It is shown that any multicriteria problem can be represented by a hierarchical system of criteria. Individual properties of the object (alternative) are evaluated at the bottom level of the system, using a criteria v...It is shown that any multicriteria problem can be represented by a hierarchical system of criteria. Individual properties of the object (alternative) are evaluated at the bottom level of the system, using a criteria vector. A composition mechanism is used to evaluate the object as a whole at the top level. The problem is solved by the method of nested scalar convolutions of vector-valued criteria. The methodology of the problem solving is based on the complementarity principle by N. Bohr and the theorem of incompleteness by K. G?del. An example is presented that helps the reader digest some of the intricacies in the methodology.展开更多
The main objective of this paper is to present an efficient structure-preserving scheme,which is based on the idea of the scalar auxiliary variable approach,for solving the twodimensional space-fractional nonlinear Sc...The main objective of this paper is to present an efficient structure-preserving scheme,which is based on the idea of the scalar auxiliary variable approach,for solving the twodimensional space-fractional nonlinear Schrodinger equation.First,we reformulate the equation as an canonical Hamiltonian system,and obtain a new equivalent system via introducing a scalar variable.Then,we construct a semi-discrete energy-preserving scheme by using the Fourier pseudo-spectral method to discretize the equivalent system in space direction.After that,applying the Crank-Nicolson method on the temporal direction gives a linearly-implicit scheme in the fully-discrete version.As expected,the proposed scheme can preserve the energy exactly and more efficient in the sense that only decoupled equations with constant coefficients need to be solved at each time step.Finally,numerical experiments are provided to demonstrate the efficiency and conservation of the scheme.展开更多
Based on the assumption of a two-quark structure of the scalar meson f0（980） ,we calculate the branching ratios and CP-violating asymmetries for the four B → f0（980） π and B → f0（980） η^（＇） decays by empl...Based on the assumption of a two-quark structure of the scalar meson f0（980） ,we calculate the branching ratios and CP-violating asymmetries for the four B → f0（980） π and B → f0（980） η^（＇） decays by employing the perturbative QCD（pQCD） factorization approach. The leading order pQCD predictions for branching ratios are,Br（B^-→ f0（980） π^-） ～ 2.5×10^-6,Br（Bˉ^0 → f0（980） π^0） ～ 2.6×10^-7,Br（Bˉ^0 → f0（980） η） ～ 2.5×10^-7 and Br（Bˉ^0 → f0（980） η ） ～ 6.7×10^-7,which are consistent with both the QCD factorization predictions and the experimental upper limits.展开更多
Based on the assumption of two-quark structure of the scalar meson K0^＊（1430）, we calculate the CP-averaged branching ratios for B→K0^＊（1430）η（＇） decays in the framework of the perturbative QCD （pQCD） app...Based on the assumption of two-quark structure of the scalar meson K0^＊（1430）, we calculate the CP-averaged branching ratios for B→K0^＊（1430）η（＇） decays in the framework of the perturbative QCD （pQCD） approach here. We perform the evaluations in two scenarios for the scalar meson spectrum. We find that： （a） the pQCD predictions for Br（B→K0^＊（1430）η（＇）） which are about 10^-5 10^-6, basically agree with the data within large theoretical uncertainty; （b） the agreement between the pQCD predictions and the data in Scenario Ⅰ is better than that in Scenario Ⅱ, which can be tested by the forthcoming LHC experiments; （c） the annihilation contributions play an important role for these considered decays.展开更多
In the two-quark model supposition for K0＊（1430）, which can be viewed as either the first excited state （ScenarioⅠ） or the lowest lying state （Scenario Ⅱ）, the branching ratios and the direct CP-violating asy...In the two-quark model supposition for K0＊（1430）, which can be viewed as either the first excited state （ScenarioⅠ） or the lowest lying state （Scenario Ⅱ）, the branching ratios and the direct CP-violating asymmetries for decays s0 → K0＊0（1430）η （’） are studied by employing the perturbative QCD factorization approach. We find the following results： （a） The CP averaged branching ratios ofs0 → K0＊0 （1430）η ands0→ K0＊0（1430）η’ are small and both in the order of 10-7 . If one views K0＊ （1430） as the lowest lying state, B（s0→K0＊0（1430）η） ≈ 3.9×10-7 and B（s0→K0＊0（1430）η’） ≈ 7.8×10-7.（b） While the direct CP-violating asymmetries of these two decays are not small： if we still take the parameters of K0＊ （1430） in scenario , ACPdir（s0→K0＊0（1430）η） ≈ 56.2% and ACPdir（s0→ K0＊0（1430）η’） ≈ 42.4%. （c） The annihilation contributions will play an important role in accounting for future data, because both the branching ratios and the direct CP asymmetries of these two decays are sensitive to the annihilation type contributions.展开更多
文摘It is shown that any multicriteria problem can be represented by a hierarchical system of criteria. Individual properties of the object (alternative) are evaluated at the bottom level of the system, using a criteria vector. A composition mechanism is used to evaluate the object as a whole at the top level. The problem is solved by the method of nested scalar convolutions of vector-valued criteria. The methodology of the problem solving is based on the complementarity principle by N. Bohr and the theorem of incompleteness by K. G?del. An example is presented that helps the reader digest some of the intricacies in the methodology.
基金supported by the National Natural Science Foundation of China(Grant Nos.12171245,11971416,11971242)the Natural Science Foundation of Henan Province(No.222300420280)the Program for Scientific and Technological Innovation Talents in Universities of Henan Province(No.22HASTIT018).
文摘The main objective of this paper is to present an efficient structure-preserving scheme,which is based on the idea of the scalar auxiliary variable approach,for solving the twodimensional space-fractional nonlinear Schrodinger equation.First,we reformulate the equation as an canonical Hamiltonian system,and obtain a new equivalent system via introducing a scalar variable.Then,we construct a semi-discrete energy-preserving scheme by using the Fourier pseudo-spectral method to discretize the equivalent system in space direction.After that,applying the Crank-Nicolson method on the temporal direction gives a linearly-implicit scheme in the fully-discrete version.As expected,the proposed scheme can preserve the energy exactly and more efficient in the sense that only decoupled equations with constant coefficients need to be solved at each time step.Finally,numerical experiments are provided to demonstrate the efficiency and conservation of the scheme.
文摘Based on the assumption of a two-quark structure of the scalar meson f0（980） ,we calculate the branching ratios and CP-violating asymmetries for the four B → f0（980） π and B → f0（980） η^（＇） decays by employing the perturbative QCD（pQCD） factorization approach. The leading order pQCD predictions for branching ratios are,Br（B^-→ f0（980） π^-） ～ 2.5×10^-6,Br（Bˉ^0 → f0（980） π^0） ～ 2.6×10^-7,Br（Bˉ^0 → f0（980） η） ～ 2.5×10^-7 and Br（Bˉ^0 → f0（980） η ） ～ 6.7×10^-7,which are consistent with both the QCD factorization predictions and the experimental upper limits.
基金Supported by National Natural Science Foundation of China (10575052,10605012,10735080)
文摘Based on the assumption of two-quark structure of the scalar meson K0^＊（1430）, we calculate the CP-averaged branching ratios for B→K0^＊（1430）η（＇） decays in the framework of the perturbative QCD （pQCD） approach here. We perform the evaluations in two scenarios for the scalar meson spectrum. We find that： （a） the pQCD predictions for Br（B→K0^＊（1430）η（＇）） which are about 10^-5 10^-6, basically agree with the data within large theoretical uncertainty; （b） the agreement between the pQCD predictions and the data in Scenario Ⅰ is better than that in Scenario Ⅱ, which can be tested by the forthcoming LHC experiments; （c） the annihilation contributions play an important role for these considered decays.
基金Supported by National Natural Science Foundation of China (11147004)Foundation of Henan University of Technology(2009BS038)
文摘In the two-quark model supposition for K0＊（1430）, which can be viewed as either the first excited state （ScenarioⅠ） or the lowest lying state （Scenario Ⅱ）, the branching ratios and the direct CP-violating asymmetries for decays s0 → K0＊0（1430）η （’） are studied by employing the perturbative QCD factorization approach. We find the following results： （a） The CP averaged branching ratios ofs0 → K0＊0 （1430）η ands0→ K0＊0（1430）η’ are small and both in the order of 10-7 . If one views K0＊ （1430） as the lowest lying state, B（s0→K0＊0（1430）η） ≈ 3.9×10-7 and B（s0→K0＊0（1430）η’） ≈ 7.8×10-7.（b） While the direct CP-violating asymmetries of these two decays are not small： if we still take the parameters of K0＊ （1430） in scenario , ACPdir（s0→K0＊0（1430）η） ≈ 56.2% and ACPdir（s0→ K0＊0（1430）η’） ≈ 42.4%. （c） The annihilation contributions will play an important role in accounting for future data, because both the branching ratios and the direct CP asymmetries of these two decays are sensitive to the annihilation type contributions.
