristic can depend on the degree,order,or type of coefficient.When determining the spherical harmonic coefficients using the least squares method,it is essential to analyze the ordering pattern of these coefficients and their positions(e.g.,indices)in the vector or matrix.A systematic analysis on the type of coefficient arrangement is presented in this paper.Moreover,the index algorithm for each coefficient ordering pattern is provided.Additionally,the structure of the normal equation matrix with different coefficient arrangement patterns is analyzed.Based on the analysis and the algorithm presented in this paper:(1)we can calculate the index of each coefficient in the vector or matrix of the normal equation;(2)we can change the structure of the normal equation matrix of the Earth’s gravity field from one type of coefficient arrangement to another.Furthermore,(3)we can directly combine different structures of the normal equation matrix,calculated from different types of gravity satellite missions,to form combined normal equations.This approach is beneficial for the determination of Earth’s gravitational model using multi-type observation data.展开更多
In this paper, applying the theory of complex-functional, not only the spaceharmonic functions in polynomial form. but aIso the spherical functions are obtained.
The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer fro...The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer from numerical overflow or underflow when the Bessel function’s order is large,the argument is small or the argument has a large imaginary part.The first two issues have been solved recently by employing small-argument asymptotic formulas of Bessel functions,while the third issue remains unsolved.In this paper,the Bessel functions in the conventional formulation of the theory are replaced by scaled Bessel functions which have good numerical properties for high loss media,and stable formulas are derived.Numerical tests show that this approach can work properly with very high lossy media.Also,this approach can be seamlessly combined with the stable computation method for cases of small argument and large order of Bessel functions.展开更多
Permanent dipole moments induced high-order harmonic generation(HHG)signals offer a potential approach to producing elliptically or even circularly polarized X-ray attosecond sources.Previous studies on this topic hav...Permanent dipole moments induced high-order harmonic generation(HHG)signals offer a potential approach to producing elliptically or even circularly polarized X-ray attosecond sources.Previous studies on this topic have mainly focused on diatomic molecules such as CO and HeH.Based on this scheme,significant HHG signals in the direction perpendicular to the molecular axis can be observed in both the high-energy and low-energy regions.However,we found that the high-order harmonics induced by the permanent dipole moments of polyatomic complex molecules involve more intricate physical processes.Using time-dependent density functional theory,we simulated the dynamics of HHG from NH2COOH and NH2COSH interacting with linearly polarized lasers.We found that the harmonic signals in the direction perpendicular to the N-C bond were significantly enhanced in the high-energy photon region.Our analysis indicates that this is due to the complex molecular configuration of NH_(2)COOH and NH_(2)COSH:while the NH_(2) group has C_(2v) symmetry,both COOH and COSH groups lack this symmetry.This structural characteristic results in permanent dipole moments being felt only when electrons return to either COSH or COOH groups,but not to NH_(2) group.Additionally,our results reveal a multi-plateau structure in HHG signal along laser polarization direction,a phenomenon arising from multi-electron and multiorbital effects during interaction between complex molecule and strong laser field.展开更多
Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or e...Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or eliminated.In order to improve the accuracy of GPS positioning,the single-epoch pseudorange multipath effects at GPS station were calculated,and firstly modeled based on the spherical cap harmonic（SCH）,which is the function of satellite longitude and latitude with the robust method.The accuracy of the kinematic point positioning technique was improved by correcting pseudorange observations with the multipath effect calculated by the SCH model,especially in the elevation direction.The spherical cap harmonic can be used to model the pseudorange multipath effect.展开更多
In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequa...In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequalities are established.展开更多
A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α...A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.展开更多
The microscopic characteristics of skeletal particles in rock and soil media have important effects on macroscopic mechanical properties.A mathematical procedure called spherical harmonic function analysis was here de...The microscopic characteristics of skeletal particles in rock and soil media have important effects on macroscopic mechanical properties.A mathematical procedure called spherical harmonic function analysis was here developed to characterize micromorphology of particles and determine the meso effects in a discrete manner.This method has strong mathematical properties with respect to orthogonality and rotating invariance.It was used here to characterize and reconstruct particle micromorphology in three-dimensional space.The applicability and accuracy of the method were assessed through comparison of basic geometric properties such as volume and surface area.The results show that the micromorphological characteristics of reproduced particles become more and more readily distinguishable as the reproduced order number of spherical harmonic function increases,and the error can be brought below 5%when the order number reaches 10.This level of precision is sharp enough to distinguish the characteristics of real particles.Reconstructed particles of the same size but different reconstructed orders were used to form cylindrical samples,and the stress-strain curves of these samples filled with different-order particles which have their mutual morphological features were compared using PFC3D.Results show that the higher the spherical harmonic order of reconstructed particles,the lower the initial compression modulus and the larger the strain at peak intensity.However,peak strength shows only a random relationship to spherical harmonic order.Microstructure reconstruction was here shown to be an efficient means of numerically simulating of multi-scale rock and soil media and studying the mechanical properties of soil samples.展开更多
We used CHAMP satellite vector data and the latest IGRF12 model to investigate the regional magnetic anomalies over China's Mainland. We assumed satellite points on the same surface （307.69 km） and constructed a...We used CHAMP satellite vector data and the latest IGRF12 model to investigate the regional magnetic anomalies over China's Mainland. We assumed satellite points on the same surface （307.69 km） and constructed a spherical cap harmonic model of the satellite magnetic anomalies for elements X, Y, Z, and F over Chinese mainland for 2010.0 （SCH2010） based on selected 498 points. We removed the external field by using the CM4 model. The pole of the spherical cap is 36N° and 104°E, and its half-angle is 30°. After checking and comparing the root mean square （RMS） error of AX, AY, and AZ and X, Y, and Z, we established the truncation level at Kmax = 9. The results suggest that the created China Geomagnetic Referenced Field at the satellite level （CGRF2010） is consistent with the CM4 model. We compared the SCH2010 with other models and found that the intensities and distributions are consistent. In view of the variation off at different altitudes, the SCH2010 model results obey the basics of the geomagnetic field. Moreover, the change rate of X, Y, and Z for SCH2010 and CM4 are consistent. The proposed model can successfully reproduce the geomagnetic data, as other data-fitting models, but the inherent sources of error have to be considered as well.展开更多
This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials (FGMs). The pressur...This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials (FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier’s equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement, strains, and stresses are determined by the exact solution to Navier’s equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.展开更多
In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with vary...In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.展开更多
The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize th...The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.展开更多
The idea of Green quasifunction method is clarified in detail by considering a free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation.A Green quasifunction is established ...The idea of Green quasifunction method is clarified in detail by considering a free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation,the irregularity of the kernel of integral equations is avoided.Finally,natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasifunction method.展开更多
Recently,the simplified spherical harmonics equations(SP)model has at tracted much att entionin modeling the light propagation in small tissue ggeometriesat visible and near-infrared wave-leng ths.In this paper,we rep...Recently,the simplified spherical harmonics equations(SP)model has at tracted much att entionin modeling the light propagation in small tissue ggeometriesat visible and near-infrared wave-leng ths.In this paper,we report an eficient numerical method for fluorescence moleeular tom-ography(FMT)that combines the advantage of SP model and adaptive hp finite elementmethod(hp-FEM).For purposes of comparison,hp-FEM and h-FEM are,respectively applied tothe reconstruction pro cess with diffusion approximation and SPs model.Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are designed to evaluate thereconstruction methods in terms of the location and the reconstructed fluorescent yield.Theexperimental results demonstrate that hp-FEM with SPy model,yield more accurate results thanh-FEM with difusion approximation model does.The phantom experiments show the potentialand feasibility of the proposed approach in FMT applications.展开更多
A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) b...A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) by generalized Salagean operator of harmonic univalent functions.We give sufficient coefficient conditions for normalized harmonic functions in the class LH_λ(α,β).These conditions are also shown to be necessary when the coefficients are negative.This leads to distortion bounds and extreme points.展开更多
The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application,...The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.展开更多
Based on the CHAMP Magsat data set, spherical cap harmonic analysis was used to model the magnetic fields over China continent. The data set used in the analysis includes the 15′×15′ gridded values of the CHAMP...Based on the CHAMP Magsat data set, spherical cap harmonic analysis was used to model the magnetic fields over China continent. The data set used in the analysis includes the 15′×15′ gridded values of the CHAMP anomaly fields (latitude φ=25°N to 50°N and longitude λ=78°E to 135°E). The pole of the cap is located at φ=35°N and λ=110°E with half-angle of 30°. The maximum index (K max) of the model is 30 and the total number of model coefficients is 961, which corresponds to the minimum wavelength at the earth's surface about 400 km. The root mean square (RMS) deviations between the calculated and observed values are ～ 4 nT for ΔX, ～ 3 nT for ΔY and ～ 3.5 nT for ΔZ, respectively. Results show that positive anomalies are found mainly at the Tarim basin with ～6- 8 nT, the Yangtze platform and North China platform with ～4 nT, and the Songliao basin with ～4-6 nT. In contrast, negative anomaly is mainly located in the Tibet orogenic belt with the amplitude ～ (-6)-(-8) nT. Upward continuation of magnetic anomalies was used to semi-quantitatively separate the magnetic anomalies in different depths of crust. The magnetic anomalies at the earth's surface are from -6 to 10 nT for upper crust, middle crust -27 to 42 nT and lower crust -12 to 18 nT, respectively. The strikes of the magnetic anomalies for the upper crust are consistent with those for the middle crust, but not for the lower crust. The high positive magnetic anomalies mainly result from the old continental nucleus and diastrophic block (e.g. middle Sichuan continental nucleus, middle Tarim basin continental nucleus, Junggar diastrophic block and Qaidam diastrophic block). The amplitudes of the magnetic anomalies of the old continental nucleus and diastrophic block are related to evolution of deep crust. These results improve our understanding of the crustal structure over China continent.展开更多
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
基金Key Research and Development Program of Liaoning Province(2020JH2/10100044)National Natural Science Foundation of China(41904037)National Key Basic Research and Development Program(973 Program)(2016YFC0803102)。
文摘In order to study the temporal and spatial variation characteristics of the regional ionosphere and the modeling accuracy,the experiment is based on the spherical harmonic function model,using the GPS,Glonass,and Galileo dual-frequency observation data from the 305th-334th day of the European CORS network in 2019 to establish a global ionospheric model.By analyzing and evaluating the accuracy of the global ionospheric puncture points,VTEC,and comparing code products,the test results showed that the GPS system has the most dense puncture electricity distribution,the Glonass system is the second,and the Galileo system is the weakest.The values of ionospheric VTEC calculated by GPS,Glonass and Galileo are slightly different,but in terms of trends,they are the same as those of ESA,JPL and UPC.GPS data has the highest accuracy in global ionospheric modeling.GPS,Glonass and Galileo have the same trend,but Glonass data is unstable and fluctuates greatly.
基金supported by The National Natural Science Foundation of China(42374004).
文摘Spherical harmonic analysis(SHA)and synthesis(SHS)are widely used by researchers in various fields.Both numerical integration and least-squares methods can be employed for analysis and synthesis.However,these approaches,when calculated via summation,are computationally intensive.Although the Fast Fourier Transform(FFT)algorithm is efficient,it is traditionally limited to processing global grid points starting from zero longitude.In this paper,we derive an improved FFT algorithm for spherical harmonic analysis and synthesis.The proposed algorithm eliminates the need for grid points to start at zero longitude,thereby expanding the applicability of FFT-based methods.Numerical experiments demonstrate that the new algorithm retains the computational efficiency of conventional FFT while achieving accuracy comparable to the summation method.Consequently,it enables direct harmonic coefficient calculation from global grid data without requiring interpolation to align with zero longitude.Additionally,the algrithm can generate grid points with equi-angular spacing using the improved FFT algorithm,starting from non-zero longitudes.To address the loss of orthogonality in latitude due to discrete spherical grids,a quadrature weight factor-dependent on grid type(e.g.,regular or Gauss grid)-is incorporated,as summarized in this study.
基金supported by The National Natural Science Foundation of China(42374004).
文摘The global gravitational model can be expressed as a series of spherical harmonic coefficients computed up to a certain degree and order.The main ordering characteristic can depend on the degree,order,or type of coefficient.When determining the spherical harmonic coefficients using the least squares method,it is essential to analyze the ordering pattern of these coefficients and their positions(e.g.,indices)in the vector or matrix.A systematic analysis on the type of coefficient arrangement is presented in this paper.Moreover,the index algorithm for each coefficient ordering pattern is provided.Additionally,the structure of the normal equation matrix with different coefficient arrangement patterns is analyzed.Based on the analysis and the algorithm presented in this paper:(1)we can calculate the index of each coefficient in the vector or matrix of the normal equation;(2)we can change the structure of the normal equation matrix of the Earth’s gravity field from one type of coefficient arrangement to another.Furthermore,(3)we can directly combine different structures of the normal equation matrix,calculated from different types of gravity satellite missions,to form combined normal equations.This approach is beneficial for the determination of Earth’s gravitational model using multi-type observation data.
文摘In this paper, applying the theory of complex-functional, not only the spaceharmonic functions in polynomial form. but aIso the spherical functions are obtained.
文摘The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer from numerical overflow or underflow when the Bessel function’s order is large,the argument is small or the argument has a large imaginary part.The first two issues have been solved recently by employing small-argument asymptotic formulas of Bessel functions,while the third issue remains unsolved.In this paper,the Bessel functions in the conventional formulation of the theory are replaced by scaled Bessel functions which have good numerical properties for high loss media,and stable formulas are derived.Numerical tests show that this approach can work properly with very high lossy media.Also,this approach can be seamlessly combined with the stable computation method for cases of small argument and large order of Bessel functions.
基金supported by the Fundamental Research Funds for the Central Universities(Grant Nos.GK202207012 and QCYRCXM-2022-241).
文摘Permanent dipole moments induced high-order harmonic generation(HHG)signals offer a potential approach to producing elliptically or even circularly polarized X-ray attosecond sources.Previous studies on this topic have mainly focused on diatomic molecules such as CO and HeH.Based on this scheme,significant HHG signals in the direction perpendicular to the molecular axis can be observed in both the high-energy and low-energy regions.However,we found that the high-order harmonics induced by the permanent dipole moments of polyatomic complex molecules involve more intricate physical processes.Using time-dependent density functional theory,we simulated the dynamics of HHG from NH2COOH and NH2COSH interacting with linearly polarized lasers.We found that the harmonic signals in the direction perpendicular to the N-C bond were significantly enhanced in the high-energy photon region.Our analysis indicates that this is due to the complex molecular configuration of NH_(2)COOH and NH_(2)COSH:while the NH_(2) group has C_(2v) symmetry,both COOH and COSH groups lack this symmetry.This structural characteristic results in permanent dipole moments being felt only when electrons return to either COSH or COOH groups,but not to NH_(2) group.Additionally,our results reveal a multi-plateau structure in HHG signal along laser polarization direction,a phenomenon arising from multi-electron and multiorbital effects during interaction between complex molecule and strong laser field.
基金Project (41374009) supported by the National Natural Science Foundation of ChinaProjects (TJES1101,TJES1203) supported by the Key Laboratory of Advanced Engineering Surveying of NASMG,China+1 种基金Project (ZR2013DM009) supported by the Shandong Natural Science Foundation of ChinaProject (201412001) supported by the Public Benefit Scientific Research Project of China
文摘Most GPS positioning errors can be eliminated or removed by the differential technique or the modeling method,but the multipath effect is a special kind of system or gross error,so it is difficult to be simulated or eliminated.In order to improve the accuracy of GPS positioning,the single-epoch pseudorange multipath effects at GPS station were calculated,and firstly modeled based on the spherical cap harmonic（SCH）,which is the function of satellite longitude and latitude with the robust method.The accuracy of the kinematic point positioning technique was improved by correcting pseudorange observations with the multipath effect calculated by the SCH model,especially in the elevation direction.The spherical cap harmonic can be used to model the pseudorange multipath effect.
基金supported by NSFC (60850005)NSF of Zhejiang Province(D7080080, Y7080185, Y607128)
文摘In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequalities are established.
基金Supported by the Key Scientific Research Fund of Inner Mongolian Educational Bureau (NJ04115)
文摘A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.
基金Project(2015CB057903)supported by the National Basic Research Program of ChinaProjects(51679071,51309089)supported by the National Natural Science Foundation of China+2 种基金Project(BK20130846)supported by the Natural Science Foundation of Jiangsu Province,ChinaProject(2013BAB06B00)supported by the National Key Technology R&D Program,ChinaProject(2015B06014)supported by the Fundamental Research Funds for the Central Universities,China
文摘The microscopic characteristics of skeletal particles in rock and soil media have important effects on macroscopic mechanical properties.A mathematical procedure called spherical harmonic function analysis was here developed to characterize micromorphology of particles and determine the meso effects in a discrete manner.This method has strong mathematical properties with respect to orthogonality and rotating invariance.It was used here to characterize and reconstruct particle micromorphology in three-dimensional space.The applicability and accuracy of the method were assessed through comparison of basic geometric properties such as volume and surface area.The results show that the micromorphological characteristics of reproduced particles become more and more readily distinguishable as the reproduced order number of spherical harmonic function increases,and the error can be brought below 5%when the order number reaches 10.This level of precision is sharp enough to distinguish the characteristics of real particles.Reconstructed particles of the same size but different reconstructed orders were used to form cylindrical samples,and the stress-strain curves of these samples filled with different-order particles which have their mutual morphological features were compared using PFC3D.Results show that the higher the spherical harmonic order of reconstructed particles,the lower the initial compression modulus and the larger the strain at peak intensity.However,peak strength shows only a random relationship to spherical harmonic order.Microstructure reconstruction was here shown to be an efficient means of numerically simulating of multi-scale rock and soil media and studying the mechanical properties of soil samples.
基金supported by the National Natural Science Foundation of China(No.41404053)Special Project for MeteoScientifi c Research in the Public Interest(No.GYHY201306073)+2 种基金the Natural Science Foundation of Jiangsu Province(No.BK20140994)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No.14KJB170012)the Training Program of Innovation and Entrepreneurship for Undergraduates of NUIST(No.201510300178)
文摘We used CHAMP satellite vector data and the latest IGRF12 model to investigate the regional magnetic anomalies over China's Mainland. We assumed satellite points on the same surface （307.69 km） and constructed a spherical cap harmonic model of the satellite magnetic anomalies for elements X, Y, Z, and F over Chinese mainland for 2010.0 （SCH2010） based on selected 498 points. We removed the external field by using the CM4 model. The pole of the spherical cap is 36N° and 104°E, and its half-angle is 30°. After checking and comparing the root mean square （RMS） error of AX, AY, and AZ and X, Y, and Z, we established the truncation level at Kmax = 9. The results suggest that the created China Geomagnetic Referenced Field at the satellite level （CGRF2010） is consistent with the CM4 model. We compared the SCH2010 with other models and found that the intensities and distributions are consistent. In view of the variation off at different altitudes, the SCH2010 model results obey the basics of the geomagnetic field. Moreover, the change rate of X, Y, and Z for SCH2010 and CM4 are consistent. The proposed model can successfully reproduce the geomagnetic data, as other data-fitting models, but the inherent sources of error have to be considered as well.
文摘This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials (FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier’s equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement, strains, and stresses are determined by the exact solution to Navier’s equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.
基金supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge,University of Rzeszów
文摘In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.
基金Project supported by the Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (IHLB201008257)Scientific Research Common Program of Beijing Municipal Commission of Education (KM200810011005)+1 种基金PHR (IHLB 201102)research grant of University of Macao MYRG142(Y1-L2)-FST111-KKI
文摘The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.
基金supported by Foundation of MOE Key Laboratory of Disaster Forecast and Control in Engineering
文摘The idea of Green quasifunction method is clarified in detail by considering a free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of simply-supported trapezoidal shallow spherical shell on Winkler foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation,the irregularity of the kernel of integral equations is avoided.Finally,natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasifunction method.
基金supported by the National Natural Science Foundation of China(Grant No.61372046)the Research Fund for the Doctoral Program of Higher Education of China(New Teachers)(Grant No.20116101120018)+6 种基金the China Postdoctoral Science Foundation Funded Project(Grant Nos.2011M501467 and 2012T50814)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2011JQ1006)the Fundamental Research Funds for the Central Universities(Grant No.GK201302007)Science and Technology Plan Program,in Shaanxi Province of China(Grant Nos.2012 KJXX-29 and 2013K12-20-12)the Science and Technology Plan Program in Xian of China(Grant No.CXY1348(2))the.GraduateInovation Project of Northwest University(Grant No.YZZ12093)the Seience and Technology Program of Educational Committee,of Shaanxi Province of China(Grant No.12JK0729).
文摘Recently,the simplified spherical harmonics equations(SP)model has at tracted much att entionin modeling the light propagation in small tissue ggeometriesat visible and near-infrared wave-leng ths.In this paper,we report an eficient numerical method for fluorescence moleeular tom-ography(FMT)that combines the advantage of SP model and adaptive hp finite elementmethod(hp-FEM).For purposes of comparison,hp-FEM and h-FEM are,respectively applied tothe reconstruction pro cess with diffusion approximation and SPs model.Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are designed to evaluate thereconstruction methods in terms of the location and the reconstructed fluorescent yield.Theexperimental results demonstrate that hp-FEM with SPy model,yield more accurate results thanh-FEM with difusion approximation model does.The phantom experiments show the potentialand feasibility of the proposed approach in FMT applications.
基金Foundation item： Supported by the Natural Science Foundation of Inner Mongolia（2009MS0113） Supported by the Higher School Research Foundation of Inner Mongolia（NJzy08150）
文摘A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) by generalized Salagean operator of harmonic univalent functions.We give sufficient coefficient conditions for normalized harmonic functions in the class LH_λ(α,β).These conditions are also shown to be necessary when the coefficients are negative.This leads to distortion bounds and extreme points.
基金Project supported by the Outstanding Youth Grant of Natural Science Foundation of China (No. 60225002), the National Basic Research Program (973) of China (No. 2004CB318000), the National Natural Science Foundation of China (Nos. 60533060 and 60473132)
文摘The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.
基金ThispaperissupportedbytheChinese" 973"Program (No .2 0 0 3CD71 650 6)
文摘Based on the CHAMP Magsat data set, spherical cap harmonic analysis was used to model the magnetic fields over China continent. The data set used in the analysis includes the 15′×15′ gridded values of the CHAMP anomaly fields (latitude φ=25°N to 50°N and longitude λ=78°E to 135°E). The pole of the cap is located at φ=35°N and λ=110°E with half-angle of 30°. The maximum index (K max) of the model is 30 and the total number of model coefficients is 961, which corresponds to the minimum wavelength at the earth's surface about 400 km. The root mean square (RMS) deviations between the calculated and observed values are ～ 4 nT for ΔX, ～ 3 nT for ΔY and ～ 3.5 nT for ΔZ, respectively. Results show that positive anomalies are found mainly at the Tarim basin with ～6- 8 nT, the Yangtze platform and North China platform with ～4 nT, and the Songliao basin with ～4-6 nT. In contrast, negative anomaly is mainly located in the Tibet orogenic belt with the amplitude ～ (-6)-(-8) nT. Upward continuation of magnetic anomalies was used to semi-quantitatively separate the magnetic anomalies in different depths of crust. The magnetic anomalies at the earth's surface are from -6 to 10 nT for upper crust, middle crust -27 to 42 nT and lower crust -12 to 18 nT, respectively. The strikes of the magnetic anomalies for the upper crust are consistent with those for the middle crust, but not for the lower crust. The high positive magnetic anomalies mainly result from the old continental nucleus and diastrophic block (e.g. middle Sichuan continental nucleus, middle Tarim basin continental nucleus, Junggar diastrophic block and Qaidam diastrophic block). The amplitudes of the magnetic anomalies of the old continental nucleus and diastrophic block are related to evolution of deep crust. These results improve our understanding of the crustal structure over China continent.
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.
