Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and ...Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.展开更多
In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the wh...In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n).展开更多
This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are ...This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.展开更多
We consider the nonlinear functional dynamic equation （p（t）[（r（t）x^△（t））^△]γ）^△＋q（t）f（x（τ（t））） =0, for t≥t0,on a time scale T, where γ〉 0 is the quotient of odd positive integers, p, r, τ- ...We consider the nonlinear functional dynamic equation （p（t）[（r（t）x^△（t））^△]γ）^△＋q（t）f（x（τ（t））） =0, for t≥t0,on a time scale T, where γ〉 0 is the quotient of odd positive integers, p, r, τ- and q are positive rd-continuous functions defined on the time scale 1F, and lirut→∞ τ（t） = ∞. The main aim of this paper is to establish some new sufficient conditions which guarantee that the equation has oscillatory solutions or the solutions tend to zero as →∞ τ. The main investigation depends on the Riccati substitution and the analysis of the associated Riccati dynamic inequality. Our results extend, complement and improve some previously obtained ones. In particular, the results provided substantial improvement for those obtained by Yu and Wang [J Comput Appl Math, 225 （2009）, 531-540]. Some examples illustrating the main results are given.展开更多
We have studied the reversal of magnetisation in Ising ferromagnet by the field having gradient along a particular direction. We employed the Monte Carlo simulation with Metropolis single spin nip algorithm. The avera...We have studied the reversal of magnetisation in Ising ferromagnet by the field having gradient along a particular direction. We employed the Monte Carlo simulation with Metropolis single spin nip algorithm. The average lifetime of the metastable state was observed to increase with the magnitude of the gradient of applied field. In the high gradient regime, the system was observed to show two distinct region of up and down spins. The interface or the domain wall was observed to move as one increases the gradient. The displacement of the mean position of the interface was observed to increase with the gradient as hyperbolic tangent function. The roughness of the interface was observed to decay exponentially as the gradient increases. The number of spin flip per site was observed to show a discontinuity in the vicinity of the domain wall. The amount of the discontinuity was found to diverge with the system size as a power law fashion with an exponent 5/3.展开更多
In this paper, the authors aim at proving two existence results of fractional differential boundary value problems of the form （Pa,bα）{D^au（x）＋f（x,u（x））=0,x∈（0,1）,u（0）=u（1）=0,D^a-3u（0）=a,u^（1）=-6w...In this paper, the authors aim at proving two existence results of fractional differential boundary value problems of the form （Pa,bα）{D^au（x）＋f（x,u（x））=0,x∈（0,1）,u（0）=u（1）=0,D^a-3u（0）=a,u^（1）=-6where 3 ≤ a 〈 4, D^ is the standard Riemann-Liouville fractional derivative and a, b are nonnegative constants. First the authors suppose that f（x, t） = -p（x）t^σ, with cr ~ （-1, 1） and p being a nonnegative continuous function that may be singular at x - 0 or x - 1 and satisfies some conditions related to the Karamata regular variation theory. Combining sharp estimates on some potential functions and the Sch^uder fixed point theorem, the authors prove the existence of a unique positive continuous solution to problem （P0,0）. Global estimates on such a solution are also obtained. To state the second existence result, the authors assume that a, b are nonnegative constants such that a ＋ b 〉 0 and f（x, t） -= tφ（x, t）, with φ（x, t） being a nonnegative continuous function in （0, 1） × [0, ∞） that is required to satisfy some suitable integrability condition. Using estimates on the Green＇s function and a perturbation argument, the authors prove the existence and uniqueness of a positive continuous solution u to problem （Pa,b）, which behaves like the unique solution of the homogeneous problem corresponding the existence results. to （Pa,b）. Some examples are given to illustrate the existence results.,展开更多
文摘Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.
文摘In this paper two sequences of generalized Landau linear positive operators are introduced. They can be applied in approximating continuous functions with arbitrary growth order, defined on a finite interval or the whole real axis. The properties of approximation are studied and their asymptotic formulae are presented. These results show that their degrees of approximation are the best among existing operator sequences of Landau type, for example, their degrees of approximation for C 2[0, 1] are O(1/n 2) but corresponding degree of ordinary Landau operators are only O(1/n).
文摘This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.
基金supported by King Saud University,Dean-ship of Scientific Research,College of Science Research Centre
文摘We consider the nonlinear functional dynamic equation （p（t）[（r（t）x^△（t））^△]γ）^△＋q（t）f（x（τ（t））） =0, for t≥t0,on a time scale T, where γ〉 0 is the quotient of odd positive integers, p, r, τ- and q are positive rd-continuous functions defined on the time scale 1F, and lirut→∞ τ（t） = ∞. The main aim of this paper is to establish some new sufficient conditions which guarantee that the equation has oscillatory solutions or the solutions tend to zero as →∞ τ. The main investigation depends on the Riccati substitution and the analysis of the associated Riccati dynamic inequality. Our results extend, complement and improve some previously obtained ones. In particular, the results provided substantial improvement for those obtained by Yu and Wang [J Comput Appl Math, 225 （2009）, 531-540]. Some examples illustrating the main results are given.
文摘We have studied the reversal of magnetisation in Ising ferromagnet by the field having gradient along a particular direction. We employed the Monte Carlo simulation with Metropolis single spin nip algorithm. The average lifetime of the metastable state was observed to increase with the magnitude of the gradient of applied field. In the high gradient regime, the system was observed to show two distinct region of up and down spins. The interface or the domain wall was observed to move as one increases the gradient. The displacement of the mean position of the interface was observed to increase with the gradient as hyperbolic tangent function. The roughness of the interface was observed to decay exponentially as the gradient increases. The number of spin flip per site was observed to show a discontinuity in the vicinity of the domain wall. The amount of the discontinuity was found to diverge with the system size as a power law fashion with an exponent 5/3.
基金funded by the National Plan for Science,Technology and Innovation(MAARIFAH),King Abdulaziz City for Science and Technology,Kingdom of Saudi Arabia,Award Number(No.13-MAT2137-02)
文摘In this paper, the authors aim at proving two existence results of fractional differential boundary value problems of the form （Pa,bα）{D^au（x）＋f（x,u（x））=0,x∈（0,1）,u（0）=u（1）=0,D^a-3u（0）=a,u^（1）=-6where 3 ≤ a 〈 4, D^ is the standard Riemann-Liouville fractional derivative and a, b are nonnegative constants. First the authors suppose that f（x, t） = -p（x）t^σ, with cr ~ （-1, 1） and p being a nonnegative continuous function that may be singular at x - 0 or x - 1 and satisfies some conditions related to the Karamata regular variation theory. Combining sharp estimates on some potential functions and the Sch^uder fixed point theorem, the authors prove the existence of a unique positive continuous solution to problem （P0,0）. Global estimates on such a solution are also obtained. To state the second existence result, the authors assume that a, b are nonnegative constants such that a ＋ b 〉 0 and f（x, t） -= tφ（x, t）, with φ（x, t） being a nonnegative continuous function in （0, 1） × [0, ∞） that is required to satisfy some suitable integrability condition. Using estimates on the Green＇s function and a perturbation argument, the authors prove the existence and uniqueness of a positive continuous solution u to problem （Pa,b）, which behaves like the unique solution of the homogeneous problem corresponding the existence results. to （Pa,b）. Some examples are given to illustrate the existence results.,
