The conceptions of theorems, laws and corollaries of hydrology were put forward. Combining with hydrology practice, several theo- rems, laws as well as corollaries of hydrology were summarized. The study provided some...The conceptions of theorems, laws and corollaries of hydrology were put forward. Combining with hydrology practice, several theo- rems, laws as well as corollaries of hydrology were summarized. The study provided some references for accelerating the development of hydrology theory in these aspects and promoting the improvement of its production technology.展开更多
If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton＇s second law of mechanics in the Planck＇s scale. This curious velocity dependent term inspires a frictional fe...If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton＇s second law of mechanics in the Planck＇s scale. This curious velocity dependent term inspires a frictional feature of the gravity. In this short letter we address that this new term modifies the effective mass and the Newtonian constant as the time dependent quantities. Thus we must have a running on the value of the effective mass on the particle mass m near the holographic screen and the G. This result has a nigh relation with the Dirac hypothesis about the large numbers hypothesis （L.N.H.）. We propose that the corrected entropie terms via Verlinde idea can be brought as a holographic evidence for the authenticity of the Dirac idea.展开更多
Self-adjoint theorem is introduced to match the corresponding functional of the given differential equations,and then Noether＇s theorem is used to determine the extended conservation laws of the original equations. F...Self-adjoint theorem is introduced to match the corresponding functional of the given differential equations,and then Noether＇s theorem is used to determine the extended conservation laws of the original equations. Finally, as the application of the method, the conservation laws of Drinfel＇d-Sokolov-Wilson equation and Benjamin-Bona-Mahony equation are constructed.展开更多
Our ability to arrive at knowledge by chains of judgment is constitutive of our rationality, likewise our ability to discern the self-evidence of logical and arithmetical laws. To count an activity as ＂thinking about...Our ability to arrive at knowledge by chains of judgment is constitutive of our rationality, likewise our ability to discern the self-evidence of logical and arithmetical laws. To count an activity as ＂thinking about the physical world＂ is to hold it assessable in the light of the laws of physics; whereas to count an activity as ＂thinking at all＂ is to hold it assessable in the light of the laws of logic. Thus, the kind of generality that distinguishes logic from the special sciences is a generality in the applicability of the norms it provides. Logical laws are more general than laws of the special sciences because they prescribe universally the way in which one ought to think, if one is to think all. Logicism is usually understood to be the thesis that all, or at least large parts of, mathematics can be reduced to logic. This thesis has two sides： （1） all mathematical concepts can be defined in terms of basic logical concepts; （2） all mathematical theorems can be deduced from basic logical truths. According to logicism all terms, including all mathematical terms, are to be given a definite meaning within the basic system. This paper aims at a comparative analysis of the contributions of Frege and Russell to the development of modem logic by reviewing in some detail their essential features and derivations. Without making any pretensions to proffering a definitive resolution of any puzzles, the discussion will, however, raise some fundamental questions, and offer a critical evaluation of the putative success or failure of the logicist programmes of Frege and Russell.展开更多
The arguments in this paper lead to a new definition of thermodynamic equilibrium that remedies the deficiencies of the current forms. This definition relates thermodynamic equilibrium to its physical causes and accou...The arguments in this paper lead to a new definition of thermodynamic equilibrium that remedies the deficiencies of the current forms. This definition relates thermodynamic equilibrium to its physical causes and accounts for all factors that determine it for all types of equilibrium. Standard definitions of thermodynamic equilibrium are incomplete. They do not take account of all factors that determine such equilibriums, discuss the impediments which may prevent them being reached or relate the properties that define equilibriums to the physical reasons that determine them when impediments are present. The laws of thermodynamics determine the requirements for equilibrium. These laws arise from the physical behaviour of the molecules in molecular systems and are consequences of the conservation of energy, the energies of molecules, statistics, Newton＇s laws of motion, and the equi-partition of energy. The standard definition of thermodynamic equilibrium correctly defines equilibrium whenever impediments are not factors. The discussion demonstrates how impediments arise, accounts for their role in defining equilibrium and how they relate to the energies of molecules at the conditions of the system. The new definition applies to all types of equilibrium.展开更多
In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two ca...In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.展开更多
We investigate a tagged particle in the exclusion processes on {1,..., N }×Zd, with different densities in different levels {k} × Zd, ? k. Ignoring the level the tagged particle lying in, we only concern its...We investigate a tagged particle in the exclusion processes on {1,..., N }×Zd, with different densities in different levels {k} × Zd, ? k. Ignoring the level the tagged particle lying in, we only concern its position in Zd,denoted by Xt. Note that the whole space is not homogeneous. We define the environment process viewed from the tagged particle, of which Xt can be expressed as a functional. It is called the tagged particle process. We show the ergodicity of the tagged particle process, then prove the strong law of large numbers. Furthermore, we show the central limit theorem of Xt provided the zero-mean condition.展开更多
In this work we study the Lagrangian and the conservation laws for a wave equation with a dissipative source. Using semi-inverse method, we show that the equation possesses a nonlocal Lagrangian with an auxiliary func...In this work we study the Lagrangian and the conservation laws for a wave equation with a dissipative source. Using semi-inverse method, we show that the equation possesses a nonlocal Lagrangian with an auxiliary function.As a result, from a modified Noether's theorem and the nonclassical Noether symmetry generators, we construct some conservation laws for this equation, which are different from the ones obtained by Ibragimov's theorem in [Y. Wang and L. Wei, Abstr. App. Anal. 2013(2013) 407908]. The results show that our method work for arbitrary functions f(u)and g(u) rather than special ones.展开更多
In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the...In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. Inthe model there are two sets of unknown parameters, one set corresponding to the marginaldistribution of V and one to autocorrelation of V. Based on discrete time observations ofthe log price the authors discuss how to estimate the parameters appearing in the marginaldistribution and find the asymptotic properties.展开更多
In this paper, we correct the Stefan–Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan–Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calcu...In this paper, we correct the Stefan–Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan–Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calculated. We find that the corrected Stefan–Boltzmann law contains two terms, the 46 Tterm and the Tterm. Due to the modifications, at the end of the black hole radiation, it will arise a limited highest temperature and leave a residue. It is interesting to note that the mass of the residue and the Planck mass is in the same order of magnitude. The modified Stefan–Boltzmann law also gives a correction to the lifespan of the black hole, although it is very small.展开更多
文摘The conceptions of theorems, laws and corollaries of hydrology were put forward. Combining with hydrology practice, several theo- rems, laws as well as corollaries of hydrology were summarized. The study provided some references for accelerating the development of hydrology theory in these aspects and promoting the improvement of its production technology.
文摘If the uncertainty principle applies to the Verlinde entropic idea, it leads to a new term in the Newton＇s second law of mechanics in the Planck＇s scale. This curious velocity dependent term inspires a frictional feature of the gravity. In this short letter we address that this new term modifies the effective mass and the Newtonian constant as the time dependent quantities. Thus we must have a running on the value of the effective mass on the particle mass m near the holographic screen and the G. This result has a nigh relation with the Dirac hypothesis about the large numbers hypothesis （L.N.H.）. We propose that the corrected entropie terms via Verlinde idea can be brought as a holographic evidence for the authenticity of the Dirac idea.
基金Supported by "Math + X" Fund of Dalian University of Technology, Science Foundation of Dalian University of Technology under Grant No. SFDUT0808the National Key Basic Research Development of China under Grant No. 2004CB318000
文摘Self-adjoint theorem is introduced to match the corresponding functional of the given differential equations,and then Noether＇s theorem is used to determine the extended conservation laws of the original equations. Finally, as the application of the method, the conservation laws of Drinfel＇d-Sokolov-Wilson equation and Benjamin-Bona-Mahony equation are constructed.
文摘Our ability to arrive at knowledge by chains of judgment is constitutive of our rationality, likewise our ability to discern the self-evidence of logical and arithmetical laws. To count an activity as ＂thinking about the physical world＂ is to hold it assessable in the light of the laws of physics; whereas to count an activity as ＂thinking at all＂ is to hold it assessable in the light of the laws of logic. Thus, the kind of generality that distinguishes logic from the special sciences is a generality in the applicability of the norms it provides. Logical laws are more general than laws of the special sciences because they prescribe universally the way in which one ought to think, if one is to think all. Logicism is usually understood to be the thesis that all, or at least large parts of, mathematics can be reduced to logic. This thesis has two sides： （1） all mathematical concepts can be defined in terms of basic logical concepts; （2） all mathematical theorems can be deduced from basic logical truths. According to logicism all terms, including all mathematical terms, are to be given a definite meaning within the basic system. This paper aims at a comparative analysis of the contributions of Frege and Russell to the development of modem logic by reviewing in some detail their essential features and derivations. Without making any pretensions to proffering a definitive resolution of any puzzles, the discussion will, however, raise some fundamental questions, and offer a critical evaluation of the putative success or failure of the logicist programmes of Frege and Russell.
文摘The arguments in this paper lead to a new definition of thermodynamic equilibrium that remedies the deficiencies of the current forms. This definition relates thermodynamic equilibrium to its physical causes and accounts for all factors that determine it for all types of equilibrium. Standard definitions of thermodynamic equilibrium are incomplete. They do not take account of all factors that determine such equilibriums, discuss the impediments which may prevent them being reached or relate the properties that define equilibriums to the physical reasons that determine them when impediments are present. The laws of thermodynamics determine the requirements for equilibrium. These laws arise from the physical behaviour of the molecules in molecular systems and are consequences of the conservation of energy, the energies of molecules, statistics, Newton＇s laws of motion, and the equi-partition of energy. The standard definition of thermodynamic equilibrium correctly defines equilibrium whenever impediments are not factors. The discussion demonstrates how impediments arise, accounts for their role in defining equilibrium and how they relate to the energies of molecules at the conditions of the system. The new definition applies to all types of equilibrium.
基金supported by the National Natural Science Foundations of China (Grant Nos.11072218 and 11272287)the Natural Science Foundations of Zhejiang Province of China (Grant No.Y6110314)
文摘In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.
基金supported by National Natural Science Foundation of China(Grant No.11371040)
文摘We investigate a tagged particle in the exclusion processes on {1,..., N }×Zd, with different densities in different levels {k} × Zd, ? k. Ignoring the level the tagged particle lying in, we only concern its position in Zd,denoted by Xt. Note that the whole space is not homogeneous. We define the environment process viewed from the tagged particle, of which Xt can be expressed as a functional. It is called the tagged particle process. We show the ergodicity of the tagged particle process, then prove the strong law of large numbers. Furthermore, we show the central limit theorem of Xt provided the zero-mean condition.
基金Supported by National Natural Science Foundation of China under Grant No.11101111Zhejiang Provincial Natural Science Foundation of China under Grant Nos.LY14A010029 and LY12A01003
文摘In this work we study the Lagrangian and the conservation laws for a wave equation with a dissipative source. Using semi-inverse method, we show that the equation possesses a nonlocal Lagrangian with an auxiliary function.As a result, from a modified Noether's theorem and the nonclassical Noether symmetry generators, we construct some conservation laws for this equation, which are different from the ones obtained by Ibragimov's theorem in [Y. Wang and L. Wei, Abstr. App. Anal. 2013(2013) 407908]. The results show that our method work for arbitrary functions f(u)and g(u) rather than special ones.
基金Project supported by the Yunnan Provincial Natural Science Foundation of China(No.00A0006R).
文摘In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. Inthe model there are two sets of unknown parameters, one set corresponding to the marginaldistribution of V and one to autocorrelation of V. Based on discrete time observations ofthe log price the authors discuss how to estimate the parameters appearing in the marginaldistribution and find the asymptotic properties.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11273009 and 11303006
文摘In this paper, we correct the Stefan–Boltzmann law by considering the generalized uncertainty principle, and with this corrected Stefan–Boltzmann law, the lifespan of the Schwarzschild-de-sitter black holes is calculated. We find that the corrected Stefan–Boltzmann law contains two terms, the 46 Tterm and the Tterm. Due to the modifications, at the end of the black hole radiation, it will arise a limited highest temperature and leave a residue. It is interesting to note that the mass of the residue and the Planck mass is in the same order of magnitude. The modified Stefan–Boltzmann law also gives a correction to the lifespan of the black hole, although it is very small.
