Aims and Scope: Numerical Mathematics:Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction,analysis and application of numerical methods for solving scientific ...Aims and Scope: Numerical Mathematics:Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction,analysis and application of numerical methods for solving scientific problems.Important research and expository papers devoted to the numerical solution of mathematical problems arising in all areas of science and technology are expected.The journal originates from the journal Numerical Mathematics:A Journal of Chinese Universities (English Edition).展开更多
In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,br...In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general coefficients.In our knowledge earlier reported results of the KE equation with specific coefficients.These obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other branches.All calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences.展开更多
Fuzzy mathematics comprehensive evaluation method is used to evaluate the geological environment suitability of rural urbanization in Qingdao City,China.A total of 5 first-level evaluation factors are selected,includi...Fuzzy mathematics comprehensive evaluation method is used to evaluate the geological environment suitability of rural urbanization in Qingdao City,China.A total of 5 first-level evaluation factors are selected,including environmental geological condition,geological resources,engineering geological condition,geological disaster and environmental geological problem,and human engineering activity.And there are 27 second-level evaluation factors,such as topography,land type and vegetation,nature reserve,water source protection area,groundwater quality division,and major engineering project.Qingdao City is divided into four districts of suitable area,relatively suitable area,moderately suitable area and relatively unsuitable area of ecological environment.And their characteristics are introduced.Suggestions for the developing direction of urban construction are put forward.Region of Laoshan District lying to the west of the Shilaoren is suitable to set up high-rise building;west Hongshiya may establish a waste landfill site;Jiaozhou Bay,the downstream of Dagu River,and Jihongtan Reservoir should be built as the key geological environment protection area and water source protection area.And the north Hongdao should be strictly monitored in order to control the expansion of urban construction to Jihongtan Reservoir.Mocheng District and the area north of it,Jiaozhou District and the area east of it are the ideal urban construction development areas in Qingdao City in the future.展开更多
It was proposed how the concentration distribution was calculated in the treble lager wall of hgdrogenation reactor according to the principle of hydrogen diffusion at the steady state in this paper. Based on the stea...It was proposed how the concentration distribution was calculated in the treble lager wall of hgdrogenation reactor according to the principle of hydrogen diffusion at the steady state in this paper. Based on the steady hydrogen permeation current density i∞ measund with the hydrogen probe at a given temperature, the hydmpen concentrationson the key interfaces and hydrogen distribution at any given mdial profile in the single, double or treble layer wall of hydrogenation reactor could be found by applying the presented equations throoph suitable parmeters ioput. The theoretical bases were provided for developing the nondestructive probing technique of the concentration of atomic hydmpen in the wallS of hydrogenation reactors.展开更多
Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number o...Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.展开更多
A new method for the determination of components in mixed acids has been developed.The mathematical model is obtained from samples of known composition and is then used to predict the concentrations of components in u...A new method for the determination of components in mixed acids has been developed.The mathematical model is obtained from samples of known composition and is then used to predict the concentrations of components in unknown sample.The practical utility of this method is demonstrated for simultaneous determination of two systems of ternary mixed acids and the results are satisfactory.展开更多
An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the li...An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the linearized perturbation approach,the symplectic transform matrix for a unit cell of the weakly nonlinear graded metamaterial is derived,which only relies on the state vector.The results of the dispersion relation obtained with the symplectic mathematical method agree well with those achieved by the Bloch theory.It is shown that wider and lower frequency bandgaps are formed when the hardening nonlinearity and incident wave intensity increase.Subsequently,the displacement response and transmission performance of nonlinear graded metamaterials with finite length are studied.The dual tunable effects of nonlinearity and gradation on the wave propagation are explored under different excitation frequencies.For small excitation frequencies,the gradient parameter plays a dominant role compared with the nonlinearity.The reason is that the gradient tuning aims at the gradient arrangement of local resonators,which is limited by the critical value of the local resonator mass.In contrast,for larger excitation frequencies,the hardening nonlinearity is dominant and will contribute to the formation of a new bandgap.展开更多
The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear d...The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.展开更多
A closed form of the title integral formula over the Gaussian-type orbitals is derived for the first time. The present closed form is analytical as the multiple hyper-geometric function of five variables.
In this paper, the authors study the effectiveness of the Japanese monetary policy set by the Bank of Japan (BOJ) to contrast the three major crises that the country has experienced since the second half of the 90s: t...In this paper, the authors study the effectiveness of the Japanese monetary policy set by the Bank of Japan (BOJ) to contrast the three major crises that the country has experienced since the second half of the 90s: that of the lost decade, that of 2008 and that of the Covid-19 pandemic. To this end, they use a particular type of mathematical-statistical model that is widely applied today in the economic field, namely a simultaneous equation model (SEM). This simultaneous equation model is estimated through an Iteratively reweighted least squares (IRLS) using quarterly historical series in the sample period Q1 1994 - Q2 2020. All data are in real terms. The results, appropriately compared with those of other authors, suggest that the monetary policy has a (limited) impact only on the interbank market. The fiscal policy, instead, has a greater ability to influence the money supply, the private consumption and the inflation expectations.展开更多
The Square Kilometre Array(SKA)is the largest radio interferometer under construction in the world.Its immense amount of visibility data poses a considerable challenge to the subsequent processing by the science data ...The Square Kilometre Array(SKA)is the largest radio interferometer under construction in the world.Its immense amount of visibility data poses a considerable challenge to the subsequent processing by the science data processor(SDP).Baseline dependent averaging(BDA),which reduces the amount of visibility data based on the baseline distribution of the radio interferometer,has become a focus of SKA SDP development.This paper developed and implemented a full-featured BDA module based on Radio Astronomy Simulation,Calibration and Imaging Library(RASCIL).Simulated observations were then performed with RASCIL based on a full-scale SKA1-LOW configuration.The performance of the BDA was systematically investigated and evaluated based on the simulated data.The experimental results confirmed that the amount of visibility data is reduced by about 50%to 85%for different time intervals(Δt_(max)).In addition,differentΔt_(max)have a significant effect on the imaging quality.The smallerΔt_(max)is,the smaller the degradation of imaging quality.展开更多
ELIMINO is a mathematical research system developed for theimplementation of Wu's method, a powerful method for polynomial equation systemsolving and geometric theorem proving. The aim of ELIMINO is to provide use...ELIMINO is a mathematical research system developed for theimplementation of Wu's method, a powerful method for polynomial equation systemsolving and geometric theorem proving. The aim of ELIMINO is to provide usera programmable interpreting environment to use Wu's method in scientific researchand engineering computation. In this paper, the development of ELIMINo systemis outlined and the techniques adopted are discussed, then some details about theobject-oriented analysis of ELIMINO are presented.展开更多
文摘Aims and Scope: Numerical Mathematics:Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction,analysis and application of numerical methods for solving scientific problems.Important research and expository papers devoted to the numerical solution of mathematical problems arising in all areas of science and technology are expected.The journal originates from the journal Numerical Mathematics:A Journal of Chinese Universities (English Edition).
文摘In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general coefficients.In our knowledge earlier reported results of the KE equation with specific coefficients.These obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other branches.All calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences.
文摘Fuzzy mathematics comprehensive evaluation method is used to evaluate the geological environment suitability of rural urbanization in Qingdao City,China.A total of 5 first-level evaluation factors are selected,including environmental geological condition,geological resources,engineering geological condition,geological disaster and environmental geological problem,and human engineering activity.And there are 27 second-level evaluation factors,such as topography,land type and vegetation,nature reserve,water source protection area,groundwater quality division,and major engineering project.Qingdao City is divided into four districts of suitable area,relatively suitable area,moderately suitable area and relatively unsuitable area of ecological environment.And their characteristics are introduced.Suggestions for the developing direction of urban construction are put forward.Region of Laoshan District lying to the west of the Shilaoren is suitable to set up high-rise building;west Hongshiya may establish a waste landfill site;Jiaozhou Bay,the downstream of Dagu River,and Jihongtan Reservoir should be built as the key geological environment protection area and water source protection area.And the north Hongdao should be strictly monitored in order to control the expansion of urban construction to Jihongtan Reservoir.Mocheng District and the area north of it,Jiaozhou District and the area east of it are the ideal urban construction development areas in Qingdao City in the future.
文摘It was proposed how the concentration distribution was calculated in the treble lager wall of hgdrogenation reactor according to the principle of hydrogen diffusion at the steady state in this paper. Based on the steady hydrogen permeation current density i∞ measund with the hydrogen probe at a given temperature, the hydmpen concentrationson the key interfaces and hydrogen distribution at any given mdial profile in the single, double or treble layer wall of hydrogenation reactor could be found by applying the presented equations throoph suitable parmeters ioput. The theoretical bases were provided for developing the nondestructive probing technique of the concentration of atomic hydmpen in the wallS of hydrogenation reactors.
基金The project supported by the National Natural Science Foundation of China
文摘Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.
基金This project is supported by National Natural Science Foundation of China
文摘A new method for the determination of components in mixed acids has been developed.The mathematical model is obtained from samples of known composition and is then used to predict the concentrations of components in unknown sample.The practical utility of this method is demonstrated for simultaneous determination of two systems of ternary mixed acids and the results are satisfactory.
基金Project supported by the National Natural Science Foundation of China(Nos.12072266,12172297,11972287,and 12072262)the Open Foundation of the State Key Laboratory of Structural Analysis for Industrial Equipment of China(No.GZ22106)。
文摘An analytical method,called the symplectic mathematical method,is proposed to study the wave propagation in a spring-mass chain with gradient arranged local resonators and nonlinear ground springs.Combined with the linearized perturbation approach,the symplectic transform matrix for a unit cell of the weakly nonlinear graded metamaterial is derived,which only relies on the state vector.The results of the dispersion relation obtained with the symplectic mathematical method agree well with those achieved by the Bloch theory.It is shown that wider and lower frequency bandgaps are formed when the hardening nonlinearity and incident wave intensity increase.Subsequently,the displacement response and transmission performance of nonlinear graded metamaterials with finite length are studied.The dual tunable effects of nonlinearity and gradation on the wave propagation are explored under different excitation frequencies.For small excitation frequencies,the gradient parameter plays a dominant role compared with the nonlinearity.The reason is that the gradient tuning aims at the gradient arrangement of local resonators,which is limited by the critical value of the local resonator mass.In contrast,for larger excitation frequencies,the hardening nonlinearity is dominant and will contribute to the formation of a new bandgap.
基金Project supported by the National Natural Science Foundation of China (Nos. 10972182,10772147,and 10632030)the National Basic Research Program of China (No. 2006CB 601202)+4 种基金the National 111 Project of China (No. B07050)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (No. GZ0802)the Doctoral Foundation of Northwestern Polytechnical University (No. CX200908)the China Postdoctoral Science Foundation (No. 20090450170)the Northwestern Polytechnical University Foundation for Fundamental Research (No. JC200938)
文摘The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.
文摘A closed form of the title integral formula over the Gaussian-type orbitals is derived for the first time. The present closed form is analytical as the multiple hyper-geometric function of five variables.
文摘In this paper, the authors study the effectiveness of the Japanese monetary policy set by the Bank of Japan (BOJ) to contrast the three major crises that the country has experienced since the second half of the 90s: that of the lost decade, that of 2008 and that of the Covid-19 pandemic. To this end, they use a particular type of mathematical-statistical model that is widely applied today in the economic field, namely a simultaneous equation model (SEM). This simultaneous equation model is estimated through an Iteratively reweighted least squares (IRLS) using quarterly historical series in the sample period Q1 1994 - Q2 2020. All data are in real terms. The results, appropriately compared with those of other authors, suggest that the monetary policy has a (limited) impact only on the interbank market. The fiscal policy, instead, has a greater ability to influence the money supply, the private consumption and the inflation expectations.
基金supported by the National SKA Program of China(2020SKA0110300)the Joint Research Fund in Astronomy(U1831204,U1931141)under cooperative agreement between the National Natural Science Foundation of China(NSFC)and the Chinese Academy of Sciences(CAS)+3 种基金the Funds for International Cooperation and Exchange of the National Natural Science Foundation of China(11961141001)the National Science Foundation for Young Scholars(11903009)supported by the Astronomical Big Data Joint Research Centerco-founded by National Astronomical Observatories,Chinese Academy of Sciences and Alibaba Cloud。
文摘The Square Kilometre Array(SKA)is the largest radio interferometer under construction in the world.Its immense amount of visibility data poses a considerable challenge to the subsequent processing by the science data processor(SDP).Baseline dependent averaging(BDA),which reduces the amount of visibility data based on the baseline distribution of the radio interferometer,has become a focus of SKA SDP development.This paper developed and implemented a full-featured BDA module based on Radio Astronomy Simulation,Calibration and Imaging Library(RASCIL).Simulated observations were then performed with RASCIL based on a full-scale SKA1-LOW configuration.The performance of the BDA was systematically investigated and evaluated based on the simulated data.The experimental results confirmed that the amount of visibility data is reduced by about 50%to 85%for different time intervals(Δt_(max)).In addition,differentΔt_(max)have a significant effect on the imaging quality.The smallerΔt_(max)is,the smaller the degradation of imaging quality.
文摘ELIMINO is a mathematical research system developed for theimplementation of Wu's method, a powerful method for polynomial equation systemsolving and geometric theorem proving. The aim of ELIMINO is to provide usera programmable interpreting environment to use Wu's method in scientific researchand engineering computation. In this paper, the development of ELIMINo systemis outlined and the techniques adopted are discussed, then some details about theobject-oriented analysis of ELIMINO are presented.
