A detailed study of some simple forms which have a given special structure have been solved, in this paper, we research the extension of this kind of special structure problems.
[ Objective] To discuss regional response of reference evapotranspiration ( ETo ) to global climate change and its influencing factors. [Method] Penman-Monteith equation was adopted to calculate ET0 in Australia fro...[ Objective] To discuss regional response of reference evapotranspiration ( ETo ) to global climate change and its influencing factors. [Method] Penman-Monteith equation was adopted to calculate ET0 in Australia from 1998 to 2007. Spatiotemporal change characteristics were analyzed by using GIS spatial analysis tools and relationships between ETo and main climate factors were also analyzed. [ Resultsl The results showed that multi-year average ET0 increased from the east and south part to the northwest part and inland, and its distribution was consistent with climate zones. Multi-year average ETo of the whole region was 1 750 mm, obtaining minimum and maximum values in 2000 and 2002 respectively. Regional ETo decreased in the order of summer, spring, autumn and winter; January and December got the highest monthly ET0, while June got the lowest value 79.55 mm. ETo positively correlated with mean temperature and solar radiation, R2 for each were 0.83 and 0.94, while the relationship between ETo and average relative humidity was negative, and precipitation had no significant relationship with ET0. [ Conclusion] This research could provide important reference for crop water requirement study and making irrigation method for Australia.展开更多
By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
Multivariate statistical process monitoring and control (MSPM&C) methods for chemical process monitoring with statistical projection techniques such as principal component analysis (PCA) and partial least squares ...Multivariate statistical process monitoring and control (MSPM&C) methods for chemical process monitoring with statistical projection techniques such as principal component analysis (PCA) and partial least squares (PLS) are surveyed in this paper. The four-step procedure of performing MSPM&C for chemical process, modeling of processes, detecting abnormal events or faults, identifying the variable(s) responsible for the faults and diagnosing the source cause for the abnormal behavior, is analyzed. Several main research directions of MSPM&C reported in the literature are discussed, such as multi-way principal component analysis (MPCA) for batch process, statistical monitoring and control for nonlinear process, dynamic PCA and dynamic PLS, and on-line quality control by inferential models. Industrial applications of MSPM&C to several typical chemical processes, such as chemical reactor, distillation column, polymerization process, petroleum refinery units, are summarized. Finally, some concluding remarks and future considerations are made.展开更多
We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion ...We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and O, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively.展开更多
Chemical process variables are always driven by random noise and disturbances. The closed-loop con-trol yields process measurements that are auto and cross correlated. The influence of auto and cross correlations on s...Chemical process variables are always driven by random noise and disturbances. The closed-loop con-trol yields process measurements that are auto and cross correlated. The influence of auto and cross correlations on statistical process control (SPC) is investigated in detail by Monte Carlo experiments. It is revealed that in the sense of average performance, the false alarms rates (FAR) of principal component analysis (PCA), dynamic PCA are not affected by the time-series structures of process variables. Nevertheless, non-independent identical distribution will cause the actual FAR to deviate from its theoretic value apparently and result in unexpected consecutive false alarms for normal operating process. Dynamic PCA and ARMA-PCA are demonstrated to be inefficient to remove the influences of auto and cross correlations. Subspace identification-based PCA (SI-PCA) is proposed to improve the monitoring of dynamic processes. Through state space modeling, SI-PCA can remove the auto and cross corre-lations efficiently and avoid consecutive false alarms. Synthetic Monte Carlo experiments and the application in Tennessee Eastman challenge process illustrate the advantages of the proposed approach.展开更多
Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to n...Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.展开更多
In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation...In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
The parameters of principal and directional extrema in a marine environment are important in marine engineering design, especially for appropriate construction of oceanic platforms and other structures. When designing...The parameters of principal and directional extrema in a marine environment are important in marine engineering design, especially for appropriate construction of oceanic platforms and other structures. When designing wave walls and break water structures, the orientation of the breakwater or seawall depends mainly on the direction of the strongest waves. However, the strength of the breakwater and the elevation of the seawall depend on the magnitude of the biggest wave height of the strongest waves. Thus, identification of directional extrema plays an important role in the design of wave factors. When calculating the directional extremum, different materials may require different specific computational methods, yet few theoretical studies have been conducted in this field of research. Based on multivariate extremnm statistical theory, this paper utilizes a discrete random variable to build a joint probability model compounded by a discrete random variable and a multivariate continuous random variable. Furthermore, this paper provides the first investigation on the theories and methodologies to deduce wave directional extrema. The results provide tools for both creating the calculation method of the directional extremum value and providing the rational directional extremum parameters for marine engineering design.展开更多
Euphausia pacific is an important source of natural astaxanthin. Studies were carried out to assess the extractability of astaxanthin from E. pacific using subcritical 1, 1, 1,2-tetrafluoroethane (R134a). To examine...Euphausia pacific is an important source of natural astaxanthin. Studies were carried out to assess the extractability of astaxanthin from E. pacific using subcritical 1, 1, 1,2-tetrafluoroethane (R134a). To examine the effects of multiple process variables on the extraction yield, astaxanthin was extracted under various conditions of pressure (30-150bar), temperature (303-343 K), time (10-50rain), flow rate (2-10gmin-1), moisture content (5.5%-63.61%), and particle size (0.25-0.109mm). The results showed that the extraction yield increased with temperature, pressure, time and flow rate, but decreased with moisture content and particle size. A maximum yield of 87.74% was obtained under conditions of 100bar, 333K, and 30min with a flow rate of 6gmin-1 and a moisture content of 5.5%. The substantial astaxanthin yield obtained under low-pressure conditions demonstrates that subcritical R134a is a good alternative to CO2 for extraction of astaxanthin from E. pacific.展开更多
In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering ...In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.展开更多
The bilinear equation of the genera/nonlinear Schrodinger equation with derivative (GDNLSE) and the N-soliton solutions are obtained through the dependent variable transformation and the Hirota method, respectively....The bilinear equation of the genera/nonlinear Schrodinger equation with derivative (GDNLSE) and the N-soliton solutions are obtained through the dependent variable transformation and the Hirota method, respectively. The bilinear equation of the nonlinear Schrodinger equation with derivative (DNLSE) and its multisoliton solutions are given by reduction.展开更多
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional sep...We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.展开更多
The cubic-quintic nonlinear Schroedinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic sol...The cubic-quintic nonlinear Schroedinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients (vCQNLS) are derived with the aid of a set of subsidiary high-order ordinary differential equations (sub-equations for short). The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.展开更多
A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, th...A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.展开更多
This paper reports the reengineering of the assembly processes of printed circuit boards (PCBs) used in computers.The new designed assembly processes are quite different from the traditional ones,and the business perf...This paper reports the reengineering of the assembly processes of printed circuit boards (PCBs) used in computers.The new designed assembly processes are quite different from the traditional ones,and the business performance is dramatically improved through establishing parallel workstations,off line workstation,merging workstations and organizing a small teamwork who cooperates in stations.“ITHINK”,a software package of business process reengineering (BPR),was used to analyze the current processes and create new processes.ITHINK is a powerful tool of BPR in modeling business processes,“soft” variables and conducting sensitivity analysis.The new assembly processes were tested over a period of 8 hours simulation.The results show that the new processes can increase throughput by 80% with only requiring less additional resources.The throughput can increase further by 17.5% when a small teamwork cooperates in some stations.展开更多
This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble (D32). The study was performed using pilot-scale equipment (0.8 m^3) that ...This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble (D32). The study was performed using pilot-scale equipment (0.8 m^3) that is up to two orders of magnitude larger than equipment used for studies performed to date by others, and incorporated the key process variables of frother type and impeller speed. The results show that each frother family exhibits a unique CCC95-HLB relationship dependent on n (number of C-atoms in alkyl group) and m (number of propylene oxide group). Empirical models were developed to predict CCC95 from HLB associated with other two parameters a and ft. The impeller speed-bubble size tests show that D32 is unaffected by increased impeller tip speed across the range of 4.6 to 9.2 m/s (representing the industrial operating range), although D32 starts to increase below 4.6 m/s. The finding is valid for both coalescing and non-coalescing conditions. The results suggest that the bubble size and bubble size distribution (BSD) being created do not change with increasing impeller speed in the quiescent zone of the flotation.展开更多
文摘A detailed study of some simple forms which have a given special structure have been solved, in this paper, we research the extension of this kind of special structure problems.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences(No.KZCX-XY-340)the Frontier Field Program of NEIGAE-CAS (No.C08Y46)~~
文摘[ Objective] To discuss regional response of reference evapotranspiration ( ETo ) to global climate change and its influencing factors. [Method] Penman-Monteith equation was adopted to calculate ET0 in Australia from 1998 to 2007. Spatiotemporal change characteristics were analyzed by using GIS spatial analysis tools and relationships between ETo and main climate factors were also analyzed. [ Resultsl The results showed that multi-year average ET0 increased from the east and south part to the northwest part and inland, and its distribution was consistent with climate zones. Multi-year average ETo of the whole region was 1 750 mm, obtaining minimum and maximum values in 2000 and 2002 respectively. Regional ETo decreased in the order of summer, spring, autumn and winter; January and December got the highest monthly ET0, while June got the lowest value 79.55 mm. ETo positively correlated with mean temperature and solar radiation, R2 for each were 0.83 and 0.94, while the relationship between ETo and average relative humidity was negative, and precipitation had no significant relationship with ET0. [ Conclusion] This research could provide important reference for crop water requirement study and making irrigation method for Australia.
文摘By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
基金Supported by the National High-Tech Development Program of China(No.863-511-920-011,2001AA411230).
文摘Multivariate statistical process monitoring and control (MSPM&C) methods for chemical process monitoring with statistical projection techniques such as principal component analysis (PCA) and partial least squares (PLS) are surveyed in this paper. The four-step procedure of performing MSPM&C for chemical process, modeling of processes, detecting abnormal events or faults, identifying the variable(s) responsible for the faults and diagnosing the source cause for the abnormal behavior, is analyzed. Several main research directions of MSPM&C reported in the literature are discussed, such as multi-way principal component analysis (MPCA) for batch process, statistical monitoring and control for nonlinear process, dynamic PCA and dynamic PLS, and on-line quality control by inferential models. Industrial applications of MSPM&C to several typical chemical processes, such as chemical reactor, distillation column, polymerization process, petroleum refinery units, are summarized. Finally, some concluding remarks and future considerations are made.
基金河南省自然科学基金,河南省教育厅自然科学基金,the Science Foundation of Henan University of Science and Technology
文摘We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and O, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively.
基金National Natural Foundation of China (No.60421002, No.70471052)
文摘Chemical process variables are always driven by random noise and disturbances. The closed-loop con-trol yields process measurements that are auto and cross correlated. The influence of auto and cross correlations on statistical process control (SPC) is investigated in detail by Monte Carlo experiments. It is revealed that in the sense of average performance, the false alarms rates (FAR) of principal component analysis (PCA), dynamic PCA are not affected by the time-series structures of process variables. Nevertheless, non-independent identical distribution will cause the actual FAR to deviate from its theoretic value apparently and result in unexpected consecutive false alarms for normal operating process. Dynamic PCA and ARMA-PCA are demonstrated to be inefficient to remove the influences of auto and cross correlations. Subspace identification-based PCA (SI-PCA) is proposed to improve the monitoring of dynamic processes. Through state space modeling, SI-PCA can remove the auto and cross corre-lations efficiently and avoid consecutive false alarms. Synthetic Monte Carlo experiments and the application in Tennessee Eastman challenge process illustrate the advantages of the proposed approach.
文摘Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
基金Supported by the National Natural Science Foundation of China (No. 40776006)Shanghai Typhoon Research Fund (No.2009ST05)
文摘The parameters of principal and directional extrema in a marine environment are important in marine engineering design, especially for appropriate construction of oceanic platforms and other structures. When designing wave walls and break water structures, the orientation of the breakwater or seawall depends mainly on the direction of the strongest waves. However, the strength of the breakwater and the elevation of the seawall depend on the magnitude of the biggest wave height of the strongest waves. Thus, identification of directional extrema plays an important role in the design of wave factors. When calculating the directional extremum, different materials may require different specific computational methods, yet few theoretical studies have been conducted in this field of research. Based on multivariate extremnm statistical theory, this paper utilizes a discrete random variable to build a joint probability model compounded by a discrete random variable and a multivariate continuous random variable. Furthermore, this paper provides the first investigation on the theories and methodologies to deduce wave directional extrema. The results provide tools for both creating the calculation method of the directional extremum value and providing the rational directional extremum parameters for marine engineering design.
基金supported by the National Natural Science Foundation of China (No.31071541)
文摘Euphausia pacific is an important source of natural astaxanthin. Studies were carried out to assess the extractability of astaxanthin from E. pacific using subcritical 1, 1, 1,2-tetrafluoroethane (R134a). To examine the effects of multiple process variables on the extraction yield, astaxanthin was extracted under various conditions of pressure (30-150bar), temperature (303-343 K), time (10-50rain), flow rate (2-10gmin-1), moisture content (5.5%-63.61%), and particle size (0.25-0.109mm). The results showed that the extraction yield increased with temperature, pressure, time and flow rate, but decreased with moisture content and particle size. A maximum yield of 87.74% was obtained under conditions of 100bar, 333K, and 30min with a flow rate of 6gmin-1 and a moisture content of 5.5%. The substantial astaxanthin yield obtained under low-pressure conditions demonstrates that subcritical R134a is a good alternative to CO2 for extraction of astaxanthin from E. pacific.
基金The project supported by the Key Project of the Chinese Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024+2 种基金Chinese Ministry of Education,the National Natural Science Foundation of China under Grant Nos.60772023 and 60372095the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)under Grant No.2005CB321901
文摘In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.
基金The project supported by National Natural Science Foundation of China under Grant No.10671121
文摘The bilinear equation of the genera/nonlinear Schrodinger equation with derivative (GDNLSE) and the N-soliton solutions are obtained through the dependent variable transformation and the Hirota method, respectively. The bilinear equation of the nonlinear Schrodinger equation with derivative (DNLSE) and its multisoliton solutions are given by reduction.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.
基金The project supported in part by Natural Science Foundation of Henan Province of China under Grant No. 2006110002 and the Science Foundation of Henan University of Science and Technology under Grant No. 2004ZD002
文摘The cubic-quintic nonlinear Schroedinger equation (CQNLS) plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients (vCQNLS) are derived with the aid of a set of subsidiary high-order ordinary differential equations (sub-equations for short). The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.
文摘A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
基金Supported by NSFC (No.79770 0 63) and Natural Sciences and En-gineering Research Council of Canada
文摘This paper reports the reengineering of the assembly processes of printed circuit boards (PCBs) used in computers.The new designed assembly processes are quite different from the traditional ones,and the business performance is dramatically improved through establishing parallel workstations,off line workstation,merging workstations and organizing a small teamwork who cooperates in stations.“ITHINK”,a software package of business process reengineering (BPR),was used to analyze the current processes and create new processes.ITHINK is a powerful tool of BPR in modeling business processes,“soft” variables and conducting sensitivity analysis.The new assembly processes were tested over a period of 8 hours simulation.The results show that the new processes can increase throughput by 80% with only requiring less additional resources.The throughput can increase further by 17.5% when a small teamwork cooperates in some stations.
基金Project supported by the Collaborative Research and Development Program of NSERC(Natural Sciences and Engineering Research Council of Canada) with Industrial Sponsorship from Vale,Teck Cominco,Xstrata Process Support,Agnico-Eagle,Shell Canada,Barrick Gold,COREM,SGS Lakefield Research and Flottec
文摘This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble (D32). The study was performed using pilot-scale equipment (0.8 m^3) that is up to two orders of magnitude larger than equipment used for studies performed to date by others, and incorporated the key process variables of frother type and impeller speed. The results show that each frother family exhibits a unique CCC95-HLB relationship dependent on n (number of C-atoms in alkyl group) and m (number of propylene oxide group). Empirical models were developed to predict CCC95 from HLB associated with other two parameters a and ft. The impeller speed-bubble size tests show that D32 is unaffected by increased impeller tip speed across the range of 4.6 to 9.2 m/s (representing the industrial operating range), although D32 starts to increase below 4.6 m/s. The finding is valid for both coalescing and non-coalescing conditions. The results suggest that the bubble size and bubble size distribution (BSD) being created do not change with increasing impeller speed in the quiescent zone of the flotation.