The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the compa...The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.展开更多
In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing...In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing triangular fuzzy numbers. We utilize the fuzzy linguistic scale to construct a linguistic preference matrix, and propose a fuzzy induced ordered weighted geometric averaging (FIOWGA) operator to aggregate linguistic preference information. A method based on the fuzzy linguistic scale and FIOWGA operator for decision-making problems is presented. Finally, an illustrative example is given to verify the developed method and to demonstrate its feasibility and effectiveness.展开更多
This paper describes a Fast Finding and Fitting (FFF)Algorithm based on the geometric symmetry of the circle. A comparison with other circle detection approaches, in par- ticular the Hough Transform and its extensions...This paper describes a Fast Finding and Fitting (FFF)Algorithm based on the geometric symmetry of the circle. A comparison with other circle detection approaches, in par- ticular the Hough Transform and its extensions is presented. A method to determine a rele- vant estimation of accuracy is also given. Experiments show that FFF possesses advantages in memory usage, high speed, reliability and accuracy are also presented.展开更多
Electron momentum distributions for 4a1 orbitals of serial freon molecules CFaC1, CF2Cl2, and CFCl3 （CFxC14-x, x=1-3） have been reanalyzed due to the severe discrepancies between theory and experiment in low momentu...Electron momentum distributions for 4a1 orbitals of serial freon molecules CFaC1, CF2Cl2, and CFCl3 （CFxC14-x, x=1-3） have been reanalyzed due to the severe discrepancies between theory and experiment in low momentum region. The tentative calculations using equilibrium geometries of molecular ions have exhibited a great improvement in agreement with the experimental data, which suggests that the molecular geometry distortion may be responsible for the observed high intensities at p〈0.5 a.u.. Further analyses show that the severe discrepancies at low momentum region mainly arise from the influence of molecular geometry distortion on C-Cl bonding electron density distributions.展开更多
The quantum-chemical calculations were performed to determine the nature of the equilibrium geometry of the ground and excited states of the 1,3,5-triazapentadiene complexes of platinum（Ⅱ） and theirs nature and str...The quantum-chemical calculations were performed to determine the nature of the equilibrium geometry of the ground and excited states of the 1,3,5-triazapentadiene complexes of platinum（Ⅱ） and theirs nature and structure of molecular orbitals.展开更多
For strictly positive operators A and B, and for x ∈ [0,1] and r ∈[-1,1], we investigate the operator power mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 If r = O, this is reduced to the geometric operator m...For strictly positive operators A and B, and for x ∈ [0,1] and r ∈[-1,1], we investigate the operator power mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 If r = O, this is reduced to the geometric operator mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 Since A #0,r B = A and A #l,r B = B, weregard A#t,rB as apath combining A and B.Our aim is to show the essential properties of St,r （AIB）. The Tsallis relative operator entropy by Yanagi, Kuriyama and Furuichi can also be expanded, and by using this, we can give an expanded operator valued a-divergence and obtain its properties.展开更多
Valence and all electron correlation energies of a large set of atoms and molecules with structural motifs from amino acids and peptides at their equilibrium as well as non-equilibrium geometries are calculated at the...Valence and all electron correlation energies of a large set of atoms and molecules with structural motifs from amino acids and peptides at their equilibrium as well as non-equilibrium geometries are calculated at the levels of MP2, RI-MP2, and CCSD （T） with Dunnings sequential correlation consistent basis sets. A two point basis set extrapolation scheme for correlation energies to the complete basis set limit based on only DZ （double-zeta） and TZ （triple-zeta） results is presented and analyzed. We show that this basis set extrapolation scheme reduces the computational cost by two to three orders of magnitude to obtain the same accuracy as simpler extrapolations from higher order basis set computations.展开更多
Studying on the buffer operator, we structure the GAWBO（Geometry Average Weakening Buffer Operator）, WAWBO（Weighed Average Weakening Buffer Operator）, WGAWBO（Weighed Geometry Average Weakening Buffer Operator） a...Studying on the buffer operator, we structure the GAWBO（Geometry Average Weakening Buffer Operator）, WAWBO（Weighed Average Weakening Buffer Operator）, WGAWBO（Weighed Geometry Average Weakening Buffer Operator） and so on, which are easy to apply and be universality. At the same time, we address their characteristics and their internal relations between these buffer operators. All this effectively resolves the questions, which often come forth in modeling forecasting of disturbed data sequence by shock wave and there are some contradictions between the quantity result and the qualitative analysis.展开更多
We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115(2015)020403]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of ...We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115(2015)020403]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states—maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.展开更多
基金The Technological Innovation Foundation of NanjingForestry University(No.163060033).
文摘The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.
基金The National Natural Science Foundation of China(79970093) the Ph.D. Dissertation Foundation of Southeast University- NARI-Relays Electric Co. Ltd.
文摘In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing triangular fuzzy numbers. We utilize the fuzzy linguistic scale to construct a linguistic preference matrix, and propose a fuzzy induced ordered weighted geometric averaging (FIOWGA) operator to aggregate linguistic preference information. A method based on the fuzzy linguistic scale and FIOWGA operator for decision-making problems is presented. Finally, an illustrative example is given to verify the developed method and to demonstrate its feasibility and effectiveness.
文摘This paper describes a Fast Finding and Fitting (FFF)Algorithm based on the geometric symmetry of the circle. A comparison with other circle detection approaches, in par- ticular the Hough Transform and its extensions is presented. A method to determine a rele- vant estimation of accuracy is also given. Experiments show that FFF possesses advantages in memory usage, high speed, reliability and accuracy are also presented.
基金V. ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.10734040） and the Chinese Academy of Science Knowledge Promotion Project （No.KJCXI-YW-N30）. The authors also gratefully acknowledge Professor C. E. Brion from University of British Columbia （UBC） in Canada for supplying the HEMS and RESFOLD programs.
文摘Electron momentum distributions for 4a1 orbitals of serial freon molecules CFaC1, CF2Cl2, and CFCl3 （CFxC14-x, x=1-3） have been reanalyzed due to the severe discrepancies between theory and experiment in low momentum region. The tentative calculations using equilibrium geometries of molecular ions have exhibited a great improvement in agreement with the experimental data, which suggests that the molecular geometry distortion may be responsible for the observed high intensities at p〈0.5 a.u.. Further analyses show that the severe discrepancies at low momentum region mainly arise from the influence of molecular geometry distortion on C-Cl bonding electron density distributions.
文摘The quantum-chemical calculations were performed to determine the nature of the equilibrium geometry of the ground and excited states of the 1,3,5-triazapentadiene complexes of platinum（Ⅱ） and theirs nature and structure of molecular orbitals.
文摘For strictly positive operators A and B, and for x ∈ [0,1] and r ∈[-1,1], we investigate the operator power mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 If r = O, this is reduced to the geometric operator mean A#x,rB=A1/2{（1-x）/＋x（a-1＊2BA-1/2）r}1/rA1/2 Since A #0,r B = A and A #l,r B = B, weregard A#t,rB as apath combining A and B.Our aim is to show the essential properties of St,r （AIB）. The Tsallis relative operator entropy by Yanagi, Kuriyama and Furuichi can also be expanded, and by using this, we can give an expanded operator valued a-divergence and obtain its properties.
文摘Valence and all electron correlation energies of a large set of atoms and molecules with structural motifs from amino acids and peptides at their equilibrium as well as non-equilibrium geometries are calculated at the levels of MP2, RI-MP2, and CCSD （T） with Dunnings sequential correlation consistent basis sets. A two point basis set extrapolation scheme for correlation energies to the complete basis set limit based on only DZ （double-zeta） and TZ （triple-zeta） results is presented and analyzed. We show that this basis set extrapolation scheme reduces the computational cost by two to three orders of magnitude to obtain the same accuracy as simpler extrapolations from higher order basis set computations.
文摘Studying on the buffer operator, we structure the GAWBO（Geometry Average Weakening Buffer Operator）, WAWBO（Weighed Average Weakening Buffer Operator）, WGAWBO（Weighed Geometry Average Weakening Buffer Operator） and so on, which are easy to apply and be universality. At the same time, we address their characteristics and their internal relations between these buffer operators. All this effectively resolves the questions, which often come forth in modeling forecasting of disturbed data sequence by shock wave and there are some contradictions between the quantity result and the qualitative analysis.
基金Supported by the National Basic Research Program of China under Grant No.2015CB921002the National Natural Science Foundation of China under Grant Nos.11175094,91221205,11275131+2 种基金Fundamental Research Funds for the Central Universities under Grant No.16CX02049Athe Shandong Provincial Natural Science Foundation under Grant No.ZR2016AQ06the Postdoctor Science Foundation under Grant No.2016M600997
文摘We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115(2015)020403]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states—maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.
