In this paper,we present monotonicity results of a function involving the inverse hyperbolic sine.From these,we obtain some lower bounds for the inverse hyperbolic sine.
This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.Thi...This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.展开更多
A high accuracy experimental system has been established for unsteady open-channel flow.Then 40 experiments were conducted to study the propagating characteristics of unsteady open-channel flow.From the experimental d...A high accuracy experimental system has been established for unsteady open-channel flow.Then 40 experiments were conducted to study the propagating characteristics of unsteady open-channel flow.From the experimental data,the variation law of propagating velocity,wave deformation rate,flow depth of wave peak and bottom,and other parameters were obtained.The experimental results show the followings.1) The propagating velocity of unsteady open-channel flows can be expressed by the sum of flow velocity and micro-amplitude wave velocity at wave peak.2) The waveform of an unsteady flow would deform when it propagates,with the rising stage becoming longer and the falling stage shorter;the deformation rate is a function of distance,period and relative amplitude of discharge.3) The flow depths of wave peak and bottom have a close relationship with the period of the unsteady flow.When the period is short,water depths of wave peak and bottom are both close to those of the average discharge in the condition of uniform flow.For a long period unsteady flow,the water depth of wave peak is close to that of the maximal discharge in the condition of uniform flow,while at the flow wave bottom,it is close to the depth of the minimum discharge in an uniform flow.4) Propagating characteristic of discharge is analogous to that of flow depth for unsteady flow.展开更多
Taking into account the Bekenstein-Hawking area law,based on the analysis of Zeng and Liu et al.that area spectrum is determined by the periodicity of an outgoing wave,we discuss on the quantization of entropy from a ...Taking into account the Bekenstein-Hawking area law,based on the analysis of Zeng and Liu et al.that area spectrum is determined by the periodicity of an outgoing wave,we discuss on the quantization of entropy from a neutral black string.In addition,applying the adiabatic invariant quantity method proposed by Majhi and Vagenas,we further verify the entropy quantum of the neutral black string.As a result,two different methods show that the quantum of entropy is △S = 2π,which is in agreement with Bekenstein's proposal.展开更多
文摘In this paper,we present monotonicity results of a function involving the inverse hyperbolic sine.From these,we obtain some lower bounds for the inverse hyperbolic sine.
文摘This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.
基金supported by the National Key Technology R & D Programof China (Grant No. 2011BAB09B01)the Chongqing Natural Science Foundation of China (Grant No. cstc2011jjA1167)
文摘A high accuracy experimental system has been established for unsteady open-channel flow.Then 40 experiments were conducted to study the propagating characteristics of unsteady open-channel flow.From the experimental data,the variation law of propagating velocity,wave deformation rate,flow depth of wave peak and bottom,and other parameters were obtained.The experimental results show the followings.1) The propagating velocity of unsteady open-channel flows can be expressed by the sum of flow velocity and micro-amplitude wave velocity at wave peak.2) The waveform of an unsteady flow would deform when it propagates,with the rising stage becoming longer and the falling stage shorter;the deformation rate is a function of distance,period and relative amplitude of discharge.3) The flow depths of wave peak and bottom have a close relationship with the period of the unsteady flow.When the period is short,water depths of wave peak and bottom are both close to those of the average discharge in the condition of uniform flow.For a long period unsteady flow,the water depth of wave peak is close to that of the maximal discharge in the condition of uniform flow,while at the flow wave bottom,it is close to the depth of the minimum discharge in an uniform flow.4) Propagating characteristic of discharge is analogous to that of flow depth for unsteady flow.
基金Supported by the Scientific Research Foundation of the Education Department of Liaoning Province under Grant No. L2011195
文摘Taking into account the Bekenstein-Hawking area law,based on the analysis of Zeng and Liu et al.that area spectrum is determined by the periodicity of an outgoing wave,we discuss on the quantization of entropy from a neutral black string.In addition,applying the adiabatic invariant quantity method proposed by Majhi and Vagenas,we further verify the entropy quantum of the neutral black string.As a result,two different methods show that the quantum of entropy is △S = 2π,which is in agreement with Bekenstein's proposal.
