This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this n...This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.展开更多
Nanograined(NG)materials often suffer from low thermal stability owing to the high volume fraction of grain boundaries(GBs).Herein,we investigate the possibility of utilizing local chemical ordering(LCO)for improving ...Nanograined(NG)materials often suffer from low thermal stability owing to the high volume fraction of grain boundaries(GBs).Herein,we investigate the possibility of utilizing local chemical ordering(LCO)for improving the thermal stability of NG FeCoNiCrMn highentropy alloys(HE As).NG HE As with two different grain sizes were considered.Tensile tests and creep test simulations were then performed to reveal the influence of LCO on the mechanical properties and thermal stability of NG HE As.After performing hybrid molecular dynamics and Monte Carlo simulations,Cr atoms were found to accumulate at GBs.By analyzing the atomic structure evolution during the deformation process,we found that the formation of LCO effectively stabilized the GBs and inhibited GB movement.In addition,dislocation nucleation from GBs and dislocation movement was also hindered.The inhibiting effect of LCO on GB movement and dislocation activity is more prominent than in the NG model with smaller grain sizes.The current simulation results suggest a possible strategy for enhancing the thermal stability of NG HEAs for service in a high-temperature environment.展开更多
Multi-principal element alloys(MPEAs)have attracted much attention as future nuclear materials due to their extraordinary radiation resistances.In this work,we have elucidated the development of local chemical orderin...Multi-principal element alloys(MPEAs)have attracted much attention as future nuclear materials due to their extraordinary radiation resistances.In this work,we have elucidated the development of local chemical orderings(LCOs)and their influences on radiation damage behavior in the typical CrFeNi MPEA by hybrid-molecular dynamics and Monte Carlo simulations.It was found that considerable LCOs consist-ing of the Cr-Cr and Ni-Fe short-range orders existed in the ordered configuration with optimized system energy.Through modeling the accumulation cascades up to 1000 recoils,we revealed that the size of de-fect clusters and dislocation loops is smaller in the ordered configuration than those in the random one,although the former formed more Frenkel pairs(i.e.,self-interstitials and vacancies).In addition,the dis-tribution of dislocation loops is relatively more dispersed in the ordered configuration,and the stair-rod dislocations related to irradiation swelling are also smaller,implying that the existence of LCOs is con-ducive to enhancing radiation damage tolerance.To understand the underlying mechanism,the effects of LCOs on the formation and evolution of defects and radiation resistance were discussed from the aspects of atomic bonding,migration path,and energy of defect diffusion,which provides theoretical guidance for the design of MPEAs with enhanced radiation resistance.展开更多
Fractional calculus is a powerful tool for modeling nonlinear systems.It is necessary to discuss the basic properties of fractional order before solving a fractional order model.Using the formula of power function def...Fractional calculus is a powerful tool for modeling nonlinear systems.It is necessary to discuss the basic properties of fractional order before solving a fractional order model.Using the formula of power function defined by local fractional derivative and the chain rule to calculate a compound function,the results are inconsistent.This shows that the chain rule of local fractional derivatives similar to classical calculus is suspicious,and fractional complex transformation based on the chain rule is also suspicious and needs further discussion.In order to overcome this inconsistency,an improved definition of local fractional derivative,which can be regarded as a fractal derivative,is proposed based on the results derived from the relationship between the mass function and the Hausdorff measure.展开更多
The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the correspondi...The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.展开更多
In this paper, a new mechanism for the emergence of scale-free distribution is proposed. It is more realistic than the existing mechanism. Based on our mechanism, a model responsible for the scale-free distribution wi...In this paper, a new mechanism for the emergence of scale-free distribution is proposed. It is more realistic than the existing mechanism. Based on our mechanism, a model responsible for the scale-free distribution with an exponent in a range of 3-to-5 is given. Moreover, this model could also reproduce the exponential distribution that is discovered in some real networks. Finally, the analytical result of the model is given and the simulation shows the validity of our result,展开更多
In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the cor...In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the corresponding well known Fredholm integral equation of second kind. The considered in this paper has been solved already numerically in [1].展开更多
The crystallization behavior of silica-filled polydimethylsiloxane(PDMS)was investigated in detail by^(1)H solid-state nuclear magnetic resonance(^(1)H SS-NMR)in combination with synchrotron radiation wide-angle X-ray...The crystallization behavior of silica-filled polydimethylsiloxane(PDMS)was investigated in detail by^(1)H solid-state nuclear magnetic resonance(^(1)H SS-NMR)in combination with synchrotron radiation wide-angle X-ray scattering(WAXS),and temperature-modulated differential scanning calorimetry(TMDSC)techniques.For neat PDMS,no apparent difference is observed for the crystallinity characterized by^(1)H SS-NMR and WAXS at low-temperature regions.However,upon filler addition,a 15%-35%lower difference in crystallinity is observed measured by^(1)H SS-NMR compared to WAXS.The origin of such mismatch was explored through multi-component structural,dynamics,and chain-order analysis of PDMS samples with different filler fractions.The 1D integrated WAXS results of PDMS with different filler fractions at different temperatures show that the packing structure as well as crystal size basically remain unchanged,but as the filler fraction increases from 0 phr to 60 phr,the rigid component’s dynamics order parameter S_(r)obtained by^(1)H SS-NMR decreases from 0.70 to 0.55.The filler fraction-dependent crystallinity calculated based on S_(r)was compared with experimental values,revealing a behavior of decreasing order in the crystalline region.Combining with the results of accelerated chain dynamics in crystalline region as reflected by T_(2)values,the molecular origin is attributed to the formation of CONDIS crystals,whose conformational order is lost but the position and orientation orders are kept.Such hypothesis is further supported by the TMDSC results,where,as the filler fraction increases from 0 phr to 60 phr,the melting range widens from 8.77 K to 14.56 K,representing a growth of166%.In addition to previous reports related to the condition for forming CONDIS mesophase,i.e.,temperature,pressure,and stretching,the nano-sized filler could also introduce the local conformational disorder for chain packing.展开更多
Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the charact...Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave number spectrum of ocean waves. As an illustrative example, a fully developed wind generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.展开更多
In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation functi...In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.展开更多
The nonlocal symmetry of the generalized fifth order KdV equation(FOKdV) is first obtained by using the related Lax pair and then localizing it in a new enlarged system by introducing some new variables. On this basis...The nonlocal symmetry of the generalized fifth order KdV equation(FOKdV) is first obtained by using the related Lax pair and then localizing it in a new enlarged system by introducing some new variables. On this basis, new Ba¨cklund transformation is obtained through Lie’s first theorem. Furthermore, the general form of Lie point symmetry for the enlarged FOKdV system is found and new interaction solutions for the generalized FOKdV equation are explored by using a symmetry reduction method.展开更多
In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solutio...In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.展开更多
The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of C...The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of China(Legislation Law) has led to two divergent views. One holds that "the local laws of cities with subordinate districts should take precedence over the regulations of provincial governments," while the other supports the exact opposite. This is a value judgment issue in legislation. To reach a solution, we need to clarify the premises based on the characteristics of the laws in question so that a basic common ground can be established for discussion. The first premise for traditional legislation is that a law should be based on experience as well as logic; the second is that the experience of authority subjects, plus the three aspects of logic should outweigh the experience of social subjects, plus the three aspects of logic. With respect to postmodern legislation, the first premise is that experience should override logic, and the second is that the experience of the authority subject should take precedence over that of social subject, with no requirements for logical consistency. Since Legislation Law fal s into the category of postmodern legislation, according to the premises, the argument that the local laws of cities with subordinate districts should take precedence enjoys wider acceptance, but the view is logically challenged in terms of conceptual consistency, system consistency and principle consistency. More studies must be conducted to facilitate the discussion.展开更多
文摘This paper deals with extensions of higher-order optimality conditions for scalar optimization to multiobjective optimization.A type of directional derivatives for a multiobjective function is proposed,and with this notion characterizations of strict local minima of order k for a multiobjective optimization problem with a nonempty set constraint are established,generalizing the corresponding scalar case obtained by Studniarski[3].Also necessary not sufficient and sufficient not necessary optimality conditions for this minima are derived based on our directional derivatives,which are generalizations of some existing scalar results and equivalent to some existing multiobjective ones.Many examples are given to illustrate them there.
基金financially supported by the National Natural Science Foundation of China(Nos.52101019,52071023,51901013,52122408)the financial support from the Fundamental Research Funds for theCentral Universities(University of Science and Technology Beijing,Nos.FRF-TP-2021-04C1,06500135)supported by USTB MatCom of Beijing Advanced Innovation Center for Materials Genome Engineering。
文摘Nanograined(NG)materials often suffer from low thermal stability owing to the high volume fraction of grain boundaries(GBs).Herein,we investigate the possibility of utilizing local chemical ordering(LCO)for improving the thermal stability of NG FeCoNiCrMn highentropy alloys(HE As).NG HE As with two different grain sizes were considered.Tensile tests and creep test simulations were then performed to reveal the influence of LCO on the mechanical properties and thermal stability of NG HE As.After performing hybrid molecular dynamics and Monte Carlo simulations,Cr atoms were found to accumulate at GBs.By analyzing the atomic structure evolution during the deformation process,we found that the formation of LCO effectively stabilized the GBs and inhibited GB movement.In addition,dislocation nucleation from GBs and dislocation movement was also hindered.The inhibiting effect of LCO on GB movement and dislocation activity is more prominent than in the NG model with smaller grain sizes.The current simulation results suggest a possible strategy for enhancing the thermal stability of NG HEAs for service in a high-temperature environment.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.51671021,11790293,51871016,52071024,and 51961160729)the Funds for Creative Research Groups of China(No.51921001)+1 种基金the 111 Project(No.B07003)the Fundamental Research Funds for the Central Universities.
文摘Multi-principal element alloys(MPEAs)have attracted much attention as future nuclear materials due to their extraordinary radiation resistances.In this work,we have elucidated the development of local chemical orderings(LCOs)and their influences on radiation damage behavior in the typical CrFeNi MPEA by hybrid-molecular dynamics and Monte Carlo simulations.It was found that considerable LCOs consist-ing of the Cr-Cr and Ni-Fe short-range orders existed in the ordered configuration with optimized system energy.Through modeling the accumulation cascades up to 1000 recoils,we revealed that the size of de-fect clusters and dislocation loops is smaller in the ordered configuration than those in the random one,although the former formed more Frenkel pairs(i.e.,self-interstitials and vacancies).In addition,the dis-tribution of dislocation loops is relatively more dispersed in the ordered configuration,and the stair-rod dislocations related to irradiation swelling are also smaller,implying that the existence of LCOs is con-ducive to enhancing radiation damage tolerance.To understand the underlying mechanism,the effects of LCOs on the formation and evolution of defects and radiation resistance were discussed from the aspects of atomic bonding,migration path,and energy of defect diffusion,which provides theoretical guidance for the design of MPEAs with enhanced radiation resistance.
基金Major Science and Technology Project in Shanxi Province of China(Nos.20181101008 and 20181102015)Supplementary Platform Project of“1331”Project in Shanxi Province in 2018,China。
文摘Fractional calculus is a powerful tool for modeling nonlinear systems.It is necessary to discuss the basic properties of fractional order before solving a fractional order model.Using the formula of power function defined by local fractional derivative and the chain rule to calculate a compound function,the results are inconsistent.This shows that the chain rule of local fractional derivatives similar to classical calculus is suspicious,and fractional complex transformation based on the chain rule is also suspicious and needs further discussion.In order to overcome this inconsistency,an improved definition of local fractional derivative,which can be regarded as a fractal derivative,is proposed based on the results derived from the relationship between the mass function and the Hausdorff measure.
文摘The solvability of the fifth-order nonlinear dispersive equation δtu＋au （δxu）^2＋βδx^3u＋γδx^5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem,it is proved that if the initial function u0 belongs to H^5（R） and s〉1/4,then the Cauchy problem has a unique solution in C（[-T,T],H^5（R）） for some T〉0.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 60374037 and 60574036）, the Program for New Century Excellent Talents of High Education of China（Grant No NCET 2005-290）, The Special Research Fund for the Doctoral Program of High Education of China （Grant No 20050055013）.Acknowledgments The authors would like to thank Réka Albert for useful discussion and are grateful to the anonymous referees for their valuable suggestions and comments, which have made this paper improved.
文摘In this paper, a new mechanism for the emergence of scale-free distribution is proposed. It is more realistic than the existing mechanism. Based on our mechanism, a model responsible for the scale-free distribution with an exponent in a range of 3-to-5 is given. Moreover, this model could also reproduce the exponential distribution that is discovered in some real networks. Finally, the analytical result of the model is given and the simulation shows the validity of our result,
文摘In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the corresponding well known Fredholm integral equation of second kind. The considered in this paper has been solved already numerically in [1].
基金financially supported by NSAF Joint Fund of China(No.U2030203)the National Natural Science Foundation of China(Nos.51973207 and 51903230)。
文摘The crystallization behavior of silica-filled polydimethylsiloxane(PDMS)was investigated in detail by^(1)H solid-state nuclear magnetic resonance(^(1)H SS-NMR)in combination with synchrotron radiation wide-angle X-ray scattering(WAXS),and temperature-modulated differential scanning calorimetry(TMDSC)techniques.For neat PDMS,no apparent difference is observed for the crystallinity characterized by^(1)H SS-NMR and WAXS at low-temperature regions.However,upon filler addition,a 15%-35%lower difference in crystallinity is observed measured by^(1)H SS-NMR compared to WAXS.The origin of such mismatch was explored through multi-component structural,dynamics,and chain-order analysis of PDMS samples with different filler fractions.The 1D integrated WAXS results of PDMS with different filler fractions at different temperatures show that the packing structure as well as crystal size basically remain unchanged,but as the filler fraction increases from 0 phr to 60 phr,the rigid component’s dynamics order parameter S_(r)obtained by^(1)H SS-NMR decreases from 0.70 to 0.55.The filler fraction-dependent crystallinity calculated based on S_(r)was compared with experimental values,revealing a behavior of decreasing order in the crystalline region.Combining with the results of accelerated chain dynamics in crystalline region as reflected by T_(2)values,the molecular origin is attributed to the formation of CONDIS crystals,whose conformational order is lost but the position and orientation orders are kept.Such hypothesis is further supported by the TMDSC results,where,as the filler fraction increases from 0 phr to 60 phr,the melting range widens from 8.77 K to 14.56 K,representing a growth of166%.In addition to previous reports related to the condition for forming CONDIS mesophase,i.e.,temperature,pressure,and stretching,the nano-sized filler could also introduce the local conformational disorder for chain packing.
文摘Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave number spectrum of ocean waves. As an illustrative example, a fully developed wind generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LY18F030023,LY17F030016,and LY18F020028)the National Natural Science Foundation of China(Grant Nos.61503338,61502422,and 61773348)
文摘In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11347183,11405110,11275129,and 11305106)the Natural Science Foundation of Zhejiang Province of China(Grant Nos.Y7080455 and LQ13A050001)
文摘The nonlocal symmetry of the generalized fifth order KdV equation(FOKdV) is first obtained by using the related Lax pair and then localizing it in a new enlarged system by introducing some new variables. On this basis, new Ba¨cklund transformation is obtained through Lie’s first theorem. Furthermore, the general form of Lie point symmetry for the enlarged FOKdV system is found and new interaction solutions for the generalized FOKdV equation are explored by using a symmetry reduction method.
文摘In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.
基金part of the results(presented in stages)of"Research on the Legislative System of Cities with Subordinate Districts"(16XFX004)-a program of National Social Sciences Fund in Western China"Empirical Research on Local Legislation"(16XW16)-a research focus of Sichuan Academy of Social Sciences under a key program launched by the Publicity Department of the CPC Sichuan Provincial Committee
文摘The lack of descriptions regarding the order of precedence between the local laws of cities with subordinate districts and the regulations of provincial governments in Legislation Law of the People's Republic of China(Legislation Law) has led to two divergent views. One holds that "the local laws of cities with subordinate districts should take precedence over the regulations of provincial governments," while the other supports the exact opposite. This is a value judgment issue in legislation. To reach a solution, we need to clarify the premises based on the characteristics of the laws in question so that a basic common ground can be established for discussion. The first premise for traditional legislation is that a law should be based on experience as well as logic; the second is that the experience of authority subjects, plus the three aspects of logic should outweigh the experience of social subjects, plus the three aspects of logic. With respect to postmodern legislation, the first premise is that experience should override logic, and the second is that the experience of the authority subject should take precedence over that of social subject, with no requirements for logical consistency. Since Legislation Law fal s into the category of postmodern legislation, according to the premises, the argument that the local laws of cities with subordinate districts should take precedence enjoys wider acceptance, but the view is logically challenged in terms of conceptual consistency, system consistency and principle consistency. More studies must be conducted to facilitate the discussion.
