The stabilities of two kinds of solutions (30 mg/mL) of Ampicillin sodium in 0.9% NaCl in water (NS, normal saline) and in sterile water (SW) in the intravenous elastomeric infusion device (Accufuser®) were ev...The stabilities of two kinds of solutions (30 mg/mL) of Ampicillin sodium in 0.9% NaCl in water (NS, normal saline) and in sterile water (SW) in the intravenous elastomeric infusion device (Accufuser®) were evaluated based on recommended solutions and storage periods. The injectable NS- and SW-Ampicillin solutions in the Accufuser® device were stored and evaluated at controlled temperature (room temperature, 25℃ ± 2℃ and cold temperature, 4℃ ± 2℃) during 7 days. Effects of the periods of storage (from 0 to 7 days) and the temperatures of storage (RT and CT) on the physico-chemical appearances and concentrations of active compounds were determined. The visual clarity, pH, and concentrations of Ampicillin were determined by stability-indicating high-performance liquid chromatography (HPLC)-ultraviolet (UV) detection. The results showed that the amount of Ampicillin in studied solutions gradually decreased with time. The Ampicillin in NS, which was stored in CT, was relatively stable, retaining 94% of its original amount up to 7 days. The solution that showed least stability was Ampicillin in SW, which was stored in RT, retaining 80% of its original amount. Generally, solutions that were stored in CT were more stable than the solutions that were stored in RT. No significant changes in physical appearance or color of the solutions were observed during the study. Particles were not detected in any solution samples. In summary, two kinds of solutions of Ampicillin sodium, in NS and SW, showed different chemical stabilities with time in intravenous infusion device without any significant physical changes and retained about 94% vs 89% and 83% vs 80% of initial concentrations after 7 days in CT and RT, respectively. We suggest that 30 mg/mL of Ampicillin sodium in NS solution in an Accufuser® infusion device which is stored in CT can be applicable for 7 days in clinical situations.展开更多
This paper is concerned with multidirectional associative memory neural network with distributed delays on almost-periodic time scales.Some sufficient conditions on the existence,uniqueness and the global exponential ...This paper is concerned with multidirectional associative memory neural network with distributed delays on almost-periodic time scales.Some sufficient conditions on the existence,uniqueness and the global exponential stability of almost-periodic solutions are established.An example is presented to illustrate the feasibility and effectiveness of the obtained results.展开更多
Numerical solutions of the steady transonic small-disturbance（TSD） potential equation are computed using the conservative Murman-Cole scheme. Multiple solutions are discovered and mapped out for the Mach number rang...Numerical solutions of the steady transonic small-disturbance（TSD） potential equation are computed using the conservative Murman-Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.展开更多
In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqu...In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.展开更多
One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one pred...One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.展开更多
In this study, the changing trend of crystal-lattice constant and the influential factors of the stability of supersaturated solid solutions with various alloying additions in the Al–X（Zn, Mg, Cu） binary alloys wer...In this study, the changing trend of crystal-lattice constant and the influential factors of the stability of supersaturated solid solutions with various alloying additions in the Al–X（Zn, Mg, Cu） binary alloys were investigated. The samples were analyzed using X-ray diffraction（XRD）,X-ray absorption fine structure（XAFS）, and scanning electron microscope（SEM）. It is found that the addition of Cu causes the largest change of crystal-lattice constant of the Al–xCu supersaturated solid solution binary alloy. The most dramatic change occurs in the initial stage of Cu addition.The change is stabilized thereafter. Also, at the same alloying element addition to the Al–X（X = Zn, Mg, Cu）binary alloys, the Al–xCu is the most unstable system.Influential factors of the stability include the lattice constant change and the type of alloying element. The larger the lattice constant changes, the more unstable the supersaturated solid solution is. The alloying element, easy to aggregate, often leads to the solid solution less stable.展开更多
In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equa...In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.展开更多
Al2O3-ZrO2 microspheres were prepared by internal gelation method.The effects of Al3+on the stability of solution and performance of gel spheres were studied.Al3+had a great influence on the stability of the solutions...Al2O3-ZrO2 microspheres were prepared by internal gelation method.The effects of Al3+on the stability of solution and performance of gel spheres were studied.Al3+had a great influence on the stability of the solutions,and the more of the amount of Al3+,the shorter of the stabilization time.Because Al3+did not copolymerize with Zr4+during the sol-gel transformation,the strength of gel sphere added with Al3+was low and deformed easily as it was squeezed.The results of our experiments well verify Glasser team’s speculation and conclusions.At the same time,based on the experimental results,we prepared Al2O3-ZrO2 composite microspheres with higher content of Al2O3 by controlling the pH of the solution.The change curve of viscosity with time and the stabilization time of the solution with different Al3+dosage were given,which could provide references for industrial mass production.Samples without hydrothermal treatment cracked severely,while the samples hydrothermally treated kept structural integrity with no cracks after calcined.Al2O3-ZrO2 microspheres with no segregation and phase separation were prepared and alumina evenly distributed in the zirconia matrix.When the content of Al2O3 was low,the tetragonal phase was stable.And the cubic phase was obtained when the content of Al2O3 was more.展开更多
In this paper, a climate dynamics model with the effects of topography and a non-constant external force, which consists of the Navier-Stokes equations and a temperature equation arising from the evolution process of ...In this paper, a climate dynamics model with the effects of topography and a non-constant external force, which consists of the Navier-Stokes equations and a temperature equation arising from the evolution process of the atmosphere, was considered.Under certain assumptions imposed on the initial data and by using some delicate estimates and compactness arguments, we proved the L^1-stability of weak solutions to the atmospheric equations.展开更多
In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable...In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.展开更多
This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" cond...This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" conditions and the velocity field and temperature enjoy the slip boundary condition and convective boundary condition, respectively. The uniform estimates with respect to both the Mach number ∈(0, ∈] and time t ∈ [0, ∞) are established by deriving a differential inequality with decay property, where ∈∈(0, 1] is a constant.As the Mach number vanishes, the global solution to full compressible Navier-Stokes equations converges to the one of isentropic incompressible Navier-Stokes equations in t ∈ [0, +∞). Moreover, we prove the exponentially asymptotic stability for the global solutions of both the compressible system and its limiting incompressible system.展开更多
In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous b...In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.展开更多
In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--lo...In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--losing point. However,according to many practical experts, it is rather difficult to put such a phaselooked loop into practice, though it has fine properties. W. C. Lindsey [3] made a展开更多
For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if perio...For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to then Eq.(1) has an mω-periodic solution p(t), for some integer m≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq.(1) has an almost periodic solution.展开更多
We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positi...We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positive periodic solution are established. The results results in [1 -6] are summarized and improved in this paper.展开更多
A series of CeO2–ZrO2–WO3（CZW）catalysts prepared by a hydrothermal synthesis method showed excellent catalytic activity for selective catalytic reduction（SCR）of NO with NH3 over a wide temperature of 150–550℃....A series of CeO2–ZrO2–WO3（CZW）catalysts prepared by a hydrothermal synthesis method showed excellent catalytic activity for selective catalytic reduction（SCR）of NO with NH3 over a wide temperature of 150–550℃.The effect of hydrothermal treatment of CZW catalysts on SCR activity was investigated in the presence of 10% H2O.The fresh catalyst showed above 90% NOx conversion at 201–459℃,which is applicable to diesel exhaust NOx purification（200–440℃）.The SCR activity results indicated that hydrothermal aging decreased the SCR activity of CZW at low temperatures（below 300℃）,while the activity was notably enhanced at high temperature（above 450℃）.The aged CZW catalyst（hydrothermal aging at 700℃ for 8 hr）showed almost 80% NOx conversion at 229–550℃,while the V2O5–WO3/TiO2 catalyst presented above 80% NOx conversion at 308–370℃.The effect of structural changes,acidity,and redox properties of CZW on the SCR activity was investigated.The results indicated that the excellent hydrothermal stability of CZW was mainly due to the CeO2–ZrO2 solid solution,amorphous WO3 phase and optimal acidity.In addition,the formation of WO3 clusters increased in size as the hydrothermal aging temperature increased,resulting in the collapse of structure,which could further affect the acidity and redox properties.展开更多
We study the quantitative stability of solutions to Markovian quadratic reflected backward stochastic differential equations(BSDEs)with bounded terminal data.By virtue of bounded mean oscillation martingale and change...We study the quantitative stability of solutions to Markovian quadratic reflected backward stochastic differential equations(BSDEs)with bounded terminal data.By virtue of bounded mean oscillation martingale and change of measure techniques,we obtain stability estimates for the variation of the solutions with different underlying forward processes.In addition,we propose a truncated discrete-time numerical scheme for quadratic reflected BSDEs and obtain the explicit rate of convergence by applying the quantitative stability result.展开更多
Purpose–The purpose of this paper is to develop a method for the existence,uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays,continuous di...Purpose–The purpose of this paper is to develop a method for the existence,uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays,continuous distributed delays and a kind of discontinuous activation functions.Design/methodology/approach–Basedonthe Leray–Schauderalternativetheoremand chainrule,by using a novel integral inequality dealing with monotone non-decreasing function,the authors obtain a delay-dependent sufficient condition with less conservativeness for robust stability of considered neural networks.Findings–Itturns out thattheauthors’delay-dependent sufficientcondition canbeformed intermsof linear matrix inequalities conditions.Two examples show the effectiveness of the obtained results.Originality/value–The novelty of the proposed approach lies in dealing with a new kind of discontinuous activation functions by using the Leray–Schauder alternative theorem,chain rule and a novel integral inequality on monotone non-decreasing function.展开更多
Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It ...Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ*> 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r^(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .展开更多
Photodynamic therapy(PDT)has shown a promising capability for cancer treatment with minimal side effects.Indocyanine green(ICG),the only clinically approved near-infrared(NIR)fluorophore,has been used as a photosensit...Photodynamic therapy(PDT)has shown a promising capability for cancer treatment with minimal side effects.Indocyanine green(ICG),the only clinically approved near-infrared(NIR)fluorophore,has been used as a photosensitizer for PDT in clinical application.However,the main obstacle of directly utilizing ICG in the clinic lies in its low singlet oxygen(1O_(2))quantum yield(QY)and instability in aqueous solution.To improve the PDT efficacy of ICG,free ICG molecules were assembled with free oxygen nanobubbles(NBs-O_(2))to fabricate ICG-NBs-O_(2) by hydrophilic-hydrophobe interactions on the gas-liquid interface.Interestingly,1O2 QY of ICG-NBs-O_(2) solution was significantly increased to 1.6%,which was estimated to be 8 times as high as that of free ICG solution.Meanwhile,ICG-NBs-O_(2) exhibited better aqueous solution stability compared with free ICG.Furthermore,through establishing tumor models in nude mice,the therapeutic efficacy of ICG-NBs-O_(2) was also assessed in the PDT treatment of oral cancer.The tumor volume in ICG-NBs-O_(2) treated group on day 14 decreased to 0.56 of the initial tumor size on day 1,while the tumor volume in free ICG treated group increased to 2.4 times.The results demonstrated that ICG-NBs-O_(2) showed excellent tumor ablation in vivo.Therefore,this facile method provided an effective strategy for enhanced PDT treatment of ICG and showed great potential in clinical application.展开更多
基金supported by Division of Molecular Therapeutics Development,Hanyang Biomedical Research Institute,Hanyang University and Woo Young Medical Co.LTD.,Seoul,South Korea.
文摘The stabilities of two kinds of solutions (30 mg/mL) of Ampicillin sodium in 0.9% NaCl in water (NS, normal saline) and in sterile water (SW) in the intravenous elastomeric infusion device (Accufuser®) were evaluated based on recommended solutions and storage periods. The injectable NS- and SW-Ampicillin solutions in the Accufuser® device were stored and evaluated at controlled temperature (room temperature, 25℃ ± 2℃ and cold temperature, 4℃ ± 2℃) during 7 days. Effects of the periods of storage (from 0 to 7 days) and the temperatures of storage (RT and CT) on the physico-chemical appearances and concentrations of active compounds were determined. The visual clarity, pH, and concentrations of Ampicillin were determined by stability-indicating high-performance liquid chromatography (HPLC)-ultraviolet (UV) detection. The results showed that the amount of Ampicillin in studied solutions gradually decreased with time. The Ampicillin in NS, which was stored in CT, was relatively stable, retaining 94% of its original amount up to 7 days. The solution that showed least stability was Ampicillin in SW, which was stored in RT, retaining 80% of its original amount. Generally, solutions that were stored in CT were more stable than the solutions that were stored in RT. No significant changes in physical appearance or color of the solutions were observed during the study. Particles were not detected in any solution samples. In summary, two kinds of solutions of Ampicillin sodium, in NS and SW, showed different chemical stabilities with time in intravenous infusion device without any significant physical changes and retained about 94% vs 89% and 83% vs 80% of initial concentrations after 7 days in CT and RT, respectively. We suggest that 30 mg/mL of Ampicillin sodium in NS solution in an Accufuser® infusion device which is stored in CT can be applicable for 7 days in clinical situations.
基金the National Natural Science Foundation of China(11671406,12071491)the Research Fund of Shenzhen Institute of Information Technology(QN201703).
文摘This paper is concerned with multidirectional associative memory neural network with distributed delays on almost-periodic time scales.Some sufficient conditions on the existence,uniqueness and the global exponential stability of almost-periodic solutions are established.An example is presented to illustrate the feasibility and effectiveness of the obtained results.
文摘Numerical solutions of the steady transonic small-disturbance（TSD） potential equation are computed using the conservative Murman-Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.
文摘In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.
基金This work is supported by National Science Foundation of China and the Fundes of Institute of Math (opened) Academic Sinica.
文摘One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.
基金financially supported by the National Natural Science Foundation of China (No. 51274046)
文摘In this study, the changing trend of crystal-lattice constant and the influential factors of the stability of supersaturated solid solutions with various alloying additions in the Al–X（Zn, Mg, Cu） binary alloys were investigated. The samples were analyzed using X-ray diffraction（XRD）,X-ray absorption fine structure（XAFS）, and scanning electron microscope（SEM）. It is found that the addition of Cu causes the largest change of crystal-lattice constant of the Al–xCu supersaturated solid solution binary alloy. The most dramatic change occurs in the initial stage of Cu addition.The change is stabilized thereafter. Also, at the same alloying element addition to the Al–X（X = Zn, Mg, Cu）binary alloys, the Al–xCu is the most unstable system.Influential factors of the stability include the lattice constant change and the type of alloying element. The larger the lattice constant changes, the more unstable the supersaturated solid solution is. The alloying element, easy to aggregate, often leads to the solid solution less stable.
文摘In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.
基金Funded by National Natural Science Foundation of China(No.91326203)。
文摘Al2O3-ZrO2 microspheres were prepared by internal gelation method.The effects of Al3+on the stability of solution and performance of gel spheres were studied.Al3+had a great influence on the stability of the solutions,and the more of the amount of Al3+,the shorter of the stabilization time.Because Al3+did not copolymerize with Zr4+during the sol-gel transformation,the strength of gel sphere added with Al3+was low and deformed easily as it was squeezed.The results of our experiments well verify Glasser team’s speculation and conclusions.At the same time,based on the experimental results,we prepared Al2O3-ZrO2 composite microspheres with higher content of Al2O3 by controlling the pH of the solution.The change curve of viscosity with time and the stabilization time of the solution with different Al3+dosage were given,which could provide references for industrial mass production.Samples without hydrothermal treatment cracked severely,while the samples hydrothermally treated kept structural integrity with no cracks after calcined.Al2O3-ZrO2 microspheres with no segregation and phase separation were prepared and alumina evenly distributed in the zirconia matrix.When the content of Al2O3 was low,the tetragonal phase was stable.And the cubic phase was obtained when the content of Al2O3 was more.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41630530, 41575109 & 91230202)
文摘In this paper, a climate dynamics model with the effects of topography and a non-constant external force, which consists of the Navier-Stokes equations and a temperature equation arising from the evolution process of the atmosphere, was considered.Under certain assumptions imposed on the initial data and by using some delicate estimates and compactness arguments, we proved the L^1-stability of weak solutions to the atmospheric equations.
文摘In this paper,we consider the periodic solution problems for the systems with unbounded delay,and the existence,uniqueness and stability of the periodic solution are dealt with unitedly.First we establish the suitable delay-differential inequality,then study seperately the problems of periodic solution for the systems with bounded delay,with unbounded delay and the Volterra integral-dlfferentlal systems with infinite delay by using the character of matrix measure and the asymptotic fixed point theorem of poincaré’s periodic operator in the different phase spaces.A series of simple criteria for the existence,uniqueness and stability of these systems are obtained.
基金supported by National Natural Science Foundation of China (Grant No. 11471334)Program for New Century Excellent Talents in University (Grant No. NCET-12-0085)
文摘This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" conditions and the velocity field and temperature enjoy the slip boundary condition and convective boundary condition, respectively. The uniform estimates with respect to both the Mach number ∈(0, ∈] and time t ∈ [0, ∞) are established by deriving a differential inequality with decay property, where ∈∈(0, 1] is a constant.As the Mach number vanishes, the global solution to full compressible Navier-Stokes equations converges to the one of isentropic incompressible Navier-Stokes equations in t ∈ [0, +∞). Moreover, we prove the exponentially asymptotic stability for the global solutions of both the compressible system and its limiting incompressible system.
基金supported by the National NSF of China(11571088)NSF of Zhejiang Province(LY13A010020)Program(HNUEYT2013)
文摘In this paper,several new constant-amplitude and variable-amplitude wave solutions（namely,traveling wave solutions） of a generalized nonlinear Schrdinger equation are investigated by using the extended homogeneous balance method,where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation,respectively.In addition,stability analysis of those solutions are also conducted by regular phase plane technique.
文摘In [1] and [2], the authors made a deep qualitative analysis of the equationwith the character of tangent detected phase and they mathematically provided atheoretical basis of why the phase looked loop has no look--losing point. However,according to many practical experts, it is rather difficult to put such a phaselooked loop into practice, though it has fine properties. W. C. Lindsey [3] made a
文摘For the operator D(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect to then Eq.(1) has an mω-periodic solution p(t), for some integer m≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance from H+ (ξ,D,f), then Eq.(1) has an almost periodic solution.
文摘We study the qualitative property of solutions of planar periodic competing otka-Volterra systems New criteria of uniform persistence of solutins and existence, uniqueness and globally asymptotical stability of positive periodic solution are established. The results results in [1 -6] are summarized and improved in this paper.
基金supported by the National Natural Science Foundation of China(Nos.U1137603,21307047)the Opening Project of Key Laboratory of Green Catalysis of Sichuan Institutes of High Education(No.LYJ1309)
文摘A series of CeO2–ZrO2–WO3（CZW）catalysts prepared by a hydrothermal synthesis method showed excellent catalytic activity for selective catalytic reduction（SCR）of NO with NH3 over a wide temperature of 150–550℃.The effect of hydrothermal treatment of CZW catalysts on SCR activity was investigated in the presence of 10% H2O.The fresh catalyst showed above 90% NOx conversion at 201–459℃,which is applicable to diesel exhaust NOx purification（200–440℃）.The SCR activity results indicated that hydrothermal aging decreased the SCR activity of CZW at low temperatures（below 300℃）,while the activity was notably enhanced at high temperature（above 450℃）.The aged CZW catalyst（hydrothermal aging at 700℃ for 8 hr）showed almost 80% NOx conversion at 229–550℃,while the V2O5–WO3/TiO2 catalyst presented above 80% NOx conversion at 308–370℃.The effect of structural changes,acidity,and redox properties of CZW on the SCR activity was investigated.The results indicated that the excellent hydrothermal stability of CZW was mainly due to the CeO2–ZrO2 solid solution,amorphous WO3 phase and optimal acidity.In addition,the formation of WO3 clusters increased in size as the hydrothermal aging temperature increased,resulting in the collapse of structure,which could further affect the acidity and redox properties.
基金supported by China Scholarship Council.Gechun Liang is partially supported by the National Natural Science Foundation of China(Grant No.12171169)Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515011338)+1 种基金GL thanks J.F.Chassagneux and A.Richou for helpful and inspiring discussions on how to extend to the state dependent volatility case.Shanjian Tang is partially supported by National Science Foundation of China(Grant No.11631004)National Key R&D Program of China(Grant No.2018YFA0703903).
文摘We study the quantitative stability of solutions to Markovian quadratic reflected backward stochastic differential equations(BSDEs)with bounded terminal data.By virtue of bounded mean oscillation martingale and change of measure techniques,we obtain stability estimates for the variation of the solutions with different underlying forward processes.In addition,we propose a truncated discrete-time numerical scheme for quadratic reflected BSDEs and obtain the explicit rate of convergence by applying the quantitative stability result.
基金supported by the National Natural Science Foundation of China No.61273022the Research Foundation of Department of Education of Liaoning Province No.JDL2017031.
文摘Purpose–The purpose of this paper is to develop a method for the existence,uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays,continuous distributed delays and a kind of discontinuous activation functions.Design/methodology/approach–Basedonthe Leray–Schauderalternativetheoremand chainrule,by using a novel integral inequality dealing with monotone non-decreasing function,the authors obtain a delay-dependent sufficient condition with less conservativeness for robust stability of considered neural networks.Findings–Itturns out thattheauthors’delay-dependent sufficientcondition canbeformed intermsof linear matrix inequalities conditions.Two examples show the effectiveness of the obtained results.Originality/value–The novelty of the proposed approach lies in dealing with a new kind of discontinuous activation functions by using the Leray–Schauder alternative theorem,chain rule and a novel integral inequality on monotone non-decreasing function.
基金supported by the National Natural Science Foundation of China(Nos.11201119,11471099)the International Cultivation of Henan Advanced Talents and the Research Foundation of Henan University(No.yqpy20140043)
文摘Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ*> 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r^(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .
基金This investigation was financially funded by the projects of the National Key Research and Development Program of China(No.2017YFA0104302)the National Natural Science Foundation of China(Nos.51832001,61821002,and 81971750)the Jiangsu Planned Projects for Postdoctoral Research Funds(No.2021K601C).
文摘Photodynamic therapy(PDT)has shown a promising capability for cancer treatment with minimal side effects.Indocyanine green(ICG),the only clinically approved near-infrared(NIR)fluorophore,has been used as a photosensitizer for PDT in clinical application.However,the main obstacle of directly utilizing ICG in the clinic lies in its low singlet oxygen(1O_(2))quantum yield(QY)and instability in aqueous solution.To improve the PDT efficacy of ICG,free ICG molecules were assembled with free oxygen nanobubbles(NBs-O_(2))to fabricate ICG-NBs-O_(2) by hydrophilic-hydrophobe interactions on the gas-liquid interface.Interestingly,1O2 QY of ICG-NBs-O_(2) solution was significantly increased to 1.6%,which was estimated to be 8 times as high as that of free ICG solution.Meanwhile,ICG-NBs-O_(2) exhibited better aqueous solution stability compared with free ICG.Furthermore,through establishing tumor models in nude mice,the therapeutic efficacy of ICG-NBs-O_(2) was also assessed in the PDT treatment of oral cancer.The tumor volume in ICG-NBs-O_(2) treated group on day 14 decreased to 0.56 of the initial tumor size on day 1,while the tumor volume in free ICG treated group increased to 2.4 times.The results demonstrated that ICG-NBs-O_(2) showed excellent tumor ablation in vivo.Therefore,this facile method provided an effective strategy for enhanced PDT treatment of ICG and showed great potential in clinical application.
