A segmented basis set of quadruple zeta valence quality plus polarization functions(QZP)for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian.This set was augmented with diffuse functions ...A segmented basis set of quadruple zeta valence quality plus polarization functions(QZP)for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian.This set was augmented with diffuse functions to describe electrons farther away from the nuclei adequately.Using the ZORA-CCSD(T)/QZP-ZORA theoretical model,atomic ionization energies and bond lengths,harmonic vibrational frequencies,and atomization energies of some molecules were calculated.The addition of core-valence corrections has been shown to improve the agreement between theoretical and experimental results for molecular properties.For atomization energies,a similar observation emerges when considering spin-orbit couplings.With the augmented QZP-ZORA set,static mean dipole polarizabilities of a set of atoms were calculated and compared with previously published recommended and experimental values.Performance evaluations of the ZORA and Douglas–Kroll–Hess Hamiltonians were made for each property studied.展开更多
Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ...Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.展开更多
A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy...A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.展开更多
A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting backg...A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting background （TPBG）, is developed to remove the information of the background, which blocks the detection of weak boundaries in the object; （2） The two-phase level set is applied multiple times for getting the multi-phase segmentation model （n-1 times for the n-phase model, n〉1）; （3） A scaling-based method is introduced to improve the basic model. Experimental results show that the proposed model is effective for detecting weak boundaries.展开更多
Let F be a family of sets in R^(d)(always d≥2).A set M■R^(d)is called F-convex,if for any pair of distinct points a,y∈M,there is a set F∈F such that x,y∈F and F■M.We obtain theΓ-convexity,when F consists of F-p...Let F be a family of sets in R^(d)(always d≥2).A set M■R^(d)is called F-convex,if for any pair of distinct points a,y∈M,there is a set F∈F such that x,y∈F and F■M.We obtain theΓ-convexity,when F consists of F-paths.AΓ-path is the union of both shorter sides of an isosceles right triangle.In this paper we first characterize some I-convex sets,bounded or unbounded,including triangles,regular polygons,subsets of balls,right cylinders and cones,unbounded planar closed convex sets,etc.Then,we investigate the F-starshaped sets,and provide some conditions for a fan,a spherical sector and a right cylinder to be F-starshaped.Finally,we study theΓ-triple-convexity,which is a discrete generalization ofΓ-convexity,and provide characterizations for all the 4-point sets,some 5-point sets and Z^(d)to beΓ-triple-convex.展开更多
This paper introduces a method of sieve which can be to calculate the number of residues of the integers 1,2,...,2a sifted by n paiwise coprime numbers.
Let f be an entire solution of the Tumura-Clunie type non-linear delay differential equation.We mainly investigate the dynamical properties of Julia sets of f,and the lower bound estimates of the measure of related li...Let f be an entire solution of the Tumura-Clunie type non-linear delay differential equation.We mainly investigate the dynamical properties of Julia sets of f,and the lower bound estimates of the measure of related limiting directions is verified.展开更多
Based on detailed analysis of advantages and disadvantages of the existing connected-component labeling （CCL） algorithm,a new algorithm for binary connected components labeling based on run-length encoding （RLE） a...Based on detailed analysis of advantages and disadvantages of the existing connected-component labeling （CCL） algorithm,a new algorithm for binary connected components labeling based on run-length encoding （RLE） and union-find sets has been put forward.The new algorithm uses RLE as the basic processing unit,converts the label merging of connected RLE into sets grouping in accordance with equivalence relation,and uses the union-find sets which is the realization method of sets grouping to solve the label merging of connected RLE.And the label merging procedure has been optimized：the union operation has been modified by adding the ＂weighted rule＂ to avoid getting a degenerated-tree,and the ＂path compression＂ has been adopted when implementing the find operation,then the time complexity of label merging is O（nα（n））.The experiments show that the new algorithm can label the connected components of any shapes very quickly and exactly,save more memory,and facilitate the subsequent image analysis.展开更多
The main factors deciding the compressive strength of binder backfill body are tailing density and binder dosage in binder backfill materials. Based on the antecedent of certain pulp density, the method of increasing ...The main factors deciding the compressive strength of binder backfill body are tailing density and binder dosage in binder backfill materials. Based on the antecedent of certain pulp density, the method of increasing the tailing density and reducing the binder dosage, or the manner of cutting down the tailing density and gaining the binder dosage are taken to guarantee the strength of backfill body. The problem that should be solved is how to determine the tailing density and the binder dosage rationally. This paper tries to realize the correct selection of the tailing density and the binder dosage in computer with the method of fuzzy mathematics.展开更多
In this paper,we mainly investigate the dynamical properties of entire solutions of complex differential equations.With some conditions on coefficients,we prove that the set of common limiting directions of Julia sets...In this paper,we mainly investigate the dynamical properties of entire solutions of complex differential equations.With some conditions on coefficients,we prove that the set of common limiting directions of Julia sets of solutions,their derivatives and their primitives must have a definite range of measure.展开更多
Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov＇s theorem for a fractional i...Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov＇s theorem for a fractional integro-differential inclusion involving Caputo＇s fractional derivative. This result allows us to obtain a continuous selection of the solution set of the problem considered.展开更多
In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete...In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.展开更多
In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies ...In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies of these measures are derived. By introducing two general formulas, we propose a new method to define the similarity measures and the distance measures between two fuzzy soft sets with different parameter sets.展开更多
基金the financial support of Conselho Nacional de Desenvolvimento Científico e Tecnológico and Coordenacao de Aperfeic oamento de Pessoal de Nível Superior (Brazilian Agencies)。
文摘A segmented basis set of quadruple zeta valence quality plus polarization functions(QZP)for H through Xe was developed to be used in conjunction with the ZORA Hamiltonian.This set was augmented with diffuse functions to describe electrons farther away from the nuclei adequately.Using the ZORA-CCSD(T)/QZP-ZORA theoretical model,atomic ionization energies and bond lengths,harmonic vibrational frequencies,and atomization energies of some molecules were calculated.The addition of core-valence corrections has been shown to improve the agreement between theoretical and experimental results for molecular properties.For atomization energies,a similar observation emerges when considering spin-orbit couplings.With the augmented QZP-ZORA set,static mean dipole polarizabilities of a set of atoms were calculated and compared with previously published recommended and experimental values.Performance evaluations of the ZORA and Douglas–Kroll–Hess Hamiltonians were made for each property studied.
文摘Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.
文摘A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.
文摘A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting background （TPBG）, is developed to remove the information of the background, which blocks the detection of weak boundaries in the object; （2） The two-phase level set is applied multiple times for getting the multi-phase segmentation model （n-1 times for the n-phase model, n〉1）; （3） A scaling-based method is introduced to improve the basic model. Experimental results show that the proposed model is effective for detecting weak boundaries.
基金supported by the NSFC(12271139,11871192)the High-end Foreign Experts Recruitment Program of People’s Republic of China(G2023003003L)+3 种基金the Program for Foreign experts of Hebei Provincethe Natural Science Foundation of Hebei Province(A2023205045)the Special Project on Science and Technology Research and Development Platforms,Hebei Province(22567610H)the program for 100 Foreign Experts Plan of Hebei Province.
文摘Let F be a family of sets in R^(d)(always d≥2).A set M■R^(d)is called F-convex,if for any pair of distinct points a,y∈M,there is a set F∈F such that x,y∈F and F■M.We obtain theΓ-convexity,when F consists of F-paths.AΓ-path is the union of both shorter sides of an isosceles right triangle.In this paper we first characterize some I-convex sets,bounded or unbounded,including triangles,regular polygons,subsets of balls,right cylinders and cones,unbounded planar closed convex sets,etc.Then,we investigate the F-starshaped sets,and provide some conditions for a fan,a spherical sector and a right cylinder to be F-starshaped.Finally,we study theΓ-triple-convexity,which is a discrete generalization ofΓ-convexity,and provide characterizations for all the 4-point sets,some 5-point sets and Z^(d)to beΓ-triple-convex.
文摘This paper introduces a method of sieve which can be to calculate the number of residues of the integers 1,2,...,2a sifted by n paiwise coprime numbers.
基金supported by the National Natural Science Foundation of China(12171050,12071047)the Fundamental Research Funds for the Central Universities(500421126)。
文摘Let f be an entire solution of the Tumura-Clunie type non-linear delay differential equation.We mainly investigate the dynamical properties of Julia sets of f,and the lower bound estimates of the measure of related limiting directions is verified.
文摘Based on detailed analysis of advantages and disadvantages of the existing connected-component labeling （CCL） algorithm,a new algorithm for binary connected components labeling based on run-length encoding （RLE） and union-find sets has been put forward.The new algorithm uses RLE as the basic processing unit,converts the label merging of connected RLE into sets grouping in accordance with equivalence relation,and uses the union-find sets which is the realization method of sets grouping to solve the label merging of connected RLE.And the label merging procedure has been optimized：the union operation has been modified by adding the ＂weighted rule＂ to avoid getting a degenerated-tree,and the ＂path compression＂ has been adopted when implementing the find operation,then the time complexity of label merging is O（nα（n））.The experiments show that the new algorithm can label the connected components of any shapes very quickly and exactly,save more memory,and facilitate the subsequent image analysis.
文摘The main factors deciding the compressive strength of binder backfill body are tailing density and binder dosage in binder backfill materials. Based on the antecedent of certain pulp density, the method of increasing the tailing density and reducing the binder dosage, or the manner of cutting down the tailing density and gaining the binder dosage are taken to guarantee the strength of backfill body. The problem that should be solved is how to determine the tailing density and the binder dosage rationally. This paper tries to realize the correct selection of the tailing density and the binder dosage in computer with the method of fuzzy mathematics.
基金supported by Shanghai Center for Mathematical Sci-ences,China Scholarship Council(201206105015)National Science Foundation of China(11171119,11001057,11571049)Natural Science Foundation of Guangdong Province in China(2014A030313422)
文摘In this paper,we mainly investigate the dynamical properties of entire solutions of complex differential equations.With some conditions on coefficients,we prove that the set of common limiting directions of Julia sets of solutions,their derivatives and their primitives must have a definite range of measure.
基金supported by CNCS grant PN-II-ID-PCE-2011-3-0198
文摘Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov＇s theorem for a fractional integro-differential inclusion involving Caputo＇s fractional derivative. This result allows us to obtain a continuous selection of the solution set of the problem considered.
基金Supported by the NSF of Henan Province(082300410040)Supported by the NSF of Zhumadian City(087006)
文摘In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.
基金Supported by the National Natural Science Foundation of China（6147323961175044） Supported by the Fundamental Research Funds for the Central Universities of China（2682014ZT28）
文摘In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies of these measures are derived. By introducing two general formulas, we propose a new method to define the similarity measures and the distance measures between two fuzzy soft sets with different parameter sets.
