Electrocatalytic water splitting provides an efficient method for the production of hydrogen.In electrocatalytic water splitting,the oxygen evolution reaction(OER)involves a kinetically sluggish four-electron transfer...Electrocatalytic water splitting provides an efficient method for the production of hydrogen.In electrocatalytic water splitting,the oxygen evolution reaction(OER)involves a kinetically sluggish four-electron transfer process,which limits the efficiency of electrocatalytic water splitting.Therefore,it is urgent to develop highly active OER catalysts to accelerate reaction kinetics.Coupling single atoms and clusters in one system is an innovative approach for developing efficient catalysts that can synergistically optimize the adsorption and configuration of intermediates and improve catalytic activity.However,research in this area is still scarce.Herein,we constructed a heterogeneous single-atom cluster system by anchoring Ir single atoms and Co clusters on the surface of Ni(OH)_(2)nanosheets.Ir single atoms and Co clusters synergistically improved the catalytic activity toward the OER.Specifically,Co_(n)Ir_(1)/Ni(OH)_(2)required an overpotential of 255 mV at a current density of 10 mA·cm^(−2),which was 60 mV and 67 mV lower than those of Co_(n)/Ni(OH)_(2)and Ir1/Ni(OH)_(2),respectively.The turnover frequency of Co_(n)Ir_(1)/Ni(OH)_(2)was 0.49 s^(−1),which was 4.9 times greater than that of Co_(n)/Ni(OH)_(2)at an overpotential of 300 mV.展开更多
A behavioral model of the photodiode is presented.The model describes the relationship between photocurrent and incident optical power,and it also illustrates the impact of the reverse bias to the variation of the jun...A behavioral model of the photodiode is presented.The model describes the relationship between photocurrent and incident optical power,and it also illustrates the impact of the reverse bias to the variation of the junction capacitance.According to this model,the photodiode and a CMOS receiver circuit are simulated and designed simultaneously under a universal circuit simulation environment.展开更多
This paper presents a general approach for determining the configuration number for any linkage: A kinematic cham (KC) can be divided into some basic kinematic chains (BKCs) and driving joints; there are only 33 kinds...This paper presents a general approach for determining the configuration number for any linkage: A kinematic cham (KC) can be divided into some basic kinematic chains (BKCs) and driving joints; there are only 33 kinds of BKCs with υ =1-4 independent loop, containing only R (revolute) joints and their configuration numbers are given; the configuration number of a KC equals to the multiplication of the configuration numbers of BKCs contained in the KC.展开更多
The hardware optimization technique of mono similarity system generation is presented based on hardware/software(HW/SW) co design.First,the coarse structure of sub graphs' matching based on full customized HW...The hardware optimization technique of mono similarity system generation is presented based on hardware/software(HW/SW) co design.First,the coarse structure of sub graphs' matching based on full customized HW/SW co design is put forward.Then,a universal sub graphs' combination method is discussed.Next,a more advanced vertexes' compression algorithm based on sub graphs' combination method is discussed with great emphasis.Experiments are done successfully with perfect results verifying all the formulas and the methods above.展开更多
In recent years,there have been numerous studies on Fenton or Fenton-like reactions mediated by nonfree radicals such as singlet oxygen(1O_(2));however,there are few studies on the synergistic effect of 1O_(2) and fre...In recent years,there have been numerous studies on Fenton or Fenton-like reactions mediated by nonfree radicals such as singlet oxygen(1O_(2));however,there are few studies on the synergistic effect of 1O_(2) and free radicals on the degradation of organic molecules,such as phenol in Fenton reaction.In this study,a cocatalyst,CoP,commonly used in photocatalysis was synthesized using a simple two-step method,and a CoP/Fe^(2+)/AM1.5 system was constructed by introducing Fe^(2+)and simulated sunlight(AM1.5)irradiation.The newly constructed CoP/Fe^(2+)/AM1.5 system could effectively degrade various organic pollutants,including dyes,phenols,and antibiotics.Radical quenching experiments and electron paramagnetic resonance detection confirmed that there were three reactive oxygen species(ROS)in the CoP/Fe^(2+)/AM1.5 system,including·OH_(ads),·O_(2)^(-),and 1O_(2).Further,combined with the liquid chromatogram of phenol,its intermediate products,and the fluorescence diagram of o-hydroxybenzoic acid,it can be concluded that a synergistic effect exists between 1O_(2) and the surface-adsorbed·OH_(ads) in the CoP/Fe^(2+)/AM1.5 system.The controllable formation of surface 1O_(2) and·OH_(ads) was achieved through the oxidation(Co^(3+))and reduction(Pδ−)centers exposed on the CoP surface,and the synergistic effect between them results in phenol’s hydroxylation,ring-opening,and degradation.The study of this new mechanism provides a new perspective for revealing the surface interface reaction between ROS and organic pollutants.展开更多
In this paper, we describe all the divisible semiring congruences on a distributive semiring S and also establish a one_to_one, inclusion_preserving mapping from the set of full, closed, self_conjagate, ideal subsemir...In this paper, we describe all the divisible semiring congruences on a distributive semiring S and also establish a one_to_one, inclusion_preserving mapping from the set of full, closed, self_conjagate, ideal subsemirings of S to the set of all divisible semiring congruences on S.展开更多
To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coup...To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.展开更多
The inclusive differential cross sections of the ^7 Li nucleus in a reaction induced by ^6He on a ^9Be target are measured at an incident energy of 25 MeV/nucleon. Finite-range distorted-wave Born approximation calcul...The inclusive differential cross sections of the ^7 Li nucleus in a reaction induced by ^6He on a ^9Be target are measured at an incident energy of 25 MeV/nucleon. Finite-range distorted-wave Born approximation calculations suggest that these ^7 Li particles are formed in a direct single-proton pickup reaction ^9Be(^6He,^7 Li)^8Li. The experimental data can be well reproduced by taking into account of the contributions of both the ground states and the first excited states of ^7Li and ^8Li.展开更多
In order to improve the reliability of the design and calculation of single piles under the combined vertical and lateral loads, the solutions were presented based on the subgrade reaction method, in which the ultimat...In order to improve the reliability of the design and calculation of single piles under the combined vertical and lateral loads, the solutions were presented based on the subgrade reaction method, in which the ultimate soil resistance was considered and the coefficient of subgrade reaction was assumed to be a constant. The corresponding computational program was developed using FORTRAN language. A comparison between the obtained solutions and the model test results was made to show the validity of the obtained solutions. The calculation results indicate that both the maximum lateral displacement and bending moment increase with the increase of the vertical and lateral loads and the pile length above ground, while decrease as the pile stiffness, the coefficient of subgrade reaction and the yielding displacement of soil increase. It is also shown that the pile head condition controls the pile responses and the vertical load may cause the instability problem to the pile. In general, the proposed method can be employed to calculate the pile responses independent of the magnitude of the pile deflection.展开更多
It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigr...It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.展开更多
The paper design a double eccentric mass driven spherical robot, the ball is also subject to eccentric force and inertia force that generate by internal drive units in movement. Due to the unique spherical shell, the ...The paper design a double eccentric mass driven spherical robot, the ball is also subject to eccentric force and inertia force that generate by internal drive units in movement. Due to the unique spherical shell, the robot in the dynamic state transition process, Friction cannot offset the robot motion state change due to internal driving motion error of small units. In order to make linear movement of the spherical robot that can smooth start, stop and speed control, the paper design a method for linear motion driven spherical robot with double eccentric mass control. The improved driving eccentric mass of robot total mass ratio is larger, that can provide the eccentric torque and inertia moment more, the robot has higher motion velocity.展开更多
A constructive theorem is established for generalized synchronization (GS) related to C<SUP>1</SUP> diffeomorphic transformations of unidirectionally coupled dynamical arrays. The theorem provides some int...A constructive theorem is established for generalized synchronization (GS) related to C<SUP>1</SUP> diffeomorphic transformations of unidirectionally coupled dynamical arrays. The theorem provides some interpretations about the underlying mechanism of various GS phenomena in nature. As a direct application of the theorem, a chaos-based secure Internet communication scheme is proposed. Moreover, a cellular neural network (CNN) of Chen's chaotic circuits with GS property is designed and studied. Numerical simulation shows that this Chen's CNN has high security and is fast and reliable for secure Internet communications.展开更多
A simple model of three coupled oscillators as an approximation of main modes behaviors in a spatial extended system is proposed. Multi-looping generalized synchronization and drift intermittent lag phase synchronizat...A simple model of three coupled oscillators as an approximation of main modes behaviors in a spatial extended system is proposed. Multi-looping generalized synchronization and drift intermittent lag phase synchronization phenomena are found in this simple model. For a certain of parameters in which chaotic-like intermittent behavior exhibit the amplitudes and phases of three modes are controlled to be synchronized states via coupling them with an external periodic mode.展开更多
AIM: To investigate the association between single nucleotide polymorphisms (SNPs) in the phosphatase and tensin homolog (PTEN) tumor suppressor gene and risk of colon cancer. METHODS: We utilized a population-based c...AIM: To investigate the association between single nucleotide polymorphisms (SNPs) in the phosphatase and tensin homolog (PTEN) tumor suppressor gene and risk of colon cancer. METHODS: We utilized a population-based casecontrol study of incident colon cancer individuals (n= 421) and controls (n = 483) aged ≥ 30 years to conduct a comprehensive tagSNP association analysis of the PTEN gene. RESULTS: None of the PTEN SNPs were statistically significantly associated with colon cancer when controlled for age, gender, and race, or when additionally adjusted for other known risk factors (P > 0.05). Haplotype analyses similarly showed no association between the PTEN gene and colon cancer. CONCLUSION: Our study does not support PTEN as a colon cancer susceptibility gene.展开更多
The digital communication in a system of two multi-mode solid state chaotic lasers is investigated theoretically. If the usual method working well in a single-mode laser system is applied to a multi-mode laser system,...The digital communication in a system of two multi-mode solid state chaotic lasers is investigated theoretically. If the usual method working well in a single-mode laser system is applied to a multi-mode laser system, the memory effect of the two nearest digits can cause high rate of mistakes when the digits are decoded through the subtraction of receiver output from the transmittal. By introducing the deviations of two nearest maximum and minimum fluctuationsof the signal to decode the digit, the message can be decoded correctly. Also, this communication method does not critically depend on the quality of the chaotic synchronization of the two multi-mode lasers.展开更多
In this paper we describe a full-integrated circuit containing all building blocks of a completed PLL-based synthesizer except for low pass filter(LPF). The frequency synthesizer is designed for a frequency hopping ...In this paper we describe a full-integrated circuit containing all building blocks of a completed PLL-based synthesizer except for low pass filter(LPF). The frequency synthesizer is designed for a frequency hopping (FH) transceiver operating up to 1.5 GHz as a local oscillator. The architecture of Voltage Controlled Oscillator (VCO) is optimized to get better performance, and a phase noise of -111.85-dBc/Hz @ 1 MHz and a tuning range of 250 MHz are gained at a centre frequency of 1.35 GHz. A novel Dual-Modulus Prescaler(DMP) is designed to achieve a very low jitter and a lower power. The settling time of PLL is 80 μs while the reference frequency is 400 KHz.This monolithic frequency synthesizer is to integrate all main building blocks of PLL except for the low pass filter, with a maximum VCO output frequency of 1.5 GHz, and is fabricated with a 0.18 μm mixed signal CMOS process. Low power dissipation, low phase noise, large tuning range and fast settling time are gained in this design.展开更多
Spin parity effect on magnetic relaxation by quantum tunneling in the biaxial spin model is studied by taking into account the transverse local stray field. It is shown that the square root time dependence in the even...Spin parity effect on magnetic relaxation by quantum tunneling in the biaxial spin model is studied by taking into account the transverse local stray field. It is shown that the square root time dependence in the even resonance occurs in the presence of a distribution of transverse anisotropic parameters, while the odd resonance always shows exponential relaxation. Magnetic relaxation under a sweeping field is also studied. The variation of the relaxation curve with the increasing distribution width of the local stray field for even resonance is qualitatively different from that of the odd resonance. The theoretical result on even resonance is in agreement with experimental results on Fe8 system, while the prediction for odd resonance awaits the experimental verification.展开更多
基金supported by the National Key Research and Development Program of China(2021YFA1500500,2019-YFA0405600)the CAS Project for Young Scientists in Basic Research(YSBR-051)+6 种基金the National Science Fund for Distinguished Young Scholars(21925204)the National Natural Science Foundation of China(22202192,U19A2015,22221003,22250007,22163002)the Collaborative Innovation Program of Hefei Science Center,CAS(2022HSCCIP004)the International Partnership,the DNL Cooperation Fund,CAS(DNL202003)the USTC Research Funds of the Double First-Class Initiative(YD9990002016,YD999000-2014)the Program of Chinese Academy of Sciences(123GJHZ2022101GC)the Fundamental Research Funds for the Central Universities(WK9990000095,WK999000-0124).
文摘Electrocatalytic water splitting provides an efficient method for the production of hydrogen.In electrocatalytic water splitting,the oxygen evolution reaction(OER)involves a kinetically sluggish four-electron transfer process,which limits the efficiency of electrocatalytic water splitting.Therefore,it is urgent to develop highly active OER catalysts to accelerate reaction kinetics.Coupling single atoms and clusters in one system is an innovative approach for developing efficient catalysts that can synergistically optimize the adsorption and configuration of intermediates and improve catalytic activity.However,research in this area is still scarce.Herein,we constructed a heterogeneous single-atom cluster system by anchoring Ir single atoms and Co clusters on the surface of Ni(OH)_(2)nanosheets.Ir single atoms and Co clusters synergistically improved the catalytic activity toward the OER.Specifically,Co_(n)Ir_(1)/Ni(OH)_(2)required an overpotential of 255 mV at a current density of 10 mA·cm^(−2),which was 60 mV and 67 mV lower than those of Co_(n)/Ni(OH)_(2)and Ir1/Ni(OH)_(2),respectively.The turnover frequency of Co_(n)Ir_(1)/Ni(OH)_(2)was 0.49 s^(−1),which was 4.9 times greater than that of Co_(n)/Ni(OH)_(2)at an overpotential of 300 mV.
文摘A behavioral model of the photodiode is presented.The model describes the relationship between photocurrent and incident optical power,and it also illustrates the impact of the reverse bias to the variation of the junction capacitance.According to this model,the photodiode and a CMOS receiver circuit are simulated and designed simultaneously under a universal circuit simulation environment.
文摘This paper presents a general approach for determining the configuration number for any linkage: A kinematic cham (KC) can be divided into some basic kinematic chains (BKCs) and driving joints; there are only 33 kinds of BKCs with υ =1-4 independent loop, containing only R (revolute) joints and their configuration numbers are given; the configuration number of a KC equals to the multiplication of the configuration numbers of BKCs contained in the KC.
文摘The hardware optimization technique of mono similarity system generation is presented based on hardware/software(HW/SW) co design.First,the coarse structure of sub graphs' matching based on full customized HW/SW co design is put forward.Then,a universal sub graphs' combination method is discussed.Next,a more advanced vertexes' compression algorithm based on sub graphs' combination method is discussed with great emphasis.Experiments are done successfully with perfect results verifying all the formulas and the methods above.
文摘In recent years,there have been numerous studies on Fenton or Fenton-like reactions mediated by nonfree radicals such as singlet oxygen(1O_(2));however,there are few studies on the synergistic effect of 1O_(2) and free radicals on the degradation of organic molecules,such as phenol in Fenton reaction.In this study,a cocatalyst,CoP,commonly used in photocatalysis was synthesized using a simple two-step method,and a CoP/Fe^(2+)/AM1.5 system was constructed by introducing Fe^(2+)and simulated sunlight(AM1.5)irradiation.The newly constructed CoP/Fe^(2+)/AM1.5 system could effectively degrade various organic pollutants,including dyes,phenols,and antibiotics.Radical quenching experiments and electron paramagnetic resonance detection confirmed that there were three reactive oxygen species(ROS)in the CoP/Fe^(2+)/AM1.5 system,including·OH_(ads),·O_(2)^(-),and 1O_(2).Further,combined with the liquid chromatogram of phenol,its intermediate products,and the fluorescence diagram of o-hydroxybenzoic acid,it can be concluded that a synergistic effect exists between 1O_(2) and the surface-adsorbed·OH_(ads) in the CoP/Fe^(2+)/AM1.5 system.The controllable formation of surface 1O_(2) and·OH_(ads) was achieved through the oxidation(Co^(3+))and reduction(Pδ−)centers exposed on the CoP surface,and the synergistic effect between them results in phenol’s hydroxylation,ring-opening,and degradation.The study of this new mechanism provides a new perspective for revealing the surface interface reaction between ROS and organic pollutants.
文摘In this paper, we describe all the divisible semiring congruences on a distributive semiring S and also establish a one_to_one, inclusion_preserving mapping from the set of full, closed, self_conjagate, ideal subsemirings of S to the set of all divisible semiring congruences on S.
基金Projects(61073187,61161006) supported by the National Nature Science Foundation of ChinaProject supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry,China
文摘To design a hyperchaotic generator and apply chaos into secure communication, a linear unidirectional coupling control is applied to two identical simplified Lorenz systems. The dynamical evolution process of the coupled system is investigated with variations of the system parameter and coupling coefficients. Particularly, the influence of coupling strength on dynamics of the coupled system is analyzed in detail. The range of the coupling strength in which the coupled system can generate hyperchaos or realize synchronization is determined, including phase portraits, Lyapunov exponents, and Poincare section. And the critical value of the system parameter between hyperchaos and synchronization is also found with fixed coupled strength. In addition, abundant dynamical behaviors such as four-wing hyperchaotic, two-wing chaotic, single-wing coexisting attractors and periodic orbits are observed and chaos synchronization error curves are also drawn by varying system parameter c. Numerical simulations are implemented to verify the results of these investigations.
文摘The inclusive differential cross sections of the ^7 Li nucleus in a reaction induced by ^6He on a ^9Be target are measured at an incident energy of 25 MeV/nucleon. Finite-range distorted-wave Born approximation calculations suggest that these ^7 Li particles are formed in a direct single-proton pickup reaction ^9Be(^6He,^7 Li)^8Li. The experimental data can be well reproduced by taking into account of the contributions of both the ground states and the first excited states of ^7Li and ^8Li.
基金Foundation item: Projects(50708093, 50808159) supported by the National Natural Science Foundation of China
文摘In order to improve the reliability of the design and calculation of single piles under the combined vertical and lateral loads, the solutions were presented based on the subgrade reaction method, in which the ultimate soil resistance was considered and the coefficient of subgrade reaction was assumed to be a constant. The corresponding computational program was developed using FORTRAN language. A comparison between the obtained solutions and the model test results was made to show the validity of the obtained solutions. The calculation results indicate that both the maximum lateral displacement and bending moment increase with the increase of the vertical and lateral loads and the pile length above ground, while decrease as the pile stiffness, the coefficient of subgrade reaction and the yielding displacement of soil increase. It is also shown that the pile head condition controls the pile responses and the vertical load may cause the instability problem to the pile. In general, the proposed method can be employed to calculate the pile responses independent of the magnitude of the pile deflection.
基金Foundation item: Supported by NSF of China(10471112) Supported by Shaanxi Provincial Natural Science Foundation(2005A15) Acknowledgement The authors express their gratitude to the referees for very helpful and detailed comments.
文摘It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.
文摘The paper design a double eccentric mass driven spherical robot, the ball is also subject to eccentric force and inertia force that generate by internal drive units in movement. Due to the unique spherical shell, the robot in the dynamic state transition process, Friction cannot offset the robot motion state change due to internal driving motion error of small units. In order to make linear movement of the spherical robot that can smooth start, stop and speed control, the paper design a method for linear motion driven spherical robot with double eccentric mass control. The improved driving eccentric mass of robot total mass ratio is larger, that can provide the eccentric torque and inertia moment more, the robot has higher motion velocity.
文摘A constructive theorem is established for generalized synchronization (GS) related to C<SUP>1</SUP> diffeomorphic transformations of unidirectionally coupled dynamical arrays. The theorem provides some interpretations about the underlying mechanism of various GS phenomena in nature. As a direct application of the theorem, a chaos-based secure Internet communication scheme is proposed. Moreover, a cellular neural network (CNN) of Chen's chaotic circuits with GS property is designed and studied. Numerical simulation shows that this Chen's CNN has high security and is fast and reliable for secure Internet communications.
文摘A simple model of three coupled oscillators as an approximation of main modes behaviors in a spatial extended system is proposed. Multi-looping generalized synchronization and drift intermittent lag phase synchronization phenomena are found in this simple model. For a certain of parameters in which chaotic-like intermittent behavior exhibit the amplitudes and phases of three modes are controlled to be synchronized states via coupling them with an external periodic mode.
文摘AIM: To investigate the association between single nucleotide polymorphisms (SNPs) in the phosphatase and tensin homolog (PTEN) tumor suppressor gene and risk of colon cancer. METHODS: We utilized a population-based casecontrol study of incident colon cancer individuals (n= 421) and controls (n = 483) aged ≥ 30 years to conduct a comprehensive tagSNP association analysis of the PTEN gene. RESULTS: None of the PTEN SNPs were statistically significantly associated with colon cancer when controlled for age, gender, and race, or when additionally adjusted for other known risk factors (P > 0.05). Haplotype analyses similarly showed no association between the PTEN gene and colon cancer. CONCLUSION: Our study does not support PTEN as a colon cancer susceptibility gene.
基金The project supported by Natural Science Foundation of Jiangsu Province of China under Grant No.BK2001138
文摘The digital communication in a system of two multi-mode solid state chaotic lasers is investigated theoretically. If the usual method working well in a single-mode laser system is applied to a multi-mode laser system, the memory effect of the two nearest digits can cause high rate of mistakes when the digits are decoded through the subtraction of receiver output from the transmittal. By introducing the deviations of two nearest maximum and minimum fluctuationsof the signal to decode the digit, the message can be decoded correctly. Also, this communication method does not critically depend on the quality of the chaotic synchronization of the two multi-mode lasers.
文摘In this paper we describe a full-integrated circuit containing all building blocks of a completed PLL-based synthesizer except for low pass filter(LPF). The frequency synthesizer is designed for a frequency hopping (FH) transceiver operating up to 1.5 GHz as a local oscillator. The architecture of Voltage Controlled Oscillator (VCO) is optimized to get better performance, and a phase noise of -111.85-dBc/Hz @ 1 MHz and a tuning range of 250 MHz are gained at a centre frequency of 1.35 GHz. A novel Dual-Modulus Prescaler(DMP) is designed to achieve a very low jitter and a lower power. The settling time of PLL is 80 μs while the reference frequency is 400 KHz.This monolithic frequency synthesizer is to integrate all main building blocks of PLL except for the low pass filter, with a maximum VCO output frequency of 1.5 GHz, and is fabricated with a 0.18 μm mixed signal CMOS process. Low power dissipation, low phase noise, large tuning range and fast settling time are gained in this design.
基金National Natural Science Foundation of China under Grant No.10575045
文摘Spin parity effect on magnetic relaxation by quantum tunneling in the biaxial spin model is studied by taking into account the transverse local stray field. It is shown that the square root time dependence in the even resonance occurs in the presence of a distribution of transverse anisotropic parameters, while the odd resonance always shows exponential relaxation. Magnetic relaxation under a sweeping field is also studied. The variation of the relaxation curve with the increasing distribution width of the local stray field for even resonance is qualitatively different from that of the odd resonance. The theoretical result on even resonance is in agreement with experimental results on Fe8 system, while the prediction for odd resonance awaits the experimental verification.