In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formula...In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formulas of the first part of the Lax pairs. Then by further discussion and doing some revisional work, we make the recursion formulas fit for the second part of Lax pairs. At last, some solutions to the MGDLW equation are worked out by using the recursion formula.展开更多
An error analysis of the dynamic shear modulus of stiff specimens from tests performed by a new resonant column device developed by the Institute of Engineering Mechanics, China was conducted. A modified approach for ...An error analysis of the dynamic shear modulus of stiff specimens from tests performed by a new resonant column device developed by the Institute of Engineering Mechanics, China was conducted. A modified approach for calculating the dynamic shear modulus of the stiff specimens is presented. The error formula of the tests was deduced and parameters that impact the accuracy of the test were identified. Using six steel specimens with known standard stiffness as a base, a revised dynamic shear modulus calculation for stiff specimens was formulated by comparing three of the models. The maximum error between the test results and the calculated results shown by curves from both the free-vibration and the resonant-vibration tests is less than 6%. The free-vibration and resonant-vibration tests for three types of stiff samples with a known modulus indicate that the maximum deviation between the actual and the tested value using the modified approach were less than 10%. As a result, the modified approach presented here is shown to be reliable and the new device can be used for testing dynamic shear modulus of any stiff materials at low shear strain levels展开更多
A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for the...A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for theperformance evaluation on control charts. This paper proposes the explicit formula for evaluating the average runlength on a two-sided modified exponentially weighted moving average chart under the observations of a first-orderautoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparisonof the explicit formula and the numerical integral technique is carried out using the absolute relative change forchecking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL ofthe explicit formula and the numerical integral equation method are hardly different, but this explicit formula ismuch faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classicalEWMA and the modified EWMA control charts are compared and the results show that the latter is better for smalland intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the healthfield as COVID-19 data in Thailand and Singapore.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10101025
文摘In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formulas of the first part of the Lax pairs. Then by further discussion and doing some revisional work, we make the recursion formulas fit for the second part of Lax pairs. At last, some solutions to the MGDLW equation are worked out by using the recursion formula.
基金Ministry of Science and Technology of Chinaand the Earthquake Science Foundation of China Under GrandNo.102033
文摘An error analysis of the dynamic shear modulus of stiff specimens from tests performed by a new resonant column device developed by the Institute of Engineering Mechanics, China was conducted. A modified approach for calculating the dynamic shear modulus of the stiff specimens is presented. The error formula of the tests was deduced and parameters that impact the accuracy of the test were identified. Using six steel specimens with known standard stiffness as a base, a revised dynamic shear modulus calculation for stiff specimens was formulated by comparing three of the models. The maximum error between the test results and the calculated results shown by curves from both the free-vibration and the resonant-vibration tests is less than 6%. The free-vibration and resonant-vibration tests for three types of stiff samples with a known modulus indicate that the maximum deviation between the actual and the tested value using the modified approach were less than 10%. As a result, the modified approach presented here is shown to be reliable and the new device can be used for testing dynamic shear modulus of any stiff materials at low shear strain levels
基金The research was supported by King Mongkut’s University of Technology North Bangkok Contract No.KMUTNB-62-KNOW-018.
文摘A modified exponentially weighted moving average (EWMA) scheme is one of the quality control charts suchthat this control chart can quickly detect a small shift. The average run length (ARL) is frequently used for theperformance evaluation on control charts. This paper proposes the explicit formula for evaluating the average runlength on a two-sided modified exponentially weighted moving average chart under the observations of a first-orderautoregressive process, referred to as AR(1) process, with an exponential white noise. The performance comparisonof the explicit formula and the numerical integral technique is carried out using the absolute relative change forchecking the correct formula and the CPU time for testing speed of calculation. The results show that the ARL ofthe explicit formula and the numerical integral equation method are hardly different, but this explicit formula ismuch faster for calculating the ARL and offered accurate values. Furthermore, the cumulative sum, the classicalEWMA and the modified EWMA control charts are compared and the results show that the latter is better for smalland intermediate shift sizes. In addition, the explicit formula is successfully applied to real-world data in the healthfield as COVID-19 data in Thailand and Singapore.
