This paper investigates the hydrodynamic characteristics of floating truncated cylinders undergoing horizontal and vertical motions due to earthquake excitations in the finite water depth.The governing equation of the...This paper investigates the hydrodynamic characteristics of floating truncated cylinders undergoing horizontal and vertical motions due to earthquake excitations in the finite water depth.The governing equation of the hydrodynamic pressure acting on the cylinder is derived based on the radiation theory with the inviscid and incompressible assumptions.The governing equation is solved by using the method of separating variables and analytical solutions are obtained by assigning reasonable boundary conditions.The analytical result is validated by a numerical model using the exact artificial boundary simulation of the infinite water.The main variation and distribution characteristics of the hydrodynamic pressure acting on the side and bottom of the cylinder are analyzed for different combinations of wide-height and immersion ratios.The added mass coefficient of the cylinder is calculated by integrating the hydrodynamic pressure and simplified formulas are proposed for engineering applications.The calculation results show that the simplified formulas are in good agreement with the analytical solutions.展开更多
This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound cor...This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis.展开更多
The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n,...The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n, the quadrature formulae with m and m ＋ 1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval（-π, π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m ≥ 3.展开更多
The problem of yield estimation merely from performance test data of qualified semiconductor devices is studied. An empirical formula is presented to calculate the yield directly by the sample mean and standard de- vi...The problem of yield estimation merely from performance test data of qualified semiconductor devices is studied. An empirical formula is presented to calculate the yield directly by the sample mean and standard de- viation of singly truncated normal samples based on the theoretical relation between process capability indices and the yield. Firstly, we compare four commonly used normality tests under different conditions, and simulation results show that the Shapiro-Wilk test is the most powerful test in recognizing singly truncated normal samples. Secondly, the maximum likelihood estimation method and the empirical formula are compared by Monte Carlo simulation. The results show that the simple empirical formulas can achieve almost the same accuracy as the max- imum likelihood estimation method but with a much lower amount of calculations when estimating yield from singly truncated normal samples. In addition, the empirical formula can also be used for doubly truncated normal samples when some specific conditions are met. Practical examples of yield estimation from academic and IC test data are given to verify the effectiveness of the proposed method.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52078010 and 52101321)the National Key Research and Development Program of China(Grant No.2022YFC3004300).
文摘This paper investigates the hydrodynamic characteristics of floating truncated cylinders undergoing horizontal and vertical motions due to earthquake excitations in the finite water depth.The governing equation of the hydrodynamic pressure acting on the cylinder is derived based on the radiation theory with the inviscid and incompressible assumptions.The governing equation is solved by using the method of separating variables and analytical solutions are obtained by assigning reasonable boundary conditions.The analytical result is validated by a numerical model using the exact artificial boundary simulation of the infinite water.The main variation and distribution characteristics of the hydrodynamic pressure acting on the side and bottom of the cylinder are analyzed for different combinations of wide-height and immersion ratios.The added mass coefficient of the cylinder is calculated by integrating the hydrodynamic pressure and simplified formulas are proposed for engineering applications.The calculation results show that the simplified formulas are in good agreement with the analytical solutions.
文摘This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis.
基金The NSF (61033012,10801023,10911140268 and 10771028) of China
文摘The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n, the quadrature formulae with m and m ＋ 1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval（-π, π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m ≥ 3.
文摘The problem of yield estimation merely from performance test data of qualified semiconductor devices is studied. An empirical formula is presented to calculate the yield directly by the sample mean and standard de- viation of singly truncated normal samples based on the theoretical relation between process capability indices and the yield. Firstly, we compare four commonly used normality tests under different conditions, and simulation results show that the Shapiro-Wilk test is the most powerful test in recognizing singly truncated normal samples. Secondly, the maximum likelihood estimation method and the empirical formula are compared by Monte Carlo simulation. The results show that the simple empirical formulas can achieve almost the same accuracy as the max- imum likelihood estimation method but with a much lower amount of calculations when estimating yield from singly truncated normal samples. In addition, the empirical formula can also be used for doubly truncated normal samples when some specific conditions are met. Practical examples of yield estimation from academic and IC test data are given to verify the effectiveness of the proposed method.
