This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t...This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), and εy′(t)=g(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), where 0<ε1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.展开更多
In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, ...In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.展开更多
Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the meth...Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.展开更多
Ionic liquids （ILs） have attracted many attentions in the dissolution of cellulose due to their unique physicochemical properties as green solvents. However, the mechanism of dissolution is still under debate. In th...Ionic liquids （ILs） have attracted many attentions in the dissolution of cellulose due to their unique physicochemical properties as green solvents. However, the mechanism of dissolution is still under debate. In this work, computational investigation for the mechanisms of dissolution of cellulose in [Bmim]Cl, [Emim]C1 and [Emim]OAc ILs was performed, and it was focused on the process of breakage of cellulose chain and ring opening using cellobiose as a model molecule. The detailed mechanism and reaction energy barriers were computed for various possible pathways by density functional theoretical method. The key finding was that 1Ls catalyze the dissolution process by synergistic effect of anion and cation, which led to the cleavage of cellulose chain and formation of derivatives of cellulose. The investigation on ring opening process ofcellobiose suggested that carbene formed in ILs played an important role in the side reaction of cellulose, and it facilitated the formation of a covalent bond between cellulose and imidazolium core. These computation results may provide new perspective to understand and apply ILs for pretreatment of cellulose.展开更多
In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing ti...In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing time pj = 1. We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them. Then we further consider a problem on unrelated processors.展开更多
The C-I bond dissociation enthalpies （BDE） of various organic iodides were calculated using high-level theoretical methods including MP2 and CCSD（T） with extrapolated basis set as well as a number of density funct...The C-I bond dissociation enthalpies （BDE） of various organic iodides were calculated using high-level theoretical methods including MP2 and CCSD（T） with extrapolated basis set as well as a number of density functional theory methods. After systematic evaluation of the theoretical results against available experimental C-I BDEs, it was found that the MPW LYPIM method gave the lowest root mean square error. We, therefore, used this method to examine the substituent effects on different categories of C（sp3）-I and C（sp2）-I bonds. Fur thermore, the remote substituent effects on the C-I BDEs of substituted iodobenzenes and substituted （iodomethyl）benzenes were also investigated at the same level. The C-I BDEs of typical heteroaromatic iodides including five-membered and six-membered heterocyclic iodides were also examined.展开更多
The subject of the legal history belongs to the interdisciplinary of the law and the history. Because of the attribute of the interdisciplinary of the subject of the legal history, the reference of the experience in t...The subject of the legal history belongs to the interdisciplinary of the law and the history. Because of the attribute of the interdisciplinary of the subject of the legal history, the reference of the experience in the development of the h/story is very important. The subject of the legal history must pay attention to the problems encountered in the process of the development of the history and the accumulated experience. The historical development since the last century displays the importance and necessity of the theory of the social science in the study of the history. The researcher of the legal history should focus on the comprehensive use of the theories and methods of the subject of the social sciences, and through the innovative use of the historical data and the use of the multidisciplinary interpretation methods, re-interpret the historical events and figures. With the aid of the comprehensive use of the methods of the multiple disciplines, further open the new situation of the study of the legal history.展开更多
The properties of dissolution in different solvents,the specific heat capacity and thermal decomposition process under the non-isothermal conditions for energetic triazole ionic salts 1,2,4-triazolium nitrate(1a),1,2,...The properties of dissolution in different solvents,the specific heat capacity and thermal decomposition process under the non-isothermal conditions for energetic triazole ionic salts 1,2,4-triazolium nitrate(1a),1,2,3-triazolium nitrate(1b),3,4,5triamino-1,2,4-triazolium nitrate(2a),3,4,5-triamino-1,2,4-triazolium dinitramide(2b)were precisely measured using a Calvet Microcalorimeter.The thermochemical equation,differential enthalpies of dissolution(△difH m ),standard molar enthalpies of dissolution(△difH m ),apparent activation energy(E),pre-exponential constant(A),kinetic equation,linear relationship of specific heat capacity with temperature over the temperature range from 283 to 353 K,standard molar heat capacity(C p,m)and enthalpy,entropy and Gibbs free energy at 283–353 K,taking 298.15 K as the benchmark for 1a,1b,2a and 2b were obtained with treating experimental data and theoretical calculation method.The kinetic and thermodynamic parameters of thermal decomposition reaction,critical temperature of thermal explosion(Tb),self-accelerating decomposition temperature(TSADT)and adiabatic time-to-explosion(t)of 1a,1b,2a and 2b were calculated.Their heat-resistance abilities were evaluated.Information was obtained on the relation between molecular structures and properties of 1a,1b,2a and 2b.展开更多
The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity mode...The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.展开更多
Transport and diffusion caused by coastal waves have different characteristics from those induced by flows. Through solving the vertical diffusion equation by an analytic method, this paper infers a theoretical formul...Transport and diffusion caused by coastal waves have different characteristics from those induced by flows. Through solving the vertical diffusion equation by an analytic method, this paper infers a theoretical formula of dispersion coefficient under the combined action of current and waves. It divides the general dispersion coefficient into six parts, including coefficients due to tidal current, Stokes drift, wave oscillation and interaction among them. It draws a conclusion that the contribution of dispersive effect induced by coastal waves is mainly produced by Stokes drift, while the contributions to time-averaged dispersion coefficient due to wave orbital motion and interaction between current and waves are very small. The results without tidal current are in agreement with the numerical and experimental results, which proves the correctness of the theoretical derivation. This paper introduces the variation characteristics of both the time-averaged and oscillating dispersion coefficients versus relative water depth, and demonstrates the physical implications of the oscillating mixing coefficient due to waves. We also apply the results to the costal vertical circulation and give its characteristics compared to Stokes drift.展开更多
文摘This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems (MVDPP) of the form x′(t)=f(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), and εy′(t)=g(x(t),x(t-τ 1(t)),...,x(t-τ m(t)),y(t),y(t-τ 1(t)),...,y(t-τ m(t))), where 0<ε1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
基金Natural Science Foundation of Shandong Province under Grant Nos.2004zx16 and Q2005A01
文摘In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.
文摘Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.
基金Supported by the National Natural Science Foundation of China(21210006,21276255,21406230,91434111)the Natural Science Foundation of Beijing of China(2131005,2142029)
文摘Ionic liquids （ILs） have attracted many attentions in the dissolution of cellulose due to their unique physicochemical properties as green solvents. However, the mechanism of dissolution is still under debate. In this work, computational investigation for the mechanisms of dissolution of cellulose in [Bmim]Cl, [Emim]C1 and [Emim]OAc ILs was performed, and it was focused on the process of breakage of cellulose chain and ring opening using cellobiose as a model molecule. The detailed mechanism and reaction energy barriers were computed for various possible pathways by density functional theoretical method. The key finding was that 1Ls catalyze the dissolution process by synergistic effect of anion and cation, which led to the cleavage of cellulose chain and formation of derivatives of cellulose. The investigation on ring opening process ofcellobiose suggested that carbene formed in ILs played an important role in the side reaction of cellulose, and it facilitated the formation of a covalent bond between cellulose and imidazolium core. These computation results may provide new perspective to understand and apply ILs for pretreatment of cellulose.
文摘In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing time pj = 1. We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them. Then we further consider a problem on unrelated processors.
文摘The C-I bond dissociation enthalpies （BDE） of various organic iodides were calculated using high-level theoretical methods including MP2 and CCSD（T） with extrapolated basis set as well as a number of density functional theory methods. After systematic evaluation of the theoretical results against available experimental C-I BDEs, it was found that the MPW LYPIM method gave the lowest root mean square error. We, therefore, used this method to examine the substituent effects on different categories of C（sp3）-I and C（sp2）-I bonds. Fur thermore, the remote substituent effects on the C-I BDEs of substituted iodobenzenes and substituted （iodomethyl）benzenes were also investigated at the same level. The C-I BDEs of typical heteroaromatic iodides including five-membered and six-membered heterocyclic iodides were also examined.
文摘The subject of the legal history belongs to the interdisciplinary of the law and the history. Because of the attribute of the interdisciplinary of the subject of the legal history, the reference of the experience in the development of the h/story is very important. The subject of the legal history must pay attention to the problems encountered in the process of the development of the history and the accumulated experience. The historical development since the last century displays the importance and necessity of the theory of the social science in the study of the history. The researcher of the legal history should focus on the comprehensive use of the theories and methods of the subject of the social sciences, and through the innovative use of the historical data and the use of the multidisciplinary interpretation methods, re-interpret the historical events and figures. With the aid of the comprehensive use of the methods of the multiple disciplines, further open the new situation of the study of the legal history.
基金supported by the National Natural Science Foundation of China (20573098)the Science and Technology Foundation of National Key Lab of Science and Technology on Combustion and Explosion in China (9140C3503030805)
文摘The properties of dissolution in different solvents,the specific heat capacity and thermal decomposition process under the non-isothermal conditions for energetic triazole ionic salts 1,2,4-triazolium nitrate(1a),1,2,3-triazolium nitrate(1b),3,4,5triamino-1,2,4-triazolium nitrate(2a),3,4,5-triamino-1,2,4-triazolium dinitramide(2b)were precisely measured using a Calvet Microcalorimeter.The thermochemical equation,differential enthalpies of dissolution(△difH m ),standard molar enthalpies of dissolution(△difH m ),apparent activation energy(E),pre-exponential constant(A),kinetic equation,linear relationship of specific heat capacity with temperature over the temperature range from 283 to 353 K,standard molar heat capacity(C p,m)and enthalpy,entropy and Gibbs free energy at 283–353 K,taking 298.15 K as the benchmark for 1a,1b,2a and 2b were obtained with treating experimental data and theoretical calculation method.The kinetic and thermodynamic parameters of thermal decomposition reaction,critical temperature of thermal explosion(Tb),self-accelerating decomposition temperature(TSADT)and adiabatic time-to-explosion(t)of 1a,1b,2a and 2b were calculated.Their heat-resistance abilities were evaluated.Information was obtained on the relation between molecular structures and properties of 1a,1b,2a and 2b.
基金Project supported by the Natural Science Foundation(No. DMS 04-07866)the "Research Team on Complex Systems" of Chinese Academy of Sciences.
文摘The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. The technique in this paper is based mainly on spectral perturbation theory for large matrices.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10672034, 51079024)the Funds for Creative Re-search Groups of China (Grant No. 50921001)
文摘Transport and diffusion caused by coastal waves have different characteristics from those induced by flows. Through solving the vertical diffusion equation by an analytic method, this paper infers a theoretical formula of dispersion coefficient under the combined action of current and waves. It divides the general dispersion coefficient into six parts, including coefficients due to tidal current, Stokes drift, wave oscillation and interaction among them. It draws a conclusion that the contribution of dispersive effect induced by coastal waves is mainly produced by Stokes drift, while the contributions to time-averaged dispersion coefficient due to wave orbital motion and interaction between current and waves are very small. The results without tidal current are in agreement with the numerical and experimental results, which proves the correctness of the theoretical derivation. This paper introduces the variation characteristics of both the time-averaged and oscillating dispersion coefficients versus relative water depth, and demonstrates the physical implications of the oscillating mixing coefficient due to waves. We also apply the results to the costal vertical circulation and give its characteristics compared to Stokes drift.
