For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for s...For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.展开更多
The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper...The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper presents a new approach to rank the alternatives by G1-coefficient of variation method.The focus of this approach is the use of the combination weighing,which is able to compensate for the deficiencies in the method of evaluation index single weighing.In the case study,an appropriate evaluation index system was established to determine the evaluation value of each ventilation mode.Then the proposed approach was used to select the best development face ventilation mode.The result shows that the proposed approach is able to rank the alternative development face ventilation mode reasonably,the combination weighing method had the advantages of both subjective and objective weighing methods in that it took into consideration of both the experience and wisdom of experts,and the new changes in objective conditions.This approach provides a more reasonable and reliable procedure to analyse and evaluate different ventilation modes.展开更多
Functional traits, specifically leaf functional traits, are core-topics to explore importance to the invasion success of invasive plant species. This study aims to address the differences in leaf functional traits and...Functional traits, specifically leaf functional traits, are core-topics to explore importance to the invasion success of invasive plant species. This study aims to address the differences in leaf functional traits and their corresponding variability of the invasive tree staghorn sumac Rhus typhina L. with different invasion success, including lower and higher invasion success, in two climatic regions in North China, including a warm temperate region and a cold temperate region. No significant differences were found for leaf functional traits of staghorn sumac across different invasion success. However, the variability of leaf chlorophyll and nitrogen concentrations of staghorn sumac under higher invasion success were approximately 66.023% and 68.615% higher than those under lower invasion success, respectively. The leaf chlorophyll and nitrogen concentrations of staghorn sumac in the warm temperate region were approximately 18.432% and 16.337% higher than those in cold temperate region, respectively. The variability of specific leaf area of staghorn sumac in warm temperate region was approximately 59.802% higher than that in cold temperate region. Accordingly, leaf chlorophyll and N concentrations as well as specific leaf area of staghorn sumac and their corresponding variability may play an essential role in shaping ecological success of studied invader along a climatic gradient.展开更多
[Objective] The aim was to analyze the differences in haploid induction rates of different inducers. [Method] Six maize inducers with purple spot and purple color were selected as the male parents to pollinate six inb...[Objective] The aim was to analyze the differences in haploid induction rates of different inducers. [Method] Six maize inducers with purple spot and purple color were selected as the male parents to pollinate six inbred lines. [Result] The mean haploid induction rates were significantly different among the inducers: KMS-3 >WY-1 >PR-2 >YP-13 >KMS-2 >KMS-1. The haploid induction rates of the different hybrid materials were significantly different: K410 >105A >103A >104A >107A >D271 >106A>L73>N21>KZ58. [Conclusion] The haploid inducer line PR-2, which had high haploid induction rate and low variation coefficient, was an elite haploid inducer.展开更多
The energy absorption capacity of the Al5083 thin-walled tube produced by parallel tubular angular pressing(PTCAP) process was evaluated. Also, microstructure, mechanical properties, and anisotropy coefficients were s...The energy absorption capacity of the Al5083 thin-walled tube produced by parallel tubular angular pressing(PTCAP) process was evaluated. Also, microstructure, mechanical properties, and anisotropy coefficients were studied in the peripheral and axial directions. Results showed that values of energy absorption decreased with processing pass increasing and the values for the unprocessed, first and second passes were obtained to be 167, 161.4 and 160.7 J, respectively. The differences between the simulation results for the energy absorption values and their experimental values for the unprocessed, the first and the second PTCAP passes samples are about 5%, 10%, and 13%, respectively. The energy absorption capacity was related to the anisotropy coefficient and microstructure. The results demonstrated that grain refinement occurred and ultimate tensile strength(UTS) and microhardness after the first and second PTCAP passes were enhanced, while the increase rate in the first pass was much severer. Also, by applying PTCAP, the deformation modes were altered, such that the deformation mode of the annealed tube was quite symmetrical and circular while for the first and second passes there have been triple and double lobes diamond. The results of the numerical simulation for the deformation mode of the annealed and PTCAPed tubes were consistent with the experimental results. The deformation mode of tubes is dependent on their mechanical properties and variation of the mechanical properties during PTCAP process.展开更多
In recent years, long-offset exploration has been widely used, especially on marine seismic surveys. Conventional AVO analysis is insufficient for long-offset seismic data. To widen the application range of AVO analys...In recent years, long-offset exploration has been widely used, especially on marine seismic surveys. Conventional AVO analysis is insufficient for long-offset seismic data. To widen the application range of AVO analysis, we present a new P-wave reflection coefficient approximation applicable to long-offset data. Our result is similar to the well known Shuey formula which can be treated as an approximation to our results for short-offset seismic data.展开更多
A new modeling concept, referred to as Modeling Surgery, has been recently developed at University of Wisconsin-Madison. It is specifically designed to diagnose coupled feedbacks between different climate components a...A new modeling concept, referred to as Modeling Surgery, has been recently developed at University of Wisconsin-Madison. It is specifically designed to diagnose coupled feedbacks between different climate components as well as climatic teleconnections within a specific component through systematically modifying the coupling configurations and teleconnective pathways. It thus provides a powerful means for identifying the causes and mechanisms of low-frequency variability in the Earth's climate system. In this paper, we will give a short review of our recent progress in this new area.展开更多
A shadow detection method using pulse couple neural network inspired by the characters of human visual system is proposed.More precisely,lateral inhibition of human vision and coefficient of variation are combined tog...A shadow detection method using pulse couple neural network inspired by the characters of human visual system is proposed.More precisely,lateral inhibition of human vision and coefficient of variation are combined together to improve the pulse couple neural network.Shadow detection is considered to be a shadow region segmentation problem.Experiment shows that the presented method is consistent with human vision compared to shadow detection methods based on HSV and pulse couple neural network(PCNN) by both subjective and objective assessments.展开更多
With the rapid development of the marine economy,the demand for marine resources development and the pressure on marine environmental protection are gradually increasing.It is critical to evaluate and analyze the driv...With the rapid development of the marine economy,the demand for marine resources development and the pressure on marine environmental protection are gradually increasing.It is critical to evaluate and analyze the driving forces of marine sustainable development in order to promote the coordinated development of the marine economy,resources and environment.Taking Jiangsu Province of China as an example,this paper constructs an evaluation index system for marine sustainable development from the three aspects of marine economy,resources and environment,and calculates the weight of the variation coefficient for each indicator.Based on the grey relational model,the average value of the relational degree,calculated by the average value method of correlation coefficients and the weighting method,is then used to evaluate the status of marine sustainable development in this province.The comprehensive index model is used to analyze the dynamic trend of the evolution of marine sustainable development.The driving forces of marine sustainable development are analyzed by the path analysis method combined with the average values of the grey relational degree for each indicator.This analysis found that the marine sustainable development in 2016 and 2012 was good,the situation in 2007 was bad,and the remaining years were intermediate.Compared with the previous years,the optimal conditions of 2008 and 2012 were obvious.The main driving factors of marine sustainable development are cargo throughput of coastal ports,economic losses caused by storm surges in coastal areas,the area of marine nature reserves in coastal areas,coastal wind power generation capacity,and marine biodiversity.展开更多
A high-performance liquid chromatography (HPLC) system was used in the reversed phase mode for the determination ofbenzalkonium chloride (BKC) in azithromycin viscous ophthalmic drops. A Venusil-XBP(L)-C18 (150...A high-performance liquid chromatography (HPLC) system was used in the reversed phase mode for the determination ofbenzalkonium chloride (BKC) in azithromycin viscous ophthalmic drops. A Venusil-XBP(L)-C18 (150 mm×4.6 mm, 5 gm) column was used at 50℃. The mobile phase consisted of a mixture of methanol-potassium phosphate (16:5, v/v). Two sample preparation methods were compared. The results suggested that, compared with an extraction procedure, a deproteinization procedure was much quicker and more convenient. Using the deproteinization procedure for sample preparation, calibration curves were linear in the range 5.0-50μg/ml. The within-day and inter-day coefficients of variation were less than 10%. The average recoveries were determined as 96.70%, 98.52%, and 97.96% at concentrations of 10.0, 30.0, and 50.0 μg/ml, respectively. Variability in precision did not exceed 5%. In conclusion, this HPLC method using a simple sample treatment procedure appears suitable for monitoring BKC content in azithromycin viscous ophthalmic drops.展开更多
Aims Litterfall is a key parameter in forest biogeochemical cycle and fire risk prediction.However,considerable uncertainty remains regarding the litterfall variations with forest ages.Quantifying the interannual vari...Aims Litterfall is a key parameter in forest biogeochemical cycle and fire risk prediction.However,considerable uncertainty remains regarding the litterfall variations with forest ages.Quantifying the interannual variation of forest litterfall is crucial for reducing uncertainties in large-scale litterfall prediction.Methods Based on the available dataset(N=318)with continuous multi-year(≥2 years)measurements of litterfall in Chinese planted and secondary forests,coefficient of variation(CV),variation percent(V_(P)),and the ratio of next-year litterfall to current-year litterfall were used as the indexes to quantify the interannual variability in litterfall.Important Findings The interannual variations of litterfall showed a declining trend with increasing age from 1 to 90 years.The litterfall variations were the largest in 1-10 years(mean CV=23.51%and mean V_(P)=−28.59%to 20.89%),which were mainly from tree growth(mean ratio of next-year to current-year=1.20).In 11-40 years,the interannual variations of litterfall gradually decreased but still varied widely,mean CV was~18%and mean V_(P) ranged from−17.69%to 21.19%.In 41-90 years,the interannual variations minimized to 8.98%in mean CV and~8%in mean V_(P).As a result,forest litterfall remained relatively low and constant when stand age was larger than 40 years.This result was different from the previous assumptions that forest litterfall reached relatively stable when stand age was larger than 30,20 or even 15 years.Our findings can improve the knowledge about forest litter ecology and provide the groundwork for carbon budget and biogeochemical cycle models at a large scale.展开更多
Autism spectrum disorder(ASD) is gathering concerns in socially developed countries. ASD is a neuropsychiatric disorder of genetic origin with high prevalence of 1%–2%. The patients with ASD characteristically show i...Autism spectrum disorder(ASD) is gathering concerns in socially developed countries. ASD is a neuropsychiatric disorder of genetic origin with high prevalence of 1%–2%. The patients with ASD characteristically show impaired social skills. Today, many genetic studies identify numerous susceptible genes and genetic loci associated with ASD. Although some genetic factors can lead to abnormal brain function linked to ASD phenotypes, the pathogenic mechanism of ASD is still unclear. Here, we discuss a new mouse model for ASD as an advanced tool to understand the mechanism of ASD.展开更多
The density of forest cover based upon reaction diffusion model for mono-species of two age classes with seed dynamics is to be attempted. The prevailing densities of young, old species and airborne seedlings are reso...The density of forest cover based upon reaction diffusion model for mono-species of two age classes with seed dynamics is to be attempted. The prevailing densities of young, old species and airborne seedlings are resolved by homotopy perturbation method which is applied in reaction diffusion model. This model is utilized to verify the effect of the density of forest cover with the following variables namely seed reproduction, seed deposition, seed establishment rates, coefficients of aging of old tree and coefficients of mortality on the space variable.展开更多
In this article,we establish exact solutions for the variable-coefficient Fisher-type equation.The solutions are obtained by the modified sine-cosine method and ansatz method.The soliton and periodic solutions and top...In this article,we establish exact solutions for the variable-coefficient Fisher-type equation.The solutions are obtained by the modified sine-cosine method and ansatz method.The soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz method.These solutions are important for the explanation of some practical physical problems.The obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients.展开更多
基金The National Natural Science Foundation of China(No.10972151,11272227)
文摘For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.
基金Projects(51504286,51374242)supported by the National Natural Science Foundation of ChinaProject(2015M572270)supported by China Postdoctoral Science FoundationProject(2015RS4004)supported by the Science and Technology Plan of Hunan Province,China
文摘The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper presents a new approach to rank the alternatives by G1-coefficient of variation method.The focus of this approach is the use of the combination weighing,which is able to compensate for the deficiencies in the method of evaluation index single weighing.In the case study,an appropriate evaluation index system was established to determine the evaluation value of each ventilation mode.Then the proposed approach was used to select the best development face ventilation mode.The result shows that the proposed approach is able to rank the alternative development face ventilation mode reasonably,the combination weighing method had the advantages of both subjective and objective weighing methods in that it took into consideration of both the experience and wisdom of experts,and the new changes in objective conditions.This approach provides a more reasonable and reliable procedure to analyse and evaluate different ventilation modes.
基金Project(31300343)supported by the National Natural Science Foundation of ChinaProject(Y20160023)supported by Open Science Research Fund of State Key Laboratory of Soil and Sustainable Agriculture,Institute of Soil Science,Chinese Academy of Sciences,China+1 种基金Project supported by Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD),ChinaProject supported by Jiangsu Collaborative Innovation Center of Technology and Material of Water Treatment
文摘Functional traits, specifically leaf functional traits, are core-topics to explore importance to the invasion success of invasive plant species. This study aims to address the differences in leaf functional traits and their corresponding variability of the invasive tree staghorn sumac Rhus typhina L. with different invasion success, including lower and higher invasion success, in two climatic regions in North China, including a warm temperate region and a cold temperate region. No significant differences were found for leaf functional traits of staghorn sumac across different invasion success. However, the variability of leaf chlorophyll and nitrogen concentrations of staghorn sumac under higher invasion success were approximately 66.023% and 68.615% higher than those under lower invasion success, respectively. The leaf chlorophyll and nitrogen concentrations of staghorn sumac in the warm temperate region were approximately 18.432% and 16.337% higher than those in cold temperate region, respectively. The variability of specific leaf area of staghorn sumac in warm temperate region was approximately 59.802% higher than that in cold temperate region. Accordingly, leaf chlorophyll and N concentrations as well as specific leaf area of staghorn sumac and their corresponding variability may play an essential role in shaping ecological success of studied invader along a climatic gradient.
基金Supported by Key Program for International S&T Cooperation Projects of China(2011DFR30840)National Key Technology Research and Development Program of Harbin(2007AA6BE047)
文摘[Objective] The aim was to analyze the differences in haploid induction rates of different inducers. [Method] Six maize inducers with purple spot and purple color were selected as the male parents to pollinate six inbred lines. [Result] The mean haploid induction rates were significantly different among the inducers: KMS-3 >WY-1 >PR-2 >YP-13 >KMS-2 >KMS-1. The haploid induction rates of the different hybrid materials were significantly different: K410 >105A >103A >104A >107A >D271 >106A>L73>N21>KZ58. [Conclusion] The haploid inducer line PR-2, which had high haploid induction rate and low variation coefficient, was an elite haploid inducer.
文摘The energy absorption capacity of the Al5083 thin-walled tube produced by parallel tubular angular pressing(PTCAP) process was evaluated. Also, microstructure, mechanical properties, and anisotropy coefficients were studied in the peripheral and axial directions. Results showed that values of energy absorption decreased with processing pass increasing and the values for the unprocessed, first and second passes were obtained to be 167, 161.4 and 160.7 J, respectively. The differences between the simulation results for the energy absorption values and their experimental values for the unprocessed, the first and the second PTCAP passes samples are about 5%, 10%, and 13%, respectively. The energy absorption capacity was related to the anisotropy coefficient and microstructure. The results demonstrated that grain refinement occurred and ultimate tensile strength(UTS) and microhardness after the first and second PTCAP passes were enhanced, while the increase rate in the first pass was much severer. Also, by applying PTCAP, the deformation modes were altered, such that the deformation mode of the annealed tube was quite symmetrical and circular while for the first and second passes there have been triple and double lobes diamond. The results of the numerical simulation for the deformation mode of the annealed and PTCAPed tubes were consistent with the experimental results. The deformation mode of tubes is dependent on their mechanical properties and variation of the mechanical properties during PTCAP process.
基金This research is sponsored by China National Natural Science Foundation (40574050, 40521002) and CNPC Key Research Program (06A 10101).
文摘In recent years, long-offset exploration has been widely used, especially on marine seismic surveys. Conventional AVO analysis is insufficient for long-offset seismic data. To widen the application range of AVO analysis, we present a new P-wave reflection coefficient approximation applicable to long-offset data. Our result is similar to the well known Shuey formula which can be treated as an approximation to our results for short-offset seismic data.
文摘A new modeling concept, referred to as Modeling Surgery, has been recently developed at University of Wisconsin-Madison. It is specifically designed to diagnose coupled feedbacks between different climate components as well as climatic teleconnections within a specific component through systematically modifying the coupling configurations and teleconnective pathways. It thus provides a powerful means for identifying the causes and mechanisms of low-frequency variability in the Earth's climate system. In this paper, we will give a short review of our recent progress in this new area.
基金Projects(61262032,61173122)supported by the National Natural Science Foundation of ChinaProject(12JJ038)supported by the Key Project of Natural Science Foundation of Hunan Province,China+1 种基金Project(2012FJ3100)supported by the Hunan Provincial Science&Technology Department,ChinaProject(12B103)supported by the Youth Project of Hunan Universities and Colleges Science Research,China
文摘A shadow detection method using pulse couple neural network inspired by the characters of human visual system is proposed.More precisely,lateral inhibition of human vision and coefficient of variation are combined together to improve the pulse couple neural network.Shadow detection is considered to be a shadow region segmentation problem.Experiment shows that the presented method is consistent with human vision compared to shadow detection methods based on HSV and pulse couple neural network(PCNN) by both subjective and objective assessments.
基金Jiangsu Social Science Fund(19GLC013,17GLB003)Open Fund of Key Laboratory of Marine Management Technology of State Oceanic Administration(2015105HX90085)。
文摘With the rapid development of the marine economy,the demand for marine resources development and the pressure on marine environmental protection are gradually increasing.It is critical to evaluate and analyze the driving forces of marine sustainable development in order to promote the coordinated development of the marine economy,resources and environment.Taking Jiangsu Province of China as an example,this paper constructs an evaluation index system for marine sustainable development from the three aspects of marine economy,resources and environment,and calculates the weight of the variation coefficient for each indicator.Based on the grey relational model,the average value of the relational degree,calculated by the average value method of correlation coefficients and the weighting method,is then used to evaluate the status of marine sustainable development in this province.The comprehensive index model is used to analyze the dynamic trend of the evolution of marine sustainable development.The driving forces of marine sustainable development are analyzed by the path analysis method combined with the average values of the grey relational degree for each indicator.This analysis found that the marine sustainable development in 2016 and 2012 was good,the situation in 2007 was bad,and the remaining years were intermediate.Compared with the previous years,the optimal conditions of 2008 and 2012 were obvious.The main driving factors of marine sustainable development are cargo throughput of coastal ports,economic losses caused by storm surges in coastal areas,the area of marine nature reserves in coastal areas,coastal wind power generation capacity,and marine biodiversity.
基金Project (No. 2008BAI55B03) supported by the Key Project of the National Science and Technology Pillar Program, China
文摘A high-performance liquid chromatography (HPLC) system was used in the reversed phase mode for the determination ofbenzalkonium chloride (BKC) in azithromycin viscous ophthalmic drops. A Venusil-XBP(L)-C18 (150 mm×4.6 mm, 5 gm) column was used at 50℃. The mobile phase consisted of a mixture of methanol-potassium phosphate (16:5, v/v). Two sample preparation methods were compared. The results suggested that, compared with an extraction procedure, a deproteinization procedure was much quicker and more convenient. Using the deproteinization procedure for sample preparation, calibration curves were linear in the range 5.0-50μg/ml. The within-day and inter-day coefficients of variation were less than 10%. The average recoveries were determined as 96.70%, 98.52%, and 97.96% at concentrations of 10.0, 30.0, and 50.0 μg/ml, respectively. Variability in precision did not exceed 5%. In conclusion, this HPLC method using a simple sample treatment procedure appears suitable for monitoring BKC content in azithromycin viscous ophthalmic drops.
基金supported by the National Key Research and Development Program of China(2017YFC0503906)the China Special Fund for Meteorological Research in the Public Interest(GYHY201406034).
文摘Aims Litterfall is a key parameter in forest biogeochemical cycle and fire risk prediction.However,considerable uncertainty remains regarding the litterfall variations with forest ages.Quantifying the interannual variation of forest litterfall is crucial for reducing uncertainties in large-scale litterfall prediction.Methods Based on the available dataset(N=318)with continuous multi-year(≥2 years)measurements of litterfall in Chinese planted and secondary forests,coefficient of variation(CV),variation percent(V_(P)),and the ratio of next-year litterfall to current-year litterfall were used as the indexes to quantify the interannual variability in litterfall.Important Findings The interannual variations of litterfall showed a declining trend with increasing age from 1 to 90 years.The litterfall variations were the largest in 1-10 years(mean CV=23.51%and mean V_(P)=−28.59%to 20.89%),which were mainly from tree growth(mean ratio of next-year to current-year=1.20).In 11-40 years,the interannual variations of litterfall gradually decreased but still varied widely,mean CV was~18%and mean V_(P) ranged from−17.69%to 21.19%.In 41-90 years,the interannual variations minimized to 8.98%in mean CV and~8%in mean V_(P).As a result,forest litterfall remained relatively low and constant when stand age was larger than 40 years.This result was different from the previous assumptions that forest litterfall reached relatively stable when stand age was larger than 30,20 or even 15 years.Our findings can improve the knowledge about forest litter ecology and provide the groundwork for carbon budget and biogeochemical cycle models at a large scale.
基金supported in part by a grant from Japan Society for the Promotion of Science and Ministry of Education,Culture,Sports,Science and Technology KAKENHI,Core Research for Evolutional Science and Technology,Strategic International Cooperative Program of Japan Science and Technology Agency,and by research grants from Takeda Science Foundation,the Naito Foundation and Terumo Life Science Foundation
文摘Autism spectrum disorder(ASD) is gathering concerns in socially developed countries. ASD is a neuropsychiatric disorder of genetic origin with high prevalence of 1%–2%. The patients with ASD characteristically show impaired social skills. Today, many genetic studies identify numerous susceptible genes and genetic loci associated with ASD. Although some genetic factors can lead to abnormal brain function linked to ASD phenotypes, the pathogenic mechanism of ASD is still unclear. Here, we discuss a new mouse model for ASD as an advanced tool to understand the mechanism of ASD.
文摘The density of forest cover based upon reaction diffusion model for mono-species of two age classes with seed dynamics is to be attempted. The prevailing densities of young, old species and airborne seedlings are resolved by homotopy perturbation method which is applied in reaction diffusion model. This model is utilized to verify the effect of the density of forest cover with the following variables namely seed reproduction, seed deposition, seed establishment rates, coefficients of aging of old tree and coefficients of mortality on the space variable.
文摘In this article,we establish exact solutions for the variable-coefficient Fisher-type equation.The solutions are obtained by the modified sine-cosine method and ansatz method.The soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz method.These solutions are important for the explanation of some practical physical problems.The obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients.