In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the notion of (α,β)-fuzzy Q-algebras, the level Q-subalgebra is introduced where α,β are any two of {...In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the notion of (α,β)-fuzzy Q-algebras, the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q. Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras. The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined, and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.展开更多
This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF met...This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.展开更多
We introduce an algebraic model to vibrations of polyatomic Bio-molecules and present, as an example, the vibrational analysis of Cm-H, Cm-C, Cm-D, Cb-Cb, pyrrol breathing and Cb-C, stretching modes of Metalloporphyri...We introduce an algebraic model to vibrations of polyatomic Bio-molecules and present, as an example, the vibrational analysis of Cm-H, Cm-C, Cm-D, Cb-Cb, pyrrol breathing and Cb-C, stretching modes of Metalloporphyrins and its substituted forms. The excited energy levels of Cb-C, pyrrol breathing stretching modes of Ni(OEP) and Ni(OEP)-d4 are calculated by using U(2) algebraic mode Hamiltonian. The higher excited energy levels of Cm-H, Cm-C, Cm-D and Cb-Cb vibrational modes of Porphyrin and its substituted forms are predicted upto second overtone. It shows that the energy levels are clustering at the higher overtones. The results obtained by this method are accuracy with experimental data.展开更多
In handing information regarding various aspects of uncertainty, non-classical-mathematics (fuzzy mathematics or great extension and development of classical mathematics) is considered to be a more powerful technique ...In handing information regarding various aspects of uncertainty, non-classical-mathematics (fuzzy mathematics or great extension and development of classical mathematics) is considered to be a more powerful technique than classical mathematics. The non-classical mathematics, therefore, has now days become a useful tool in applications mathematics and computer science. The purpose of this paper is to apply the concept of the fuzzy sets to some algebraic structures such as an ideal, upper semilattice, lower semilattice, lattice and sub-algebra and gives some properties of these algebraic structures by using the concept of fuzzy sets. Finally, related properties are investigated in fuzzy BCK-algebras.展开更多
文摘In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the notion of (α,β)-fuzzy Q-algebras, the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q. Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras. The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined, and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.
基金Project supported by the National Natural Science Foundation of China （Grant No 60771038）.
文摘This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.
文摘We introduce an algebraic model to vibrations of polyatomic Bio-molecules and present, as an example, the vibrational analysis of Cm-H, Cm-C, Cm-D, Cb-Cb, pyrrol breathing and Cb-C, stretching modes of Metalloporphyrins and its substituted forms. The excited energy levels of Cb-C, pyrrol breathing stretching modes of Ni(OEP) and Ni(OEP)-d4 are calculated by using U(2) algebraic mode Hamiltonian. The higher excited energy levels of Cm-H, Cm-C, Cm-D and Cb-Cb vibrational modes of Porphyrin and its substituted forms are predicted upto second overtone. It shows that the energy levels are clustering at the higher overtones. The results obtained by this method are accuracy with experimental data.
文摘In handing information regarding various aspects of uncertainty, non-classical-mathematics (fuzzy mathematics or great extension and development of classical mathematics) is considered to be a more powerful technique than classical mathematics. The non-classical mathematics, therefore, has now days become a useful tool in applications mathematics and computer science. The purpose of this paper is to apply the concept of the fuzzy sets to some algebraic structures such as an ideal, upper semilattice, lower semilattice, lattice and sub-algebra and gives some properties of these algebraic structures by using the concept of fuzzy sets. Finally, related properties are investigated in fuzzy BCK-algebras.
