The stabilization problem via the linear output feedback controller is addressed for a class of nonlinear systems subject to time-delay.The uncertainty of the system satisfies the lower-triangular growth condition and...The stabilization problem via the linear output feedback controller is addressed for a class of nonlinear systems subject to time-delay.The uncertainty of the system satisfies the lower-triangular growth condition and it is affected by time-delay. A linear output feedback controller with a tunable scaling gain is constructed.By selecting an appropriate Lyapunov-Krasovskii functional the scaling gain can be adjusted to render the closed-loop system globally asymptotically stable.The results can also be extended to the non-triangular nonlinear time-delay systems. The proposed control law together with the observer is linear and memoryless in nature and therefore it is easy to implement in practice. Two computer simulations are conducted to illustrate the effectiveness of the proposed theoretical results.展开更多
Hydrology plays a dominant role in wetland plant distribution and microbial composition, but few studies explicitly attempted to relate the linkage between wetland vegetation and microbial community. The present study...Hydrology plays a dominant role in wetland plant distribution and microbial composition, but few studies explicitly attempted to relate the linkage between wetland vegetation and microbial community. The present study consisted of five wetland plant communities along three adjacent flood gradients zones(zone 1 dominated by Carex appendiculat, zone 2 dominated by Eleocharis ovate, and zone 3 dominated by Phragmites australis/Bidens pilosa/Calamagrostis angustifolia, which formed separate, monoculture patches). Gram negative and arbuscular mycorrhizal fungal phospholipid fatty acid(PLFA) are more abundant in the site with short flooding period(zone 3) than in the site with long flooding period(zone 1), and they are also different in the P. australis, B. spilosa and C. angustifolia of zone 3. Principle Component Analysis(PCA) showed that the flooding period could explain 92.4% of variance in microbial composition. Redundancy Analysis(RDA) showed that available nitrogen(AN), total nitrogen(TN) and soil organic matter(SOM) could explain the 79.5% of variance in microbial composition among E. ovata, P. australis, B. pilosa and C. angustifolia. Results demonstrated that flooding period was the main factor in driving the microbial composition and plant-derived resources could influence soil microbial composition in the seasonally flooded zones.展开更多
The authors obtain some sufficient conditions for the stability of zero solutions to some types of the functional equation. (x)(t)+ p(t)-x(t)+q(t)x(t)+f (t, xt)=0 by transformations and the Liapunov's Second metho...The authors obtain some sufficient conditions for the stability of zero solutions to some types of the functional equation. (x)(t)+ p(t)-x(t)+q(t)x(t)+f (t, xt)=0 by transformations and the Liapunov's Second method. The obtained conclusions generalize some results of Stability of Equation (x)(t)+p(t)(x)(t)+q(t)x(t)=0 and Jack Hale in his paper of Theory of Functional Differential Equations.展开更多
We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R...We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R^3.The equation describes the propagation of the time-harmonic electric field R{E(χ)e^(iwt)}in a nonlinear isotropic material ? withλ=-μεω~2≤0,where μ andεstand for the permeability and the linear part of the permittivity of the material.The nonlinear term|E|^(P-2)E with 2<p≤2*=6 comes from the nonlinear polarization and the boundary conditions are those for?surrounded by a perfect conductor.The problem has a variational structure;however the energy functional associated with the problem is strongly indefinite and does not satisfy the Palais-Smale condition.We show the underlying difficulties of the problem and enlist some open questions.展开更多
In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomts...In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili- Benjamin-Bona Mahony （KP-BBM）. As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations （FDEs） and it can be applied to other nonlinear FDEs.展开更多
The structural, electronic and spectroscopic properties of monomer FPt (2-(4′,6′-difluorophenyl)pyridinato-N,C2′)(2,4-pentanedionato-O,O) (1) and dimer [FPt]2 (2) were explored within the density functional theory ...The structural, electronic and spectroscopic properties of monomer FPt (2-(4′,6′-difluorophenyl)pyridinato-N,C2′)(2,4-pentanedionato-O,O) (1) and dimer [FPt]2 (2) were explored within the density functional theory (DFT) and time-dependent DFT (TD-DFT). The calculated geometry parameters and spectroscopic results agree well with the experimental observation. In the ground state, FPt exists in the form of monomer, while in the excited state, dimer [FPt]2 forms with a Pt-Pt contraction of 0.05 nm due to the promotion of σ[dz2(Pt2)] to π*(phenylryridyl) and σ[pz(Pt2)]. Transition properties of monomer and excimer are different in nature: the former originates from mixed transitions of 3MLCT and 3ILCT, while the latter is dominated by 3MMLCT transition.展开更多
A series of polypyridine ruthenium （II） acetylide complexes, [（tpy）（bpy）RuC≡CC6H4R]^＋ （tpy = 2,2＇：6＇,2＂-terpyridine, bpy = 2,2＇-bipyridine; R = F （1）, C1 （2）, H （3）, Me （4） and OMe （5）） are in...A series of polypyridine ruthenium （II） acetylide complexes, [（tpy）（bpy）RuC≡CC6H4R]^＋ （tpy = 2,2＇：6＇,2＂-terpyridine, bpy = 2,2＇-bipyridine; R = F （1）, C1 （2）, H （3）, Me （4） and OMe （5）） are investigated theoretically to explore their electronic structures and spectroscopic properties. Their ground/excited state geometries, electronic structures and spectroscopic properties are first calculated using density functional theory （DFT） and time-dependent DFT （TDDFT）. The absorption and emission spectra of the complexes in acetonitrile solution are also obtained by using TDDFT （B3LYP） method associated with the CPCM model. The calculations show that the energy levels of HOMOs for 1-5 are sensitive to the substituent on phenylacetylide ligand and increase with the same order of the electron-donating ability of the substituents; however, those of polypyridine-based LUMOs vary slightly. The lowest-energy absorptions and emissions for 1-5 are progressively red-shifted in the order of 1 ~ 2 〈 3 〈 4 〈 5 when the electron-donating groups are introduced into the phenylacetylide [igand. The phosphorescence of 1 are attributed to {[dxz（Ru） ＋π（C≡C）]→[π^＊（tpy）]} （3MLCT/3LLCT） transition, whereas those of 2-5 are originated from { [dxz/dxy（Ru）＋ π（C ≡C）＋g（C6H4R）] → [＊（tpy/bpy）] } （3MLCT/3LLCT） transitions.展开更多
In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the n...In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.展开更多
This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that t...This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.展开更多
This paper deals with the robust stability analysis of dynamic systems with interval time- varying delay and uncertainties. The innovation of the method includes employment of a tighter integral inequality and constru...This paper deals with the robust stability analysis of dynamic systems with interval time- varying delay and uncertainties. The innovation of the method includes employment of a tighter integral inequality and construction of an appropriate type of Lyapunov functional. The stability criteria derived from this method have less conservatism than some existing ones. Numerical examples are given to illustrate the effectiveness of the orooosed method.展开更多
absorption and phosphorescent mechanism of three Au（III） complexes, Au（2,5-F2C6H3-C^CAC）（C = C-C6H4N（C6Hs）2 [Au25FPh], Au（3,5-F2C6Ha-CACAC）（C=C-C6H4N（C6Hs）2 [Au35FPh], and Au（3,5-F2C6H3-CAC^C）（C=C-C6H4N...absorption and phosphorescent mechanism of three Au（III） complexes, Au（2,5-F2C6H3-C^CAC）（C = C-C6H4N（C6Hs）2 [Au25FPh], Au（3,5-F2C6Ha-CACAC）（C=C-C6H4N（C6Hs）2 [Au35FPh], and Au（3,5-F2C6H3-CAC^C）（C=C-C6H4N（1H- indole）2 [Au35FID], are calculated and compared using density functional theory （DFT） and time-dependent DFT （TDDFT）. The calculated results reveal that enlarging the center CACAC ligand will result in the enhanced LMCT participation. This theoretical contribution allows design of new Au（III） complexes with higher phosphorescence efficiency.展开更多
基金The National Natural Science Foundation of China(No.61273119,61174076,61004046,61374038)the Natural Science Foundation of Jiangsu Province(No.BK2011253)the Research Fund for the Doctoral Program of Higher Education of China(No.20110092110021)
文摘The stabilization problem via the linear output feedback controller is addressed for a class of nonlinear systems subject to time-delay.The uncertainty of the system satisfies the lower-triangular growth condition and it is affected by time-delay. A linear output feedback controller with a tunable scaling gain is constructed.By selecting an appropriate Lyapunov-Krasovskii functional the scaling gain can be adjusted to render the closed-loop system globally asymptotically stable.The results can also be extended to the non-triangular nonlinear time-delay systems. The proposed control law together with the observer is linear and memoryless in nature and therefore it is easy to implement in practice. Two computer simulations are conducted to illustrate the effectiveness of the proposed theoretical results.
基金Under the auspices of National Natural Science Foundation of China(No.41361015,41271106,41271107,41501105)Open Fund of the State Environmental Protection Key Laboratory of Wetland Ecology and Vegetation Restoration,Northeast Normal University(No.130028630)
文摘Hydrology plays a dominant role in wetland plant distribution and microbial composition, but few studies explicitly attempted to relate the linkage between wetland vegetation and microbial community. The present study consisted of five wetland plant communities along three adjacent flood gradients zones(zone 1 dominated by Carex appendiculat, zone 2 dominated by Eleocharis ovate, and zone 3 dominated by Phragmites australis/Bidens pilosa/Calamagrostis angustifolia, which formed separate, monoculture patches). Gram negative and arbuscular mycorrhizal fungal phospholipid fatty acid(PLFA) are more abundant in the site with short flooding period(zone 3) than in the site with long flooding period(zone 1), and they are also different in the P. australis, B. spilosa and C. angustifolia of zone 3. Principle Component Analysis(PCA) showed that the flooding period could explain 92.4% of variance in microbial composition. Redundancy Analysis(RDA) showed that available nitrogen(AN), total nitrogen(TN) and soil organic matter(SOM) could explain the 79.5% of variance in microbial composition among E. ovata, P. australis, B. pilosa and C. angustifolia. Results demonstrated that flooding period was the main factor in driving the microbial composition and plant-derived resources could influence soil microbial composition in the seasonally flooded zones.
文摘The authors obtain some sufficient conditions for the stability of zero solutions to some types of the functional equation. (x)(t)+ p(t)-x(t)+q(t)x(t)+f (t, xt)=0 by transformations and the Liapunov's Second method. The obtained conclusions generalize some results of Stability of Equation (x)(t)+p(t)(x)(t)+q(t)x(t)=0 and Jack Hale in his paper of Theory of Functional Differential Equations.
基金supported by the National Science Centre of Poland (Grant No. 2013/09/B/ST1/01963)
文摘We survey recent results on ground and bound state solutions E:?→R^3 of the problem {▽(▽×E)+}λE=|E|^(P-2)E in Ω,v×E=0 on Ω on a bounded Lipschitz domain ??R^3,where?×denotes the curl operator in R^3.The equation describes the propagation of the time-harmonic electric field R{E(χ)e^(iwt)}in a nonlinear isotropic material ? withλ=-μεω~2≤0,where μ andεstand for the permeability and the linear part of the permittivity of the material.The nonlinear term|E|^(P-2)E with 2<p≤2*=6 comes from the nonlinear polarization and the boundary conditions are those for?surrounded by a perfect conductor.The problem has a variational structure;however the energy functional associated with the problem is strongly indefinite and does not satisfy the Palais-Smale condition.We show the underlying difficulties of the problem and enlist some open questions.
文摘In the present article, He＇s fractional derivative, the ansatz method, the （ C / G）-expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili- Benjamin-Bona Mahony （KP-BBM）. As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations （FDEs） and it can be applied to other nonlinear FDEs.
基金supported by the Research Fund for the Doctoral Program of Higher Education of China (200801831004)the Fundamental Research Funds for the Central Universities (HIT.NSRIF.2009083)+1 种基金the National Natural Science Foundation of China (20703015)the Program for New Century Excellent Talents of Common Universities of Heilongjiang Province (1154-NCET-010)
文摘The structural, electronic and spectroscopic properties of monomer FPt (2-(4′,6′-difluorophenyl)pyridinato-N,C2′)(2,4-pentanedionato-O,O) (1) and dimer [FPt]2 (2) were explored within the density functional theory (DFT) and time-dependent DFT (TD-DFT). The calculated geometry parameters and spectroscopic results agree well with the experimental observation. In the ground state, FPt exists in the form of monomer, while in the excited state, dimer [FPt]2 forms with a Pt-Pt contraction of 0.05 nm due to the promotion of σ[dz2(Pt2)] to π*(phenylryridyl) and σ[pz(Pt2)]. Transition properties of monomer and excimer are different in nature: the former originates from mixed transitions of 3MLCT and 3ILCT, while the latter is dominated by 3MMLCT transition.
基金supported by the National Natural Science Foundation of China(Grant No.51073048)the National Natural Science Foundation ofHei Long Jiang Province of China(Grant No.B201102)+1 种基金the Science Foundation for Leaders in Academe of Harbin City of China(Grant No.2013RFXXJ024)the Science Foundation for Elitists of Harbin University of Science and Technology
文摘A series of polypyridine ruthenium （II） acetylide complexes, [（tpy）（bpy）RuC≡CC6H4R]^＋ （tpy = 2,2＇：6＇,2＂-terpyridine, bpy = 2,2＇-bipyridine; R = F （1）, C1 （2）, H （3）, Me （4） and OMe （5）） are investigated theoretically to explore their electronic structures and spectroscopic properties. Their ground/excited state geometries, electronic structures and spectroscopic properties are first calculated using density functional theory （DFT） and time-dependent DFT （TDDFT）. The absorption and emission spectra of the complexes in acetonitrile solution are also obtained by using TDDFT （B3LYP） method associated with the CPCM model. The calculations show that the energy levels of HOMOs for 1-5 are sensitive to the substituent on phenylacetylide ligand and increase with the same order of the electron-donating ability of the substituents; however, those of polypyridine-based LUMOs vary slightly. The lowest-energy absorptions and emissions for 1-5 are progressively red-shifted in the order of 1 ~ 2 〈 3 〈 4 〈 5 when the electron-donating groups are introduced into the phenylacetylide [igand. The phosphorescence of 1 are attributed to {[dxz（Ru） ＋π（C≡C）]→[π^＊（tpy）]} （3MLCT/3LLCT） transition, whereas those of 2-5 are originated from { [dxz/dxy（Ru）＋ π（C ≡C）＋g（C6H4R）] → [＊（tpy/bpy）] } （3MLCT/3LLCT） transitions.
基金supported by the Hong Kong General Research Fund (Grant Nos. 202112, 15302214 and 509213)National Natural Science Foundation of China/Research Grants Council Joint Research Scheme (Grant Nos. N HKBU204/12 and 11261160486)+1 种基金National Natural Science Foundation of China (Grant No. 11471046)the Ministry of Education Program for New Century Excellent Talents Project (Grant No. NCET-12-0053)
文摘In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.
基金supported by the National Natural Science Foundation of China(Nos.11171110,11371087)the Science and Technology Commission of Shanghai Municipality(No.13dz2260400)the Shanghai Leading Academic Discipline Project(No.B407)
文摘This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.
基金supported by National Nature Science Foundation of China under Grant Nos.60174032,61004019the Key Project of Science&Technology Commission of Shanghai under Grant No.10JC140500
文摘This paper deals with the robust stability analysis of dynamic systems with interval time- varying delay and uncertainties. The innovation of the method includes employment of a tighter integral inequality and construction of an appropriate type of Lyapunov functional. The stability criteria derived from this method have less conservatism than some existing ones. Numerical examples are given to illustrate the effectiveness of the orooosed method.
基金financially supported by the National Natural Science Foundation of China (20973076, 21003057 and 21173096)Specialized Research Fund for the Doctoral Program of Higher Education(20110061110018)
文摘absorption and phosphorescent mechanism of three Au（III） complexes, Au（2,5-F2C6H3-C^CAC）（C = C-C6H4N（C6Hs）2 [Au25FPh], Au（3,5-F2C6Ha-CACAC）（C=C-C6H4N（C6Hs）2 [Au35FPh], and Au（3,5-F2C6H3-CAC^C）（C=C-C6H4N（1H- indole）2 [Au35FID], are calculated and compared using density functional theory （DFT） and time-dependent DFT （TDDFT）. The calculated results reveal that enlarging the center CACAC ligand will result in the enhanced LMCT participation. This theoretical contribution allows design of new Au（III） complexes with higher phosphorescence efficiency.
