Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers e...Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W(t)=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.展开更多
Olefin oligomerization reaction catalyzed by new catalyst systems(a Br?nsted‐acidic ionic liquid as the main catalyst and tricaprylylmethylammonium chloride as the co‐catalyst) has been investigat‐ed. The synthe...Olefin oligomerization reaction catalyzed by new catalyst systems(a Br?nsted‐acidic ionic liquid as the main catalyst and tricaprylylmethylammonium chloride as the co‐catalyst) has been investigat‐ed. The synthesized Br?nsted acidic ionic liquids were characterized by Fourier transform infrared spectroscopy(FT‐IR), ultraviolet‐visible spectroscopy(UV), ^1H nuclear magnetic resonance(NMR), and ^13 C NMR to analyze their structures and acidities. The influence of different ionic liquids, ionic liquid loading, different co‐catalysts, catalyst ratios(mole ratio of ionic liquid to co‐catalyst), reac‐tion time, pressure, temperature, solvent, source of reactants, and the recycling of catalyst systems was studied. Among the synthesized ionic liquids, 1‐(4‐sulfonic acid)butyl‐3‐hexylimidazolium hydrogen sulfate([HIMBs]HSO4) exhibited the best catalytic activity under the tested reaction con‐ditions. The conversion of isobutene and selectivity of trimers were 83.21% and 35.80%, respec‐tively, at the optimum reaction conditions. Furthermore, the catalyst system can be easily separated and reused; a feasible reaction mechanism is proposed on the basis of the distribution of experi‐mental products.展开更多
Based on homogeneous balance method, sofiton solutions to a generalized nonlinear Sehr6dinger equation (NLSE) with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-lik...Based on homogeneous balance method, sofiton solutions to a generalized nonlinear Sehr6dinger equation (NLSE) with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-like spatial solitons can be formed in the Kerr nonlinear media in the cylindrical symmetric geometry. It is shown by numerical simulation that these soliton profiles are stable.展开更多
Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation (BT) for (3-k l)-Dimensional Jimbo-Miwa (JM) equation. The auto-BT obtain...Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation (BT) for (3-k l)-Dimensional Jimbo-Miwa (JM) equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the (3+1)-Dimensional JM equation is obtained.展开更多
The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of op...The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art classical supercomputers.展开更多
Text alignment is crucial to the accuracy of MT (Machine Translation) systems, some NLP (Natural Language Processing) tools or any other text processing tasks requiring bilingual data. This research proposes a lan...Text alignment is crucial to the accuracy of MT (Machine Translation) systems, some NLP (Natural Language Processing) tools or any other text processing tasks requiring bilingual data. This research proposes a language independent sentence alignment approach based on Polish (not position-sensitive language) to English experiments. This alignment approach was developed on the TED (Translanguage English Database) talks corpus, but can be used for any text domain or language pair. The proposed approach implements various heuristics for sentence recognition. Some of them value synonyms and semantic text structure analysis as a part of additional information. Minimization of data loss was ensured. The solution is compared to other sentence alignment implementations. Also an improvement in MT system score with text processed with the described tool is shown.展开更多
BrФnsted-acidic zeolite and zeotype materials are potential catalysts for the conversion of ethene to higher alkenes. In this study, two materials with AFI structure but different acid strength, H-SAPO-5 and H-SSZ-24...BrФnsted-acidic zeolite and zeotype materials are potential catalysts for the conversion of ethene to higher alkenes. In this study, two materials with AFI structure but different acid strength, H-SAPO-5 and H-SSZ-24, were subject to studies of ethene, cis-2-butene and ethene-butene mixture conversion under conditions where C3-C5 alkene formation is thermodynamically favoured over higher hydrocarbons(673-823 K, 1 atm). Ethene and cis-2-butene partial pressures were varied in the range 9-60 and 0.9-8.1 kPa, respectively, and contact times were varied in the range 3.78-756 and 0.573-76.4 s.μmol H+/cm^3 over H-SAPO-5 and H-SSZ-24, respectively. Less than 1% conversion of ethene and less than 10% conversion of butene was obtained in the range of conditions used for elucidation of rate parameters. The ethene conversion rates were more than an order of magnitude higher over the more acidic H-SSZ-24 than over H-SAPO-5(6.5 vs. 0.3 mmol/mol H+.s at 748 K, Pethene = 33 kP a), with corresponding lower reaction order in ethene(1.5 vs. 2.0 at 673 K) and lower apparent activation energy(52 vs. 80 kJ/mol at 698-823 K). Propene selectivity was substantially higher over H-SSZ-24 than over H-SAPO-5(68% vs. 36% at 0.5% ethene conversion). A similar difference in apparent reaction rates was observed for cis-2-butene conversion over the two catalysts, and for co-feeds of ethene and cis-2-butene. However, the cis-2-butene conversion to C3-C5 alkenes was found to be severely influenced by thermodynamic limitations, impeding a detailed kinetic analysis, and leading predominantly to isobutene formation at the highest temperatures.展开更多
Two definitions are given that Definitionl: an induced subgraph by a vertex vie G and its neighbors in G is defined as a vertex adjacent closed subgraph, and denoted by Qi (=G[V(Nvi)]), with the vertex vi called ...Two definitions are given that Definitionl: an induced subgraph by a vertex vie G and its neighbors in G is defined as a vertex adjacent closed subgraph, and denoted by Qi (=G[V(Nvi)]), with the vertex vi called the hub; and Definition2: A r(k,I)-I vertices graph is called the (k,l)-Ramsey graph, denoted by RG(k,1), if RG(k,1) only contains cliques Kk.1 and the intersect QiNQj of any two nonadjacent vertices vi and vj of RG(k,I) contains only Kk-2. Meanwhile, the RG(k,l)'s complement RG(I,k) contains only cliques Kl.l, and the intersect QiNQj of any two nonadjacent vertices vi and vj of RG(I,k) contains only Ki.2. On the basis of those definitions, two theorems are put forward and proved in this paper. They are Theoreml: the biggest clique in G is contained in some Qi of G, and Theorem 2: r(k,1) = [V(RG(k,I))I + 1. With those definitions and theorems as well as analysis of chord property, a method for quick inspection and building RG(k,1) is proposed. Accordingly, RG(4,6) is built, it is a strongly 14-regular graph on order 35. We have tested RG(4,6) and its complement, as a result, they meet the defintion2, so we proclaim that r(4,6)=36.展开更多
The interference alignment (IA) algorithm based on FDPM subspace tracking (FDPM-ST IA) is proposed for MIMO cognitive network (CRN) with multiple primary users in this paper. The feasibility conditions of FDPM-S...The interference alignment (IA) algorithm based on FDPM subspace tracking (FDPM-ST IA) is proposed for MIMO cognitive network (CRN) with multiple primary users in this paper. The feasibility conditions of FDPM-ST IA is also got. Futherly, IA scheme of secondary network and IA scheme of primary network are given respectively without assuming a priori knowledge of interference covariance matrices. Moreover, the paper analyses the computational complexity of FDPM-ST IA. Simulation results and theoretical calculations show that the proposed algorithm can achieve higher sum rate with lower computational complexity.展开更多
The (1+1)-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general (3+1)-dimensional nonlinear Schr6dinger equa...The (1+1)-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general (3+1)-dimensional nonlinear Schr6dinger equation (NLSE) with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The (3+1)D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.展开更多
Oleanolic acid (OA) and ursolic acid (UA) are isomeric tritcrpenes that are difficult to separate chromatographically. Studies have indicated that both OA and UA have antifertility properties in several livestock ...Oleanolic acid (OA) and ursolic acid (UA) are isomeric tritcrpenes that are difficult to separate chromatographically. Studies have indicated that both OA and UA have antifertility properties in several livestock species, suppressing attainment of puberty, gonad function and gamete production. Being able to determine the presence and quantity of the OA and UA in moringa and pawpaw seeds will allow for calculation of optimal inclusion levels of these acids in animal diets for antifertility-activity. The purpose of the study was thus to quantify the levels of OA and UA in Moringa and pawpaw seed powder by means of ultra-high performance liquid chromatography with electrospray ionization tandem mass spectrometry (UHPLC-ESI-MS/MS). Only OA was detected in moringa seeds at a concentration level of 0.508 p.g/g + 0.032 pg/g dry weight. UA and OA could not be detected in pawpaw seeds used in this study. The presence of OA in moringa seeds suggest that the seeds can be included in tilapia diets as a potential antifertility treatment to control precocious breeding in tilapia culture in small scale farming systems in Sub-Saharan Africa. Further studies are warranted to determine the levels of OA and UA composition in moringa seeds from other parts of the Sub-Saharan Africa (other than Zambia).展开更多
In this paper,the(0.1)-form heat kernel of a complex projective space of dimensions n is constructed cxplicitely.As an application of the(0.1)-form heat kernel,the(0.1)type Green Form of CP~
Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional ...Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional operators Ml with function b(x) in BMO(R^n), respectively.展开更多
The Moore-Penrose metric generalized inverse T+ of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moo...The Moore-Penrose metric generalized inverse T+ of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T+ is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T+ will be given, and some properties of T+ will be investigated in this paper.展开更多
文摘Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W(t)=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.
基金supported by the National Natural Science Foundation of China(21473225)
文摘Olefin oligomerization reaction catalyzed by new catalyst systems(a Br?nsted‐acidic ionic liquid as the main catalyst and tricaprylylmethylammonium chloride as the co‐catalyst) has been investigat‐ed. The synthesized Br?nsted acidic ionic liquids were characterized by Fourier transform infrared spectroscopy(FT‐IR), ultraviolet‐visible spectroscopy(UV), ^1H nuclear magnetic resonance(NMR), and ^13 C NMR to analyze their structures and acidities. The influence of different ionic liquids, ionic liquid loading, different co‐catalysts, catalyst ratios(mole ratio of ionic liquid to co‐catalyst), reac‐tion time, pressure, temperature, solvent, source of reactants, and the recycling of catalyst systems was studied. Among the synthesized ionic liquids, 1‐(4‐sulfonic acid)butyl‐3‐hexylimidazolium hydrogen sulfate([HIMBs]HSO4) exhibited the best catalytic activity under the tested reaction con‐ditions. The conversion of isobutene and selectivity of trimers were 83.21% and 35.80%, respec‐tively, at the optimum reaction conditions. Furthermore, the catalyst system can be easily separated and reused; a feasible reaction mechanism is proposed on the basis of the distribution of experi‐mental products.
基金Supported by the Xianning University Foundation of Hubei Province under Grant No.2010CDB05103Xianning University Foundation under Grant No.BK001
文摘Based on homogeneous balance method, sofiton solutions to a generalized nonlinear Sehr6dinger equation (NLSE) with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-like spatial solitons can be formed in the Kerr nonlinear media in the cylindrical symmetric geometry. It is shown by numerical simulation that these soliton profiles are stable.
基金Supported by National Natural Science Foundation of China under Grant No.11071209 the Natural Science Foundation of the Higer Education Institutions of Jiangsu Province under Grant No.10KJB110011
文摘Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation (BT) for (3-k l)-Dimensional Jimbo-Miwa (JM) equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the (3+1)-Dimensional JM equation is obtained.
基金support from NYU Shanghai,the National Natural Science Foundation of China(No.21903054)the Hefei National Laboratory for Physical Sciences at the Microscale(No.KF2020008)+1 种基金the Shanghai Sailing Program(No.19YF1435600)the Program for Eastern Young Scholar at Shanghai Institutions of Higher Learning。
文摘The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art classical supercomputers.
文摘Text alignment is crucial to the accuracy of MT (Machine Translation) systems, some NLP (Natural Language Processing) tools or any other text processing tasks requiring bilingual data. This research proposes a language independent sentence alignment approach based on Polish (not position-sensitive language) to English experiments. This alignment approach was developed on the TED (Translanguage English Database) talks corpus, but can be used for any text domain or language pair. The proposed approach implements various heuristics for sentence recognition. Some of them value synonyms and semantic text structure analysis as a part of additional information. Minimization of data loss was ensured. The solution is compared to other sentence alignment implementations. Also an improvement in MT system score with text processed with the described tool is shown.
文摘BrФnsted-acidic zeolite and zeotype materials are potential catalysts for the conversion of ethene to higher alkenes. In this study, two materials with AFI structure but different acid strength, H-SAPO-5 and H-SSZ-24, were subject to studies of ethene, cis-2-butene and ethene-butene mixture conversion under conditions where C3-C5 alkene formation is thermodynamically favoured over higher hydrocarbons(673-823 K, 1 atm). Ethene and cis-2-butene partial pressures were varied in the range 9-60 and 0.9-8.1 kPa, respectively, and contact times were varied in the range 3.78-756 and 0.573-76.4 s.μmol H+/cm^3 over H-SAPO-5 and H-SSZ-24, respectively. Less than 1% conversion of ethene and less than 10% conversion of butene was obtained in the range of conditions used for elucidation of rate parameters. The ethene conversion rates were more than an order of magnitude higher over the more acidic H-SSZ-24 than over H-SAPO-5(6.5 vs. 0.3 mmol/mol H+.s at 748 K, Pethene = 33 kP a), with corresponding lower reaction order in ethene(1.5 vs. 2.0 at 673 K) and lower apparent activation energy(52 vs. 80 kJ/mol at 698-823 K). Propene selectivity was substantially higher over H-SSZ-24 than over H-SAPO-5(68% vs. 36% at 0.5% ethene conversion). A similar difference in apparent reaction rates was observed for cis-2-butene conversion over the two catalysts, and for co-feeds of ethene and cis-2-butene. However, the cis-2-butene conversion to C3-C5 alkenes was found to be severely influenced by thermodynamic limitations, impeding a detailed kinetic analysis, and leading predominantly to isobutene formation at the highest temperatures.
文摘Two definitions are given that Definitionl: an induced subgraph by a vertex vie G and its neighbors in G is defined as a vertex adjacent closed subgraph, and denoted by Qi (=G[V(Nvi)]), with the vertex vi called the hub; and Definition2: A r(k,I)-I vertices graph is called the (k,l)-Ramsey graph, denoted by RG(k,1), if RG(k,1) only contains cliques Kk.1 and the intersect QiNQj of any two nonadjacent vertices vi and vj of RG(k,I) contains only Kk-2. Meanwhile, the RG(k,l)'s complement RG(I,k) contains only cliques Kl.l, and the intersect QiNQj of any two nonadjacent vertices vi and vj of RG(I,k) contains only Ki.2. On the basis of those definitions, two theorems are put forward and proved in this paper. They are Theoreml: the biggest clique in G is contained in some Qi of G, and Theorem 2: r(k,1) = [V(RG(k,I))I + 1. With those definitions and theorems as well as analysis of chord property, a method for quick inspection and building RG(k,1) is proposed. Accordingly, RG(4,6) is built, it is a strongly 14-regular graph on order 35. We have tested RG(4,6) and its complement, as a result, they meet the defintion2, so we proclaim that r(4,6)=36.
基金the National Nature Science Foundation of China under Grant No.61271259 and 61301123,the Chongqing Nature Science Foundation under Grant No.CTSC2011jjA40006,and the Research Project of Chongqing Education Commission under Grant No.KJ120501 and KJ120502
文摘The interference alignment (IA) algorithm based on FDPM subspace tracking (FDPM-ST IA) is proposed for MIMO cognitive network (CRN) with multiple primary users in this paper. The feasibility conditions of FDPM-ST IA is also got. Futherly, IA scheme of secondary network and IA scheme of primary network are given respectively without assuming a priori knowledge of interference covariance matrices. Moreover, the paper analyses the computational complexity of FDPM-ST IA. Simulation results and theoretical calculations show that the proposed algorithm can achieve higher sum rate with lower computational complexity.
基金Supported by National Science Foundation of China under Grant No. 2006CB921605
文摘The (1+1)-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general (3+1)-dimensional nonlinear Schr6dinger equation (NLSE) with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The (3+1)D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.
文摘Oleanolic acid (OA) and ursolic acid (UA) are isomeric tritcrpenes that are difficult to separate chromatographically. Studies have indicated that both OA and UA have antifertility properties in several livestock species, suppressing attainment of puberty, gonad function and gamete production. Being able to determine the presence and quantity of the OA and UA in moringa and pawpaw seeds will allow for calculation of optimal inclusion levels of these acids in animal diets for antifertility-activity. The purpose of the study was thus to quantify the levels of OA and UA in Moringa and pawpaw seed powder by means of ultra-high performance liquid chromatography with electrospray ionization tandem mass spectrometry (UHPLC-ESI-MS/MS). Only OA was detected in moringa seeds at a concentration level of 0.508 p.g/g + 0.032 pg/g dry weight. UA and OA could not be detected in pawpaw seeds used in this study. The presence of OA in moringa seeds suggest that the seeds can be included in tilapia diets as a potential antifertility treatment to control precocious breeding in tilapia culture in small scale farming systems in Sub-Saharan Africa. Further studies are warranted to determine the levels of OA and UA composition in moringa seeds from other parts of the Sub-Saharan Africa (other than Zambia).
基金This subject supported by NSF of ChinaThis subject supported by the Henan Fundations of Scientific Committee.
文摘In this paper,the(0.1)-form heat kernel of a complex projective space of dimensions n is constructed cxplicitely.As an application of the(0.1)-form heat kernel,the(0.1)type Green Form of CP~
基金the National Natural Science Foundation of China(1057101410571158).
文摘Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional operators Ml with function b(x) in BMO(R^n), respectively.
基金the National Natural Science Foundation of China(No.19971023)the Heilongjiang Provincial Natural Science Foundation of China.
文摘The Moore-Penrose metric generalized inverse T+ of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T+ is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T+ will be given, and some properties of T+ will be investigated in this paper.