This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilt...This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.展开更多
Based on the features of the non-standard equipment executing work, a project management and decision support system oriented to the non-standard equipment is developed, and the information model, function model as we...Based on the features of the non-standard equipment executing work, a project management and decision support system oriented to the non-standard equipment is developed, and the information model, function model as well as the structure framework of the system are also introduced in this paper.展开更多
The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are...The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.展开更多
Recently,the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations.Different forms of non-standard Lagrangia...Recently,the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations.Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties.One interesting form related to the inverse variational problem is the logarithmic Lagrangian,which has a number of motivating features related to the Li′enard-type and Emden nonlinear differential equations.Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians.In this communication,we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians.One interesting consequence concerns the emergence of an extra pressure term,which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field.The case of the stellar halo of the Milky Way is considered.展开更多
. Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with l.... Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with lattice point counting. More precisely, by using combinatorial tools, we prove that there exists a polytope such that the image of Hilbert function in some degree is equal to the number of lattice points of this polytope.展开更多
A series of new physics scenarios predict the existence of the extra charged gauge boson W’,which can induce charged-current(CC)non-standard neutrino interactions(NSIs).The theoretical constraints on the simplified W...A series of new physics scenarios predict the existence of the extra charged gauge boson W’,which can induce charged-current(CC)non-standard neutrino interactions(NSIs).The theoretical constraints on the simplified W’model and further on the CC NSI parameters ε_(αβ)^-qq'Y from partial wave unitarity and W’decays are considered.The sensitivity of the process pp→W’→lv to the W’model at the LHC and high-luminosity(HL)LHC experiments is investigated by estimating the expected constraints on ε_(αβ)^-qq'Y (α=β=e orμ)using a Monte-Carlo(MC)simulation.We find that the interference effect plays an important role,and the LHC can strongly constrain ε_(αβ)^-qq'L .Compared with those at the 13 TeV LHC with L=139 fb^(-1),the expected constraints at the 14TeV LHC with L=3 ab^(-1)can be strengthened to approximately one order of magnitude.展开更多
Analysis of free fall and acceleration of the mass on the Earth shows that using abstract entities such as absolute space or inertial space to explain mass dynamics leads to the violation of the principle of action an...Analysis of free fall and acceleration of the mass on the Earth shows that using abstract entities such as absolute space or inertial space to explain mass dynamics leads to the violation of the principle of action and reaction. Many scientists including Newton, Mach, and Einstein recognized that inertial force has no reaction that originates on mass. Einstein calls the lack of reaction to the inertial force a serious criticism of the space-time continuum concept. Presented is the hypothesis that the inertial force develops in an interaction of two masses via the force field. The inertial force created by such a field has reaction force. The dynamic gravitational field predicted is strong enough to be detected in the laboratory. This article describes the laboratory experiment which can prove or disprove the hypothesis of the dynamic gravitational field. The inertial force, calculated using the equation for the dynamic gravitational field, agrees with the behavior of inertial force observed in the experiments on the Earth. The movement of the planets in our solar system calculated using that equation is the same as that calculated using Newton’s method. The space properties calculated by the candidate equation explain the aberration of light and the results of light propagation experiments. The dynamic gravitational field can explain the discrepancy between the observed velocity of stars in the galaxy and those predicted by Newton’s theory of gravitation without the need for the dark matter hypothesis.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11572212 and 11272227)the Innovation Program of Suzhou University of Science and Technology,China(Grant No.SKYCX16 012)
文摘This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.
文摘Based on the features of the non-standard equipment executing work, a project management and decision support system oriented to the non-standard equipment is developed, and the information model, function model as well as the structure framework of the system are also introduced in this paper.
基金Supported by the National Natural Science Foundation of China(12272248,11972241)。
文摘The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,respectively.The criterion equations of canonical transformation are established,and four basic forms of canonical transformations are given.The dynamic equations with non-standard Lagrangians admit Lie algebraic structure.From this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved quantities.Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.
文摘Recently,the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations.Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties.One interesting form related to the inverse variational problem is the logarithmic Lagrangian,which has a number of motivating features related to the Li′enard-type and Emden nonlinear differential equations.Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians.In this communication,we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians.One interesting consequence concerns the emergence of an extra pressure term,which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field.The case of the stellar halo of the Milky Way is considered.
文摘. Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with lattice point counting. More precisely, by using combinatorial tools, we prove that there exists a polytope such that the image of Hilbert function in some degree is equal to the number of lattice points of this polytope.
基金Supported by the National Natural Science Foundation of China(11875157,12147214)the Natural Science Foundation of the Liaoning Scientific Committee(LJKZ0978)the Outstanding Research Cultivation Program of Liaoning Normal University(21GDL004)。
文摘A series of new physics scenarios predict the existence of the extra charged gauge boson W’,which can induce charged-current(CC)non-standard neutrino interactions(NSIs).The theoretical constraints on the simplified W’model and further on the CC NSI parameters ε_(αβ)^-qq'Y from partial wave unitarity and W’decays are considered.The sensitivity of the process pp→W’→lv to the W’model at the LHC and high-luminosity(HL)LHC experiments is investigated by estimating the expected constraints on ε_(αβ)^-qq'Y (α=β=e orμ)using a Monte-Carlo(MC)simulation.We find that the interference effect plays an important role,and the LHC can strongly constrain ε_(αβ)^-qq'L .Compared with those at the 13 TeV LHC with L=139 fb^(-1),the expected constraints at the 14TeV LHC with L=3 ab^(-1)can be strengthened to approximately one order of magnitude.
文摘Analysis of free fall and acceleration of the mass on the Earth shows that using abstract entities such as absolute space or inertial space to explain mass dynamics leads to the violation of the principle of action and reaction. Many scientists including Newton, Mach, and Einstein recognized that inertial force has no reaction that originates on mass. Einstein calls the lack of reaction to the inertial force a serious criticism of the space-time continuum concept. Presented is the hypothesis that the inertial force develops in an interaction of two masses via the force field. The inertial force created by such a field has reaction force. The dynamic gravitational field predicted is strong enough to be detected in the laboratory. This article describes the laboratory experiment which can prove or disprove the hypothesis of the dynamic gravitational field. The inertial force, calculated using the equation for the dynamic gravitational field, agrees with the behavior of inertial force observed in the experiments on the Earth. The movement of the planets in our solar system calculated using that equation is the same as that calculated using Newton’s method. The space properties calculated by the candidate equation explain the aberration of light and the results of light propagation experiments. The dynamic gravitational field can explain the discrepancy between the observed velocity of stars in the galaxy and those predicted by Newton’s theory of gravitation without the need for the dark matter hypothesis.
