In this paper, we prove that for any given positive masses the variational minimization solutions of the 3-body problem in R^3 or R^2 are precisely the planar equilateral triangle circular solutions found by J. Lagran...In this paper, we prove that for any given positive masses the variational minimization solutions of the 3-body problem in R^3 or R^2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular rostricted 3-body problem in R^3 or R^2 are also planar equilateral triangle circular solutions.展开更多
Using variational minimizing methods,we prove the existence of the odd symmetric parabolic or hyperbolic orbit for the restricted 3-body problems with weak forces.
We study the charged 3-body problem with the potential function being （-a）-homogeneous on the mutual distances of any two particles via the variational method and try to find the geometric characterizations of the m...We study the charged 3-body problem with the potential function being （-a）-homogeneous on the mutual distances of any two particles via the variational method and try to find the geometric characterizations of the minimizers. We prove that if the charged 3-body problem admits a triangular central configuration, then the variational minimizing solutions of the problem in the τ/2-antiperiodic function space are exactly defined by the circular motions of this triangular central configuration.展开更多
For any given positive masses it is proved that the variational minimization solutions of the 3-body problem in 3 or 2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and...For any given positive masses it is proved that the variational minimization solutions of the 3-body problem in 3 or 2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular restricted 3-body problem in 3 or 2 are also planar equilateral triangle circular solutions.展开更多
Control signaling is mandatory for the operation and management of all types of communication networks,including the Third Generation Partnership Project(3GPP)mobile broadband networks.However,they consume important a...Control signaling is mandatory for the operation and management of all types of communication networks,including the Third Generation Partnership Project(3GPP)mobile broadband networks.However,they consume important and scarce network resources such as bandwidth and processing power.There have been several reports of these control signaling turning into signaling storms halting network operations and causing the respective Telecom companies big financial losses.This paper draws its motivation from such real network disaster incidents attributed to signaling storms.In this paper,we present a thorough survey of the causes,of the signaling storm problems in 3GPP-based mobile broadband networks and discuss in detail their possible solutions and countermeasures.We provide relevant analytical models to help quantify the effect of the potential causes and benefits of their corresponding solutions.Another important contribution of this paper is the comparison of the possible causes and solutions/countermeasures,concerning their effect on several important network aspects such as architecture,additional signaling,fidelity,etc.,in the form of a table.This paper presents an update and an extension of our earlier conference publication.To our knowledge,no similar survey study exists on the subject.展开更多
The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution a...The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution analysis,which is also a key research issue of the problem.In this paper,we prove that given 3 control points,if the camera's optical center lies on the so-called“danger cylinder”and is enough far from the supporting plane of control points,the corresponding P3P problem must have 3 positive solutions.This result can bring some new insights into a better understanding of the multi-solution problem.For example,it is shown in the literature that the solution of the P3P problem is instable if the optical center lies on this danger cylinder,we think such occurrence of triple-solution is the primary source of this instability.展开更多
The key problems of cold power spinning of Ti-15-3 alloy are studied. Reasonable billet preparation methods are presented to improve crystal structure and avoid crack of billet. Influences of original wall thickness,...The key problems of cold power spinning of Ti-15-3 alloy are studied. Reasonable billet preparation methods are presented to improve crystal structure and avoid crack of billet. Influences of original wall thickness, reduction rate and feed rate on expanding in diameter are analyzed and some methods to prevent expanding in diameter are given.展开更多
A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evol...A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evolution is mainly composed of the eigenstates of the problem Hamiltonian, which are Hamming close to the solution state. And the instantaneous ground state immediately after the starting is mainly formed of low energy eigenstates of the problem Hamiltonian. These results are then applied to estimate the minimum gap for a special case.展开更多
We propose the exact solution of the equation in separated variable which appears in the process of constructing solutions to the quantum Calogero-Moser three-particle problem with elliptic two-particle potential . Th...We propose the exact solution of the equation in separated variable which appears in the process of constructing solutions to the quantum Calogero-Moser three-particle problem with elliptic two-particle potential . This solution is found for special values of coupling constants . It can be used for solving three-particle Calogero-Moser problem under the appropriate boundary conditions.展开更多
The 3-partitioning problem is to decide whether a given multiset of nonnegative integers can be partitioned into triples that all have the same sum. It is considerably used to prove the strong NP-hardness of many sche...The 3-partitioning problem is to decide whether a given multiset of nonnegative integers can be partitioned into triples that all have the same sum. It is considerably used to prove the strong NP-hardness of many scheduling problems. In this paper, we consider four optimization versions of the 3-partitioning problem, and then present four polynomial time approximation schemes for these problems.展开更多
We find that having the scale factor close to zero due to a given magnetic field value, an early universe magnetic field affects how we would interpret Mukhanov’s chapter on “self reproduction of the universe”. We ...We find that having the scale factor close to zero due to a given magnetic field value, an early universe magnetic field affects how we would interpret Mukhanov’s chapter on “self reproduction of the universe”. We extend such arguments, and refer to the possibility of modified gravity. We hope that some of the issues raised by Kobayashi and Seto as to allowed inflation models may be addressed, once further refinement of these preliminary results commences. We close with statements as to the value of α in a gravitational potential proportional to r?α and how this adjustment affects the 3 body problem.展开更多
A generalized upwind scheme with fractional steps for 3-D mathematical models of convection dominating groundwater quality is suggested. The mass transport equation is split into a convection equation and a dispersive...A generalized upwind scheme with fractional steps for 3-D mathematical models of convection dominating groundwater quality is suggested. The mass transport equation is split into a convection equation and a dispersive equation. The generalized upwind scheme is used to solve the convection equation and the finite element method is used to compute the dispersive equation.These procedures which not only overcome the phenomenon of the negative concentration and numerical dispersion appear frequently with normal FEM or FDM to solve models of convection dominating groundwater transport but also avoid the step for computing each node velocity give a more suitable method to calculate the concentrations of the well points.展开更多
The 3X + 1 problem (Collatz conjecture) has been proposed for many years, however no major breakthrough has been made so far. As we know, the Crandall conjecture is a well-known generalization of the 3X + 1 problem. I...The 3X + 1 problem (Collatz conjecture) has been proposed for many years, however no major breakthrough has been made so far. As we know, the Crandall conjecture is a well-known generalization of the 3X + 1 problem. It is worth noting that, both conjectures are infamous for their simplicity in stating but intractability in solving. In this paper, I aim to provide a clear explanation about the reason why these two problems are difficult to handle and have very different characteristics on convergence of the series via creatively applying the probability theory and global expectancy value E(n) of energy contraction index. The corresponding convergence analysis explicitly shows that a = 3 leads to a difficult problem, while a > 3 leads to a divergent series. To the best of my knowledge, this is the first work to point out the difference between these cases. The corresponding results not only propose a new angle to analyze the 3X + 1 problem, but also shed some light on the future research.展开更多
This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change ...This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change by the Collatz conjecture. 1) This positive integer will change to an odd number;2) The odd number must change to a number of LiKe’s second sequence {3<sup>n</sup> – 1| n ∈ Z<sup>+</sup>};3) Then this 3<sup>n</sup> - 1 will change to a smaller 3<sup>n </sup>– 1 and gradually decrease to 8 (that is 3<sup>2</sup> - 1) then back to 1 in the end. If we can determine each step, the Collatz conjecture will be true. This is certainly more valuable than 2<sup>n</sup> (it might even explain 2<sup>n</sup>). And to illustrate the importance of this rule, introduced some important funny corollaries related to it.展开更多
In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in a multilayered domain. We consider the metal concentration in the 3 layered peat blocks. Using experiment...In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in a multilayered domain. We consider the metal concentration in the 3 layered peat blocks. Using experimental data the mathematical model for calculating the concentration of metal at different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for the partial differential equations （PDEs） of the elliptic type of second order with piece-wise diffusion coefficients in the three layer domain. We develop here a finite-difference method for solving a problem of the above type with the periodical boundary condition in x direction. This procedure allows reducing the 3-D problem to a system of 2-D problems by using a circulant matrix.展开更多
基金Partially supported by the NNSF and MCME of China. the Qiu Shi Sci. and Tech. Foundation.Edn. Comm. of Tianjun CityAssociate Member of the ICTP.Partially supported by the NNSF of China
文摘In this paper, we prove that for any given positive masses the variational minimization solutions of the 3-body problem in R^3 or R^2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular rostricted 3-body problem in R^3 or R^2 are also planar equilateral triangle circular solutions.
基金supported by National Natural Science Foundation of China (Grant No. 11071175)a grant for advisor and PhD students from educational committee of China
文摘Using variational minimizing methods,we prove the existence of the odd symmetric parabolic or hyperbolic orbit for the restricted 3-body problems with weak forces.
基金The authors thank sincerely Professor Shanzhong Sun for his careful reading and helpful comments on the manuscript of this paper. The first author was partially supported by the Doctoral Innovation Project of Nankai University. The second author was partially supported by the National Natural Science Foundation of China （Grant No. 11131004）, MCME, LPMC of Ministry of Education of China, Nankai University, and the BCMIIS at Capital Normal University.
文摘We study the charged 3-body problem with the potential function being （-a）-homogeneous on the mutual distances of any two particles via the variational method and try to find the geometric characterizations of the minimizers. We prove that if the charged 3-body problem admits a triangular central configuration, then the variational minimizing solutions of the problem in the τ/2-antiperiodic function space are exactly defined by the circular motions of this triangular central configuration.
文摘For any given positive masses it is proved that the variational minimization solutions of the 3-body problem in 3 or 2 are precisely the planar equilateral triangle circular solutions found by J. Lagrange in 1772, and that the variational minimization solutions of the circular restricted 3-body problem in 3 or 2 are also planar equilateral triangle circular solutions.
基金the Deanship of Graduate Studies and Scientific Research at Qassim University for financial support(QU-APC-2024-9/1).
文摘Control signaling is mandatory for the operation and management of all types of communication networks,including the Third Generation Partnership Project(3GPP)mobile broadband networks.However,they consume important and scarce network resources such as bandwidth and processing power.There have been several reports of these control signaling turning into signaling storms halting network operations and causing the respective Telecom companies big financial losses.This paper draws its motivation from such real network disaster incidents attributed to signaling storms.In this paper,we present a thorough survey of the causes,of the signaling storm problems in 3GPP-based mobile broadband networks and discuss in detail their possible solutions and countermeasures.We provide relevant analytical models to help quantify the effect of the potential causes and benefits of their corresponding solutions.Another important contribution of this paper is the comparison of the possible causes and solutions/countermeasures,concerning their effect on several important network aspects such as architecture,additional signaling,fidelity,etc.,in the form of a table.This paper presents an update and an extension of our earlier conference publication.To our knowledge,no similar survey study exists on the subject.
基金Supported by"973"Program(2002CB312104)National Natural Science Foundation of P.R.China(60375006)the Research Foundation of North China Unversity of Technology University
文摘The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution analysis,which is also a key research issue of the problem.In this paper,we prove that given 3 control points,if the camera's optical center lies on the so-called“danger cylinder”and is enough far from the supporting plane of control points,the corresponding P3P problem must have 3 positive solutions.This result can bring some new insights into a better understanding of the multi-solution problem.For example,it is shown in the literature that the solution of the P3P problem is instable if the optical center lies on this danger cylinder,we think such occurrence of triple-solution is the primary source of this instability.
文摘The key problems of cold power spinning of Ti-15-3 alloy are studied. Reasonable billet preparation methods are presented to improve crystal structure and avoid crack of billet. Influences of original wall thickness, reduction rate and feed rate on expanding in diameter are analyzed and some methods to prevent expanding in diameter are given.
基金Project supported by the National Natural Science Foundation of China(Grant No.61173050)
文摘A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evolution is mainly composed of the eigenstates of the problem Hamiltonian, which are Hamming close to the solution state. And the instantaneous ground state immediately after the starting is mainly formed of low energy eigenstates of the problem Hamiltonian. These results are then applied to estimate the minimum gap for a special case.
文摘We propose the exact solution of the equation in separated variable which appears in the process of constructing solutions to the quantum Calogero-Moser three-particle problem with elliptic two-particle potential . This solution is found for special values of coupling constants . It can be used for solving three-particle Calogero-Moser problem under the appropriate boundary conditions.
文摘The 3-partitioning problem is to decide whether a given multiset of nonnegative integers can be partitioned into triples that all have the same sum. It is considerably used to prove the strong NP-hardness of many scheduling problems. In this paper, we consider four optimization versions of the 3-partitioning problem, and then present four polynomial time approximation schemes for these problems.
文摘We find that having the scale factor close to zero due to a given magnetic field value, an early universe magnetic field affects how we would interpret Mukhanov’s chapter on “self reproduction of the universe”. We extend such arguments, and refer to the possibility of modified gravity. We hope that some of the issues raised by Kobayashi and Seto as to allowed inflation models may be addressed, once further refinement of these preliminary results commences. We close with statements as to the value of α in a gravitational potential proportional to r?α and how this adjustment affects the 3 body problem.
文摘A generalized upwind scheme with fractional steps for 3-D mathematical models of convection dominating groundwater quality is suggested. The mass transport equation is split into a convection equation and a dispersive equation. The generalized upwind scheme is used to solve the convection equation and the finite element method is used to compute the dispersive equation.These procedures which not only overcome the phenomenon of the negative concentration and numerical dispersion appear frequently with normal FEM or FDM to solve models of convection dominating groundwater transport but also avoid the step for computing each node velocity give a more suitable method to calculate the concentrations of the well points.
文摘The 3X + 1 problem (Collatz conjecture) has been proposed for many years, however no major breakthrough has been made so far. As we know, the Crandall conjecture is a well-known generalization of the 3X + 1 problem. It is worth noting that, both conjectures are infamous for their simplicity in stating but intractability in solving. In this paper, I aim to provide a clear explanation about the reason why these two problems are difficult to handle and have very different characteristics on convergence of the series via creatively applying the probability theory and global expectancy value E(n) of energy contraction index. The corresponding convergence analysis explicitly shows that a = 3 leads to a difficult problem, while a > 3 leads to a divergent series. To the best of my knowledge, this is the first work to point out the difference between these cases. The corresponding results not only propose a new angle to analyze the 3X + 1 problem, but also shed some light on the future research.
文摘This article introduces a change rule of 3x + 1 problem (Collatz conjecture), it’s named LiKe’s Rule. It’s a map of 3x + 1 problem, and details the path of each step of the change: For any positive integer, change by the Collatz conjecture. 1) This positive integer will change to an odd number;2) The odd number must change to a number of LiKe’s second sequence {3<sup>n</sup> – 1| n ∈ Z<sup>+</sup>};3) Then this 3<sup>n</sup> - 1 will change to a smaller 3<sup>n </sup>– 1 and gradually decrease to 8 (that is 3<sup>2</sup> - 1) then back to 1 in the end. If we can determine each step, the Collatz conjecture will be true. This is certainly more valuable than 2<sup>n</sup> (it might even explain 2<sup>n</sup>). And to illustrate the importance of this rule, introduced some important funny corollaries related to it.
文摘In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in a multilayered domain. We consider the metal concentration in the 3 layered peat blocks. Using experimental data the mathematical model for calculating the concentration of metal at different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for the partial differential equations （PDEs） of the elliptic type of second order with piece-wise diffusion coefficients in the three layer domain. We develop here a finite-difference method for solving a problem of the above type with the periodical boundary condition in x direction. This procedure allows reducing the 3-D problem to a system of 2-D problems by using a circulant matrix.
