Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fund...Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.展开更多
ZTE’s cost-effective GSM solutions provide world class service to over 70 million subscribers in more than 30 countries,and have helped us build strong partnerships with 12 of the world’s top thirty telecoms operators.
The drag-reducing characteristics of a cationic surfactant solution flow in copper pipe have been investigated experimentally.The tested drag-reducing fluid was an aqueous solution of the cationic surfactant cetyltrim...The drag-reducing characteristics of a cationic surfactant solution flow in copper pipe have been investigated experimentally.The tested drag-reducing fluid was an aqueous solution of the cationic surfactant cetyltrimethyl ammonium chloride(CTAC).The experimental results show that the maximum drag reduction percentage reduces with the increase of fluid temperature at low concentration of CTAC,such as 100×10-6 or 150×10-6.Furthermore,the concentration and temperature changes of CTAC solution have significant influences on the drag-reducing ability.The drag-reducing effect of CTAC additives shows great potentials in the application in a district heating/cooling(DHC)system,especially for the radiant floor heating(RFH)system.展开更多
We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains ...We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains more arbitrary autocephalous parameters.In addition,a lumpoff solution is also derived based on the general lump solutions and a stripe soliton.Furthermore,we figure out instanton/rogue wave solutions via introducing two stripe solitons.Finally,one can better illustrate these propagation phenomena of these solutions by analyzing images.展开更多
In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution ...In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.展开更多
This paper uses the boundary layer theory to obtain an asymptotic solution of the nonlinear educed wave equation. This solution is valid in the secular region where the geometrical optics result fails. However it agre...This paper uses the boundary layer theory to obtain an asymptotic solution of the nonlinear educed wave equation. This solution is valid in the secular region where the geometrical optics result fails. However it agrees with the geometrical optics result when the field is away from the secular region. By using this solution the self-focusing length can also be obtained.展开更多
In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduce...In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell-Bloch equations with solitary wave, cnoidal periodic wave, and soliton-cnoidal interactional wave solutions in an explicit form. Particularly, the soliton-cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell-Bloch equations. Finally, we present some figures to show properties of the explicit soliton-cnoidal interactional wave solutions as well as some new dynamical phenomena.展开更多
Investigation in this paper is given to the reduced Maxwell-Bloeh equations with variable coetcients, describing the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric ...Investigation in this paper is given to the reduced Maxwell-Bloeh equations with variable coetcients, describing the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. We apply the Hirota method and symbolic computation to study such equations. With the help of the dependent variable transformations, we present the variable-coetteient-dependent bilinear forms. Then, we construct the one-, two- and N- soliton solutions in analytic forms for them.展开更多
The flow field with a high order scheme is usually calculated so as to solve complex flow problems and describe the flow structure accurately. However, there are two problems, i.e., the reduced-order boundary is inevi...The flow field with a high order scheme is usually calculated so as to solve complex flow problems and describe the flow structure accurately. However, there are two problems, i.e., the reduced-order boundary is inevitable and the order of the scheme at the discontinuous shock wave contained in the flow field as the supersonic flow field is low. It is questionable whether the reduced-order boundary and the low-order scheme at the shock wave have an effect on the numerical solution and accuracy of the flow field inside. In this paper, according to the actual situation of the direct numerical simulation of the flow field, two model equations with the exact solutions are solved, which are steady and unsteady, respectively, to study the question with a high order scheme at the interior of the domain and the reduced-order method at the boundary and center of the domain. Comparing with the exact solutions, it is found that the effect of reduced-order exists and cannot be ignored. In addition, the other two model equations with the exact solutions, which are often used in fluid mechanics, are also studied with the same process for the reduced-order problem.展开更多
Cu2O@Cu2O core-shell nanoparticles (NPs) were prepared by using solution phase strategy. It was found that Cu2O@Cu2O NPs were easily converted to Cu2O@Cu NPs with the help of polyvinylpyrrolidine (PVP) and excessive a...Cu2O@Cu2O core-shell nanoparticles (NPs) were prepared by using solution phase strategy. It was found that Cu2O@Cu2O NPs were easily converted to Cu2O@Cu NPs with the help of polyvinylpyrrolidine (PVP) and excessive ascorbic acid (AA) in air at room temperature, which was an interesting phenomenon. The features of the two kinds of NPs were characterized by XRD, TEM and extinction spectra. Cu2O@Cu NPs with different shell thicknesses showed wide tunable optical properties for the localized surface plasmon (LSP) in metallic Cu. But Cu2O@Cu2O NPs did not indicate this feature. FTIR results reveal that Cu+ ions on the surface of Cu2O shell coordinate with N and O atoms in PVP and are further reduced to metallic Cu by excessive AA and then form a nucleation site on the surface of Cu2O nanocrystalline. PVP binds onto different sites to proceed with the reduction utill all the Cu sources in Cu2O shell are completely assumed.展开更多
In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symm...In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.展开更多
We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(...We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(1+1)-dimensional partial differential systems,but also derive bright solitons,dark solitons,kink or anti-kink solutions and the localized instanton solution.展开更多
In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the （2＋1）-dimensional hyperbolic nonlinear Schr6dinger （HNLS） equation and reduce the （2＋1）-dimensional HNLS equ...In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the （2＋1）-dimensional hyperbolic nonlinear Schr6dinger （HNLS） equation and reduce the （2＋1）-dimensional HNLS equation to some （1 ＋ 1 ）-dimensional partial differential systems. Finally, many exact travelling solutions of the （2＋1）-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.展开更多
In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.T...In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.展开更多
AIM:To evaluate the effectiveness of our proposed bowel preparation method for colon capsule endoscopy.METHODS:A pilot,multicenter,randomized controlled trial compared our proposed "reduced volume method"(gr...AIM:To evaluate the effectiveness of our proposed bowel preparation method for colon capsule endoscopy.METHODS:A pilot,multicenter,randomized controlled trial compared our proposed "reduced volume method"(group A) with the "conventional volume method"(group B) preparation regimens.Group A did not drink polyethylene glycol electrolyte lavage solution(PEGELS) the day before the capsule procedure,while group B drank 2 L.During the procedure day,groups A and B drank 2 L and 1 L of PEG-ELS,respectively,and swallowed the colon capsule(PillCam COLON capsule).Two hours later the first booster of 100 g magnesium citrate mixed with 900 mL water was administered to both groups,and the second booster was administered six hours post capsule ingestion as long as the capsule had not been excreted by that time.Capsule videos were reviewed for grading of cleansing level,RESULTS:Sixty-four subjects were enrolled,with results from 60 analyzed.Groups A and B included 31 and 29 subjects,respectively.Twenty-nine(94%) subjects in group A and 25(86%) subjects in group B had adequate bowel preparation(ns).Twenty-two(71%) of the 31 subjects in group A excreted the capsule within its battery life compared to 16(55%) of the 29 subjects in group B(ns).Of the remaining 22 subjects whose capsules were not excreted within the battery life,all of the capsules reached the left side colon before they stopped functioning.A single adverse event was reported in one subject who had mild symptoms of nausea and vomiting one hour after starting to drink PEG-ELS,due to ingesting the PEG-ELS faster than recommended.CONCLUSION:Our proposed reduced volume bowel preparation method for colon capsule without PEG-ELS during the days before the procedure was as effective as the conventional volume method.展开更多
This paper formulates an efficient numerical method for solving the convection diffusion solute transport equations coupled to blood flow equations in vessel networks.The reduced coupled model describes the variations...This paper formulates an efficient numerical method for solving the convection diffusion solute transport equations coupled to blood flow equations in vessel networks.The reduced coupled model describes the variations of vessel cross-sectional area,radially averaged blood momentum and solute concentration in large vessel networks.For the discretization of the reduced transport equation,we combine an interior penalty discontinuous Galerkin method in space with a novel locally implicit time stepping scheme.The stability and the convergence are proved.Numerical results show the impact of the choice for the steady-state axial velocity profile on the numerical solutions in a fifty-five vessel network with physiological boundary data.展开更多
文摘Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.
文摘ZTE’s cost-effective GSM solutions provide world class service to over 70 million subscribers in more than 30 countries,and have helped us build strong partnerships with 12 of the world’s top thirty telecoms operators.
基金Sponsored by the National Nature Science Foundation of China(Grant No.50908064)the Ph.D. Programs Foundation of Ministry of Education of China(Grant No.20090460912)
文摘The drag-reducing characteristics of a cationic surfactant solution flow in copper pipe have been investigated experimentally.The tested drag-reducing fluid was an aqueous solution of the cationic surfactant cetyltrimethyl ammonium chloride(CTAC).The experimental results show that the maximum drag reduction percentage reduces with the increase of fluid temperature at low concentration of CTAC,such as 100×10-6 or 150×10-6.Furthermore,the concentration and temperature changes of CTAC solution have significant influences on the drag-reducing ability.The drag-reducing effect of CTAC additives shows great potentials in the application in a district heating/cooling(DHC)system,especially for the radiant floor heating(RFH)system.
基金Project supported by the National Natural Science Foundation of China(Grant No.11971475)。
文摘We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains more arbitrary autocephalous parameters.In addition,a lumpoff solution is also derived based on the general lump solutions and a stripe soliton.Furthermore,we figure out instanton/rogue wave solutions via introducing two stripe solitons.Finally,one can better illustrate these propagation phenomena of these solutions by analyzing images.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11675084 and 11435005)the Fund from the Educational Commission of Zhejiang Province,China(Grant No.Y201737177)+1 种基金Ningbo Natural Science Foundation(Grant No.2015A610159)the K C Wong Magna Fund in Ningbo University
文摘In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.
文摘This paper uses the boundary layer theory to obtain an asymptotic solution of the nonlinear educed wave equation. This solution is valid in the secular region where the geometrical optics result fails. However it agrees with the geometrical optics result when the field is away from the secular region. By using this solution the self-focusing length can also be obtained.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11675054 and 11435005)+3 种基金the Outstanding Doctoral Dissertation Cultivation Plan of Action(Grant No.YB2016039)Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(Grant No.ZF1213)the UTRGV President Endowed Professorship(Grant No.450000123)the UTRGV College of Science Seed Grant(Grant No.240000013)for partial support
文摘In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell-Bloch equations with solitary wave, cnoidal periodic wave, and soliton-cnoidal interactional wave solutions in an explicit form. Particularly, the soliton-cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell-Bloch equations. Finally, we present some figures to show properties of the explicit soliton-cnoidal interactional wave solutions as well as some new dynamical phenomena.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11772017,11272023,11471050the Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),China(IPOC:2017ZZ05)the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02
文摘Investigation in this paper is given to the reduced Maxwell-Bloeh equations with variable coetcients, describing the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. We apply the Hirota method and symbolic computation to study such equations. With the help of the dependent variable transformations, we present the variable-coetteient-dependent bilinear forms. Then, we construct the one-, two- and N- soliton solutions in analytic forms for them.
基金Project supported by the National Key Research and Development Project of China(No.2016YFA0401200)the National Natural Science Foundation of China(Nos.11672205 and11332007)
文摘The flow field with a high order scheme is usually calculated so as to solve complex flow problems and describe the flow structure accurately. However, there are two problems, i.e., the reduced-order boundary is inevitable and the order of the scheme at the discontinuous shock wave contained in the flow field as the supersonic flow field is low. It is questionable whether the reduced-order boundary and the low-order scheme at the shock wave have an effect on the numerical solution and accuracy of the flow field inside. In this paper, according to the actual situation of the direct numerical simulation of the flow field, two model equations with the exact solutions are solved, which are steady and unsteady, respectively, to study the question with a high order scheme at the interior of the domain and the reduced-order method at the boundary and center of the domain. Comparing with the exact solutions, it is found that the effect of reduced-order exists and cannot be ignored. In addition, the other two model equations with the exact solutions, which are often used in fluid mechanics, are also studied with the same process for the reduced-order problem.
基金Projects(41172110,61107090)supported by the National Natural Science Foundation of China
文摘Cu2O@Cu2O core-shell nanoparticles (NPs) were prepared by using solution phase strategy. It was found that Cu2O@Cu2O NPs were easily converted to Cu2O@Cu NPs with the help of polyvinylpyrrolidine (PVP) and excessive ascorbic acid (AA) in air at room temperature, which was an interesting phenomenon. The features of the two kinds of NPs were characterized by XRD, TEM and extinction spectra. Cu2O@Cu NPs with different shell thicknesses showed wide tunable optical properties for the localized surface plasmon (LSP) in metallic Cu. But Cu2O@Cu2O NPs did not indicate this feature. FTIR results reveal that Cu+ ions on the surface of Cu2O shell coordinate with N and O atoms in PVP and are further reduced to metallic Cu by excessive AA and then form a nucleation site on the surface of Cu2O nanocrystalline. PVP binds onto different sites to proceed with the reduction utill all the Cu sources in Cu2O shell are completely assumed.
基金supported by the National Natural Science Foundation of China under Grant No.60821002the National Key Basic Research Program of China under Grant No.2004CB318000
文摘In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10875106 and 11175158
文摘We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(1+1)-dimensional partial differential systems,but also derive bright solitons,dark solitons,kink or anti-kink solutions and the localized instanton solution.
基金Supported by the National Natural Science Foundation of China under Grant No.10875106
文摘In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the （2＋1）-dimensional hyperbolic nonlinear Schr6dinger （HNLS） equation and reduce the （2＋1）-dimensional HNLS equation to some （1 ＋ 1 ）-dimensional partial differential systems. Finally, many exact travelling solutions of the （2＋1）-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.
文摘In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.
基金Supported by Foundation for Promotion of Cancer Research by Ministry of Health,Labor and Welfare in Japan
文摘AIM:To evaluate the effectiveness of our proposed bowel preparation method for colon capsule endoscopy.METHODS:A pilot,multicenter,randomized controlled trial compared our proposed "reduced volume method"(group A) with the "conventional volume method"(group B) preparation regimens.Group A did not drink polyethylene glycol electrolyte lavage solution(PEGELS) the day before the capsule procedure,while group B drank 2 L.During the procedure day,groups A and B drank 2 L and 1 L of PEG-ELS,respectively,and swallowed the colon capsule(PillCam COLON capsule).Two hours later the first booster of 100 g magnesium citrate mixed with 900 mL water was administered to both groups,and the second booster was administered six hours post capsule ingestion as long as the capsule had not been excreted by that time.Capsule videos were reviewed for grading of cleansing level,RESULTS:Sixty-four subjects were enrolled,with results from 60 analyzed.Groups A and B included 31 and 29 subjects,respectively.Twenty-nine(94%) subjects in group A and 25(86%) subjects in group B had adequate bowel preparation(ns).Twenty-two(71%) of the 31 subjects in group A excreted the capsule within its battery life compared to 16(55%) of the 29 subjects in group B(ns).Of the remaining 22 subjects whose capsules were not excreted within the battery life,all of the capsules reached the left side colon before they stopped functioning.A single adverse event was reported in one subject who had mild symptoms of nausea and vomiting one hour after starting to drink PEG-ELS,due to ingesting the PEG-ELS faster than recommended.CONCLUSION:Our proposed reduced volume bowel preparation method for colon capsule without PEG-ELS during the days before the procedure was as effective as the conventional volume method.
基金Puelz was supported in part by the Research Training Group in Modeling and Simulation funded by NSF via grant RTG/DMS-1646339Riviere acknowledged the support of NSF via Grant DMS 1913291.
文摘This paper formulates an efficient numerical method for solving the convection diffusion solute transport equations coupled to blood flow equations in vessel networks.The reduced coupled model describes the variations of vessel cross-sectional area,radially averaged blood momentum and solute concentration in large vessel networks.For the discretization of the reduced transport equation,we combine an interior penalty discontinuous Galerkin method in space with a novel locally implicit time stepping scheme.The stability and the convergence are proved.Numerical results show the impact of the choice for the steady-state axial velocity profile on the numerical solutions in a fifty-five vessel network with physiological boundary data.
