Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of ...Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#'_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.展开更多
We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an actio...We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.展开更多
123I is the most widely used cyclotron-produced radio-halogen in medical research. In this paper, excitation function formulae for the nuclear reactions of 123I production are introduced. 124Te (p, 2n)123I and 127I (p...123I is the most widely used cyclotron-produced radio-halogen in medical research. In this paper, excitation function formulae for the nuclear reactions of 123I production are introduced. 124Te (p, 2n)123I and 127I (p, 5n)123Xe → 123I nuclear reactions have been studied as a function of the energy of the neutrons. Both two formulae were created using the least squares regression of the experimental cross sections data, which were obtained from the Experimental Nuclear Reaction Data EXFOR Database version of 2023. The proposed formulae were evaluated using two statistical indicators for goodness-of-fit. High agreement was observed between the empirical and experimental results for both nuclear processes.展开更多
Let H be a finite-dimensional weak Hopf algebra over a field κ and A an associative algebra, and A#;H a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cot...Let H be a finite-dimensional weak Hopf algebra over a field κ and A an associative algebra, and A#;H a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cotorsion dimension of A#;H in terms of the corresponding data for H and A.展开更多
We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rin...We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rings, skew strongly reversible rings and strongly M-reversible rings. Some well-known results on this subject are generalized and extended.展开更多
Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal cros...Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal crossed product in the sense of Hopf algebras.The result that the product in B#A is non-degenerate is given.Next,the definition of the comultiplicationΔ#on B#A is introduced,which is composed of the multiplierΔB(b)on B⊗B and the multiplierΔA(a)on A⊗A,and the elementΔ#(b⊗a)is a two-side multiplier of B#A⊗B#A,for any b∈B and a∈A.Then,a sufficient condition for B#A to be a regular multiplier Hopf algebra is described.In particular,Delvaux's main theorem in the case of smash products is generalized.Finally,these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.展开更多
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left...Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.展开更多
First,the group crossed product over the Hopf group-algebras is defined,and the necessary and sufficient conditions for the group crossed product to be a group algebra are given.The cleft extension theory of the Hopf ...First,the group crossed product over the Hopf group-algebras is defined,and the necessary and sufficient conditions for the group crossed product to be a group algebra are given.The cleft extension theory of the Hopf group algebra is introduced,and it is proved that the crossed product of the Hopf group algebra is equivalent to the cleft extension.The necessary and sufficient conditions for the crossed product equivalence of two Hopf groups are then given.Finally,combined with the equivalence theory of the Hopf group crossed product and cleft extension,the group crossed product constructed by the general 2-cocycle as algebra is determined to be isomorphic to the group crossed product of the 2-cocycle with a convolutional invertible map of the 2-cocycle.The unit property of a general 2-cocycle is equivalent to the convolutional invertible map of the 2-cocycle,and the combination condition of the weak action is equivalent to the convolutional invertible map of the 2-cocycle and the combination condition of the weak action.Similarly,crossed product algebra constructed by the general 2-cocycle is isomorphic to the Hopfπ-crossed product algebra constructed by the 2-cocycle with a convolutional invertible map.展开更多
This article is based on a recent model specifically defining magnetic field values around electrical wires. With this model, calculations of field around parallel wires were obtained. Now, this model is extended with...This article is based on a recent model specifically defining magnetic field values around electrical wires. With this model, calculations of field around parallel wires were obtained. Now, this model is extended with the new concept of magnetic equipotential surface to magnetic field curves around crossing wires. Cases of single, double, and triple wires are described. Subsequent article will be conducted for more general scenarios where wires are neither infinite nor parallel.展开更多
A DH population derived from C49S-87/01Y1-1069 was used to study the inheritance of wheat haploid embryo production frequency(EPF) in wheat × maize cross with the mixed major gene and polygene inheritance model...A DH population derived from C49S-87/01Y1-1069 was used to study the inheritance of wheat haploid embryo production frequency(EPF) in wheat × maize cross with the mixed major gene and polygene inheritance model of quantitative traits. The results showed that the EPF of wheat × maize cross was controlled by two dominant epistatic genes and polygene with gene effects of 1.95 for the first major gene, 6.69 for the second one and 2.80 for the polygene. The inheritability of major genes was as high as 72.09%, suggesting that the differences in EPF among wheat materials were mainly influenced by genotype. However, non-genetic factors were still important, especially for wheat materials with low EPF.展开更多
In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash produc...In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.展开更多
In order to increase productivity and reduce energy consumption of steelmaking-continuous casting(SCC) production process, especially with complicated technological routes, the cross entropy(CE) method was adopted to ...In order to increase productivity and reduce energy consumption of steelmaking-continuous casting(SCC) production process, especially with complicated technological routes, the cross entropy(CE) method was adopted to optimize the SCC production scheduling(SCCPS) problem. Based on the CE method, a matrix encoding scheme was proposed and a backward decoding method was used to generate a reasonable schedule. To describe the distribution of the solution space, a probability distribution model was built and used to generate individuals. In addition, the probability updating mechanism of the probability distribution model was proposed which helps to find the optimal individual gradually. Because of the poor stability and premature convergence of the standard cross entropy(SCE) algorithm, the improved cross entropy(ICE) algorithm was proposed with the following improvements: individual generation mechanism combined with heuristic rules, retention mechanism of the optimal individual, local search mechanism and dynamic parameters of the algorithm. Simulation experiments validate that the CE method is effective in solving the SCCPS problem with complicated technological routes and the ICE algorithm proposed has superior performance to the SCE algorithm and the genetic algorithm(GA).展开更多
Under improper transformations,the traditional transformation laws for cross products,the permutation tensor,and rotations are incorrect.For a cross product,using a counter-example the left-hand rule is proved wrong.T...Under improper transformations,the traditional transformation laws for cross products,the permutation tensor,and rotations are incorrect.For a cross product,using a counter-example the left-hand rule is proved wrong.The unique rule for a cross product is the right-hand rule.Coordinate systems have handedness,while a cross product is frame-indifference.Since the permutation tensor is defined as a triple product including a cross product,the law for the permutation tensor is false.For a rotation,its pseudovector representation is incorrect,because the mirror is an auxiliary device to produce the virtual image rather than a new coordinate system or reference frame.展开更多
A cross section database on excitation functions of reactions produced by charged particles is essential for many areas of nuclear research. Particularly, accurate knowledge on nuclear cross sections for the cyclotron...A cross section database on excitation functions of reactions produced by charged particles is essential for many areas of nuclear research. Particularly, accurate knowledge on nuclear cross sections for the cyclotron production of radioisotopes is very important for nuclear medicine. In the present paper, the cross section calculations for the production of^(43),^(34)Sc,^(45)Ti,^(51)Cr,^(54)Mn, and^(55) Fe radioisotopes were carried out by the use of ALICE/ASH code using the Fermi gas model, Kataria Ramamurthy Fermi gas model, and superfluid nuclear model for nuclear level density. Thereby, these model calculations were compared with the available measured data.展开更多
The crossing number of cartesian products of paths and cycles with 5-vertex graphs mostly are known, but only few cartesian products of 5-vertex graphs with star K 1,n are known. In this paper, we will extent those re...The crossing number of cartesian products of paths and cycles with 5-vertex graphs mostly are known, but only few cartesian products of 5-vertex graphs with star K 1,n are known. In this paper, we will extent those results, and determine the crossing numbers of cartesian products of two 5-vertex graphs with star K 1,n .展开更多
This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the def...This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.展开更多
A matrix encoding scheme for the steelmaking continuous casting( SCC) production scheduling( SCCPS) problem and the corresponding decoding method are proposed. Based on it,a cross entropy( CE) method is adopted and an...A matrix encoding scheme for the steelmaking continuous casting( SCC) production scheduling( SCCPS) problem and the corresponding decoding method are proposed. Based on it,a cross entropy( CE) method is adopted and an improved cross entropy( ICE) algorithm is proposed to solve the SCCPS problem to minimize total power consumption. To describe the distribution of the solution space of the CE method,a probability model is built and used to generate individuals by sampling and a probability updating mechanism is introduced to trace the promising samples. For the ICE algorithm,some samples are generated by the heuristic rules for the shortest makespan due to the relation between the makespan and the total power consumption,which can reduce the search space greatly. The optimal sample in each iteration is retained through a retention mechanism to ensure that the historical optimal sample is not lost so as to improve the efficiency and global convergence. A local search procedure is carried out on a part of better samples so as to improve the local exploitation capability of the ICE algorithm and get a better result. The parameter setting is investigated by the Taguchi method of design-of-experiment. A number of simulation experiments are implemented to validate the effectiveness of the ICE algorithm in solving the SCCPS problem and also the superiority of the ICE algorithm is verified through the comparison with the standard cross entropy( SCE) algorithm.展开更多
The experimental data of Mαβ X-ray production cross sections for Pb and Bi by 9–40 keV electron impact have been given. Thin films with thick carbon substrates are used in the experiment. The effects of target stru...The experimental data of Mαβ X-ray production cross sections for Pb and Bi by 9–40 keV electron impact have been given. Thin films with thick carbon substrates are used in the experiment. The effects of target structure on the Mαβ X-ray production cross sections are corrected by using the Monte Carlo method. The corrected experimental data are compared with calculated cross sections in terms of the distorted-wave Born approximation(DWBA) theory. The measured Mαβ X-ray production cross sections for Pb and Bi are lower than the DWBA calculations. The atomic relaxation parameters used in comparing the DWBA values with experimental results affect the degree of difference.展开更多
The calculation methods of production cross sections of γ-rays for thermal-neutron captures are briefly presented. The check of intensity balance is made. The examples are given to illustrate its application.
基金The National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK2012736)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Innovation Program for College Graduates of Jiangsu Province(No.KYLX15_0109)
文摘Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#'_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.
文摘We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.
文摘123I is the most widely used cyclotron-produced radio-halogen in medical research. In this paper, excitation function formulae for the nuclear reactions of 123I production are introduced. 124Te (p, 2n)123I and 127I (p, 5n)123Xe → 123I nuclear reactions have been studied as a function of the energy of the neutrons. Both two formulae were created using the least squares regression of the experimental cross sections data, which were obtained from the Experimental Nuclear Reaction Data EXFOR Database version of 2023. The proposed formulae were evaluated using two statistical indicators for goodness-of-fit. High agreement was observed between the empirical and experimental results for both nuclear processes.
基金The NSF(KJ2016A545,KJ2015B12,2017ZR08zd)of Anhui Provincethe key projectsoutstanding young talent support program(gxyq ZD2016353)of Anhui Province
文摘Let H be a finite-dimensional weak Hopf algebra over a field κ and A an associative algebra, and A#;H a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cotorsion dimension of A#;H in terms of the corresponding data for H and A.
基金The NSF(11601005) of Chinathe Jiangsu Planned Projects(1601151C) for Postdoctoral Research Funds+1 种基金the Provincial NSF(KJ2017A040) of Anhui Provincethe Graduate Students Innovation Projects(2016141) of Anhui University of Technology
文摘We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rings, skew strongly reversible rings and strongly M-reversible rings. Some well-known results on this subject are generalized and extended.
基金The National Natural Science Foundation of China(No.11371088,11571173,11871144)the Natural Science Foundation of Jiangsu Province(No.BK20171348)。
文摘Let A and B be two regular multiplier Hopf algebras.First,the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra,which is a generalization of the diagonal crossed product in the sense of Hopf algebras.The result that the product in B#A is non-degenerate is given.Next,the definition of the comultiplicationΔ#on B#A is introduced,which is composed of the multiplierΔB(b)on B⊗B and the multiplierΔA(a)on A⊗A,and the elementΔ#(b⊗a)is a two-side multiplier of B#A⊗B#A,for any b∈B and a∈A.Then,a sufficient condition for B#A to be a regular multiplier Hopf algebra is described.In particular,Delvaux's main theorem in the case of smash products is generalized.Finally,these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.
基金Foundationitem:The NSF(10271081)of Chinathe NSF(1042004)of Beijing City
文摘Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.
基金The National Natural Science Foundation of China(No.11871144,11901240).
文摘First,the group crossed product over the Hopf group-algebras is defined,and the necessary and sufficient conditions for the group crossed product to be a group algebra are given.The cleft extension theory of the Hopf group algebra is introduced,and it is proved that the crossed product of the Hopf group algebra is equivalent to the cleft extension.The necessary and sufficient conditions for the crossed product equivalence of two Hopf groups are then given.Finally,combined with the equivalence theory of the Hopf group crossed product and cleft extension,the group crossed product constructed by the general 2-cocycle as algebra is determined to be isomorphic to the group crossed product of the 2-cocycle with a convolutional invertible map of the 2-cocycle.The unit property of a general 2-cocycle is equivalent to the convolutional invertible map of the 2-cocycle,and the combination condition of the weak action is equivalent to the convolutional invertible map of the 2-cocycle and the combination condition of the weak action.Similarly,crossed product algebra constructed by the general 2-cocycle is isomorphic to the Hopfπ-crossed product algebra constructed by the 2-cocycle with a convolutional invertible map.
文摘This article is based on a recent model specifically defining magnetic field values around electrical wires. With this model, calculations of field around parallel wires were obtained. Now, this model is extended with the new concept of magnetic equipotential surface to magnetic field curves around crossing wires. Cases of single, double, and triple wires are described. Subsequent article will be conducted for more general scenarios where wires are neither infinite nor parallel.
基金Supported by National High Technology Research and Development Program of China(863 Program)(2011AA10A106)Yunnan Provincial Fund for Applied Basic Researches(2010CC001)Key New Product Development Plan of Yunnan Province(2012BB015)~~
文摘A DH population derived from C49S-87/01Y1-1069 was used to study the inheritance of wheat haploid embryo production frequency(EPF) in wheat × maize cross with the mixed major gene and polygene inheritance model of quantitative traits. The results showed that the EPF of wheat × maize cross was controlled by two dominant epistatic genes and polygene with gene effects of 1.95 for the first major gene, 6.69 for the second one and 2.80 for the polygene. The inheritability of major genes was as high as 72.09%, suggesting that the differences in EPF among wheat materials were mainly influenced by genotype. However, non-genetic factors were still important, especially for wheat materials with low EPF.
基金Foundation item: Supported by the Scientific Research Foundation for Doctoral Scientists of Henan University of Science and Technology(09001303) Supported by the National Natural Science Foundation of China(11101128)
文摘In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.
基金Supported by the Fundamental Research Fund for the Central Uuiversities(KYZ201125)Grant for Young Teachers of College of Science,Nanjing Agricultural University(LXY20090101)
基金Project(ZR2014FM036)supported by Shandong Provincial Natural Science Foundation of ChinaProject(ZR2010FZ001)supported by the Key Program of Shandong Provincial Natural Science Foundation of China
文摘In order to increase productivity and reduce energy consumption of steelmaking-continuous casting(SCC) production process, especially with complicated technological routes, the cross entropy(CE) method was adopted to optimize the SCC production scheduling(SCCPS) problem. Based on the CE method, a matrix encoding scheme was proposed and a backward decoding method was used to generate a reasonable schedule. To describe the distribution of the solution space, a probability distribution model was built and used to generate individuals. In addition, the probability updating mechanism of the probability distribution model was proposed which helps to find the optimal individual gradually. Because of the poor stability and premature convergence of the standard cross entropy(SCE) algorithm, the improved cross entropy(ICE) algorithm was proposed with the following improvements: individual generation mechanism combined with heuristic rules, retention mechanism of the optimal individual, local search mechanism and dynamic parameters of the algorithm. Simulation experiments validate that the CE method is effective in solving the SCCPS problem with complicated technological routes and the ICE algorithm proposed has superior performance to the SCE algorithm and the genetic algorithm(GA).
基金National Natural Science Foundation of China(No.51978166)the Research Fund of Sanjiang University(No.2018SJKY005)。
文摘Under improper transformations,the traditional transformation laws for cross products,the permutation tensor,and rotations are incorrect.For a cross product,using a counter-example the left-hand rule is proved wrong.The unique rule for a cross product is the right-hand rule.Coordinate systems have handedness,while a cross product is frame-indifference.Since the permutation tensor is defined as a triple product including a cross product,the law for the permutation tensor is false.For a rotation,its pseudovector representation is incorrect,because the mirror is an auxiliary device to produce the virtual image rather than a new coordinate system or reference frame.
文摘A cross section database on excitation functions of reactions produced by charged particles is essential for many areas of nuclear research. Particularly, accurate knowledge on nuclear cross sections for the cyclotron production of radioisotopes is very important for nuclear medicine. In the present paper, the cross section calculations for the production of^(43),^(34)Sc,^(45)Ti,^(51)Cr,^(54)Mn, and^(55) Fe radioisotopes were carried out by the use of ALICE/ASH code using the Fermi gas model, Kataria Ramamurthy Fermi gas model, and superfluid nuclear model for nuclear level density. Thereby, these model calculations were compared with the available measured data.
基金Supported by the Scientific Research Fund of Education Department of Hunan Province(08C518)
文摘The crossing number of cartesian products of paths and cycles with 5-vertex graphs mostly are known, but only few cartesian products of 5-vertex graphs with star K 1,n are known. In this paper, we will extent those results, and determine the crossing numbers of cartesian products of two 5-vertex graphs with star K 1,n .
基金Project supported by the National Natural Science Foundation of China (Grant No 10472091 and 10332030) and Natural Science Foundation of Shaanxi Province, China (Grant No 2003A03). The author gratefully acknowledges the support of Youth for NPU Teachers Scientific and Technological Innovation Foundation.
文摘This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.
基金Key Project of Shandong Provincial Natural Science Foundation,China(No.ZR2010FZ001)National High-Tech Research and Development Program of China(863 Program)(No.2007AA04Z157)
文摘A matrix encoding scheme for the steelmaking continuous casting( SCC) production scheduling( SCCPS) problem and the corresponding decoding method are proposed. Based on it,a cross entropy( CE) method is adopted and an improved cross entropy( ICE) algorithm is proposed to solve the SCCPS problem to minimize total power consumption. To describe the distribution of the solution space of the CE method,a probability model is built and used to generate individuals by sampling and a probability updating mechanism is introduced to trace the promising samples. For the ICE algorithm,some samples are generated by the heuristic rules for the shortest makespan due to the relation between the makespan and the total power consumption,which can reduce the search space greatly. The optimal sample in each iteration is retained through a retention mechanism to ensure that the historical optimal sample is not lost so as to improve the efficiency and global convergence. A local search procedure is carried out on a part of better samples so as to improve the local exploitation capability of the ICE algorithm and get a better result. The parameter setting is investigated by the Taguchi method of design-of-experiment. A number of simulation experiments are implemented to validate the effectiveness of the ICE algorithm in solving the SCCPS problem and also the superiority of the ICE algorithm is verified through the comparison with the standard cross entropy( SCE) algorithm.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11275071 ).
文摘The experimental data of Mαβ X-ray production cross sections for Pb and Bi by 9–40 keV electron impact have been given. Thin films with thick carbon substrates are used in the experiment. The effects of target structure on the Mαβ X-ray production cross sections are corrected by using the Monte Carlo method. The corrected experimental data are compared with calculated cross sections in terms of the distorted-wave Born approximation(DWBA) theory. The measured Mαβ X-ray production cross sections for Pb and Bi are lower than the DWBA calculations. The atomic relaxation parameters used in comparing the DWBA values with experimental results affect the degree of difference.
文摘The calculation methods of production cross sections of γ-rays for thermal-neutron captures are briefly presented. The check of intensity balance is made. The examples are given to illustrate its application.