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
采用CALPHAD(calculation of phase diagram)方法对Fe-V和Ni-V二元系进行了热力学优化,并结合第一性原理计算,利用(A,B)_(10)(A,B)_(4)(A,B)_(16)三亚点阵模型描述σ相,首次成功地描述了σ相的占位分数。使用优化的模型参数不仅可以描述...采用CALPHAD(calculation of phase diagram)方法对Fe-V和Ni-V二元系进行了热力学优化,并结合第一性原理计算,利用(A,B)_(10)(A,B)_(4)(A,B)_(16)三亚点阵模型描述σ相,首次成功地描述了σ相的占位分数。使用优化的模型参数不仅可以描述Fe-V和Ni-V系热化学性质,而且可以很好地重现Fe-V和Ni-V系的相平衡关系,为高熵合金多组元热力学数据库的建立奠定基础。展开更多
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
We investigate the elastic and the thermodynamic properties of nanolaminate V2GeC by using the ab initio pseudopotential total energy method. The axial compressibility shows that the c axis is always stiffer than the ...We investigate the elastic and the thermodynamic properties of nanolaminate V2GeC by using the ab initio pseudopotential total energy method. The axial compressibility shows that the c axis is always stiffer than the a axis. The elastic constant calculations demonstrate that the structural stability is within 0-800 GPa. The calculations of Young's and shear moduli reveal the softening behaviour at about 300 GPa. The Possion ratio makes a higher ionic or a weaker covalent contribution to intra-atomic bonding and the degree of ionicity increases with pressure. The relationship between brittleness and ductility shows that V2GeC is brittle in ambient conditions and the brittleness decreases and ductility increases with pressure. Moveover, we find that V2CeC is largely isotropic in compression and in shear, and the degree of isotropy decreases with pressure. The Griineisen parameter, the Debye temperature and the thermal expansion coefficient are also successfully obtained for the first time.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
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
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
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.
文摘采用CALPHAD(calculation of phase diagram)方法对Fe-V和Ni-V二元系进行了热力学优化,并结合第一性原理计算,利用(A,B)_(10)(A,B)_(4)(A,B)_(16)三亚点阵模型描述σ相,首次成功地描述了σ相的占位分数。使用优化的模型参数不仅可以描述Fe-V和Ni-V系热化学性质,而且可以很好地重现Fe-V和Ni-V系的相平衡关系,为高熵合金多组元热力学数据库的建立奠定基础。
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Project supported by the National Natural Science Foundation of China (Grant Nos. 10974139, 10964002 and 11104247)the Natural Science Foundation of Guizhou Province, China (Grant No. [2009]2066)+1 种基金the Project of Aiding Elites' Research Condition of Guizhou Province, China (Grant No. TZJF-2008-42)the Science Foundation from Education Ministry of Zhejiang Province,China (Grant No. Y201121807)
文摘We investigate the elastic and the thermodynamic properties of nanolaminate V2GeC by using the ab initio pseudopotential total energy method. The axial compressibility shows that the c axis is always stiffer than the a axis. The elastic constant calculations demonstrate that the structural stability is within 0-800 GPa. The calculations of Young's and shear moduli reveal the softening behaviour at about 300 GPa. The Possion ratio makes a higher ionic or a weaker covalent contribution to intra-atomic bonding and the degree of ionicity increases with pressure. The relationship between brittleness and ductility shows that V2GeC is brittle in ambient conditions and the brittleness decreases and ductility increases with pressure. Moveover, we find that V2CeC is largely isotropic in compression and in shear, and the degree of isotropy decreases with pressure. The Griineisen parameter, the Debye temperature and the thermal expansion coefficient are also successfully obtained for the first time.
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.
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.
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.