This paper is a sequel to a previous paper （Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69（2）, 1364-1375 （2008）） in which the n...This paper is a sequel to a previous paper （Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69（2）, 1364-1375 （2008）） in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.展开更多
In the real world,one of the most common problems in project management is the unpredictability of resources and timelines.An efficient way to resolve uncertainty problems and overcome such obstacles is through an ext...In the real world,one of the most common problems in project management is the unpredictability of resources and timelines.An efficient way to resolve uncertainty problems and overcome such obstacles is through an extended fuzzy approach,often known as neutrosophic logic.Our rigorous proposed model has led to the creation of an advanced technique for computing the triangular single-valued neutrosophic number.This innovative approach evaluates the inherent uncertainty in project durations of the planning phase,which enhances the potential significance of the decision-making process in the project.Our proposed method,for the first time in the neutrosophic set literature,not only solves existing problems but also introduces a new set of problems not yet explored in previous research.A comparative study using Python programming was conducted to examine the effectiveness of responsive and adaptive planning,as well as their differences from other existing models such as the classical critical path problem and the fuzzy critical path problem.The study highlights the use of neutrosophic logic in handling complex projects by illustrating an innovative dynamic programming framework that is robust and flexible,according to the derived results,and sets the stage for future discussions on its scalability and application across different industries.展开更多
The Beijing SHRIMP Centre(BSC)celebrates its 10th Anniversary on 18 December 2011.It has become known as one of the most successful ion microprobe laboratories world-wide and is a world-class platform for isotopic dat...The Beijing SHRIMP Centre(BSC)celebrates its 10th Anniversary on 18 December 2011.It has become known as one of the most successful ion microprobe laboratories world-wide and is a world-class platform for isotopic dating.It has helped countless scientists to resolve critical geological problems and thus greatly promoting the development of the geological sciences in and outside China.展开更多
In this paper,we study the following critical elliptic problem with a variable exponent:{-Δu=u^(p+ϵa(x))inΩ,u>0 inΩ,u=0 on∂Ω,where a(x)2∈C^(2)(Ω),p=N+2/N-2,∈>0,andΩis a smooth bounded domain in R^(N)(N&g...In this paper,we study the following critical elliptic problem with a variable exponent:{-Δu=u^(p+ϵa(x))inΩ,u>0 inΩ,u=0 on∂Ω,where a(x)2∈C^(2)(Ω),p=N+2/N-2,∈>0,andΩis a smooth bounded domain in R^(N)(N>4).We show that for∈small enough,there exists a family of bubble solutions concentrating at the negative stable critical point of the function a(x).This is a new perturbation to the critical elliptic equation in contrast to the usual subcritical or supercritical perturbation,and gives the first existence result for the critical elliptic problem with a variable exponent.展开更多
The critical node problem(CNP)aims to deal with critical node identification in a graph,which has extensive applications in many fields.Solving CNP is a challenging task due to its computational complexity,and it attr...The critical node problem(CNP)aims to deal with critical node identification in a graph,which has extensive applications in many fields.Solving CNP is a challenging task due to its computational complexity,and it attracts much attention from both academia and industry.In this paper,we propose a population-based heuristic search algorithm called CPHS(Cut Point Based Heuristic Search)to solve CNP,which integrates two main ideas.The first one is a cut point based greedy strategy in the local search,and the second one involves the functions used to update the solution pool of the algorithm.Besides,a mutation strategy is applied to solutions with probability based on the overall average similarity to maintain the diversity of the solution pool.Experiments are performed on a synthetic benchmark,a real-world benchmark,and a large-scale network benchmark to evaluate our algorithm.Compared with state-of-the-art algorithms,our algorithm has better performance in terms of both solution quality and run time on all the three benchmarks.展开更多
The critical cross-section identification problem(CCIP)presents a significant and highly challenging issue in power grid analysis,aiming to identify a partition of the graph into two disjoint cuts that maximize the to...The critical cross-section identification problem(CCIP)presents a significant and highly challenging issue in power grid analysis,aiming to identify a partition of the graph into two disjoint cuts that maximize the total weight of the cut.Traditionally,critical cross-sections have been determined through manual experience or mechanistic analysis,and effective intelligent methods to address these issues are lacking.Therefore,we propose a deep reinforcement learning framework based on a greedy approach(DEER)to solve the CCIP problem.Initially,proven to be NP-hard,a greedy vertex merging approach is proposed that enables the acquisition of all CCIP solutions through vertex merging.To prevent the greedy algorithm from converging to local optima,a deep reinforcement learning(DRL)framework combined with vertex marking is proposed to simulate the Markov decision process of vertex merging.Through training the DRL model,repetitive searches for vertex marking can be effectively avoided.Furthermore,the greedy algorithm can be augmented with genetic algorithms to address CCIP.Extensive experiments demonstrate the effectiveness of the proposed methods in addressing CCIP.展开更多
Dictated handwriting samples are widely used in practice due to their simplicity,convenience,and practicality.However,dictation is typically listed as one of the many collection methods in textbooks and monographs,and...Dictated handwriting samples are widely used in practice due to their simplicity,convenience,and practicality.However,dictation is typically listed as one of the many collection methods in textbooks and monographs,and there is usually no separate section focusing on dictated handwriting samples.Therefore,further study of dictated handwriting samples will have important practical significance.Consideration of the definition,existing problems,collection techniques,and critical aspects of dictated handwriting samples willsupport investigators and document examiners in their professional abilities and contribute to the theoretical system of document examination.In this article,an exploratory analysis will be conducted and ideas about dictated handwriting samples will be shared,including the definition of dictated samples,their relationship to experimental samples,practical problems,feasible collection methods,and some critical points that require special attention.Dictation is widely used but problematic because of a lack of quantity and low levels of comparability.Those difficulties are mainly caused by a lack of theoreticalstudy and understanding of the requirements and collection techniques of dictated handwriting samples among first‑line investigators.Dictated samples should be collected based on subjective and objective conditions of formation with aims to improve comparability and five similarities.Further studies are needed to improve the theoretical system and practical use of dictated samples so that they can contribute to successfully reaching conclusions in investigations.展开更多
The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation o...The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval[a,b] R{-u＇＇=（λf（x,u）＋g（u））h（u＇）,in（a,b）,u（a）=u（b）=0under ppropriate hypotheses.We exhibit the existence of at least three（weak）solutions and,and the results are illustrated by examples.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10871096)the Foun-dation of Major Project of Science and Technology of Chinese Education Ministry (No. 205056)+2 种基金the Project of Graduate Education Innovation of Jiangsu Province (No. CX09B_284Z)the Foundation for Outstanding Doctoral Dissertation of Nanjing Normal Universitythe Foundation for Young Teachers of Jiangnan University (No. 2008LQN008)
文摘This paper is a sequel to a previous paper （Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69（2）, 1364-1375 （2008）） in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.
文摘In the real world,one of the most common problems in project management is the unpredictability of resources and timelines.An efficient way to resolve uncertainty problems and overcome such obstacles is through an extended fuzzy approach,often known as neutrosophic logic.Our rigorous proposed model has led to the creation of an advanced technique for computing the triangular single-valued neutrosophic number.This innovative approach evaluates the inherent uncertainty in project durations of the planning phase,which enhances the potential significance of the decision-making process in the project.Our proposed method,for the first time in the neutrosophic set literature,not only solves existing problems but also introduces a new set of problems not yet explored in previous research.A comparative study using Python programming was conducted to examine the effectiveness of responsive and adaptive planning,as well as their differences from other existing models such as the classical critical path problem and the fuzzy critical path problem.The study highlights the use of neutrosophic logic in handling complex projects by illustrating an innovative dynamic programming framework that is robust and flexible,according to the derived results,and sets the stage for future discussions on its scalability and application across different industries.
文摘The Beijing SHRIMP Centre(BSC)celebrates its 10th Anniversary on 18 December 2011.It has become known as one of the most successful ion microprobe laboratories world-wide and is a world-class platform for isotopic dating.It has helped countless scientists to resolve critical geological problems and thus greatly promoting the development of the geological sciences in and outside China.
基金supported by National Natural Science Foundation of China(Grant No.11971147)supported by National Natural Science Foundation of China(Grant Nos.11831009 and 12171183)the Fundamental Research Funds for the Central Universities(Grant No.KJ02072020-0319).
文摘In this paper,we study the following critical elliptic problem with a variable exponent:{-Δu=u^(p+ϵa(x))inΩ,u>0 inΩ,u=0 on∂Ω,where a(x)2∈C^(2)(Ω),p=N+2/N-2,∈>0,andΩis a smooth bounded domain in R^(N)(N>4).We show that for∈small enough,there exists a family of bubble solutions concentrating at the negative stable critical point of the function a(x).This is a new perturbation to the critical elliptic equation in contrast to the usual subcritical or supercritical perturbation,and gives the first existence result for the critical elliptic problem with a variable exponent.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant Nos.XDA0320000 and XDA0320300the National Natural Science Foundation of China under Grant No.61972063.
文摘The critical node problem(CNP)aims to deal with critical node identification in a graph,which has extensive applications in many fields.Solving CNP is a challenging task due to its computational complexity,and it attracts much attention from both academia and industry.In this paper,we propose a population-based heuristic search algorithm called CPHS(Cut Point Based Heuristic Search)to solve CNP,which integrates two main ideas.The first one is a cut point based greedy strategy in the local search,and the second one involves the functions used to update the solution pool of the algorithm.Besides,a mutation strategy is applied to solutions with probability based on the overall average similarity to maintain the diversity of the solution pool.Experiments are performed on a synthetic benchmark,a real-world benchmark,and a large-scale network benchmark to evaluate our algorithm.Compared with state-of-the-art algorithms,our algorithm has better performance in terms of both solution quality and run time on all the three benchmarks.
基金supported by the Science and Technology Project of State Grid:Research on artificial intelligence analysis technology of available transmission capacity(ATC)of the key section under multiple power grid operation modes(5100-202255020A-1-1-ZN).
文摘The critical cross-section identification problem(CCIP)presents a significant and highly challenging issue in power grid analysis,aiming to identify a partition of the graph into two disjoint cuts that maximize the total weight of the cut.Traditionally,critical cross-sections have been determined through manual experience or mechanistic analysis,and effective intelligent methods to address these issues are lacking.Therefore,we propose a deep reinforcement learning framework based on a greedy approach(DEER)to solve the CCIP problem.Initially,proven to be NP-hard,a greedy vertex merging approach is proposed that enables the acquisition of all CCIP solutions through vertex merging.To prevent the greedy algorithm from converging to local optima,a deep reinforcement learning(DRL)framework combined with vertex marking is proposed to simulate the Markov decision process of vertex merging.Through training the DRL model,repetitive searches for vertex marking can be effectively avoided.Furthermore,the greedy algorithm can be augmented with genetic algorithms to address CCIP.Extensive experiments demonstrate the effectiveness of the proposed methods in addressing CCIP.
文摘Dictated handwriting samples are widely used in practice due to their simplicity,convenience,and practicality.However,dictation is typically listed as one of the many collection methods in textbooks and monographs,and there is usually no separate section focusing on dictated handwriting samples.Therefore,further study of dictated handwriting samples will have important practical significance.Consideration of the definition,existing problems,collection techniques,and critical aspects of dictated handwriting samples willsupport investigators and document examiners in their professional abilities and contribute to the theoretical system of document examination.In this article,an exploratory analysis will be conducted and ideas about dictated handwriting samples will be shared,including the definition of dictated samples,their relationship to experimental samples,practical problems,feasible collection methods,and some critical points that require special attention.Dictation is widely used but problematic because of a lack of quantity and low levels of comparability.Those difficulties are mainly caused by a lack of theoreticalstudy and understanding of the requirements and collection techniques of dictated handwriting samples among first‑line investigators.Dictated samples should be collected based on subjective and objective conditions of formation with aims to improve comparability and five similarities.Further studies are needed to improve the theoretical system and practical use of dictated samples so that they can contribute to successfully reaching conclusions in investigations.
基金supported in part by grant from IPM(No.89350020)
文摘The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval[a,b] R{-u＇＇=（λf（x,u）＋g（u））h（u＇）,in（a,b）,u（a）=u（b）=0under ppropriate hypotheses.We exhibit the existence of at least three（weak）solutions and,and the results are illustrated by examples.
