To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal charac...To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal characters but X1X2X3X4 is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.展开更多
In this paper,we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition(in the sense of expec- tation).Our main idea is to decompose the stochastic process ...In this paper,we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition(in the sense of expec- tation).Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value.Then by using the contraction mapping principle and Leray-Schauder fixed point theorem,we obtain the existence theorem.Finally,we explain our main results by an elementary example.展开更多
Multi-constrained Quality-of-Service (QoS) routing is a big challenge for Mobile Ad hoc Networks (MANETs) where the topology may change constantly. In this paper a novel QoS Routing Algorithm based on Simulated Anneal...Multi-constrained Quality-of-Service (QoS) routing is a big challenge for Mobile Ad hoc Networks (MANETs) where the topology may change constantly. In this paper a novel QoS Routing Algorithm based on Simulated Annealing (SA_RA) is proposed. This algorithm first uses an energy function to translate multiple QoS weights into a single mixed metric and then seeks to find a feasible path by simulated annealing. The pa- per outlines simulated annealing algorithm and analyzes the problems met when we apply it to Qos Routing (QoSR) in MANETs. Theoretical analysis and experiment results demonstrate that the proposed method is an effective approximation algorithms showing better performance than the other pertinent algorithm in seeking the (approximate) optimal configuration within a period of polynomial time.展开更多
This paper reviews and adds to previous arguments for the thesis that Karl Popper was mistaken to have rejected hypothetico-deductive confirmation. By turning from the positive idea of verification to the negative ide...This paper reviews and adds to previous arguments for the thesis that Karl Popper was mistaken to have rejected hypothetico-deductive confirmation. By turning from the positive idea of verification to the negative idea of criticism, Popper believed that he had turned his back on induction. He believed he had "solved" the "problem of induction" by providing a non-inductive account of corroboration. Popper used the term "corroboration" rather than confirmation which he believed was too closely allied to the notion of the inductive or probabilistic support that a theory can receive from evidence. Wesley Salmon's (1967) "concept of confirming evidence" and Clark Glymour's (1980) "bootstrap conception of evidence for theory" both defended respectively the thesis that passed tests can be confirmed by evidence or warranted by the degree of probability. Using a sequence of symbols in logical form or analysis, I shall further defend the concept to hypothetico-deductive confirmation in order to show that the known weaknesses of Popper's critical rationalism are remediable, once the notion of evidence for theories is brought back into consideration.展开更多
The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, ...The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, as well as quantum key distribution (QKD), which can perfectly protect direct lines, Combining the advantages of the quantum and multipath transmission paradigm, as well as rigorously analyzing the security of such combined techniques, is possible by virtue of game-theory. Based on a game-theoretic measure of channel vulnerability, the authors prove the problem of setting up infrastructures for QKD-based multipath transmission to be NP-complete. The authors consider the problem in two flavors, both being computationally hard. Remarkably, the authors' results indicate that the P-vs-NP-question is only of minor effect for confidentiality, because either nowadays public-key cryptosystems remain secure (in case that P, NP) or infrastructures facilitating perfectly confidential communication can be constructed efficiently (in case that P = NP).展开更多
It has been extensively recognized that the engineering structures are becoming increasingly precise and complex,which makes the requirements of design and analysis more and more rigorous.Therefore the uncertainty eff...It has been extensively recognized that the engineering structures are becoming increasingly precise and complex,which makes the requirements of design and analysis more and more rigorous.Therefore the uncertainty effects are indispensable during the process of product development.Besides,iterative calculations,which are usually unaffordable in calculative efforts,are unavoidable if we want to achieve the best design.Taking uncertainty effects into consideration,matrix perturbation methodpermits quick sensitivity analysis and structural dynamic re-analysis,it can also overcome the difficulties in computational costs.Owing to the situations above,matrix perturbation method has been investigated by researchers worldwide recently.However,in the existing matrix perturbation methods,correlation coefficient matrix of random structural parameters,which is barely achievable in engineering practice,has to be given or to be assumed during the computational process.This has become the bottleneck of application for matrix perturbation method.In this paper,we aim to develop an executable approach,which contributes to the application of matrix perturbation method.In the present research,the first-order perturbation of structural vibration eigenvalues and eigenvectors is derived on the basis of the matrix perturbation theory when structural parameters such as stiffness and mass have changed.Combining the first-order perturbation of structural vibration eigenvalues and eigenvectors with the probability theory,the variance of structural random eigenvalue is derived from the perturbation of stiffness matrix,the perturbation of mass matrix and the eigenvector of baseline-structure directly.Hence the Direct-VarianceAnalysis(DVA)method is developed to assess the variation range of the structural random eigenvalues without correlation coefficient matrix being involved.The feasibility of the DVA method is verified with two numerical examples(one is trusssystem and the other is wing structure of MA700 commercial aircraft),in which the DVA method also shows superiority in computational efficiency when compared to the Monte-Carlo method.展开更多
基金Supported by the National Natural Science Foundation of China(10171076)Supported by the Scientific and Technical Committee Foundation of Shanghai(03JC14027)
文摘To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal characters but X1X2X3X4 is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.
文摘In this paper,we present a new technique to study nonlinear stochastic differential equations with periodic boundary value condition(in the sense of expec- tation).Our main idea is to decompose the stochastic process into a deterministic term and a new stochastic term with zero mean value.Then by using the contraction mapping principle and Leray-Schauder fixed point theorem,we obtain the existence theorem.Finally,we explain our main results by an elementary example.
基金Supported by the National Natural Science Foundation of China (No.60472104), the Natural Science Research Program of Jiangsu Province (No.04KJB510094).
文摘Multi-constrained Quality-of-Service (QoS) routing is a big challenge for Mobile Ad hoc Networks (MANETs) where the topology may change constantly. In this paper a novel QoS Routing Algorithm based on Simulated Annealing (SA_RA) is proposed. This algorithm first uses an energy function to translate multiple QoS weights into a single mixed metric and then seeks to find a feasible path by simulated annealing. The pa- per outlines simulated annealing algorithm and analyzes the problems met when we apply it to Qos Routing (QoSR) in MANETs. Theoretical analysis and experiment results demonstrate that the proposed method is an effective approximation algorithms showing better performance than the other pertinent algorithm in seeking the (approximate) optimal configuration within a period of polynomial time.
文摘This paper reviews and adds to previous arguments for the thesis that Karl Popper was mistaken to have rejected hypothetico-deductive confirmation. By turning from the positive idea of verification to the negative idea of criticism, Popper believed that he had turned his back on induction. He believed he had "solved" the "problem of induction" by providing a non-inductive account of corroboration. Popper used the term "corroboration" rather than confirmation which he believed was too closely allied to the notion of the inductive or probabilistic support that a theory can receive from evidence. Wesley Salmon's (1967) "concept of confirming evidence" and Clark Glymour's (1980) "bootstrap conception of evidence for theory" both defended respectively the thesis that passed tests can be confirmed by evidence or warranted by the degree of probability. Using a sequence of symbols in logical form or analysis, I shall further defend the concept to hypothetico-deductive confirmation in order to show that the known weaknesses of Popper's critical rationalism are remediable, once the notion of evidence for theories is brought back into consideration.
文摘The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, as well as quantum key distribution (QKD), which can perfectly protect direct lines, Combining the advantages of the quantum and multipath transmission paradigm, as well as rigorously analyzing the security of such combined techniques, is possible by virtue of game-theory. Based on a game-theoretic measure of channel vulnerability, the authors prove the problem of setting up infrastructures for QKD-based multipath transmission to be NP-complete. The authors consider the problem in two flavors, both being computationally hard. Remarkably, the authors' results indicate that the P-vs-NP-question is only of minor effect for confidentiality, because either nowadays public-key cryptosystems remain secure (in case that P, NP) or infrastructures facilitating perfectly confidential communication can be constructed efficiently (in case that P = NP).
基金supported by the AVIC Research Project(Grant No.cxy2012BH07)the National Natural Science Foundation of China(Grant Nos.10872017,90816024,10876100)+1 种基金the Defense Industrial Technology Development Program(Grant Nos.A2120110001,B2120110011,A082013-2001)"111" Project(Grant No.B07009)
文摘It has been extensively recognized that the engineering structures are becoming increasingly precise and complex,which makes the requirements of design and analysis more and more rigorous.Therefore the uncertainty effects are indispensable during the process of product development.Besides,iterative calculations,which are usually unaffordable in calculative efforts,are unavoidable if we want to achieve the best design.Taking uncertainty effects into consideration,matrix perturbation methodpermits quick sensitivity analysis and structural dynamic re-analysis,it can also overcome the difficulties in computational costs.Owing to the situations above,matrix perturbation method has been investigated by researchers worldwide recently.However,in the existing matrix perturbation methods,correlation coefficient matrix of random structural parameters,which is barely achievable in engineering practice,has to be given or to be assumed during the computational process.This has become the bottleneck of application for matrix perturbation method.In this paper,we aim to develop an executable approach,which contributes to the application of matrix perturbation method.In the present research,the first-order perturbation of structural vibration eigenvalues and eigenvectors is derived on the basis of the matrix perturbation theory when structural parameters such as stiffness and mass have changed.Combining the first-order perturbation of structural vibration eigenvalues and eigenvectors with the probability theory,the variance of structural random eigenvalue is derived from the perturbation of stiffness matrix,the perturbation of mass matrix and the eigenvector of baseline-structure directly.Hence the Direct-VarianceAnalysis(DVA)method is developed to assess the variation range of the structural random eigenvalues without correlation coefficient matrix being involved.The feasibility of the DVA method is verified with two numerical examples(one is trusssystem and the other is wing structure of MA700 commercial aircraft),in which the DVA method also shows superiority in computational efficiency when compared to the Monte-Carlo method.