A novel aperiodically intermittent impulse control(AIIC)method is proposed to investigate the exponential synchronization in mean square(ESMS)of a class of impulsive stochastic infinite-dimensional systems with Poisso...A novel aperiodically intermittent impulse control(AIIC)method is proposed to investigate the exponential synchronization in mean square(ESMS)of a class of impulsive stochastic infinite-dimensional systems with Poisson jumps(ISIDSP).The AIIC control strategy inherits the flexibility of aperiodically intermittent control,including the variable control period,adjustable control interval length,and the discretization of impulsive control.In addition,this article introduces a novel mild Itô's formula.By leveraging semigroup theory,the contraction mapping principle,and graph theory,along with constructing the Lyapunov function,the criterion for the existence and uniqueness of a mild solution of ISIDSP is thereby established.Furthermore,the mean-square exponential synchronization problem of the above systems is resolved,and the constraints within the mild solution domain are alleviated.These criteria clarify the impact of control parameters,control intervals and network topology on ESMS.The theoretical results are subsequently applied to a class of neural networks with reaction-diffusion processes,and the validity of the results is verified using numerical simulations.展开更多
This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theo...This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results.展开更多
In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equ...In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equation,but also analyze the dynamical behaviors of nonlinear local wave propagation in shallow water.Firstly,based on the Hirota bilinear approach,one to four-order soliton solutions of the YTSF equation are obtained,and the effects of different parameters on the amplitude,propagation trajectory,and displacement of solitons are investigated.Secondly,using the long wave limit approach,one to three-order lump solutions and various physical quantities of the YTSF equation are derived.It is found that the real and imaginary parts of the parameter pi dominate the propagation trajectory and the shape of lump waves,respectively.Furthermore,we construct the hybrid solution for the YTSF equation,leading to the conclusion that the interaction between lumps and solitons constitutes an elastic collision.To intuitively understand the dynamic behaviors of these solutions,we conduct numerical simulations to present vivid three-dimensional visualizations.展开更多
By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions o...By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.展开更多
For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy princi...For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.展开更多
We study a novel class of two-dimensional maps with infinitely many coexisting attractors.Firstly,the mathematical model of these maps is formulated by introducing a sinusoidal function.The existence and the stability...We study a novel class of two-dimensional maps with infinitely many coexisting attractors.Firstly,the mathematical model of these maps is formulated by introducing a sinusoidal function.The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable.In particular,a computer searching program is employed to explore the chaotic attractors in these maps,and a simple map is exemplified to show their complex dynamics.Interestingly,this map contains infinitely many coexisting attractors which has been rarely reported in the literature.Further studies on these coexisting attractors are carried out by investigating their time histories,phase trajectories,basins of attraction,Lyapunov exponents spectrum,and Lyapunov(Kaplan–Yorke)dimension.Bifurcation analysis reveals that the map has periodic and chaotic solutions,and more importantly,exhibits extreme multi-stability.展开更多
Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient con...Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical ＇σ/σx＇-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.展开更多
In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the ...In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the help of them any two elements in real infinite dimensional linear space can be compared.展开更多
The reaction of triphenylphosphine with AgNO3 yielded an unusual nitrate anion bridging one-dimensional infinite chain [Ag(PPh3)NO3] in which the silver(I) atom is three-coordinated by one P atom of triphenylphosphine...The reaction of triphenylphosphine with AgNO3 yielded an unusual nitrate anion bridging one-dimensional infinite chain [Ag(PPh3)NO3] in which the silver(I) atom is three-coordinated by one P atom of triphenylphosphine and two O atoms of two bridging nitrate anions to form a scalene triangle. The complex [Ag(PPh3)NO3] crystallizes in the monoclinic system, space group P21/c with a = 10.281(2), b = 18.596(5), c = 9.180(2) , = 90.60(1), V = 1755.1(7) 3, Z = 4, Mr = 432.15, Dc = 1.635 g/cm3, F(000) = 864 and = 1.254 mm-1. The final R = 0.0606 and wR = 0.1400 for 2188 observed reflections with I > 2(I) out of 3057 unique ones (Rint = 0.0539). IR and elemental analysis of the complex are characterized.展开更多
On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node fi...On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node finite elements to compute the compression distortion of the prestressed anchorage segment. The results indicate that when the prestressed force acts on the anchorage head and segment, the stresses and the displacements in the rock around the anchorage head and segment concentrate on the zone center with the anchor axis, and they decrease with exponential forms. Therefore,the stresses and the displacement spindles are formed. The calculating results of the infinite element are close to the theoretical results. This indicates the method is right. This article introduces a new way to study the mechanism of prestressed anchors. The obtained results have an important role in the research of the anchor mechanism and engineering application.展开更多
With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.展开更多
In this article,a Generalized Calogero-Bogoyavlenskii-Schiff(CBS)equation is studied,serving as an extended shallow water wave model in higher dimensions.Firstly,utilizing the Bell polynomial method,the bilinear form ...In this article,a Generalized Calogero-Bogoyavlenskii-Schiff(CBS)equation is studied,serving as an extended shallow water wave model in higher dimensions.Firstly,utilizing the Bell polynomial method,the bilinear form of the equation,bilinear Bäcklund transformation,Lax pair and infinite conservation laws are derived,confirming the equation’s complete integrability in the context of the Lax pair.Subsequently,the nonlinear superposition formula of the equation is constructed based on the derived bilinear Bäcklund transformation and an array of infinite superposition soliton solutions of the equation are formulated using this nonlinear superposition formula.Lastly,leveraging the obtained bilinear equation,infinite superposition solutions of various functional types are constructed.Their dynamic characteristics are analyzed through illustrated solution images.It is noteworthy that this paper not only uncovers a multitude of properties through the Bell polynomial method but also derives both infinite linear and nonlinear superposition solutions,enriching the diversity of solutions,these aspects have not been previously explored in existing literature.展开更多
A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This p...A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.展开更多
One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite...One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.展开更多
Industrial linear accelerators often contain many bunches when their pulse widths are extended to microseconds.As they typically operate at low electron energies and high currents,the interactions among bunches cannot...Industrial linear accelerators often contain many bunches when their pulse widths are extended to microseconds.As they typically operate at low electron energies and high currents,the interactions among bunches cannot be neglected.In this study,an algorithm is introduced for calculating the space charge force of a train with infinite bunches.By utilizing the ring charge model and the particle-in-cell(PIC)method and combining analytical and numerical methods,the proposed algorithm efficiently calculates the space charge force of infinite bunches,enabling the accurate design of accelerator parameters and a comprehensive understanding of the space charge force.This is a significant improvement on existing simulation software such as ASTRA and PARMELA that can only handle a single bunch or a small number of bunches.The PIC algorithm is validated in long drift space transport by comparing it with existing models,such as the infinite-bunch,ASTRA single-bunch,and PARMELA several-bunch algorithms.The space charge force calculation results for the external acceleration field are also verified.The reliability of the proposed algorithm provides a foundation for the design and optimization of industrial accelerators.展开更多
This paper proposes a novel cargo loading algorithm applicable to automated conveyor-type loading systems.The algorithm offers improvements in computational efficiency and robustness by utilizing the concept of discre...This paper proposes a novel cargo loading algorithm applicable to automated conveyor-type loading systems.The algorithm offers improvements in computational efficiency and robustness by utilizing the concept of discrete derivatives and introducing logistics-related constraints.Optional consideration of the rotation of the cargoes was made to further enhance the optimality of the solutions,if possible to be physically implemented.Evaluation metrics were developed for accurate evaluation and enhancement of the algorithm’s ability to efficiently utilize the loading space and provide a high level of dynamic stability.Experimental results demonstrate the extensive robustness of the proposed algorithm to the diversity of cargoes present in Business-to-Consumer environments.This study contributes practical advancements in both cargo loading optimization and automation of the logistics industry,with potential applications in last-mile delivery services,warehousing,and supply chain management.展开更多
Let I be the set of all infinitely divisible random variables with finite second moments,I_(0)={X∈I;Var(X)>0},P_(I)=inf_(x∈I)P{|X-E[X]|≤√Var(X)}and P_(I_(0))=inf P{|X-E[X]|<√Var(X)}.Firstly,we prove that P_...Let I be the set of all infinitely divisible random variables with finite second moments,I_(0)={X∈I;Var(X)>0},P_(I)=inf_(x∈I)P{|X-E[X]|≤√Var(X)}and P_(I_(0))=inf P{|X-E[X]|<√Var(X)}.Firstly,we prove that P_(I)≥P_(I_(0))>0.Secondly,we find_(x∈I_(0))the exact values of inf P{|X-E[X]|≤√Var(X)}and inf P{|X-E[X]|<√Var(X)}for the cases that J is the set of all geometric random variables,symmetric geometric random variables,Poisson random variables and symmetric Poisson random variables,respectively.As a consequence,we obtain that P_(I)≤e^(-1)^(∞)∑_(k=0)1/2^(2k)(k!)^(2)≈0.46576 and P_(I_(0))≤e^(-1)≈0.36788.展开更多
The fracture and migration patterns of direct roofs play a critical role in excavation stability and mining pressure.However,current methods fail to capture the irregular three-dimensional(3D)behavior of these roofs.I...The fracture and migration patterns of direct roofs play a critical role in excavation stability and mining pressure.However,current methods fail to capture the irregular three-dimensional(3D)behavior of these roofs.In this study,the problem was solved by introducing an innovative 2.5-dimensional(2.5D)Voronoi numerical simulation method,dividing rock layers into 2.5D Voronoi blocks and developing cohesive element-based failure models,supported by a strain-softening HoekeBrown model.The method was applied to the 8311 working face in the Taishan Mine in China,and its accuracy was confirmed through physical experiments.The following conclusions were drawn.The first roof break typically followed an"O-X"pattern.The direct roof did not break randomly over time;instead,it followed three distinct scenarios:(1)A complete break of the direct roof occurred,followed by a sequential collapse(ScenarioⅠ).(2)Regional irregular stacking in one area was followed by sequential collapse in other zones(ScenarioⅡ).(3)The staged breakdown of the direct roof led to separate and sequential collapses on the left and right flanks(ScenarioⅢ).Scenario I was quite common during the 400 m advance of the working face and occurred five times.The fracture characteristics in Scenario I led to widespread pressure on the hydraulic supports in the middle of the working face.Finally,the direct roof from the working face towards the goaf area underwent phases of overhanging,hinging,and collapsing plates.After the first and periodic breaks,the basic roof formed stable hinged plate structures reinforced by overhanging plates and irregular accumulations of the direct roof.展开更多
Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equatio...Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.展开更多
In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilin...In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.展开更多
基金supported in part by the National Natural Science Foundation of China(12471422,62573274,12371173)the Natural Science Foundation of Shandong Province of China(ZR2022LLZ003,ZR2024MF001)the Funding for Visiting Studies and Research by Teachers in Ordinary Undergraduate Colleges and Universities in Shandong Province。
文摘A novel aperiodically intermittent impulse control(AIIC)method is proposed to investigate the exponential synchronization in mean square(ESMS)of a class of impulsive stochastic infinite-dimensional systems with Poisson jumps(ISIDSP).The AIIC control strategy inherits the flexibility of aperiodically intermittent control,including the variable control period,adjustable control interval length,and the discretization of impulsive control.In addition,this article introduces a novel mild Itô's formula.By leveraging semigroup theory,the contraction mapping principle,and graph theory,along with constructing the Lyapunov function,the criterion for the existence and uniqueness of a mild solution of ISIDSP is thereby established.Furthermore,the mean-square exponential synchronization problem of the above systems is resolved,and the constraints within the mild solution domain are alleviated.These criteria clarify the impact of control parameters,control intervals and network topology on ESMS.The theoretical results are subsequently applied to a class of neural networks with reaction-diffusion processes,and the validity of the results is verified using numerical simulations.
基金Supported by the National Natural Science Foundation of China(11361047)Fundamental Research Program of Shanxi Province(20210302124529)。
文摘This paper is concerned with a class of nonlinear fractional differential equations with a disturbance parameter in the integral boundary conditions on the infinite interval.By using Guo-Krasnoselskii fixed point theorem,fixed point index theory and the analytic technique,we give the bifurcation point of the parameter which divides the range of parameter for the existence of at least two,one and no positive solutions for the problem.And,by using a fixed point theorem of generalized concave operator and cone theory,we establish the maximum parameter interval for the existence of the unique positive solution for the problem and show that such a positive solution continuously depends on the parameter.In the end,some examples are given to illustrate our main results.
基金Supported by the National Natural Science Foundation of China(12001424,12271324)the Natural Science Basic research program of Shaanxi Province(2021JZ-21)+1 种基金the China Postdoctoral Science Foundation(2020M673332)Xi’an University,Xi’an Science and Technology Plan Wutongshu Technology Transfer Action Innovation Team(25WTZD07)。
文摘In this article,by employing the Hirota bilinear approach and the long wave limit method,we not only derive soliton solutions,lump solutions,and hybrid solutions for the(2+1)-dimensional Yu-Toda-Sasa-Fukuyama(YTSF)equation,but also analyze the dynamical behaviors of nonlinear local wave propagation in shallow water.Firstly,based on the Hirota bilinear approach,one to four-order soliton solutions of the YTSF equation are obtained,and the effects of different parameters on the amplitude,propagation trajectory,and displacement of solitons are investigated.Secondly,using the long wave limit approach,one to three-order lump solutions and various physical quantities of the YTSF equation are derived.It is found that the real and imaginary parts of the parameter pi dominate the propagation trajectory and the shape of lump waves,respectively.Furthermore,we construct the hybrid solution for the YTSF equation,leading to the conclusion that the interaction between lumps and solitons constitutes an elastic collision.To intuitively understand the dynamic behaviors of these solutions,we conduct numerical simulations to present vivid three-dimensional visualizations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11462020,11262017,and 11262012)the Key Project of Inner Mongolia Normal University,China(Grant No.2014ZD03)
文摘By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.
基金Supported by the National Natural Science Foundation of China under Grant No. 10962004the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070126002+1 种基金the Natural Science Foundation of Inner Mongolia under Grant No. 20080404MS0104the Research Foundation for Talented Scholars of Inner Mongolia University under Grant No. 207066
文摘For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.
基金National Natural Science Foundation of China(Grant Nos.11672257,11632008,11772306,and 11972173)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20161314)+1 种基金the 5th 333 High-level Personnel Training Project of Jiangsu Province of China(Grant No.BRA2018324)the Excellent Scientific and Technological Innovation Team of Jiangsu University.
文摘We study a novel class of two-dimensional maps with infinitely many coexisting attractors.Firstly,the mathematical model of these maps is formulated by introducing a sinusoidal function.The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable.In particular,a computer searching program is employed to explore the chaotic attractors in these maps,and a simple map is exemplified to show their complex dynamics.Interestingly,this map contains infinitely many coexisting attractors which has been rarely reported in the literature.Further studies on these coexisting attractors are carried out by investigating their time histories,phase trajectories,basins of attraction,Lyapunov exponents spectrum,and Lyapunov(Kaplan–Yorke)dimension.Bifurcation analysis reveals that the map has periodic and chaotic solutions,and more importantly,exhibits extreme multi-stability.
基金Project supported by the National Natural Science Foundation of China （Grant No 10562002） and the Natural Science Foundation of Nei Mongol, China （Grant No 200508010103）.
文摘Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical ＇σ/σx＇-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.
文摘In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the help of them any two elements in real infinite dimensional linear space can be compared.
基金NNSFC (No. 20001007 20131020) and Natural Science Foundation of the Chinese Academy of Sciences (KJCX2-H3) and Fujian Province (2000F006)
文摘The reaction of triphenylphosphine with AgNO3 yielded an unusual nitrate anion bridging one-dimensional infinite chain [Ag(PPh3)NO3] in which the silver(I) atom is three-coordinated by one P atom of triphenylphosphine and two O atoms of two bridging nitrate anions to form a scalene triangle. The complex [Ag(PPh3)NO3] crystallizes in the monoclinic system, space group P21/c with a = 10.281(2), b = 18.596(5), c = 9.180(2) , = 90.60(1), V = 1755.1(7) 3, Z = 4, Mr = 432.15, Dc = 1.635 g/cm3, F(000) = 864 and = 1.254 mm-1. The final R = 0.0606 and wR = 0.1400 for 2188 observed reflections with I > 2(I) out of 3057 unique ones (Rint = 0.0539). IR and elemental analysis of the complex are characterized.
文摘On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node finite elements to compute the compression distortion of the prestressed anchorage segment. The results indicate that when the prestressed force acts on the anchorage head and segment, the stresses and the displacements in the rock around the anchorage head and segment concentrate on the zone center with the anchor axis, and they decrease with exponential forms. Therefore,the stresses and the displacement spindles are formed. The calculating results of the infinite element are close to the theoretical results. This indicates the method is right. This article introduces a new way to study the mechanism of prestressed anchors. The obtained results have an important role in the research of the anchor mechanism and engineering application.
基金financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
文摘With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic computation,we find out,on one hand,a set of bilinear auto-Backlund transformations,which could connect certain solutions of that equation with other solutions of that equation itself,and on the other hand,a set of similarity reductions,which could go from that equation to a known ordinary differential equation.The results in this paper depend on all the oceanic variable coefficients in that equation.
基金the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2024MS01003)the First-Class Disciplines Project,Inner Mongolia Autonomous Region,China(Grant Nos.YLXKZX-NSD-001 and YLXKZX-NSD-009)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2414).
文摘In this article,a Generalized Calogero-Bogoyavlenskii-Schiff(CBS)equation is studied,serving as an extended shallow water wave model in higher dimensions.Firstly,utilizing the Bell polynomial method,the bilinear form of the equation,bilinear Bäcklund transformation,Lax pair and infinite conservation laws are derived,confirming the equation’s complete integrability in the context of the Lax pair.Subsequently,the nonlinear superposition formula of the equation is constructed based on the derived bilinear Bäcklund transformation and an array of infinite superposition soliton solutions of the equation are formulated using this nonlinear superposition formula.Lastly,leveraging the obtained bilinear equation,infinite superposition solutions of various functional types are constructed.Their dynamic characteristics are analyzed through illustrated solution images.It is noteworthy that this paper not only uncovers a multitude of properties through the Bell polynomial method but also derives both infinite linear and nonlinear superposition solutions,enriching the diversity of solutions,these aspects have not been previously explored in existing literature.
文摘A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.
基金Supported by the Guiding Project of Science and Technology Research Plan of Hubei Provincial Department of Education(B2022458)。
文摘One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.
基金supported by the National Key Research and Development Program(No.2022YFC2402300)。
文摘Industrial linear accelerators often contain many bunches when their pulse widths are extended to microseconds.As they typically operate at low electron energies and high currents,the interactions among bunches cannot be neglected.In this study,an algorithm is introduced for calculating the space charge force of a train with infinite bunches.By utilizing the ring charge model and the particle-in-cell(PIC)method and combining analytical and numerical methods,the proposed algorithm efficiently calculates the space charge force of infinite bunches,enabling the accurate design of accelerator parameters and a comprehensive understanding of the space charge force.This is a significant improvement on existing simulation software such as ASTRA and PARMELA that can only handle a single bunch or a small number of bunches.The PIC algorithm is validated in long drift space transport by comparing it with existing models,such as the infinite-bunch,ASTRA single-bunch,and PARMELA several-bunch algorithms.The space charge force calculation results for the external acceleration field are also verified.The reliability of the proposed algorithm provides a foundation for the design and optimization of industrial accelerators.
基金supported by the BK21 FOUR funded by the Ministry of Education of Korea and National Research Foundation of Korea,a Korea Agency for Infrastructure Technology Advancement(KAIA)grant funded by the Ministry of Land,Infrastructure,and Transport(Grant 1615013176)IITP(Institute of Information&Coummunications Technology Planning&Evaluation)-ICAN(ICT Challenge and Advanced Network of HRD)grant funded by the Korea government(Ministry of Science and ICT)(RS-2024-00438411).
文摘This paper proposes a novel cargo loading algorithm applicable to automated conveyor-type loading systems.The algorithm offers improvements in computational efficiency and robustness by utilizing the concept of discrete derivatives and introducing logistics-related constraints.Optional consideration of the rotation of the cargoes was made to further enhance the optimality of the solutions,if possible to be physically implemented.Evaluation metrics were developed for accurate evaluation and enhancement of the algorithm’s ability to efficiently utilize the loading space and provide a high level of dynamic stability.Experimental results demonstrate the extensive robustness of the proposed algorithm to the diversity of cargoes present in Business-to-Consumer environments.This study contributes practical advancements in both cargo loading optimization and automation of the logistics industry,with potential applications in last-mile delivery services,warehousing,and supply chain management.
基金supported by the National Natural Science Foundation of China(12161029,12171335)the National Natural Science Foundation of Hainan Province(121RC149)+1 种基金the Science Development Project of Sichuan University(2020SCUNL201)the Natural Sciences and Engineering Research Council of Canada(4394-2018).
文摘Let I be the set of all infinitely divisible random variables with finite second moments,I_(0)={X∈I;Var(X)>0},P_(I)=inf_(x∈I)P{|X-E[X]|≤√Var(X)}and P_(I_(0))=inf P{|X-E[X]|<√Var(X)}.Firstly,we prove that P_(I)≥P_(I_(0))>0.Secondly,we find_(x∈I_(0))the exact values of inf P{|X-E[X]|≤√Var(X)}and inf P{|X-E[X]|<√Var(X)}for the cases that J is the set of all geometric random variables,symmetric geometric random variables,Poisson random variables and symmetric Poisson random variables,respectively.As a consequence,we obtain that P_(I)≤e^(-1)^(∞)∑_(k=0)1/2^(2k)(k!)^(2)≈0.46576 and P_(I_(0))≤e^(-1)≈0.36788.
基金supported by the Autonomous General Projects of the State Key Laboratory of Coal Mine Disaster Dynamics and Control,Chongqing University,China(Grant No.2011DA105287-MS202209)the National Natural Science Foundation of China,China(Grant Nos.52304149 and 52204127).
文摘The fracture and migration patterns of direct roofs play a critical role in excavation stability and mining pressure.However,current methods fail to capture the irregular three-dimensional(3D)behavior of these roofs.In this study,the problem was solved by introducing an innovative 2.5-dimensional(2.5D)Voronoi numerical simulation method,dividing rock layers into 2.5D Voronoi blocks and developing cohesive element-based failure models,supported by a strain-softening HoekeBrown model.The method was applied to the 8311 working face in the Taishan Mine in China,and its accuracy was confirmed through physical experiments.The following conclusions were drawn.The first roof break typically followed an"O-X"pattern.The direct roof did not break randomly over time;instead,it followed three distinct scenarios:(1)A complete break of the direct roof occurred,followed by a sequential collapse(ScenarioⅠ).(2)Regional irregular stacking in one area was followed by sequential collapse in other zones(ScenarioⅡ).(3)The staged breakdown of the direct roof led to separate and sequential collapses on the left and right flanks(ScenarioⅢ).Scenario I was quite common during the 400 m advance of the working face and occurred five times.The fracture characteristics in Scenario I led to widespread pressure on the hydraulic supports in the middle of the working face.Finally,the direct roof from the working face towards the goaf area underwent phases of overhanging,hinging,and collapsing plates.After the first and periodic breaks,the basic roof formed stable hinged plate structures reinforced by overhanging plates and irregular accumulations of the direct roof.
文摘Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.
基金supported by the National Natural Science Foundation of China,Grant No.12375006。
文摘In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.
