In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to ea...In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to each other.展开更多
The newly formulated non-Newtonian rivulet flows streaming down an inclined planar surface,with additional periodic perturbations arising from the application of the 2nd Stokes problem to the investigation of rivulet ...The newly formulated non-Newtonian rivulet flows streaming down an inclined planar surface,with additional periodic perturbations arising from the application of the 2nd Stokes problem to the investigation of rivulet dynamics,are demonstrated in the current research.Hereby,the 2nd Stokes problem assumes that the surface,with a thin shared layer of the fluid on it,oscillates in a harmonic manner along the x-axis of the rivulet flow,which coincides with the main flow direction streaming down the underlying surface.We obtain the exact extension of the rivulet flow family,clarifying the structure of the pressure field,which fully absorbs the arising perturbation.The profile of the velocity field is assumed to be Gaussian-type with a non-zero level of plasticity.Hence,the absolutely non-Newtonian case of the viscoplastic flow solution,which satisfies the motion and continuity equations,is considered(with particular cases of exact solutions for pressure).The perturbed governing equations of motion for rivulet flows then result in the Riccati-type ordinary differential equation(ODE),describing the dynamics of the coordinate x(t).The approximated schematic dynamics are presented in graphical plots.展开更多
This paper focuses on the 2-median location improvement problem on tree networks and the problem is to modify the weights of edges at the minimum cost such that the overall sum of the weighted distance of the vertices...This paper focuses on the 2-median location improvement problem on tree networks and the problem is to modify the weights of edges at the minimum cost such that the overall sum of the weighted distance of the vertices to the respective closest one of two prescribed vertices in the modified network is upper bounded by a given value.l1 norm and l∞norm are used to measure the total modification cost. These two problems have a strong practical application background and important theoretical research value. It is shown that such problems can be transformed into a series of sum-type and bottleneck-type continuous knapsack problems respectively.Based on the property of the optimal solution two O n2 algorithms for solving the two problems are proposed where n is the number of vertices on the tree.展开更多
In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact pr...In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact problem.The analytic expressions of contact stresses in the phonon and phason fields were obtained for a flat rigid punch,which showed that：（1） for the finite frictional contact problem,the contact stress exhibited power-type singularities at the edge of the contact zone;（2） for the adhesive contact problem,the contact stress exhibited oscillatory singularities at the edge of the contact zone.The distribution regulation of contact stress under punch was illustrated;and the low friction property of quasicrystals was verified graphically.展开更多
This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the...This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.展开更多
Dear editor,The advent of modern molecular mechanism’s approach to disease treatment is highly advancing to mitigate/normalize the symptoms of disease i.e.hyperglycemia by targeting at least eight different pathophys...Dear editor,The advent of modern molecular mechanism’s approach to disease treatment is highly advancing to mitigate/normalize the symptoms of disease i.e.hyperglycemia by targeting at least eight different pathophysiological approaches popularly known as omnious octet[1].Importantly,type 2 diabetes is a展开更多
Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum leng...Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.展开更多
We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability(Q2SAT)problem,which is a generalization of 2-satisfiability(2SAT)problem.For a Q2SAT problem,we construct the Hamiltonian which is similar...We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability(Q2SAT)problem,which is a generalization of 2-satisfiability(2SAT)problem.For a Q2SAT problem,we construct the Hamiltonian which is similar to that of a Heisenberg chain.All the solutions of the given Q2SAT problem span the subspace of the degenerate ground states.The Hamiltonian is adiabatically evolved so that the system stays in the degenerate subspace.Our numerical results suggest that the time complexity of our algorithm is O(n^(3.9))for yielding non-trivial solutions for problems with the number of clauses m=dn(n-1)/2(d■0.1).We discuss the advantages of our algorithm over the known quantum and classical algorithms.展开更多
The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models...The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.展开更多
This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive soluti...This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.展开更多
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
The Diver Gas Recovery System(DGRS)is an important accessory equipment of the 300m Saturation Dive System. The system facilitates the recycling of the breathing gases for divers,therefore,it has great economic benefit...The Diver Gas Recovery System(DGRS)is an important accessory equipment of the 300m Saturation Dive System. The system facilitates the recycling of the breathing gases for divers,therefore,it has great economic benefits. In April 1995, a 300 m unmanned test and a 100 m manned test on the HY2031 DGRSwere carried out successively.Ten months later,another manned test on the HY2032 DGRS展开更多
For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint ...For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint model data, in noise-free case. The accuracy is quite good.展开更多
Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, de...Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.展开更多
Modeling the elastic behavior of solids in energy conversion and storage devices such as fuel cells and lithium-ion batteries is usually difficult because of the nonlinear characteristics and the coupled chemo-mechani...Modeling the elastic behavior of solids in energy conversion and storage devices such as fuel cells and lithium-ion batteries is usually difficult because of the nonlinear characteristics and the coupled chemo-mechanical behavior of these solids.In this work,a perturbation finite element(FE)formulation is developed to analyze chemo-elastic boundary value problems(BVPs)under chemical equilibrium.The perturbation method is applied to the FE equations because of the nonlinearity in the chemical potential expression as a function of solute concentration.The compositional expansion coefficient is used as the perturbation parameter.After the perturbation expansion,a system of partial differential equations for the displacement and dimensionless solute concentration functions is obtained and solved in consecutive steps.The presence of a numerical solution enables modeling 3D chemo-elastic solids,such as battery electrodes or ionic gels,of any geometric shape with defects of different shapes.The proposed method is tested in several numerical examples such as plates with circular or elliptical holes,and cracks.The numerical examples showed how the shape of the defect can change the distribution of solute concentration around the defect.Cracks in chemo-elastic solids create sharp peaks in solute concentration around crack tips,and the intensity of these peaks increases as the far field solute concentration decreases.展开更多
2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding in...2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding interpolations are given here.展开更多
This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe...This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.展开更多
Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19871096), QSSTE and MOST.
文摘In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to each other.
文摘The newly formulated non-Newtonian rivulet flows streaming down an inclined planar surface,with additional periodic perturbations arising from the application of the 2nd Stokes problem to the investigation of rivulet dynamics,are demonstrated in the current research.Hereby,the 2nd Stokes problem assumes that the surface,with a thin shared layer of the fluid on it,oscillates in a harmonic manner along the x-axis of the rivulet flow,which coincides with the main flow direction streaming down the underlying surface.We obtain the exact extension of the rivulet flow family,clarifying the structure of the pressure field,which fully absorbs the arising perturbation.The profile of the velocity field is assumed to be Gaussian-type with a non-zero level of plasticity.Hence,the absolutely non-Newtonian case of the viscoplastic flow solution,which satisfies the motion and continuity equations,is considered(with particular cases of exact solutions for pressure).The perturbed governing equations of motion for rivulet flows then result in the Riccati-type ordinary differential equation(ODE),describing the dynamics of the coordinate x(t).The approximated schematic dynamics are presented in graphical plots.
基金The National Natural Science Foundation of China(No.10801031)
文摘This paper focuses on the 2-median location improvement problem on tree networks and the problem is to modify the weights of edges at the minimum cost such that the overall sum of the weighted distance of the vertices to the respective closest one of two prescribed vertices in the modified network is upper bounded by a given value.l1 norm and l∞norm are used to measure the total modification cost. These two problems have a strong practical application background and important theoretical research value. It is shown that such problems can be transformed into a series of sum-type and bottleneck-type continuous knapsack problems respectively.Based on the property of the optimal solution two O n2 algorithms for solving the two problems are proposed where n is the number of vertices on the tree.
基金Project supported by the National Natural Science Foundation of China(Nos.11362018,11261045 and 11261401)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116401110002)
文摘In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact problem.The analytic expressions of contact stresses in the phonon and phason fields were obtained for a flat rigid punch,which showed that：（1） for the finite frictional contact problem,the contact stress exhibited power-type singularities at the edge of the contact zone;（2） for the adhesive contact problem,the contact stress exhibited oscillatory singularities at the edge of the contact zone.The distribution regulation of contact stress under punch was illustrated;and the low friction property of quasicrystals was verified graphically.
基金Project supported by the National Natural Science Foundation of China(No.11074170)the State Key Laboratory Foundation of Shanghai Jiao Tong University(No.MSVMS201105)
文摘This paper describes formulation and implementation of the fast multipole boundary element method （FMBEM） for 2D acoustic problems. The kernel function expansion theory is summarized, and four building blocks of the FMBEM are described in details. They are moment calculation, moment to moment translation, moment to local translation, and local to local translation. A data structure for the quad-tree construction is proposed which can facilitate implementation. An analytical moment expression is derived, which is more accurate, stable, and efficient than direct numerical computation. Numerical examples are presented to demonstrate the accuracy and efficiency of the FMBEM, and radiation of a 2D vibration rail mode is simulated using the FMBEM.
文摘Dear editor,The advent of modern molecular mechanism’s approach to disease treatment is highly advancing to mitigate/normalize the symptoms of disease i.e.hyperglycemia by targeting at least eight different pathophysiological approaches popularly known as omnious octet[1].Importantly,type 2 diabetes is a
基金supported by the National Natural Science Foundation of China(No.12301425)。
文摘Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.
基金Project supported by the National Key R&D Program of China(Grant Nos.2017YFA0303302 and 2018YFA0305602)the National Natural Science Foundation of China(Grant No.11921005)Shanghai Municipal Science and Technology Major Project,China(Grant No.2019SHZDZX01)。
文摘We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability(Q2SAT)problem,which is a generalization of 2-satisfiability(2SAT)problem.For a Q2SAT problem,we construct the Hamiltonian which is similar to that of a Heisenberg chain.All the solutions of the given Q2SAT problem span the subspace of the degenerate ground states.The Hamiltonian is adiabatically evolved so that the system stays in the degenerate subspace.Our numerical results suggest that the time complexity of our algorithm is O(n^(3.9))for yielding non-trivial solutions for problems with the number of clauses m=dn(n-1)/2(d■0.1).We discuss the advantages of our algorithm over the known quantum and classical algorithms.
基金the National Natural Science Foundation of China(https://www.nsfc.gov.cn/,Project No.11972179)the Natural Science Foundation of Guangdong Province(http://gdstc.gd.gov.cn/,No.2020A1515010685)the Department of Education of Guangdong Province(http://edu.gd.gov.cn/,No.2020ZDZX2008).
文摘The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.
基金Research supported by the National Natural Science Foundation of China (10871116)the Natural Science Foundation of Shandong Province of China (ZR2010AM005)the Doctoral Program Foundation of Education Ministry of China (200804460001)
文摘This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.
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The Diver Gas Recovery System(DGRS)is an important accessory equipment of the 300m Saturation Dive System. The system facilitates the recycling of the breathing gases for divers,therefore,it has great economic benefits. In April 1995, a 300 m unmanned test and a 100 m manned test on the HY2031 DGRSwere carried out successively.Ten months later,another manned test on the HY2032 DGRS
文摘For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint model data, in noise-free case. The accuracy is quite good.
文摘Sufficient conditions for the existence and uniqueness of second boundary value problems of two kinds of even order nonlinear differential equations are obtained. The proofs are based on the lemma on bilinear form, developed by A.C.Lazer, Schauder fixed point theorem and the Leray-Schauder degree theory, respectively.
文摘Modeling the elastic behavior of solids in energy conversion and storage devices such as fuel cells and lithium-ion batteries is usually difficult because of the nonlinear characteristics and the coupled chemo-mechanical behavior of these solids.In this work,a perturbation finite element(FE)formulation is developed to analyze chemo-elastic boundary value problems(BVPs)under chemical equilibrium.The perturbation method is applied to the FE equations because of the nonlinearity in the chemical potential expression as a function of solute concentration.The compositional expansion coefficient is used as the perturbation parameter.After the perturbation expansion,a system of partial differential equations for the displacement and dimensionless solute concentration functions is obtained and solved in consecutive steps.The presence of a numerical solution enables modeling 3D chemo-elastic solids,such as battery electrodes or ionic gels,of any geometric shape with defects of different shapes.The proposed method is tested in several numerical examples such as plates with circular or elliptical holes,and cracks.The numerical examples showed how the shape of the defect can change the distribution of solute concentration around the defect.Cracks in chemo-elastic solids create sharp peaks in solute concentration around crack tips,and the intensity of these peaks increases as the far field solute concentration decreases.
文摘2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding interpolations are given here.
基金Project supported by the National Natural Science Foundation of China (No. 10962004)the Special-ized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)+1 种基金the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)the Natural Science Foundation of Inner Mongolia (No. 2009BS0101)
文摘This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.
文摘Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.
