The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating ...The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating with Lyapunov-Krasovskii functional method and adding ＂zeros＂ matrix through the correlation of each item in Newton-Leibniz formula, we present a sufficient condition via the feedback stabilization based on linear matrix inequality （LMI）. LMI is a new delay dependent condition that is much less conservative, and it guarantees that the system is robust asymptotically stable via state feedback controller. Neither the model transformation nor the bounding cross terms is employed. Finally, a numerical example is presented and it demonstrates the effectiveness of the offered method.展开更多
This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
The design of decentralized robust H_∞ state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices was investigat...The design of decentralized robust H_∞ state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices was investigated. Based on the bounded real lemma a sufficient condition for the existence of a decentralized robust H_∞ state feedback controller was derived. This condition is expressed as the feasibility problem of a certain nonlinear matrix inequality. The controller, which makes the closed-loop large-scale system robust stable and satisfies the given H_∞ performance, is obtained by the offered homotopy iterative linear matrix inequality method. A numerical example is given to demonstrate the effectiveness of the proposed method.展开更多
The unconnected gas-bearing pores in shale gas reservoirs may be transformed into“potential recoverable pores”after large scale hydraulic fracturing.However,the mainstream pore classification methods of shale gas re...The unconnected gas-bearing pores in shale gas reservoirs may be transformed into“potential recoverable pores”after large scale hydraulic fracturing.However,the mainstream pore classification methods of shale gas reservoirs,do not take the unconnected pores into account,which impacts the evaluation accuracy of reservoir pore effectiveness.To solve this problem,this paper took the shale of Lower Silurian Longmaxi Formation in the southern Sichuan Basin as the research object to carry out experiments on core porosity,centrifugal+gradual drying NMR after saturated with brine and NMR freezeethaw using plunger samples and crushed samples to analyze the volume,main development location and main pore size distribution range of unconnected pores.Then,the pore systems were classified,and the lower limit of effective pore size of connected gas-bearing pores was determined.Finally,the total pore effectiveness of shale gas reservoirs was evaluated,and the influence of unconnected pores on the development of shale gas was discussed.And the following research results were obtained.First,there are a large number of unconnected pores in the shale gas reservoirs of the study area,accounting for 30.23%.Most of them are mainly developed in organic matters and a few are developed in clay minerals.The distribution of pore size ranges from 5 nm to 30 nm.Second,T_(2)cut-off value of clay bound water in the shale gas reservoirs of the study area is 0.26 ms,whose corresponding pore size is 5.35 nm,which is the lower limit of the effective pore size.Third,large-scale hydraulic fracturing can improve the unconnected pores with the size more than 5.35 nm,so effective development of shale gas will be realized.Fourth,after hydraulic fracturing stimulation,the unconnected pores can increase the storage space of fracturing fluid in the matrix,absorb the fracturing fluid in the fractures,replace the shale gas in the pores and promote the automatic alleviation of water lock in shale gas reservoirs,so the single-well shale gas production will be increased.In conclusion,fluid occurrence and pore system in shale pores can be quantitatively divided by means of centrifugal+gradual temperature drying method combined with NMR experiments,mobile water and capillary bound water can be determined by the high speed centrifugal+NMR experiments,and capillary bound water and clay bound water can be determined by the gradual drying t NMR experiments.展开更多
In the present paper,we generalize some classical results in convergence and integrability for trigonometric series with varying coefficients(may change signs),by introducing a new ultimate condition upon coefficient ...In the present paper,we generalize some classical results in convergence and integrability for trigonometric series with varying coefficients(may change signs),by introducing a new ultimate condition upon coefficient sequences.This is a comprehensive systematic work on the topic.展开更多
We obtain effective lower bounds for certain linear combinations of the valuesat algebraic points of a class of p-adic G-functions defined over a completion of analgebraic closure of a p-adio field.
In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fou...In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting.In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.展开更多
基金Supported by the National Natural Science Foundation of China (60634020)the Natural Science Foundation of Hunan Province (06JJ50145)
文摘The present paper investigated the delay-dependent robust control for linear value bounded uncertain systems with state delay. By introducing the idea of matrix decomposition into the synthesis problem, incorporating with Lyapunov-Krasovskii functional method and adding ＂zeros＂ matrix through the correlation of each item in Newton-Leibniz formula, we present a sufficient condition via the feedback stabilization based on linear matrix inequality （LMI）. LMI is a new delay dependent condition that is much less conservative, and it guarantees that the system is robust asymptotically stable via state feedback controller. Neither the model transformation nor the bounding cross terms is employed. Finally, a numerical example is presented and it demonstrates the effectiveness of the offered method.
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
基金Project (60474003) supported by the National Natural Science Foundation of China project(20050533028) supported bythe Specialized Research Fund for the Doctoral Programof Higher Education of China
文摘The design of decentralized robust H_∞ state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices was investigated. Based on the bounded real lemma a sufficient condition for the existence of a decentralized robust H_∞ state feedback controller was derived. This condition is expressed as the feasibility problem of a certain nonlinear matrix inequality. The controller, which makes the closed-loop large-scale system robust stable and satisfies the given H_∞ performance, is obtained by the offered homotopy iterative linear matrix inequality method. A numerical example is given to demonstrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China“Research on nanopore structure characterization and seepage mechanism of shale reservoirs”(No.:51674044)Chongqing Key Industry Common Key Technology Innovation Special Project“Exploration and development key technology and its application of shale gas in Chongqing”(No.:cstc2017zdcyzdyfx0040)+1 种基金Sichuan Applied Basic Research Project“Research on intelligent evaluation system of marine shale gas construction and production core area(provincial key project)”(No.:2019YJ0340)Sichuan Promising Key Project“Study on evaluation of the fracturing effect of shale gas reservoirs based on the law of fracturing fluid flow back”(No.:2019JDRC0095).
文摘The unconnected gas-bearing pores in shale gas reservoirs may be transformed into“potential recoverable pores”after large scale hydraulic fracturing.However,the mainstream pore classification methods of shale gas reservoirs,do not take the unconnected pores into account,which impacts the evaluation accuracy of reservoir pore effectiveness.To solve this problem,this paper took the shale of Lower Silurian Longmaxi Formation in the southern Sichuan Basin as the research object to carry out experiments on core porosity,centrifugal+gradual drying NMR after saturated with brine and NMR freezeethaw using plunger samples and crushed samples to analyze the volume,main development location and main pore size distribution range of unconnected pores.Then,the pore systems were classified,and the lower limit of effective pore size of connected gas-bearing pores was determined.Finally,the total pore effectiveness of shale gas reservoirs was evaluated,and the influence of unconnected pores on the development of shale gas was discussed.And the following research results were obtained.First,there are a large number of unconnected pores in the shale gas reservoirs of the study area,accounting for 30.23%.Most of them are mainly developed in organic matters and a few are developed in clay minerals.The distribution of pore size ranges from 5 nm to 30 nm.Second,T_(2)cut-off value of clay bound water in the shale gas reservoirs of the study area is 0.26 ms,whose corresponding pore size is 5.35 nm,which is the lower limit of the effective pore size.Third,large-scale hydraulic fracturing can improve the unconnected pores with the size more than 5.35 nm,so effective development of shale gas will be realized.Fourth,after hydraulic fracturing stimulation,the unconnected pores can increase the storage space of fracturing fluid in the matrix,absorb the fracturing fluid in the fractures,replace the shale gas in the pores and promote the automatic alleviation of water lock in shale gas reservoirs,so the single-well shale gas production will be increased.In conclusion,fluid occurrence and pore system in shale pores can be quantitatively divided by means of centrifugal+gradual temperature drying method combined with NMR experiments,mobile water and capillary bound water can be determined by the high speed centrifugal+NMR experiments,and capillary bound water and clay bound water can be determined by the gradual drying t NMR experiments.
文摘In the present paper,we generalize some classical results in convergence and integrability for trigonometric series with varying coefficients(may change signs),by introducing a new ultimate condition upon coefficient sequences.This is a comprehensive systematic work on the topic.
文摘We obtain effective lower bounds for certain linear combinations of the valuesat algebraic points of a class of p-adic G-functions defined over a completion of analgebraic closure of a p-adio field.
基金Supported by the European Research Council Advanced Grant(Grant No.267055)
文摘In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting.In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.
