In physics,our expectations for system behavior are often guided by intuitive arithmetic.For systems composed of identical units,we anticipate synergy of the contributions from these units,where 1+1=2.Conversely,for s...In physics,our expectations for system behavior are often guided by intuitive arithmetic.For systems composed of identical units,we anticipate synergy of the contributions from these units,where 1+1=2.Conversely,for systems built from opposing units,we expect cancellation of their contributions,where 1-1=0.This intuitive arithmetic has long underpinned our understanding of physical properties of materials,from electronic transport to optical responses.However,scientific breakthroughs often occur when nature reveals ways to circumvent these seemingly fundamental rules,opening new possibilities that challenge our deepest assumptions about material behavior.展开更多
Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further ...Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further that b is any integer satisfying some necessary congruent conditions.The solvability of linear equation a_(1)p_(1)+a_(2)p_(2)+a_(3)p_(3)=b(p_(j)=l_(j)(mod k),1≤j≤3)with prime variables pi,p_(2),ps is investigated.It is proved that if ai,a_(2),a_(3)are all positive,then the above equation is solvable whenever b≥K^(25);if a,a_(2),a_(3)are not all of the same sign,then the above equation has a solution p_(1),p_(2),p_(3)satisfying max(p_(1),p_(2),p_(3))≤3|b|+K^(25).展开更多
In this paper,we present a novel first-order digitalΣΔconverter tailored for digital-to-analog applications,focusing on achieving both high yield and reduced silicon estate.Our approach incorporates a substantial le...In this paper,we present a novel first-order digitalΣΔconverter tailored for digital-to-analog applications,focusing on achieving both high yield and reduced silicon estate.Our approach incorporates a substantial level of dithering noise into the input signal,strategically aimed at mitigating the spurious frequencies commonly encountered in such converters.Validation of our design is performed through simulations using a high-level simulator specialized in mixed-signal circuit analysis.The results underscore the enhanced performance of our circuit,especially in reducing spurious frequencies,highlighting its efficiency and effectiveness.The final circuit exhibits an effective number of bits of 13.展开更多
Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an...Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an approach for the long-term extreme-response analysis of floating structures. A modified gradient-based retrieval algorithm in conjunction with the inverse first-order reliability method(IFORM) is proposed to enable the use of convolution models in long-term extreme analysis of structures with an analytical formula of response amplitude operator(RAO). The proposed algorithm ensures convergence stability and iteration accuracy and exhibits a higher computational efficiency than the traditional backtracking method. However, when the RAO of general offshore structures cannot be analytically expressed, the convolutional integration method fails to function properly. A numerical discretization approach is further proposed for offshore structures in the case when the analytical expression of the RAO is not feasible. Through iterative discretization of environmental contours(ECs) and RAOs, a detailed procedure is proposed to calculate the long-term response extremes of offshore structures. The validity and accuracy of the proposed approach are tested using a floating offshore wind turbine as a numerical example. The long-term extreme heave responses of various return periods are calculated via the IFORM in conjunction with a numerical discretization approach. The environmental data corresponding to N-year structural responses are located inside the ECs, which indicates that the selection of design points directly along the ECs yields conservative design results.展开更多
In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic i...In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic is reviewed. Then the characteristics of road networks, which are different from general networks, are analyzed. Under this condition, an improved recursive decomposition arithmetic is put forward which fits road networks better. Furthermore, detailed calculation steps are presented which are convenient for the computer, and the advantage of the approximate arithmetic is analyzed based on this improved arithmetic. This improved recursive decomposition arithmetic directly produces disjoint minipaths and avoids the non-polynomial increasing problems. And because the characteristics of road networks are considered, this arithmetic is greatly simplified. Finally, an example is given to prove its validity.展开更多
Conventional PI control encounters some problems when dealing with large lag process in the presence of parameter uncertainties.For the typical first-order process,an observerbased linear active disturbance rejection ...Conventional PI control encounters some problems when dealing with large lag process in the presence of parameter uncertainties.For the typical first-order process,an observerbased linear active disturbance rejection control(LADRC)scheme is presented to cope with the difficulties,and a reduced-order observer scheme is proposed further.Some quantitative dynamic results with regard to non-overshoot characteristics are obtained.Finally,the performance boundaries of LADRC and PI control are explicitly compared with each other,which shows that the former is more superior in most cases.展开更多
In this paper, we analyse a new chaos-based cryptosystem with an embedded adaptive arithmetic coder, which was proposed by Li Heng-Jian and Zhang J S （Li H J and Zhang J S 2010 Chin. Phys. B 19 050508）. Although thi...In this paper, we analyse a new chaos-based cryptosystem with an embedded adaptive arithmetic coder, which was proposed by Li Heng-Jian and Zhang J S （Li H J and Zhang J S 2010 Chin. Phys. B 19 050508）. Although this new method has a better compression performance than its original version, it is found that there are some problems with its security and decryption processes. In this paper, it is shown how to obtain a great deal of plain text from the cipher text without prior knowledge of the secret key. After discussing the security and decryption problems of the Li Heng-Jian et al. algorithm, we propose an improved chaos-based cryptosystem with an embedded adaptive arithmetic coder that is more secure.展开更多
Consensus problems of first-order multi-agent systems with multiple time delays are investigated in this paper. We discuss three cases： 1） continuous, 2） discrete, and 3） a continuous system with a proportional pl...Consensus problems of first-order multi-agent systems with multiple time delays are investigated in this paper. We discuss three cases： 1） continuous, 2） discrete, and 3） a continuous system with a proportional plus derivative controller. In each case, the system contains simultaneous communication and input time delays. Supposing a dynamic multi-agent system with directed topology that contains a globally reachable node, the sufficient convergence condition of the system is discussed with respect to each of the three cases based on the generalized Nyquist criterion and the frequency-domain analysis approach, yielding conclusions that are either less conservative than or agree with previously published results. We know that the convergence condition of the system depends mainly on each agent’s input time delay and the adjacent weights but is independent of the communication delay between agents, whether the system is continuous or discrete. Finally, simulation examples are given to verify the theoretical analysis.展开更多
A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlat...A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation,and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.展开更多
Dynamic fault tree analysis is widely used for the reliability analysis of the complex system with dynamic failure characteristics. In many circumstances, the exact value of system reliability is difficult to obtain d...Dynamic fault tree analysis is widely used for the reliability analysis of the complex system with dynamic failure characteristics. In many circumstances, the exact value of system reliability is difficult to obtain due to absent or insufficient data for failure probabilities or failure rates of components. The traditional fuzzy operation arithmetic based on extension principle or interval theory may lead to fuzzy accumulations. Moreover, the existing fuzzy dynamic fault tree analysis methods are restricted to the case that all system components follow exponential time-to-failure distributions. To overcome these problems, a new fuzzy dynamic fault tree analysis approach based on the weakest n-dimensional t-norm arithmetic and developed sequential binary decision diagrams method is proposed to evaluate system fuzzy reliability. Compared with the existing approach,the proposed method can effectively reduce fuzzy cumulative and be applicable to any time-tofailure distribution type for system components. Finally, a case study is presented to illustrate the application and advantages of the proposed approach.展开更多
A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged Navier-Stokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations are ...A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged Navier-Stokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations are transformed into the σ-coordinate system and the eddy viscosity is calculated with the standard k-ε turbulence model. The control volume method is used to discrete the equations, and the boundary conditions at the bed for shallow water models only include vertical diffusion terms expressed with wall functions. And the semi-implicit method for pressure linked equation arithmetic is adopted to solve the equations. The model is applied to the 2D vertical plane flow of a current over two steep-sided trenches for which experiment data are available for comparison and good agreement is obtained. And the model is used to predicting the flow in a channel with a steep-sided submerged breakwater at the bottom, and the streamline is drawn.展开更多
When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite ...When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method (FEM). The two parameters, median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. ne solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2 n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.展开更多
For protecting the copyright of a text and recovering its original content harmlessly,this paper proposes a novel reversible natural language watermarking method that combines arithmetic coding and synonym substitutio...For protecting the copyright of a text and recovering its original content harmlessly,this paper proposes a novel reversible natural language watermarking method that combines arithmetic coding and synonym substitution operations.By analyzing relative frequencies of synonymous words,synonyms employed for carrying payload are quantized into an unbalanced and redundant binary sequence.The quantized binary sequence is compressed by adaptive binary arithmetic coding losslessly to provide a spare for accommodating additional data.Then,the compressed data appended with the watermark are embedded into the cover text via synonym substitutions in an invertible manner.On the receiver side,the watermark and compressed data can be extracted by decoding the values of synonyms in the watermarked text,as a result of which the original context can be perfectly recovered by decompressing the extracted compressed data and substituting the replaced synonyms with their original synonyms.Experimental results demonstrate that the proposed method can extract the watermark successfully and achieve a lossless recovery of the original text.Additionally,it achieves a high embedding capacity.展开更多
Let φ(n) denote the Euler-totient function, we study the distribution of solutions of φ(n) ≤ x in arithmetic progressions, where n ≡ l(mod q) and an asymptotic formula was obtained by Perron formula.
For any x ∈ （0, 1] （except at most countably many points）, there exists a unique sequence {dn（x）}n≥1 of integers, called the digit sequence of x, such that x =∞ ∑j=1 1/d1（x）（d1（x）-1）……dj-1（x）（dj-1...For any x ∈ （0, 1] （except at most countably many points）, there exists a unique sequence {dn（x）}n≥1 of integers, called the digit sequence of x, such that x =∞ ∑j=1 1/d1（x）（d1（x）-1）……dj-1（x）（dj-1（x）-1）dj（x）. The dexter infinite series expansion is called the Liiroth expansion of x. This paper is con- cerned with the size of the set of points x whose digit sequence in its Liiroth expansion is strictly increasing and contains arbitrarily long arithmetic progressions with arbitrary com- mon difference. More precisely, we determine the Hausdorff dimension of the above set.展开更多
The use of peat for the removal of nickel from aqueous solutions has been investigated at various pH values by means of static conditions. The present research shows that the ability of Ni to bind to peat increases as...The use of peat for the removal of nickel from aqueous solutions has been investigated at various pH values by means of static conditions. The present research shows that the ability of Ni to bind to peat increases as the pH value increases. The solutions reach adsorption equilibrium rapidly. A reasonable kinetic model, first-order in nickel concentration, has been developed and fitted to the adsorption of nickel （Ⅱ） onto peat. The first-order model provides a good correlation to the experimental data. The characteristic parameters of the Langmuir isotherm were determined at various temperatures. The relationship between kinetics and equilibrium isotherms was established through the forward- and backward-rate-constants, k~ and k2, and the equilibrium constant, K.展开更多
An approximately optimal adaptive arithmetic coding (AC) system using a forbidden symbol (FS) over noisy channels was proposed which allows one to jointly and adaptively design the source decoding and channel correcti...An approximately optimal adaptive arithmetic coding (AC) system using a forbidden symbol (FS) over noisy channels was proposed which allows one to jointly and adaptively design the source decoding and channel correcting in a single process, with superior performance compared with traditional separated techniques. The concept of adaptiveness is applied not only to the source model but also to the amount of coding redundancy. In addition, an improved branch metric computing algorithm and a faster sequential searching algorithm compared with the system proposed by Grangetto were proposed. The proposed system is tested in the case of image transmission over the AWGN channel, and compared with traditional separated system in terms of packet error rate and complexity. Both hard and soft decoding were taken into account.展开更多
This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are...This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.展开更多
Modular arithmetic is a fundamental operation and plays an important role in public key cryptosystem. A new method and its theory evidence on the basis of modular arithmetic with large integer modulus-changeable modul...Modular arithmetic is a fundamental operation and plays an important role in public key cryptosystem. A new method and its theory evidence on the basis of modular arithmetic with large integer modulus-changeable modulus algorithm is proposed to improve the speed of the modular arithmetic in the presented paper. For changeable modulus algorithm, when modular computation of modulo n is difficult, it can be realized by computation of modulo n-1 and n-2 on the perquisite of easy modular computations of modulo n-1 and modulo n-2. The conclusion is that the new method is better than the direct method by computing the modular arithmetic operation with large modulus. Especially, when computations of modulo n-1 and modulo n-2 are easy and computation of modulo n is difficult, this new method will be faster and has more advantages than other algorithms on modular arithmetic. Lastly, it is suggested that the proposed method be applied in public key cryptography based on modular multiplication and modular exponentiation with large integer modulus effectively展开更多
基金supported by the National Natural Science Foundation of China (Grant No.12374109)the National Key Research and Development Program of China (Grant No.2023YFA1406600)。
文摘In physics,our expectations for system behavior are often guided by intuitive arithmetic.For systems composed of identical units,we anticipate synergy of the contributions from these units,where 1+1=2.Conversely,for systems built from opposing units,we expect cancellation of their contributions,where 1-1=0.This intuitive arithmetic has long underpinned our understanding of physical properties of materials,from electronic transport to optical responses.However,scientific breakthroughs often occur when nature reveals ways to circumvent these seemingly fundamental rules,opening new possibilities that challenge our deepest assumptions about material behavior.
文摘Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further that b is any integer satisfying some necessary congruent conditions.The solvability of linear equation a_(1)p_(1)+a_(2)p_(2)+a_(3)p_(3)=b(p_(j)=l_(j)(mod k),1≤j≤3)with prime variables pi,p_(2),ps is investigated.It is proved that if ai,a_(2),a_(3)are all positive,then the above equation is solvable whenever b≥K^(25);if a,a_(2),a_(3)are not all of the same sign,then the above equation has a solution p_(1),p_(2),p_(3)satisfying max(p_(1),p_(2),p_(3))≤3|b|+K^(25).
文摘In this paper,we present a novel first-order digitalΣΔconverter tailored for digital-to-analog applications,focusing on achieving both high yield and reduced silicon estate.Our approach incorporates a substantial level of dithering noise into the input signal,strategically aimed at mitigating the spurious frequencies commonly encountered in such converters.Validation of our design is performed through simulations using a high-level simulator specialized in mixed-signal circuit analysis.The results underscore the enhanced performance of our circuit,especially in reducing spurious frequencies,highlighting its efficiency and effectiveness.The final circuit exhibits an effective number of bits of 13.
基金Supported by the National Natural Science Foundation of China (Grant Nos.52088102 and 51879287)National Key Research and Development Program of China (Grant No.2022YFB2602301)。
文摘Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an approach for the long-term extreme-response analysis of floating structures. A modified gradient-based retrieval algorithm in conjunction with the inverse first-order reliability method(IFORM) is proposed to enable the use of convolution models in long-term extreme analysis of structures with an analytical formula of response amplitude operator(RAO). The proposed algorithm ensures convergence stability and iteration accuracy and exhibits a higher computational efficiency than the traditional backtracking method. However, when the RAO of general offshore structures cannot be analytically expressed, the convolutional integration method fails to function properly. A numerical discretization approach is further proposed for offshore structures in the case when the analytical expression of the RAO is not feasible. Through iterative discretization of environmental contours(ECs) and RAOs, a detailed procedure is proposed to calculate the long-term response extremes of offshore structures. The validity and accuracy of the proposed approach are tested using a floating offshore wind turbine as a numerical example. The long-term extreme heave responses of various return periods are calculated via the IFORM in conjunction with a numerical discretization approach. The environmental data corresponding to N-year structural responses are located inside the ECs, which indicates that the selection of design points directly along the ECs yields conservative design results.
基金The National Key Technology R& D Program of Chinaduring the 11th Five-Year Plan Period (No.2006BAJ18B03).
文摘In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic is reviewed. Then the characteristics of road networks, which are different from general networks, are analyzed. Under this condition, an improved recursive decomposition arithmetic is put forward which fits road networks better. Furthermore, detailed calculation steps are presented which are convenient for the computer, and the advantage of the approximate arithmetic is analyzed based on this improved arithmetic. This improved recursive decomposition arithmetic directly produces disjoint minipaths and avoids the non-polynomial increasing problems. And because the characteristics of road networks are considered, this arithmetic is greatly simplified. Finally, an example is given to prove its validity.
基金supported by the National Natural Science Foundation of China(60774088)the National High Technology Research and Development Program of China(863 Program)(2009AA04Z132)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20090031110029)
文摘Conventional PI control encounters some problems when dealing with large lag process in the presence of parameter uncertainties.For the typical first-order process,an observerbased linear active disturbance rejection control(LADRC)scheme is presented to cope with the difficulties,and a reduced-order observer scheme is proposed further.Some quantitative dynamic results with regard to non-overshoot characteristics are obtained.Finally,the performance boundaries of LADRC and PI control are explicitly compared with each other,which shows that the former is more superior in most cases.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60573172 and 60973152)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No. 20070141014)the Natural Science Foundation of Liaoning Province of China (Grant No. 20082165)
文摘In this paper, we analyse a new chaos-based cryptosystem with an embedded adaptive arithmetic coder, which was proposed by Li Heng-Jian and Zhang J S （Li H J and Zhang J S 2010 Chin. Phys. B 19 050508）. Although this new method has a better compression performance than its original version, it is found that there are some problems with its security and decryption processes. In this paper, it is shown how to obtain a great deal of plain text from the cipher text without prior knowledge of the secret key. After discussing the security and decryption problems of the Li Heng-Jian et al. algorithm, we propose an improved chaos-based cryptosystem with an embedded adaptive arithmetic coder that is more secure.
基金Project supported in part by the National Natural Science Foundation of China (Grant Nos. 60973114 and 61170249)in part by the Natural Science Foundation of CQCSTC (Grant Nos. 2009BA2024 and cstc2011jjA1320)in part by the State Key Laboratory of Power Transmission Equipment & System Securityand New Technology, Chongqing University (Grant No. 2007DA10512711206)
文摘Consensus problems of first-order multi-agent systems with multiple time delays are investigated in this paper. We discuss three cases： 1） continuous, 2） discrete, and 3） a continuous system with a proportional plus derivative controller. In each case, the system contains simultaneous communication and input time delays. Supposing a dynamic multi-agent system with directed topology that contains a globally reachable node, the sufficient convergence condition of the system is discussed with respect to each of the three cases based on the generalized Nyquist criterion and the frequency-domain analysis approach, yielding conclusions that are either less conservative than or agree with previously published results. We know that the convergence condition of the system depends mainly on each agent’s input time delay and the adjacent weights but is independent of the communication delay between agents, whether the system is continuous or discrete. Finally, simulation examples are given to verify the theoretical analysis.
基金supported by the National Natural Science Foundation for Excellent Young Scholars(Grant 51222502)the National Natural Science Foundation of China(Grant 11172096)the Funds for State Key Laboratory of Construction Machinery(SKLCM2014-1)
文摘A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation,and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.
基金supported by the National Defense Basic Scientific Research program of China (No.61325102)
文摘Dynamic fault tree analysis is widely used for the reliability analysis of the complex system with dynamic failure characteristics. In many circumstances, the exact value of system reliability is difficult to obtain due to absent or insufficient data for failure probabilities or failure rates of components. The traditional fuzzy operation arithmetic based on extension principle or interval theory may lead to fuzzy accumulations. Moreover, the existing fuzzy dynamic fault tree analysis methods are restricted to the case that all system components follow exponential time-to-failure distributions. To overcome these problems, a new fuzzy dynamic fault tree analysis approach based on the weakest n-dimensional t-norm arithmetic and developed sequential binary decision diagrams method is proposed to evaluate system fuzzy reliability. Compared with the existing approach,the proposed method can effectively reduce fuzzy cumulative and be applicable to any time-tofailure distribution type for system components. Finally, a case study is presented to illustrate the application and advantages of the proposed approach.
文摘A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged Navier-Stokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations are transformed into the σ-coordinate system and the eddy viscosity is calculated with the standard k-ε turbulence model. The control volume method is used to discrete the equations, and the boundary conditions at the bed for shallow water models only include vertical diffusion terms expressed with wall functions. And the semi-implicit method for pressure linked equation arithmetic is adopted to solve the equations. The model is applied to the 2D vertical plane flow of a current over two steep-sided trenches for which experiment data are available for comparison and good agreement is obtained. And the model is used to predicting the flow in a channel with a steep-sided submerged breakwater at the bottom, and the streamline is drawn.
文摘When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method (FEM). The two parameters, median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. ne solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2 n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.
基金This project is supported by National Natural Science Foundation of China(No.61202439)partly supported by Scientific Research Foundation of Hunan Provincial Education Department of China(No.16A008)partly supported by Hunan Key Laboratory of Smart Roadway and Cooperative Vehicle-Infrastructure Systems(No.2017TP1016).
文摘For protecting the copyright of a text and recovering its original content harmlessly,this paper proposes a novel reversible natural language watermarking method that combines arithmetic coding and synonym substitution operations.By analyzing relative frequencies of synonymous words,synonyms employed for carrying payload are quantized into an unbalanced and redundant binary sequence.The quantized binary sequence is compressed by adaptive binary arithmetic coding losslessly to provide a spare for accommodating additional data.Then,the compressed data appended with the watermark are embedded into the cover text via synonym substitutions in an invertible manner.On the receiver side,the watermark and compressed data can be extracted by decoding the values of synonyms in the watermarked text,as a result of which the original context can be perfectly recovered by decompressing the extracted compressed data and substituting the replaced synonyms with their original synonyms.Experimental results demonstrate that the proposed method can extract the watermark successfully and achieve a lossless recovery of the original text.Additionally,it achieves a high embedding capacity.
基金Supported by the National Natural Science Foundation of China（11271249） Supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission（1601213） Supported by the Scientific Research Program of Yangtze Normal University（2012XJYBO31）
文摘Let φ(n) denote the Euler-totient function, we study the distribution of solutions of φ(n) ≤ x in arithmetic progressions, where n ≡ l(mod q) and an asymptotic formula was obtained by Perron formula.
文摘For any x ∈ （0, 1] （except at most countably many points）, there exists a unique sequence {dn（x）}n≥1 of integers, called the digit sequence of x, such that x =∞ ∑j=1 1/d1（x）（d1（x）-1）……dj-1（x）（dj-1（x）-1）dj（x）. The dexter infinite series expansion is called the Liiroth expansion of x. This paper is con- cerned with the size of the set of points x whose digit sequence in its Liiroth expansion is strictly increasing and contains arbitrarily long arithmetic progressions with arbitrary com- mon difference. More precisely, we determine the Hausdorff dimension of the above set.
基金Projects [2006]331 supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars070712 by the Key Laboratory ofNuclear Resources and Environment,Ministry of Education of China
文摘The use of peat for the removal of nickel from aqueous solutions has been investigated at various pH values by means of static conditions. The present research shows that the ability of Ni to bind to peat increases as the pH value increases. The solutions reach adsorption equilibrium rapidly. A reasonable kinetic model, first-order in nickel concentration, has been developed and fitted to the adsorption of nickel （Ⅱ） onto peat. The first-order model provides a good correlation to the experimental data. The characteristic parameters of the Langmuir isotherm were determined at various temperatures. The relationship between kinetics and equilibrium isotherms was established through the forward- and backward-rate-constants, k~ and k2, and the equilibrium constant, K.
文摘An approximately optimal adaptive arithmetic coding (AC) system using a forbidden symbol (FS) over noisy channels was proposed which allows one to jointly and adaptively design the source decoding and channel correcting in a single process, with superior performance compared with traditional separated techniques. The concept of adaptiveness is applied not only to the source model but also to the amount of coding redundancy. In addition, an improved branch metric computing algorithm and a faster sequential searching algorithm compared with the system proposed by Grangetto were proposed. The proposed system is tested in the case of image transmission over the AWGN channel, and compared with traditional separated system in terms of packet error rate and complexity. Both hard and soft decoding were taken into account.
基金supported by the National Natural Science Foundation of China(Grant Nos.52109144,52025094 and 52222905).
文摘This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.
基金Supported by the National Natural Science Foun-dation of China (60373087)
文摘Modular arithmetic is a fundamental operation and plays an important role in public key cryptosystem. A new method and its theory evidence on the basis of modular arithmetic with large integer modulus-changeable modulus algorithm is proposed to improve the speed of the modular arithmetic in the presented paper. For changeable modulus algorithm, when modular computation of modulo n is difficult, it can be realized by computation of modulo n-1 and n-2 on the perquisite of easy modular computations of modulo n-1 and modulo n-2. The conclusion is that the new method is better than the direct method by computing the modular arithmetic operation with large modulus. Especially, when computations of modulo n-1 and modulo n-2 are easy and computation of modulo n is difficult, this new method will be faster and has more advantages than other algorithms on modular arithmetic. Lastly, it is suggested that the proposed method be applied in public key cryptography based on modular multiplication and modular exponentiation with large integer modulus effectively
