From the hypotheses that the position-representation of a physical state is the Fourier transform of its momentum-representation and that the timerepresentation is the inverse Fourier transform of its energy-represent...From the hypotheses that the position-representation of a physical state is the Fourier transform of its momentum-representation and that the timerepresentation is the inverse Fourier transform of its energy-representation, we are able to obtain the Planck relation E = hν , the de Broglie relation p = h /λ , the Dirac fundamental commutation relation, the Schr?dinger equations, the Heisenberg uncertainty principle in quantum mechanics, and the annihilation/creation of a photon from excitation/de-excitation of an atom following Bohr.展开更多
An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the pola...An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.展开更多
The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
The uncertainty principle proposed by German physicist Heisenberg in 1927 is a basic principle of quantum mechanics and signal processing.Since linear canonical transformation has been widely used in various fields of...The uncertainty principle proposed by German physicist Heisenberg in 1927 is a basic principle of quantum mechanics and signal processing.Since linear canonical transformation has been widely used in various fields of signal processing recently and Heisenberg uncertainty principle has been endowed with new expressive meaning in linear canonical transforms domain,in this manuscript,an improved Heisenberg uncertainty principle is obtained in linear canonical trans-forms domain.展开更多
Using density functional theory calculations, we investigate the tetragonal distortion, electronic structure and magnetic property of Pt2MnSn. The results indicate that, when the volume-conserving tetragonal distortio...Using density functional theory calculations, we investigate the tetragonal distortion, electronic structure and magnetic property of Pt2MnSn. The results indicate that, when the volume-conserving tetragonal distortion occurs, the energy minimum appears at c/a = 0.84, and the energy difference between the minimum and cubic phase is as high as 107 me V/f. u. Thus from the point of view of thermodynamics, martensitie transformation may occur in Pt2MnSn with decreasing the temperature. The electronic structure of its cubic and martensitic phases also approves this. Moreover, both the cubic and tetragonal phases of Pt2MnSn are ferromagnetic structures and their total magnetic moments are 4.26 μB and 4.12 μB, respectively.展开更多
In this letter,the new concept of Relative Principle Component (RPC) and method of RPC Analysis (RPCA) are put forward. Meanwhile,the concepts such as Relative Transform (RT),Ro-tundity Scatter (RS) and so on are intr...In this letter,the new concept of Relative Principle Component (RPC) and method of RPC Analysis (RPCA) are put forward. Meanwhile,the concepts such as Relative Transform (RT),Ro-tundity Scatter (RS) and so on are introduced. This new method can overcome some disadvantages of the classical Principle Component Analysis (PCA) when data are rotundity scatter. The RPC selected by RPCA are more representative,and their significance of geometry is more notable,so that the application of the new algorithm will be very extensive. The performance and effectiveness are simply demonstrated by the geometrical interpretation proposed.展开更多
The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate...The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.展开更多
Boron carbide (B4C) is a rhombic structure composed of icosahedra and atomic chains, which has an important application in armored materials. The application of B4C under super high pressure without failure is a hot s...Boron carbide (B4C) is a rhombic structure composed of icosahedra and atomic chains, which has an important application in armored materials. The application of B4C under super high pressure without failure is a hot spot of research. Previous studies have unmasked the essential cause of B4C failure, i.e., its structure will change subjected to impact, especially under the non-hydrostatic pressure and shear stress. However, the change of structure has not been clearly understood nor accurately determined. Here in this paper, we propose several B4C polymorphs including B4C high pressure phases with non-icosahedra, which are denoted as post-B4C and their structures are formed due to icosahedra broken and may be obtained through high pressure and high temperature (HPHT). The research of their physical properties indicates that these B4C polymorphs have outstanding mechanical and electrical properties. For instance, aP10, mC10, mP20, and oP10-B4C are conductive superhard materials. We hope that our research will enrich the cognition of high pressure structural deformation of B4C and broaden the application scope of B4C.展开更多
The purpose of the present study is to develop a counterpart of the special relativity theory that is consistent with the existence of a preferred frame but, like the standard relativity theory, is based on the relati...The purpose of the present study is to develop a counterpart of the special relativity theory that is consistent with the existence of a preferred frame but, like the standard relativity theory, is based on the relativity principle and the universality of the (two-way) speed of light. The synthesis of such seemingly incompatible concepts as the existence of preferred frame and the relativity principle is possible at the expense of the freedom in assigning the one-way speeds of light that exists in special relativity. In the framework developed, a degree of anisotropy of the one-way speed acquires meaning of a characteristic of the really existing anisotropy caused by motion of an inertial frame relative to the preferred frame. The anisotropic special relativity kinematics is developed based on the symmetry principles: 1) Space-time transformations between inertial frames leave the equation of anisotropic light propagation invariant and 2) a set of the transformations possesses a group structure. The Lie group theory apparatus is applied to define groups of transformations between inertial frames. Applying the transformations to the problem of calculating the CMB temperature distribution yields a relation in which the angular dependence coincides with that obtained on the basis of the standard relativity theory but the mean temperature is corrected by the terms second order in the observer velocity.展开更多
Western Liaoning Province is characterized by huge areas of lowly-efficient Chinese pine (Pinus tabulaeformis Carr.) pure plantations. How to transform these plantations has become an increasingly significant manageme...Western Liaoning Province is characterized by huge areas of lowly-efficient Chinese pine (Pinus tabulaeformis Carr.) pure plantations. How to transform these plantations has become an increasingly significant management problem. In this study, the authors summarized the approaches, which are based on close-to-nature silvicultural system, to transform the pure pine plantations. Native broadleaved trees were planted in three methods: 1) after strip clearcutting, 2) after patch clearcutting; 3) on the open forestland and the forest edge. The transformation targets and the selection of tree species were expatiated in this paper. The key techniques and their application conditions for each method were analyzed and discussed. Through investigation and contrastive analysis, the assessment was made to the stands transformed by strip method. Results showed that the mixed stands at 16 years after transformation had an obvious layered structure and the species richness of understorey vegetation increased by 23.5%–52.9%. Soil enzyme activities of urease, phosphatase and sucrase increased by 6%–142%, 46%–99% and 31%–200%, respetively. Moreover, the transformed stands could effectively control the occurrence of pine caterpillars in plantations. Consequently the transformations enhanced the function of soil and water conservation. Keywords Pinus tabulaeformis - Monoculture - Transformation - Principles and methods - Assessment CLC number S791.254 - S727.22 Document code A Foundation item: This research was supported by grants from the Chinese Academy of Sciences (KZCX3-SW-418), National Natural Science Foundation of China (30100144), and National Key Technologies R & D Program of China (96-007-01-06).Biography: ZENG De-hui (1965-), male, Ph.D. professor in the Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang 110016, P. R. ChinaResponsible editor: Zhu Hong展开更多
Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers e...Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.展开更多
文摘From the hypotheses that the position-representation of a physical state is the Fourier transform of its momentum-representation and that the timerepresentation is the inverse Fourier transform of its energy-representation, we are able to obtain the Planck relation E = hν , the de Broglie relation p = h /λ , the Dirac fundamental commutation relation, the Schr?dinger equations, the Heisenberg uncertainty principle in quantum mechanics, and the annihilation/creation of a photon from excitation/de-excitation of an atom following Bohr.
基金supported by Startup Foundation for Phd Research of Henan Normal University(No.5101119170155).
文摘An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.
文摘The aim of this paper is to establish an extension of qualitative and quantitative uncertainty principles for the Fourier transform connected with the spherical mean operator.
文摘The uncertainty principle proposed by German physicist Heisenberg in 1927 is a basic principle of quantum mechanics and signal processing.Since linear canonical transformation has been widely used in various fields of signal processing recently and Heisenberg uncertainty principle has been endowed with new expressive meaning in linear canonical transforms domain,in this manuscript,an improved Heisenberg uncertainty principle is obtained in linear canonical trans-forms domain.
基金Supported by the National Natural Science Foundation of China under Grant Nos 51301119,51301195,51171206 and 51401140the National Science Foundation for Young Scientists of Shanxi Province under Grant No 2013021010-1the Youth Foundation of Taiyuan University of Technology under Grant No 1205-04020102
文摘Using density functional theory calculations, we investigate the tetragonal distortion, electronic structure and magnetic property of Pt2MnSn. The results indicate that, when the volume-conserving tetragonal distortion occurs, the energy minimum appears at c/a = 0.84, and the energy difference between the minimum and cubic phase is as high as 107 me V/f. u. Thus from the point of view of thermodynamics, martensitie transformation may occur in Pt2MnSn with decreasing the temperature. The electronic structure of its cubic and martensitic phases also approves this. Moreover, both the cubic and tetragonal phases of Pt2MnSn are ferromagnetic structures and their total magnetic moments are 4.26 μB and 4.12 μB, respectively.
基金Supported by the National Natural Science Foundation of China (No.60434020, No.60374020)International Coop-eration Item of Henan Province (No.0446650006)Henan Province Outstanding Youth Science Fund (No.0312001900).
文摘In this letter,the new concept of Relative Principle Component (RPC) and method of RPC Analysis (RPCA) are put forward. Meanwhile,the concepts such as Relative Transform (RT),Ro-tundity Scatter (RS) and so on are introduced. This new method can overcome some disadvantages of the classical Principle Component Analysis (PCA) when data are rotundity scatter. The RPC selected by RPCA are more representative,and their significance of geometry is more notable,so that the application of the new algorithm will be very extensive. The performance and effectiveness are simply demonstrated by the geometrical interpretation proposed.
文摘The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 51871114 and 12064013)the Natural Science Foundation of Jiangxi Province, China (Grant No. 20202BAB214010)+3 种基金the Research Foundation of the Education Department of Jiangxi Province, China (Grant Nos. GJJ180433 and GJJ180477)the Open Funds of the State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, China (Grant No. 201906)the Ganzhou Science and Technology Innovation Project, China (Grant No. 201960)the Jiangxi University of Science and Technology Scientific Research Starting Foundation, China (Grant No. jxxjbs17053).
文摘Boron carbide (B4C) is a rhombic structure composed of icosahedra and atomic chains, which has an important application in armored materials. The application of B4C under super high pressure without failure is a hot spot of research. Previous studies have unmasked the essential cause of B4C failure, i.e., its structure will change subjected to impact, especially under the non-hydrostatic pressure and shear stress. However, the change of structure has not been clearly understood nor accurately determined. Here in this paper, we propose several B4C polymorphs including B4C high pressure phases with non-icosahedra, which are denoted as post-B4C and their structures are formed due to icosahedra broken and may be obtained through high pressure and high temperature (HPHT). The research of their physical properties indicates that these B4C polymorphs have outstanding mechanical and electrical properties. For instance, aP10, mC10, mP20, and oP10-B4C are conductive superhard materials. We hope that our research will enrich the cognition of high pressure structural deformation of B4C and broaden the application scope of B4C.
文摘The purpose of the present study is to develop a counterpart of the special relativity theory that is consistent with the existence of a preferred frame but, like the standard relativity theory, is based on the relativity principle and the universality of the (two-way) speed of light. The synthesis of such seemingly incompatible concepts as the existence of preferred frame and the relativity principle is possible at the expense of the freedom in assigning the one-way speeds of light that exists in special relativity. In the framework developed, a degree of anisotropy of the one-way speed acquires meaning of a characteristic of the really existing anisotropy caused by motion of an inertial frame relative to the preferred frame. The anisotropic special relativity kinematics is developed based on the symmetry principles: 1) Space-time transformations between inertial frames leave the equation of anisotropic light propagation invariant and 2) a set of the transformations possesses a group structure. The Lie group theory apparatus is applied to define groups of transformations between inertial frames. Applying the transformations to the problem of calculating the CMB temperature distribution yields a relation in which the angular dependence coincides with that obtained on the basis of the standard relativity theory but the mean temperature is corrected by the terms second order in the observer velocity.
基金This research was supported by grants from the Chinese Academy of Sciences (KZCX3-SW-418) National Natural Science Founda-tion of China (30100144)and National Key Technologies R & D
文摘Western Liaoning Province is characterized by huge areas of lowly-efficient Chinese pine (Pinus tabulaeformis Carr.) pure plantations. How to transform these plantations has become an increasingly significant management problem. In this study, the authors summarized the approaches, which are based on close-to-nature silvicultural system, to transform the pure pine plantations. Native broadleaved trees were planted in three methods: 1) after strip clearcutting, 2) after patch clearcutting; 3) on the open forestland and the forest edge. The transformation targets and the selection of tree species were expatiated in this paper. The key techniques and their application conditions for each method were analyzed and discussed. Through investigation and contrastive analysis, the assessment was made to the stands transformed by strip method. Results showed that the mixed stands at 16 years after transformation had an obvious layered structure and the species richness of understorey vegetation increased by 23.5%–52.9%. Soil enzyme activities of urease, phosphatase and sucrase increased by 6%–142%, 46%–99% and 31%–200%, respetively. Moreover, the transformed stands could effectively control the occurrence of pine caterpillars in plantations. Consequently the transformations enhanced the function of soil and water conservation. Keywords Pinus tabulaeformis - Monoculture - Transformation - Principles and methods - Assessment CLC number S791.254 - S727.22 Document code A Foundation item: This research was supported by grants from the Chinese Academy of Sciences (KZCX3-SW-418), National Natural Science Foundation of China (30100144), and National Key Technologies R & D Program of China (96-007-01-06).Biography: ZENG De-hui (1965-), male, Ph.D. professor in the Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang 110016, P. R. ChinaResponsible editor: Zhu Hong
文摘Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.
