It is critical to establish a direct and precise method with a high sensitivity and selectivity in analytical chemistry. In this research, making use of a well known phenomenon of capillary flow, we have proposed an...It is critical to establish a direct and precise method with a high sensitivity and selectivity in analytical chemistry. In this research, making use of a well known phenomenon of capillary flow, we have proposed an image analysis method of nucleic acids at the price of a small amount of sample. When a droplet of the supramolecular complex solution, formed by neutral red and nucleic acids(NA) under an approximate neutral condition, was placed on the hydrophobic surface of dimethyl dichlorosilane pretreated glass slides, and it was evaporated, the supramolecular complex exhibited the periphery of the droplet due to the capillary effect, and accumulated there to form a red capillary flow directed assembly ring(CFDAR). A typical CFDAR has an outer diameter of (2 r ) about 1.18 mm and a ring width(2 δ ) of about 41 μm. Depending on the experimental conditions, a variety of CFDAR can be assembled. The experimental results are in agreement with our former theoretical discussion. It was found that when a droplet volume is 0.1 μL, the fluorescence intensity of the CFDAR formed by the NR NA is in proportion to the content of calf thymus DNA in the range of 0-0.28 ng, fish sperm DNA of 0-0.24 ng and yeast RNA of 0-0.16 ng with the limit of detection(3 σ ) of 1 7, 1.4 and 0.9 pg, respectively for the three nucleic acids.展开更多
The Daning River is a very important tributary in the Three Gorges Reservoir area. It is also a famous scenic spot. Anomalies appeared after water storage of the reservoir in June, 2003. In September, 2003, eutrophica...The Daning River is a very important tributary in the Three Gorges Reservoir area. It is also a famous scenic spot. Anomalies appeared after water storage of the reservoir in June, 2003. In September, 2003, eutrophication monitoring in the 135-m backwater reach of the Daning River was conducted and the data were simply analyzed. The assessment result is that water body in the segment from Shuanglong to Longmen was mesotrophic or eutrophic. At the same time, the causes of its nutritional change were discussed, and counter-measures have been proposed.展开更多
We apply random matrix theory to small metallic grains in different spin-states of S=0,1/2,1,3/2,2,5/2,...,and find that there exist theoretical critical level spacings dc at which the superconductivity would break do...We apply random matrix theory to small metallic grains in different spin-states of S=0,1/2,1,3/2,2,5/2,...,and find that there exist theoretical critical level spacings dc at which the superconductivity would break down.We also find that the higher the spin-state,the smaller the critical level spacing,and for the state of S=0 there actually exists the superconducting enhancement.展开更多
By solving the eigenvalue equation for the quark-antiquark potential which emerges from an effective dilatongluon coupling inspired by superstring theory, we obtain the spin-averaged energy levels of charmonium (cc) a...By solving the eigenvalue equation for the quark-antiquark potential which emerges from an effective dilatongluon coupling inspired by superstring theory, we obtain the spin-averaged energy levels of charmonium (cc) and bottonium (bb) and show that the masses of the cc and bb states are well in agreement with the available experimental data.展开更多
The energy levels of the odd-odd nucleus ^(86)Nb at low spins are calculated by using quasi-particles plus a rotor model. The distribution of the nearest-neighbour spacing and the spectral rigidity are studied. We fin...The energy levels of the odd-odd nucleus ^(86)Nb at low spins are calculated by using quasi-particles plus a rotor model. The distribution of the nearest-neighbour spacing and the spectral rigidity are studied. We find that the chaotic degree of the energy spectra increases with the increasing spin and reaches a maximum at I = 10;then it decreases gradually for spins above I = 10. The recoil term in the model Haniltonian makes the energy spectra slightly regular. The Coriolis force, however, makes the spectra chaotic and plays a major role in the spectral statistics of the odd-odd nucleus ^(86)Nb.展开更多
Superconductivity in small metallic grains is carefully checked as their size is decreased to a few nm when the average level spacing d could be compared with the bulk gapΔ.Using random matrix theory to the mean fiel...Superconductivity in small metallic grains is carefully checked as their size is decreased to a few nm when the average level spacing d could be compared with the bulk gapΔ.Using random matrix theory to the mean field,we find that the average theoretical values of the critical level spacing for both odd and even numbers of electrons and the transition temperature Tc in three Gauss ensembles are quite different for those from the model of uniformly spaced levels.For Sz=1/2,as grain size is reduced,the transition temperature or the granular gap decreases monotonously,and the relation 2△(0)/kB T_(c)≤3.53 always exists.展开更多
In this paper,the axial symmetry rotor plus quasiparticle model is generalized from odd nuclei to odd-odd nuclei.Energy spectra of yrast bands for nuclei ^(160)Ho,^(162)Tm and ^(164)Tm are calculated by using the meth...In this paper,the axial symmetry rotor plus quasiparticle model is generalized from odd nuclei to odd-odd nuclei.Energy spectra of yrast bands for nuclei ^(160)Ho,^(162)Tm and ^(164)Tm are calculated by using the method.Signature inversions in these three nuclei are reproduced,and one possible signature inversion mechanism connected with the calculation is also discussed.展开更多
Using the molecular electronegativity distance vector descriptors derived directly from the molecular topological structures, the relative retention time (RRT) of polybrominated diphenyl ethers (PBDEs) were predic...Using the molecular electronegativity distance vector descriptors derived directly from the molecular topological structures, the relative retention time (RRT) of polybrominated diphenyl ethers (PBDEs) were predicted. A four-variable regression model (M30) with the correlation coefficient of 0.9816 and the root mean square errors of 0.061 was developed using a training set including 30 PBDEs. The correlation coefficient of 0.9841 and the root mean square errors of 0.054 between the values of RRT predicted by M30 and the RRT observed for 16 external PBDEs show a good predictive potential of M30. The descriptors included in the M30 represent four interactions between four pairs of atom types, i.e., atom -C= and -C=, -C= and 〉C=, 〉C= and 〉C=, -C= and -Br.展开更多
The relationships between the changes of relative water content (RWC), malondialdehyde (MDA) contents, superoxide dismutase (SOD) activity and free proline contents in sweet potato leaves, and drought resistant ...The relationships between the changes of relative water content (RWC), malondialdehyde (MDA) contents, superoxide dismutase (SOD) activity and free proline contents in sweet potato leaves, and drought resistant ability under different concentration of polyethylene glycol (PEG) treatment applied at rhizosphere of sweet potato seedlings were studied. A highly positive correlation between RWC and drought resistance (r =0.783, P〈0.01), a highly negative correlation between MDA contents and drought resistance (r = -0.848, P〈0.01), a highly positive correlation between SOD activity and drought resistance (r = 0.777, P〈0.01) was observed. Free proline contents in leaves was not related obviously to the sweet potato drought resistance under 25% PEG treatment. The stronger the drought resistance of variety, the less decrease of RWC and increase of MDA contents, the more increase of SOD activity. By determining these physiological indices in sweet potato leaves under 25% PEG treatment, rapid identification of drought resistant ability of different varieties can be obtained in the lab.展开更多
Let D be N+1 connected bounded domain in plane. Suppose the contour of D consists of N+1 simple-ly closed curves <sub>0</sub>, <sub>1</sub>…, <sub>N</sub> and <sub>1</s...Let D be N+1 connected bounded domain in plane. Suppose the contour of D consists of N+1 simple-ly closed curves <sub>0</sub>, <sub>1</sub>…, <sub>N</sub> and <sub>1</sub>… <sub>N</sub> are in the interior of domain circumscribed byC<sub>μ</sub><sup>1</sup>(0 【μ【 1). In addition, assume that there are n mutually exclusive contour γ<sub>,</sub>j=1,…,n,in interi-or of D,γ=γ<sub>i</sub>; ∈C<sub>μ</sub><sup>1</sup>. Denote D<sub>j</sub> is the bounded domain circumscribed by γ<sub>j</sub>,j=1,…,n, D<sup>-</sup>=D<sub>1</sub>+…+D.,D<sup>+</sup>=D-D<sup>-</sup>,D<sub>t</sub><sup> </sup>=D<sup> </sup>×E, E=[0,T] (T】0), z=0∈D<sup>+</sup>.We consider the following pseudoparabolic complex equation on D<sub>t</sub><sup> </sup> : / t[W<sub>Z</sub>- Q<sub>1</sub>(z)W<sub>z</sub>- Q<sub>2</sub>(z) <sub> </sub>- A<sub>1</sub>(z)W - A<sub>2</sub>(Z) ]= H(t,z,W,W-<sub>2</sub>,W<sub>2</sub>), (z,t) ∈D<sub>t</sub><sup> </sup>, (1)展开更多
1 Newton imbedding method for nonlinear elliptic complex equation of first orderWe discuss the following nonlinear elliptic complex equation of first order on D;where D is N+1 connected bounded domain. Without loss of...1 Newton imbedding method for nonlinear elliptic complex equation of first orderWe discuss the following nonlinear elliptic complex equation of first order on D;where D is N+1 connected bounded domain. Without loss of generality, D is supposed to be N+ 1 con-nected circular domain in |z|【 1 and its boundary contour is = <sub>j</sub>, <sub>j</sub>= {|z-z<sub>j</sub>|=r<sub>j</sub>},j=1,…,N, <sub>0</sub>= <sub>N</sub>+1= {|z|=1},z=0∈D.First, we introduce two conditions satisfying (1. 1).Condition C; For any function W(z) continuous on D and any complex numbers V<sub>1</sub>,V<sub>2</sub>, the followinginequalities展开更多
In this paper,the ground state wave function of four parameters is developed and expression of the ground state level is derived for the helium atom when the radial Schrodinger equation of the helium atom is solved. T...In this paper,the ground state wave function of four parameters is developed and expression of the ground state level is derived for the helium atom when the radial Schrodinger equation of the helium atom is solved. The ground energy is respectively computed by the optimized aJgorithms of Matlab 7.0 and the Monte Carlo methods. Furthermore, the ground state wave function is obtained. Compared with the experiment value and the value with the variation calculus in reference, the results of this paper show that in the four-parameter scheme, not only the calculations become more simplified and precise, but also the radial wave function of the helium atom meets the space symmetry automatically in ground state.展开更多
The important fact that the second kind of moment of inertia J(2)is larger than the first kind of moment of inertia J(1)can be derived naturally from the 2-parameter expression for the rotational spectra,E(I)=a(√1+bI...The important fact that the second kind of moment of inertia J(2)is larger than the first kind of moment of inertia J(1)can be derived naturally from the 2-parameter expression for the rotational spectra,E(I)=a(√1+bI(I+1)-1),in its derivation the nuclear triaxiality has been taken into account.展开更多
Energy spectrum of yrast band for ^(122)Cs is studied by using particle-rotor model(PRM)of odd-odd nuclei,in which special attention is paid to the model basis accounting for the effect of the instabilityγvibration p...Energy spectrum of yrast band for ^(122)Cs is studied by using particle-rotor model(PRM)of odd-odd nuclei,in which special attention is paid to the model basis accounting for the effect of the instabilityγvibration perturbation around axial symmetry.In order to check the assignments of this band,two calculation schemes are put into practice.The first one is for previousπh11/2 vg7/2 configuration with bandhead spin I_(0)=(6^(-))which was obtained from cranked shell model(CSM)calculation,and the other one is forπh_(11/2) vh_(11/2) configuration with I_(0)=(9^(+))supported by the systematic analyses of experimental data.A qualitative comparison between the present PRM calculation and that of CSM has also been made.The results indicate that,rather thanπh_(11/2) vg_(7/2) I_(0)=(6^(-)),πh_(11/2) vh_(11/2) with I_(0)=(9^(+))is a more reasonable assignment to the yrast band in ^(122)Cs.展开更多
The behaviour of dilaton-gluon coupling (DGC) potential is investigated by studying charmonium spectra, annihilation rates and E1 transition rates systematically. We find that in the non-relativistic quantum chromod...The behaviour of dilaton-gluon coupling (DGC) potential is investigated by studying charmonium spectra, annihilation rates and E1 transition rates systematically. We find that in the non-relativistic quantum chromodynamics approximation, the charmonium properties can be described by the DGC potential.展开更多
The vacuum properties at finite temperature for the linear sigma model are studied by using the effective potential formalism.It is found that the light hadronic masses drop fast with increasing temperature.An extensi...The vacuum properties at finite temperature for the linear sigma model are studied by using the effective potential formalism.It is found that the light hadronic masses drop fast with increasing temperature.An extensive scaling behavior of light hadronic masses is observed and is found to follow the scaling law postulated in dense matter.展开更多
It is shown that the meson exchange interaction between dynamical quarks generated by the chiral symmetry breaking is of crucial importance to explain the empirical value of the pion-nucleonσ-term.The large contribut...It is shown that the meson exchange interaction between dynamical quarks generated by the chiral symmetry breaking is of crucial importance to explain the empirical value of the pion-nucleonσ-term.The large contribution of ss and gluon to a nucleon mass is predicted by using the QCD energy-momentum trace anomaly from the pion-nucleonσ-term.展开更多
Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper,...Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper, we have proved that: let (?) be a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A an artinian ZG-module with all irreducible ZG-factors of A being finite; if G ∈ (?), f(∞) ≡ f(p) . f(p)≠φ for each p ∈ π, A has an (?)-decomposition.展开更多
基金Supported by the NationalNaturalScience Foundation of China( No. 2 0 175 0 1) and U niversity Key Teachers Programdirected under the Ministry of Education ofP.R.China( No. 2 0 0 0 - 6 5 )
文摘It is critical to establish a direct and precise method with a high sensitivity and selectivity in analytical chemistry. In this research, making use of a well known phenomenon of capillary flow, we have proposed an image analysis method of nucleic acids at the price of a small amount of sample. When a droplet of the supramolecular complex solution, formed by neutral red and nucleic acids(NA) under an approximate neutral condition, was placed on the hydrophobic surface of dimethyl dichlorosilane pretreated glass slides, and it was evaporated, the supramolecular complex exhibited the periphery of the droplet due to the capillary effect, and accumulated there to form a red capillary flow directed assembly ring(CFDAR). A typical CFDAR has an outer diameter of (2 r ) about 1.18 mm and a ring width(2 δ ) of about 41 μm. Depending on the experimental conditions, a variety of CFDAR can be assembled. The experimental results are in agreement with our former theoretical discussion. It was found that when a droplet volume is 0.1 μL, the fluorescence intensity of the CFDAR formed by the NR NA is in proportion to the content of calf thymus DNA in the range of 0-0.28 ng, fish sperm DNA of 0-0.24 ng and yeast RNA of 0-0.16 ng with the limit of detection(3 σ ) of 1 7, 1.4 and 0.9 pg, respectively for the three nucleic acids.
文摘The Daning River is a very important tributary in the Three Gorges Reservoir area. It is also a famous scenic spot. Anomalies appeared after water storage of the reservoir in June, 2003. In September, 2003, eutrophication monitoring in the 135-m backwater reach of the Daning River was conducted and the data were simply analyzed. The assessment result is that water body in the segment from Shuanglong to Longmen was mesotrophic or eutrophic. At the same time, the causes of its nutritional change were discussed, and counter-measures have been proposed.
基金Supported by the National Natural Science Foundation of China under Grant No.19875040Chongqing Commission of Science and Technology,Shanghai Commission of Education and Shanghai Teachers' University.
文摘We apply random matrix theory to small metallic grains in different spin-states of S=0,1/2,1,3/2,2,5/2,...,and find that there exist theoretical critical level spacings dc at which the superconductivity would break down.We also find that the higher the spin-state,the smaller the critical level spacing,and for the state of S=0 there actually exists the superconducting enhancement.
基金Supported in part by the Foundation of the Education Minis try of China under Grand No.99108.
文摘By solving the eigenvalue equation for the quark-antiquark potential which emerges from an effective dilatongluon coupling inspired by superstring theory, we obtain the spin-averaged energy levels of charmonium (cc) and bottonium (bb) and show that the masses of the cc and bb states are well in agreement with the available experimental data.
基金Supported by the National Natural Science Foundation of China under Grant No.19875040.
文摘The energy levels of the odd-odd nucleus ^(86)Nb at low spins are calculated by using quasi-particles plus a rotor model. The distribution of the nearest-neighbour spacing and the spectral rigidity are studied. We find that the chaotic degree of the energy spectra increases with the increasing spin and reaches a maximum at I = 10;then it decreases gradually for spins above I = 10. The recoil term in the model Haniltonian makes the energy spectra slightly regular. The Coriolis force, however, makes the spectra chaotic and plays a major role in the spectral statistics of the odd-odd nucleus ^(86)Nb.
基金Supported in part by the Science and Technology Commission of Chongqing City under Grant No.97-4730 and Key Laboratory Fund of Jiangsu Province.
文摘Superconductivity in small metallic grains is carefully checked as their size is decreased to a few nm when the average level spacing d could be compared with the bulk gapΔ.Using random matrix theory to the mean field,we find that the average theoretical values of the critical level spacing for both odd and even numbers of electrons and the transition temperature Tc in three Gauss ensembles are quite different for those from the model of uniformly spaced levels.For Sz=1/2,as grain size is reduced,the transition temperature or the granular gap decreases monotonously,and the relation 2△(0)/kB T_(c)≤3.53 always exists.
基金Supported by the National Natural Science Foundation of China,。
文摘In this paper,the axial symmetry rotor plus quasiparticle model is generalized from odd nuclei to odd-odd nuclei.Energy spectra of yrast bands for nuclei ^(160)Ho,^(162)Tm and ^(164)Tm are calculated by using the method.Signature inversions in these three nuclei are reproduced,and one possible signature inversion mechanism connected with the calculation is also discussed.
基金the National Basic Research Program of China(2003CB415002)the National Natural Science Foundation of China(No.20377022) the Guangxi Natural Science Fund(No.0236063)for their financial supports.
文摘Using the molecular electronegativity distance vector descriptors derived directly from the molecular topological structures, the relative retention time (RRT) of polybrominated diphenyl ethers (PBDEs) were predicted. A four-variable regression model (M30) with the correlation coefficient of 0.9816 and the root mean square errors of 0.061 was developed using a training set including 30 PBDEs. The correlation coefficient of 0.9841 and the root mean square errors of 0.054 between the values of RRT predicted by M30 and the RRT observed for 16 external PBDEs show a good predictive potential of M30. The descriptors included in the M30 represent four interactions between four pairs of atom types, i.e., atom -C= and -C=, -C= and 〉C=, 〉C= and 〉C=, -C= and -Br.
文摘The relationships between the changes of relative water content (RWC), malondialdehyde (MDA) contents, superoxide dismutase (SOD) activity and free proline contents in sweet potato leaves, and drought resistant ability under different concentration of polyethylene glycol (PEG) treatment applied at rhizosphere of sweet potato seedlings were studied. A highly positive correlation between RWC and drought resistance (r =0.783, P〈0.01), a highly negative correlation between MDA contents and drought resistance (r = -0.848, P〈0.01), a highly positive correlation between SOD activity and drought resistance (r = 0.777, P〈0.01) was observed. Free proline contents in leaves was not related obviously to the sweet potato drought resistance under 25% PEG treatment. The stronger the drought resistance of variety, the less decrease of RWC and increase of MDA contents, the more increase of SOD activity. By determining these physiological indices in sweet potato leaves under 25% PEG treatment, rapid identification of drought resistant ability of different varieties can be obtained in the lab.
文摘Let D be N+1 connected bounded domain in plane. Suppose the contour of D consists of N+1 simple-ly closed curves <sub>0</sub>, <sub>1</sub>…, <sub>N</sub> and <sub>1</sub>… <sub>N</sub> are in the interior of domain circumscribed byC<sub>μ</sub><sup>1</sup>(0 【μ【 1). In addition, assume that there are n mutually exclusive contour γ<sub>,</sub>j=1,…,n,in interi-or of D,γ=γ<sub>i</sub>; ∈C<sub>μ</sub><sup>1</sup>. Denote D<sub>j</sub> is the bounded domain circumscribed by γ<sub>j</sub>,j=1,…,n, D<sup>-</sup>=D<sub>1</sub>+…+D.,D<sup>+</sup>=D-D<sup>-</sup>,D<sub>t</sub><sup> </sup>=D<sup> </sup>×E, E=[0,T] (T】0), z=0∈D<sup>+</sup>.We consider the following pseudoparabolic complex equation on D<sub>t</sub><sup> </sup> : / t[W<sub>Z</sub>- Q<sub>1</sub>(z)W<sub>z</sub>- Q<sub>2</sub>(z) <sub> </sub>- A<sub>1</sub>(z)W - A<sub>2</sub>(Z) ]= H(t,z,W,W-<sub>2</sub>,W<sub>2</sub>), (z,t) ∈D<sub>t</sub><sup> </sup>, (1)
文摘1 Newton imbedding method for nonlinear elliptic complex equation of first orderWe discuss the following nonlinear elliptic complex equation of first order on D;where D is N+1 connected bounded domain. Without loss of generality, D is supposed to be N+ 1 con-nected circular domain in |z|【 1 and its boundary contour is = <sub>j</sub>, <sub>j</sub>= {|z-z<sub>j</sub>|=r<sub>j</sub>},j=1,…,N, <sub>0</sub>= <sub>N</sub>+1= {|z|=1},z=0∈D.First, we introduce two conditions satisfying (1. 1).Condition C; For any function W(z) continuous on D and any complex numbers V<sub>1</sub>,V<sub>2</sub>, the followinginequalities
基金The project supported by National Natural Science Foundation of China under Grant No. 10147207, the Natural Science Foundation of Chongqing Science and Technology Committee under Grant No. 2005BB8267, and the Fundamental Research Foundation of Chongqing Education Committee under Grant No. KJ060813
文摘In this paper,the ground state wave function of four parameters is developed and expression of the ground state level is derived for the helium atom when the radial Schrodinger equation of the helium atom is solved. The ground energy is respectively computed by the optimized aJgorithms of Matlab 7.0 and the Monte Carlo methods. Furthermore, the ground state wave function is obtained. Compared with the experiment value and the value with the variation calculus in reference, the results of this paper show that in the four-parameter scheme, not only the calculations become more simplified and precise, but also the radial wave function of the helium atom meets the space symmetry automatically in ground state.
文摘The important fact that the second kind of moment of inertia J(2)is larger than the first kind of moment of inertia J(1)can be derived naturally from the 2-parameter expression for the rotational spectra,E(I)=a(√1+bI(I+1)-1),in its derivation the nuclear triaxiality has been taken into account.
基金Supported by the National Natural Science Foundation of China under Grant No.19475030。
文摘Energy spectrum of yrast band for ^(122)Cs is studied by using particle-rotor model(PRM)of odd-odd nuclei,in which special attention is paid to the model basis accounting for the effect of the instabilityγvibration perturbation around axial symmetry.In order to check the assignments of this band,two calculation schemes are put into practice.The first one is for previousπh11/2 vg7/2 configuration with bandhead spin I_(0)=(6^(-))which was obtained from cranked shell model(CSM)calculation,and the other one is forπh_(11/2) vh_(11/2) configuration with I_(0)=(9^(+))supported by the systematic analyses of experimental data.A qualitative comparison between the present PRM calculation and that of CSM has also been made.The results indicate that,rather thanπh_(11/2) vg_(7/2) I_(0)=(6^(-)),πh_(11/2) vh_(11/2) with I_(0)=(9^(+))is a more reasonable assignment to the yrast band in ^(122)Cs.
基金Supported partially by the National Natural Science Foundation of China under Grants Nos 10447130 and 10375074.
文摘The behaviour of dilaton-gluon coupling (DGC) potential is investigated by studying charmonium spectra, annihilation rates and E1 transition rates systematically. We find that in the non-relativistic quantum chromodynamics approximation, the charmonium properties can be described by the DGC potential.
基金Supported in part by the National Natural Science Foundation of China under Grant No.19375048。
文摘The vacuum properties at finite temperature for the linear sigma model are studied by using the effective potential formalism.It is found that the light hadronic masses drop fast with increasing temperature.An extensive scaling behavior of light hadronic masses is observed and is found to follow the scaling law postulated in dense matter.
文摘It is shown that the meson exchange interaction between dynamical quarks generated by the chiral symmetry breaking is of crucial importance to explain the empirical value of the pion-nucleonσ-term.The large contribution of ss and gluon to a nucleon mass is predicted by using the QCD energy-momentum trace anomaly from the pion-nucleonσ-term.
文摘Let (?) be a formation locally defined by f(P), G ∈ (?) and A a ZG-module, where p ∈ π = { all primes and symbol ∞}. Then a p-main-factor U/V of G is said to be (?)-central in G if G/CG(U/V) ∈f(p). In this paper, we have proved that: let (?) be a locally defined formation consisting of locally soluble groups, G a hyper-(cyclic or finite) locally soluble group and A an artinian ZG-module with all irreducible ZG-factors of A being finite; if G ∈ (?), f(∞) ≡ f(p) . f(p)≠φ for each p ∈ π, A has an (?)-decomposition.