With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the it...With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.展开更多
Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the...Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions展开更多
In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operato...In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.展开更多
A two-phase monadic approach is presented for monadically slicing programs with procedures. In the monadic slice algorithm for interprocedural programs, phase 1 initializes the slice table of formal parameters in a pr...A two-phase monadic approach is presented for monadically slicing programs with procedures. In the monadic slice algorithm for interprocedural programs, phase 1 initializes the slice table of formal parameters in a procedure with the given labels, and then captures the callees' influence on callers when analyzing call statements. Phase 2 captures the callees' dependence on callers by replacing all given labels appearing in the corresponding sets of formal parameters. By the introduction of given labels, this slice method can obtain similar summary information in system-dependence-graph(SDG)-based algorithms for addressing the calling-context problem. With the use of the slice monad transformer, this monadic slicing approach achieves a high level of modularity and flexibility. It shows that the monadic interprocedural algorithm has less complexity and it is not less precise than SDG algorithms.展开更多
In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x...By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.展开更多
The electronic structure of catalytic active sites can be influenced by modulating the coordination bonding of the central single metal atom,but it is difficult to achieve.Herein,we reported the single Zn-atom incorpo...The electronic structure of catalytic active sites can be influenced by modulating the coordination bonding of the central single metal atom,but it is difficult to achieve.Herein,we reported the single Zn-atom incorporated dual doped P,N carbon framework(Zn-N_(4)P/C)for ORR via engineering the surrounding coordination environment of active centers.The Zn-N_(4)P/C catalyst exhibited comparable ORR activity(E_(1/2)=0.86 V)and significantly better ORR stability than that of Pt/C catalyst.It also shows respectable performance in terms of maximum peak power density(249.6 mW cm^(-2)),specific capacitance(779 mAh g^(-1)),and charge-discharge cycling stability for 150 hours in Zn-air battery.The high catalytic activity is attributed to the uniform active sites,tunable electronic/geometric configuration,optimized intrinsic activity,and faster mass transfer during ORR-pathway.Further,theoretical results exposed that the Zn-N_(4)P configuration is more electrochemically active as compared to Zn-N_(4) structure for the oxygen reduction reaction.展开更多
In this paper we introduce two sequences of operator functions and their dualfunctions: fk(t) = (flogt)k-(t-1)k/log^k+2t (k = 1,2,...), gk(t) = (t-1)k-logkt /log^k+1t (k = 1,2,...) and fk(t)tklog^k...In this paper we introduce two sequences of operator functions and their dualfunctions: fk(t) = (flogt)k-(t-1)k/log^k+2t (k = 1,2,...), gk(t) = (t-1)k-logkt /log^k+1t (k = 1,2,...) and fk(t)tklog^k+1t/(tlogt)k-(t-1)^k(k=1,2…),gk(t)=t^klog^k+1t/(t-1)^k-log^kt(k=1,2…)defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t+1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].展开更多
This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used t...This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving (H, η)-monotone mappings.展开更多
An analytic phenomenological shell model mass formula for light nuclei is constructed. The formula takes into account the non locality of the self consistent single particle potential and the special features of light...An analytic phenomenological shell model mass formula for light nuclei is constructed. The formula takes into account the non locality of the self consistent single particle potential and the special features of light nuclei, namely: (a) charge and mass distributions are closer to a Gaussian shape than to the shape characteristic in medium and heavy nuclei; (b) the central charge and mass densities are larger than, and decrease towards, the "asymptotic" values that are the reference parameters for nuclear matter; and (c) after a shell closure, the next level has a larger orbital angular momentum and a noticeably larger mean square radius. Only then a good numerical fit is obtained with parameters consistent with optical model analysis and empirical spin-orbit couplings. A correlation between the "skin effect" and the symmetry dependence of the optical potential is established. Towards the neutron drip line the potential well depth, the spin-orbit splitting of the single particle levels and the gap between major shells decrease, as has been observed. The ensuing shift and contraction of the single particle level scheme may lead to: (a) to strong configuration mixing and new magic numbers, and (b) the onset of the halo effect, to avoid the expulsion of single particle levels to the continuum.展开更多
In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational ineq...In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.展开更多
The syntheses and structures of trinuclear Mo (W)-Fe-S cluster[MFe2S2(CO)8 (S,CNSEt2)]- (M=Mo, W), hexanuclear Fe-S cluster [Fe6S6-(CO)12]2- and undecanuclear Cu-Fe-S cluster [Cu5Fe6S6(CO)18(PPh3)2]-, containingFe2S2(...The syntheses and structures of trinuclear Mo (W)-Fe-S cluster[MFe2S2(CO)8 (S,CNSEt2)]- (M=Mo, W), hexanuclear Fe-S cluster [Fe6S6-(CO)12]2- and undecanuclear Cu-Fe-S cluster [Cu5Fe6S6(CO)18(PPh3)2]-, containingFe2S2(CO)6-units bave been summarized and the important vestiges left in their struc-tures reflecting the formation processes of the clusters have been found and discussed.Further inspecting some other typical clusters a regular unit construction in the forma-tion of the metal cluster compounds containing Fe2S2(CO)6-units has been figured outand applied to speculate and predict several new cluster compounds containing Fe2S2(CO)6-units.展开更多
Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ) of the Schrodinger algebra S(1)are dete...Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ) of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.展开更多
Abstrac In this paper, we discuss the existence of the solution and coupled minimal and maximal quasi-solutions for nonlinear non-monotone operator equation x = A(x, x), improved and generalized many relevant results.
We utilize Park's maximal element theorem in H-space to prove the existence theorems of solutions of the complementarity problems for multivalued non-monotone operators in Banach spaces.
In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further,...In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.展开更多
In this paper we modify approximate trust region methods via three precon ditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, ...In this paper we modify approximate trust region methods via three precon ditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, we employ the stable Bunch-Parlett factorization method of symmetric matrices and use the unit lower triangular matrix as a preconditioner of the optimal path and modified gradient path. In order to accelerate the preconditional conjugate gradient path, we use preconditioner to improve the eigenvalue distribution of Hessian matrix. Based on the trial steps produced by the trust region subproblem along the three curvilinear paths providing a direction of sufficient descent, we mix a strategy using both trust region and nonmonotonic line search techniques which switch to back tracking steps when a trial step is unacceptable. Theoretical analysis is given to prove that the proposed algorithms are globally convergent and have a local su-pcrlinear convergent rate under some reasonable conditions. The results of the numerical experiment are reported to show the effectiveness of the proposed algorithms.展开更多
By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s (Ω) of nonlinear boundary value probl...By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s (Ω) of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈+∞, and 2N/N+1 〈 p ≤ 2 for N(≥ 1) which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.展开更多
In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved tha...In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that ue converges weakly in W1,P(Ω) (and even in some multiscale sense), as ε→ 0 to the solution uo of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results.展开更多
文摘With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.
文摘Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions
文摘In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.
基金The National Outstanding Young Scientist Foundation by NSFC(No.60703086,60503020)
文摘A two-phase monadic approach is presented for monadically slicing programs with procedures. In the monadic slice algorithm for interprocedural programs, phase 1 initializes the slice table of formal parameters in a procedure with the given labels, and then captures the callees' influence on callers when analyzing call statements. Phase 2 captures the callees' dependence on callers by replacing all given labels appearing in the corresponding sets of formal parameters. By the introduction of given labels, this slice method can obtain similar summary information in system-dependence-graph(SDG)-based algorithms for addressing the calling-context problem. With the use of the slice monad transformer, this monadic slicing approach achieves a high level of modularity and flexibility. It shows that the monadic interprocedural algorithm has less complexity and it is not less precise than SDG algorithms.
文摘In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
基金Supported by the Scientific Research Foundation of Henan Provincial Education Com mittee(1999110018)
文摘By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.
文摘The electronic structure of catalytic active sites can be influenced by modulating the coordination bonding of the central single metal atom,but it is difficult to achieve.Herein,we reported the single Zn-atom incorporated dual doped P,N carbon framework(Zn-N_(4)P/C)for ORR via engineering the surrounding coordination environment of active centers.The Zn-N_(4)P/C catalyst exhibited comparable ORR activity(E_(1/2)=0.86 V)and significantly better ORR stability than that of Pt/C catalyst.It also shows respectable performance in terms of maximum peak power density(249.6 mW cm^(-2)),specific capacitance(779 mAh g^(-1)),and charge-discharge cycling stability for 150 hours in Zn-air battery.The high catalytic activity is attributed to the uniform active sites,tunable electronic/geometric configuration,optimized intrinsic activity,and faster mass transfer during ORR-pathway.Further,theoretical results exposed that the Zn-N_(4)P configuration is more electrochemically active as compared to Zn-N_(4) structure for the oxygen reduction reaction.
文摘In this paper we introduce two sequences of operator functions and their dualfunctions: fk(t) = (flogt)k-(t-1)k/log^k+2t (k = 1,2,...), gk(t) = (t-1)k-logkt /log^k+1t (k = 1,2,...) and fk(t)tklog^k+1t/(tlogt)k-(t-1)^k(k=1,2…),gk(t)=t^klog^k+1t/(t-1)^k-log^kt(k=1,2…)defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t+1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].
文摘This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving (H, η)-monotone mappings.
文摘An analytic phenomenological shell model mass formula for light nuclei is constructed. The formula takes into account the non locality of the self consistent single particle potential and the special features of light nuclei, namely: (a) charge and mass distributions are closer to a Gaussian shape than to the shape characteristic in medium and heavy nuclei; (b) the central charge and mass densities are larger than, and decrease towards, the "asymptotic" values that are the reference parameters for nuclear matter; and (c) after a shell closure, the next level has a larger orbital angular momentum and a noticeably larger mean square radius. Only then a good numerical fit is obtained with parameters consistent with optical model analysis and empirical spin-orbit couplings. A correlation between the "skin effect" and the symmetry dependence of the optical potential is established. Towards the neutron drip line the potential well depth, the spin-orbit splitting of the single particle levels and the gap between major shells decrease, as has been observed. The ensuing shift and contraction of the single particle level scheme may lead to: (a) to strong configuration mixing and new magic numbers, and (b) the onset of the halo effect, to avoid the expulsion of single particle levels to the continuum.
文摘In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.
文摘The syntheses and structures of trinuclear Mo (W)-Fe-S cluster[MFe2S2(CO)8 (S,CNSEt2)]- (M=Mo, W), hexanuclear Fe-S cluster [Fe6S6-(CO)12]2- and undecanuclear Cu-Fe-S cluster [Cu5Fe6S6(CO)18(PPh3)2]-, containingFe2S2(CO)6-units bave been summarized and the important vestiges left in their struc-tures reflecting the formation processes of the clusters have been found and discussed.Further inspecting some other typical clusters a regular unit construction in the forma-tion of the metal cluster compounds containing Fe2S2(CO)6-units has been figured outand applied to speculate and predict several new cluster compounds containing Fe2S2(CO)6-units.
文摘Over an algebraically closed field of characteristic p>2,based on the results on the representation theory of special linear Lie algebra sl(2),restricted simple modules L(λ) of the Schrodinger algebra S(1)are determined,and all derivations of S(1)on L(λ)are also obtained.As an application,the first cohomology of S(1)with the coefficient in L(λ)is determined.
文摘Abstrac In this paper, we discuss the existence of the solution and coupled minimal and maximal quasi-solutions for nonlinear non-monotone operator equation x = A(x, x), improved and generalized many relevant results.
基金the Foundation of Jiangsu Education Committee (04KJD110170)the Foundation of Univer-sity of Science and Technology of Suzhou.
文摘We utilize Park's maximal element theorem in H-space to prove the existence theorems of solutions of the complementarity problems for multivalued non-monotone operators in Banach spaces.
基金Supported by the Natural Science Foundation of Guizhou university(200101007)
文摘In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.
文摘In this paper we modify approximate trust region methods via three precon ditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, we employ the stable Bunch-Parlett factorization method of symmetric matrices and use the unit lower triangular matrix as a preconditioner of the optimal path and modified gradient path. In order to accelerate the preconditional conjugate gradient path, we use preconditioner to improve the eigenvalue distribution of Hessian matrix. Based on the trial steps produced by the trust region subproblem along the three curvilinear paths providing a direction of sufficient descent, we mix a strategy using both trust region and nonmonotonic line search techniques which switch to back tracking steps when a trial step is unacceptable. Theoretical analysis is given to prove that the proposed algorithms are globally convergent and have a local su-pcrlinear convergent rate under some reasonable conditions. The results of the numerical experiment are reported to show the effectiveness of the proposed algorithms.
基金This research is supported by the National Natural Science Foundation of China(No. 10471033).
文摘By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s (Ω) of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈+∞, and 2N/N+1 〈 p ≤ 2 for N(≥ 1) which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.
文摘In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that ue converges weakly in W1,P(Ω) (and even in some multiscale sense), as ε→ 0 to the solution uo of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results.