In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr’s correspondence principle. Using Fourier expansions for the classical and quantum dist...In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr’s correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume that the Fourier coefficients coincide for the case of large quantum number. We illustrate the procedure by analyzing the classical limit for the quantum harmonic oscillator and the particle in a box, although the method is quite general. We find, in an analytical fashion, the classical distribution arising from the quantum one as the zeroth order term in an expansion in powers of Planck’s constant. We interpret the correction terms as residual quantum effects at the microscopic-macroscopic boundary.展开更多
The correspondence principle and the condition of supplementation were introduced by N. Bohr for the sub-mission of light phenomena, taking into account the wave nature of electromagnetic radiation on one hand, and it...The correspondence principle and the condition of supplementation were introduced by N. Bohr for the sub-mission of light phenomena, taking into account the wave nature of electromagnetic radiation on one hand, and its quantum structures on the other. In this paper, correspondence principle combines two models of matter, namely, the classical point of view of environment can be considered as an ensemble no equally-frequencies oscillators, i.e. electrons in the surrounding various atoms (molecules) of the matter and characterized by its own set of frequencies (but not hesitant in the absence of an energy source) and the quantum - environment could be presented as a set (ensemble) two-level systems, a wide range of Bohr fre-quencies. According to the correspondence principle Bohr jump-frequencies of atoms (molecules or nano particles) and natural frequencies oscillations of electrons of the same environment - oscillators are equal to each other. The dispersion characteristics of the environment in the every study range of optical frequencies correspond to the model of the classical harmonic oscillator of Lorenz, capable oscillates with Bohr fre-quency. Using the laws of classical mechanics to describe the environment and its dispersion properties, and the simultaneous presentation of light radiation in the form of a beam interacting with the environment of photons (quanta, corpuscles) helps explain peculiarities of the spectral composition Raleigh light scattered.展开更多
1 INTRODUCTIONThe CSP(Corresponding States Principle)has been considered to be a useful methodfor the prediction of fluid properties from a minimum amount of information.One ofits form,the shape factor methods is deve...1 INTRODUCTIONThe CSP(Corresponding States Principle)has been considered to be a useful methodfor the prediction of fluid properties from a minimum amount of information.One ofits form,the shape factor methods is developed through relating the pVT of any interestedpure fluid"a"to that of another"0"by展开更多
In the two-parameter corresponding states principle(CSP), the critical compressibility factors of the fluid under study(called 'a' fluid) and the reference fluid(called 'o' fluid) must be identical. Th...In the two-parameter corresponding states principle(CSP), the critical compressibility factors of the fluid under study(called 'a' fluid) and the reference fluid(called 'o' fluid) must be identical. This is not generally observed in nature. To overcome this limitation, a perfect shape factor CSP is proposed in which the compressibility factors of 'a' and 'o' fluids are corresponded perfectly by introducing a new pressure shape factor 8. Using methane as the 'o' fluid, the shape factors of many fluids are calculated from PVT properties at saturation state and the second virial coefficients. Models are also formulated for the shape factors with the assumption of is a function of temperature and volume while 6 and 5 are temperature dependent only. The models described the shape factors satisfactorily in whole region including vapor, liquid and their co-existing phases. The perfect shape factor CSP could be applied for both polar and non-polar fluids.展开更多
The virial equation can well describe gas state at high temperature and pressure, but the difficulties in virial coefficient calculation limit the use of virial equation. Simple extended corresponding state principle(...The virial equation can well describe gas state at high temperature and pressure, but the difficulties in virial coefficient calculation limit the use of virial equation. Simple extended corresponding state principle(SE-CSP) is introduced in virial equation. Based on a corresponding state equation, including three characteristic parameters, an extended parameter is introduced to describe the second virial coefficient expressions of main products of propellant gas. The modified SE-CSP second virial coefficient expression was extrapolated based on the virial coefficients experimental temperature, and the second virial coefficients obtained are in good agreement with the experimental data at a low temperature and the theoretical values at high temperature. The maximum pressure in the closed bomb test was calculated with modified SE-CSP virial coefficient expressions with the calculated error of less than 2%, and the error was smaller than the result calculated with the reported values under the same calculation conditions. The modified SE-CSP virial coefficient expression provides a convenient and efficient method for practical virial coefficient calculation without resorting to complicated molecular model design and integral calculation.展开更多
Pragmatic vagueness is frequently used in business correspondences and it offers benefits to the addressers by making business letter more flexible,appropriate and polite.This paper focuses on the employment of vague ...Pragmatic vagueness is frequently used in business correspondences and it offers benefits to the addressers by making business letter more flexible,appropriate and polite.This paper focuses on the employment of vague language in international business correspondences based on the Politeness Principle.In this study,the pragmatic effect of vague language in business correspondence is illustrated and summarized as a motivated factor to better show politeness and respect.The use of vague language motivated by politeness consequently leads to a more smooth,successful and desired communication in business world.展开更多
Business correspondence are the indispensable tool in the practical process of business communication and interchange.Especially,as the communicated body of information,their language possesses specific characteristic...Business correspondence are the indispensable tool in the practical process of business communication and interchange.Especially,as the communicated body of information,their language possesses specific characteristics.Rooted from the "Politeness Principle" and the "Cooperative Principle",the most distinctive epitome of it is the seven "C" principles.Based on the discussion of the seven "C" principles,this paper devotes itself to the analyses of the contradictory characteristics which occur frequently in the concrete business contexts,and then to examine the causes of these features.Ultimately,it will suggest more flexible and more widened perspective towards the creation of business correspondence and the language applied in them.展开更多
The paper shows that the variational principle serves as an element of the mathematical structure of a quantum theory. The experimentally confirmed properties of the corpuscular-wave duality of a quantum particle are ...The paper shows that the variational principle serves as an element of the mathematical structure of a quantum theory. The experimentally confirmed properties of the corpuscular-wave duality of a quantum particle are elements of the analysis. A Lagrangian density that yields the equations of motion of a given quantum theory of a massive particle is analyzed. It is proved that if this Lagrangian density is a Lorentz scalar whose dimension is ?then the associated action consistently defines the required phase of the quantum particle. The dimension of this Lagrangian density proves that also the quantum function ?has dimension. This result provides new criteria for the acceptability of quantum theories. An examination of the first order Dirac equation demonstrates that it satisfies the new criteria whereas the second order Klein-Gordon equation fails to do that.展开更多
Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly c...Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function of bosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant A introduced in generalized uncertainty principle takes a proper value, we derive Bekenstein- Hawking entropy and the correction value corresponding cosmologicaJ horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small mass approximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropy of the black string cosmological horizon in non-spherical coordinate spacetime.展开更多
Modeling the earth's fluid and elastic response to the melting of the glaciers of the last ice age is the most direct way to infer the earth's radial viscosity profile.Here,we compare two methods for calculati...Modeling the earth's fluid and elastic response to the melting of the glaciers of the last ice age is the most direct way to infer the earth's radial viscosity profile.Here,we compare two methods for calculating the viscoelastic response to surface loading.In one,the elastic equation of motion is converted to a viscoelastic equation using the Correspondence Principle.In the other,elastic deformation is added to the viscous flow as isostatic adjustment proceeds.The two modeling methods predict adjustment histories that are different enough to potentially impact the interpretation of the observed glacial isostatic adjustment(GIA).The differences arise from buoyancy and whether fluid displacements are subjected to hydrostatic pre-stress.The methods agree if they use the same equations and boundary conditions.The origin of the differences is determined by varying the boundary conditions and pre-stress application.展开更多
文摘In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr’s correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume that the Fourier coefficients coincide for the case of large quantum number. We illustrate the procedure by analyzing the classical limit for the quantum harmonic oscillator and the particle in a box, although the method is quite general. We find, in an analytical fashion, the classical distribution arising from the quantum one as the zeroth order term in an expansion in powers of Planck’s constant. We interpret the correction terms as residual quantum effects at the microscopic-macroscopic boundary.
文摘The correspondence principle and the condition of supplementation were introduced by N. Bohr for the sub-mission of light phenomena, taking into account the wave nature of electromagnetic radiation on one hand, and its quantum structures on the other. In this paper, correspondence principle combines two models of matter, namely, the classical point of view of environment can be considered as an ensemble no equally-frequencies oscillators, i.e. electrons in the surrounding various atoms (molecules) of the matter and characterized by its own set of frequencies (but not hesitant in the absence of an energy source) and the quantum - environment could be presented as a set (ensemble) two-level systems, a wide range of Bohr fre-quencies. According to the correspondence principle Bohr jump-frequencies of atoms (molecules or nano particles) and natural frequencies oscillations of electrons of the same environment - oscillators are equal to each other. The dispersion characteristics of the environment in the every study range of optical frequencies correspond to the model of the classical harmonic oscillator of Lorenz, capable oscillates with Bohr fre-quency. Using the laws of classical mechanics to describe the environment and its dispersion properties, and the simultaneous presentation of light radiation in the form of a beam interacting with the environment of photons (quanta, corpuscles) helps explain peculiarities of the spectral composition Raleigh light scattered.
文摘1 INTRODUCTIONThe CSP(Corresponding States Principle)has been considered to be a useful methodfor the prediction of fluid properties from a minimum amount of information.One ofits form,the shape factor methods is developed through relating the pVT of any interestedpure fluid"a"to that of another"0"by
基金Supported by the National Natural Science Foundation of China (No.29876033), the Doctoral Foundation of Ministry of Education of China (No. 98033508) and the Zhejiang Natural Science Foundation (No. 298030).
文摘In the two-parameter corresponding states principle(CSP), the critical compressibility factors of the fluid under study(called 'a' fluid) and the reference fluid(called 'o' fluid) must be identical. This is not generally observed in nature. To overcome this limitation, a perfect shape factor CSP is proposed in which the compressibility factors of 'a' and 'o' fluids are corresponded perfectly by introducing a new pressure shape factor 8. Using methane as the 'o' fluid, the shape factors of many fluids are calculated from PVT properties at saturation state and the second virial coefficients. Models are also formulated for the shape factors with the assumption of is a function of temperature and volume while 6 and 5 are temperature dependent only. The models described the shape factors satisfactorily in whole region including vapor, liquid and their co-existing phases. The perfect shape factor CSP could be applied for both polar and non-polar fluids.
文摘The virial equation can well describe gas state at high temperature and pressure, but the difficulties in virial coefficient calculation limit the use of virial equation. Simple extended corresponding state principle(SE-CSP) is introduced in virial equation. Based on a corresponding state equation, including three characteristic parameters, an extended parameter is introduced to describe the second virial coefficient expressions of main products of propellant gas. The modified SE-CSP second virial coefficient expression was extrapolated based on the virial coefficients experimental temperature, and the second virial coefficients obtained are in good agreement with the experimental data at a low temperature and the theoretical values at high temperature. The maximum pressure in the closed bomb test was calculated with modified SE-CSP virial coefficient expressions with the calculated error of less than 2%, and the error was smaller than the result calculated with the reported values under the same calculation conditions. The modified SE-CSP virial coefficient expression provides a convenient and efficient method for practical virial coefficient calculation without resorting to complicated molecular model design and integral calculation.
文摘Pragmatic vagueness is frequently used in business correspondences and it offers benefits to the addressers by making business letter more flexible,appropriate and polite.This paper focuses on the employment of vague language in international business correspondences based on the Politeness Principle.In this study,the pragmatic effect of vague language in business correspondence is illustrated and summarized as a motivated factor to better show politeness and respect.The use of vague language motivated by politeness consequently leads to a more smooth,successful and desired communication in business world.
文摘Business correspondence are the indispensable tool in the practical process of business communication and interchange.Especially,as the communicated body of information,their language possesses specific characteristics.Rooted from the "Politeness Principle" and the "Cooperative Principle",the most distinctive epitome of it is the seven "C" principles.Based on the discussion of the seven "C" principles,this paper devotes itself to the analyses of the contradictory characteristics which occur frequently in the concrete business contexts,and then to examine the causes of these features.Ultimately,it will suggest more flexible and more widened perspective towards the creation of business correspondence and the language applied in them.
文摘The paper shows that the variational principle serves as an element of the mathematical structure of a quantum theory. The experimentally confirmed properties of the corpuscular-wave duality of a quantum particle are elements of the analysis. A Lagrangian density that yields the equations of motion of a given quantum theory of a massive particle is analyzed. It is proved that if this Lagrangian density is a Lorentz scalar whose dimension is ?then the associated action consistently defines the required phase of the quantum particle. The dimension of this Lagrangian density proves that also the quantum function ?has dimension. This result provides new criteria for the acceptability of quantum theories. An examination of the first order Dirac equation demonstrates that it satisfies the new criteria whereas the second order Klein-Gordon equation fails to do that.
基金Supported by the Shanxi Natural Science Foundation of China under Grant No.2006011012the Doctoral Scientific Research Starting Foundation of Shanxi Datong University
文摘Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function of bosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant A introduced in generalized uncertainty principle takes a proper value, we derive Bekenstein- Hawking entropy and the correction value corresponding cosmologicaJ horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small mass approximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropy of the black string cosmological horizon in non-spherical coordinate spacetime.
文摘Modeling the earth's fluid and elastic response to the melting of the glaciers of the last ice age is the most direct way to infer the earth's radial viscosity profile.Here,we compare two methods for calculating the viscoelastic response to surface loading.In one,the elastic equation of motion is converted to a viscoelastic equation using the Correspondence Principle.In the other,elastic deformation is added to the viscous flow as isostatic adjustment proceeds.The two modeling methods predict adjustment histories that are different enough to potentially impact the interpretation of the observed glacial isostatic adjustment(GIA).The differences arise from buoyancy and whether fluid displacements are subjected to hydrostatic pre-stress.The methods agree if they use the same equations and boundary conditions.The origin of the differences is determined by varying the boundary conditions and pre-stress application.
