By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （...By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.展开更多
The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryf...The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.展开更多
Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broe...Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.展开更多
We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads ...We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.展开更多
The separation characteristic of raw coal from Luoyang mining area, China, was investigated by applying a dry coal beneficiation flowsheet with the dense medium gas-solid fluidized bed as main separating equipment. Th...The separation characteristic of raw coal from Luoyang mining area, China, was investigated by applying a dry coal beneficiation flowsheet with the dense medium gas-solid fluidized bed as main separating equipment. The experimental and simulation results indicate that the dense medium gas-solid fluidized bed can provide uniform distribution and stable fluctuation of bed densities at various heights. Two types of different separating approaches were compared using the dry coal beneficiation flowsheet. Compared with obtaining cleaning coal in the first stage of the flowsheet, a higher yield of the cleaning coal and better separation efficiency can be achieved when discharging gangue in the first stage. Finally, the results indicate that 64.86% pure cleaning coal with an ash content of 11.77% and 13.53% middlings were obtained, and 21.61% gangue was removed in two successive separation stages with the probable errors of 0.05 and 0.07 g/cm3, respectively.展开更多
The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partial differential equation. Applying the B?cklund transformation and introducing the arbitrary...The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partial differential equation. Applying the B?cklund transformation and introducing the arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types of solutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functions appropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the number of the peaks.展开更多
A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we c...A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite general solution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.展开更多
By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, ring...By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, fractal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.展开更多
In this paper,the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation.The equation is reduced to some(...In this paper,the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation.The equation is reduced to some(1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test technique.Based on this idea and with the aid of symbolic computation,some new explicit solutions can be obtained.展开更多
By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal...By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal' formula is defined, and then, rich coherent structures canbe found by selecting corresponding functions appropriately.展开更多
High-quality standard oil synthetic zeolite-13(SSZ-13) membranes with thickness only ~ 1.0 μm were prepared on tubular supports by the new seeded-gel approach. Seeded-gel approach is simpler than the normal secondary...High-quality standard oil synthetic zeolite-13(SSZ-13) membranes with thickness only ~ 1.0 μm were prepared on tubular supports by the new seeded-gel approach. Seeded-gel approach is simpler than the normal secondary-growth one since adding seeds in the gel is simpler than seeding on the support surface. The synthesis time was greatly reduced from 3.0 to 1.0 d after synthesis modification of gel aging and seed sizes. Low temperature ozone calcination was used for the removal of the organic structural directing agent. The best SSZ-13 membrane displayed CO_(2)permeances of 1.3 × 10^(-6) and 1.5 × 10^(-6) mol·m^(-2)·s^(-1)·Pa^(-1) and CO_(2)/CH_(4) and CO_(2)/N_(2) selectivities of 125 and 27 for equimolar CO_(2)/CH_(4) and CO_(2)/N2mixtures at 0.2 MPa pressure drop and 298 K, respectively. Separation performance of the membrane in the two binary mixtures is higher than that of most zeolite membranes. Three SSZ-13 membranes were reproducibly prepared on tubular supports by seeded-gel approach and the standard deviation ratios of CO_(2) permeance and CO_(2)/CH_(4) selectivity are 12.5% and 7%, respectively. It suggests that this new synthesis approach is creditable. The effects of temperature and pressure on separation performance of the thin SSZ-13 membranes were studied in the two binary mixtures. The tubular SSZ-13 membranes displayed great potentials for CO_(2) capture from natural gas, biogas and flue gas.展开更多
Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution...Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.展开更多
Based on the different hydrophobicities of the intermediates of proteins the various conformational intermediates of the refolding of a-amylase originally denatured with 8.0 mol/L urea solution were separated with hi...Based on the different hydrophobicities of the intermediates of proteins the various conformational intermediates of the refolding of a-amylase originally denatured with 8.0 mol/L urea solution were separated with high performance hydrophobic interaction chromatography(HPHIC). Compared to the separation of the same intermediates with weak anion exchange chromatography and size-exclusion chromatography the result obtained with HPHIC is the best It would be expected that HPHIC may be a strongly potential tool to separate intermediates of some proteins which cannot be, or cannot completely be refolded by HPHIC.展开更多
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05010 Acknowledgments The authors would like to thank professor Chun-Long Zheng for his fruitful and helpful suggestions.
文摘By means of an improved mapping method and a variable separation method, a series of variable separation solutions including solitary wave solutions, periodic wave solutions and rational function solutions） to the （2＋1）-dimensional breaking soliton system is derived. Based on the derived solitary wave excitation, we obtain some special annihilation solitons and chaotic solitons in this short note.
基金The project supported by National Natural Science Foundation of China
文摘The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.
文摘Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.
文摘We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.
基金Projects(51221462)supported by the National Natural Science Foundation of ChinaProject(2014QNA28)supported by the Fundamental Research Funds for the Central Universities,China
文摘The separation characteristic of raw coal from Luoyang mining area, China, was investigated by applying a dry coal beneficiation flowsheet with the dense medium gas-solid fluidized bed as main separating equipment. The experimental and simulation results indicate that the dense medium gas-solid fluidized bed can provide uniform distribution and stable fluctuation of bed densities at various heights. Two types of different separating approaches were compared using the dry coal beneficiation flowsheet. Compared with obtaining cleaning coal in the first stage of the flowsheet, a higher yield of the cleaning coal and better separation efficiency can be achieved when discharging gangue in the first stage. Finally, the results indicate that 64.86% pure cleaning coal with an ash content of 11.77% and 13.53% middlings were obtained, and 21.61% gangue was removed in two successive separation stages with the probable errors of 0.05 and 0.07 g/cm3, respectively.
文摘The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partial differential equation. Applying the B?cklund transformation and introducing the arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types of solutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functions appropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the number of the peaks.
文摘A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite general solution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.
文摘By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, fractal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.
文摘In this paper,the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation.The equation is reduced to some(1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test technique.Based on this idea and with the aid of symbolic computation,some new explicit solutions can be obtained.
文摘By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal' formula is defined, and then, rich coherent structures canbe found by selecting corresponding functions appropriately.
基金Financial supports from the National Natural Science Foundation of China (21921006, 21938007 and 21576131)the open project of the State Key Laboratory of Materials-Oriented Chemical Engineering of China (KL21-04)。
文摘High-quality standard oil synthetic zeolite-13(SSZ-13) membranes with thickness only ~ 1.0 μm were prepared on tubular supports by the new seeded-gel approach. Seeded-gel approach is simpler than the normal secondary-growth one since adding seeds in the gel is simpler than seeding on the support surface. The synthesis time was greatly reduced from 3.0 to 1.0 d after synthesis modification of gel aging and seed sizes. Low temperature ozone calcination was used for the removal of the organic structural directing agent. The best SSZ-13 membrane displayed CO_(2)permeances of 1.3 × 10^(-6) and 1.5 × 10^(-6) mol·m^(-2)·s^(-1)·Pa^(-1) and CO_(2)/CH_(4) and CO_(2)/N_(2) selectivities of 125 and 27 for equimolar CO_(2)/CH_(4) and CO_(2)/N2mixtures at 0.2 MPa pressure drop and 298 K, respectively. Separation performance of the membrane in the two binary mixtures is higher than that of most zeolite membranes. Three SSZ-13 membranes were reproducibly prepared on tubular supports by seeded-gel approach and the standard deviation ratios of CO_(2) permeance and CO_(2)/CH_(4) selectivity are 12.5% and 7%, respectively. It suggests that this new synthesis approach is creditable. The effects of temperature and pressure on separation performance of the thin SSZ-13 membranes were studied in the two binary mixtures. The tubular SSZ-13 membranes displayed great potentials for CO_(2) capture from natural gas, biogas and flue gas.
基金National Natural Science Foundation of China under Grant No.10675065the Science Research Foundation of the Education Department of Zhejiang Province under Grant No.20070979+1 种基金the Natural Science Foundation of Zhejiang Province under Grant No.Y604036the State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation\PLN0402
文摘Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.
文摘Based on the different hydrophobicities of the intermediates of proteins the various conformational intermediates of the refolding of a-amylase originally denatured with 8.0 mol/L urea solution were separated with high performance hydrophobic interaction chromatography(HPHIC). Compared to the separation of the same intermediates with weak anion exchange chromatography and size-exclusion chromatography the result obtained with HPHIC is the best It would be expected that HPHIC may be a strongly potential tool to separate intermediates of some proteins which cannot be, or cannot completely be refolded by HPHIC.
