• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.65-79
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• 2007

An optimal 3-point quadrature formula of closed type is derived. It is shown that the optimal quadrature formula has a better error bound than the well-known Simpson's rule. A corrected formula is also considered. Various error inequalities for these formulas are established. Applications in numerical integration are given.

• International Journal of Fluid Machinery and Systems
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• v.8 no.4
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• pp.311-317
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• 2015

It is difficulty to calculate velocity circulation in centrifugal pump impeller outlet accurately. Velocity circulations of a double-blade pump impeller outlet were calculated with Stodola formula, Weisner formula and Stechkin formula. Simultaneously, the internal flow of impeller for the double-blade pump were measured with PIV technology and average velocity circulations at the 0.8, 1.0 and 1.2 times of design flow were obtained. All the experimental values were compared with the above calculation values at the three conditions. The results show that calculation values of velocity circulations with Weisner formula is close to the experimental values. On the basis of the above, velocity circulations of impeller outlet were corrected. The results of experimental verification show that the corrected calculation errors, whose maximum error is 3.65%, are greatly reduced than the uncorrected calculation errors. The research results could provide good references for establishment of theoretical head and multi-condition hydraulic optimization of double-blade pumps.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.17 no.3
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• pp.119-126
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• 2003

The size of low voltage level conductor cables can be installed with a long length just like a aviation field, shall be determined for considering the ampacity of cable and the drop of voltage for the power system. Therefore, The size of the conductor cables may be larger one for considering the tolerable voltage drop comparatively, although the allowable ampacity of the conductor cables may have a margin in comparison with the rated full load current In this case, the conductor cables' allowable ampacity will be very larger than the rated full load current and the generated heat of the conductor will be relatively downed. The conductor cables' alternating current resistance corrected with the maximum allowable temperature of the conductors, has been applied on the general formula for the calculating the voltage drop in determinating the size of low voltage level conductor cables, and the resistance is larger than the resistance corrected with the actual temperature of the conductor cables. This paper was studied for the purpose of the conductor resistance corrected with the actual temperature rise of the conductor and address the economic design formula so that this studies shall minimize the errors which can be occurred in comparison with the general formula and which can be applied in design work for determining the size of low voltage level conductor cables.

• East Asian mathematical journal
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• v.22 no.1
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• pp.71-77
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• 2006

By applying various known summation theorems to a general transformation formula based upon Bailey's transformation theorem due to Slater, Exton has obtained numerous and new quadratic transformations involving hypergeometric functions of order greater than two(some of which have typographical errors). We aim at first deriving a general quadratic transformation formula due to Exton and next providing a list of quadratic formulas(including the corrected forms of Exton's results) and some more results.

• East Asian mathematical journal
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• v.34 no.3
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• pp.239-248
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• 2018

In this paper, we derive a closed-form formula of a second-order approximation for a European corrected option price under stochastic elasticity of variance model mentioned in Kim et al. (2014) [1] [J.-H. Kim, J Lee, S.-P. Zhu, S.-H. Yu, A multiscale correction to the Black-Scholes formula, Appl. Stoch. Model. Bus. 30 (2014)]. To find the explicit-form correction to the option price, we use Mellin transform approaches.

• Nuclear Engineering and Technology
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• v.3 no.1
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• pp.3-7
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• 1971

A method for determining dead times of a G.M. detector as a function of the count rate has been investigated using the Mn$^{56}$ radioactive sample. The formula, (equation omitted), seems to be useful for determining a relation between the dead time and the count rate. Here (equation omitted)(N$_1$) is the dead time for the count rate N$_1$, N$_1$is the count rate at time zero, Nt is the count rate at time t, λ is the radioactive decay constant of the sample used, and t is the time between the first and second runs. When all the counting data were corrected for the dead times evaluated with this formula and then a variation of these corrected counting data with rime was observed, the results showed quite a good agreement with the published data for the radioactive decay of Mn$^{56}$ . Besides, it appears that the dead time decreases as the count rate increases in a dead time-to-count rate relation obtained by the same formula.

• Progress in Superconductivity and Cryogenics
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• v.20 no.4
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• pp.6-10
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• 2018

Low-noise amplifiers in the radio-frequency (RF) band based on the direct current (DC) superconducting quantum interference device (SQUID) can be used for quantum-limited measurements in precision physics experiments. For the prediction of peak-gain frequency of these amplifiers, we need a reliable design formula for the resonance frequency of the microstrip circuit. We improved the formula for the resonance frequency, determined by parameters of the DC SQUID and the input coil, and compared the design values with experimental values. The proposed formula showed much accurate results than the conventional formula. Minor deviation of the experimental results from the theory can be corrected by using the measured geometrical parameters of the input coil line.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.373-381
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• 2009

Evidence of linkage is expressed as a decreasing trend of the squared trait difference of two siblings with increasing identical by descent scores. In contrast to successes in the application of a parametric approach of Haseman-Elston regression, notably low powers are demonstrated in the nonparametric linkage analysis methods for complex traits and diseases with sib-pairs data. We report that the Genehunter nonparametric linkage statistic is biased and furthermore the variance formula that they used is an inflated one, and this is one reason for a low performance. Thus, we propose bias-corrected nonparametric linkage statistics. Simulation studies comparing our proposed nonparametric test statistics versus the existing test statistics suggest that the bias-corrected new nonparametric test statistics are more powerful and attains efficiencies close to that of Haseman-Elston regression.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.573-591
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• 2013

In this paper, we improve the error corrected Euler method(ECEM) introduced in [11] by evaluating function values only at local nodes in each time interval. As a result, one can avoid computations of Jacobian matrices on each time interval so that the algorithms become simpler to implement in solving various class of time dependent differential equations numerically. The proposed ECEM formula resembles to the Runge-Kutta method in its representations but both methods have different characteristic properties.

• Structural Engineering and Mechanics
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• v.50 no.1
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• pp.37-52
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• 2014

The accurate determination of cable tension is important to the monitoring of the condition of a cable-stayed bridge. When applying a vibration-based formula to identify the tension of a real cable under sag, stiffness and boundary conditions, the resulting error must not be overlooked. In this work, by resolving the implicit frequency function of a real cable under the above conditions numerically, indirect methods of determining the cable force and a method to calculate the corresponding cable mode frequency are investigated. The error in the tension is studied by numerical simulation, and an empirical error correction formula is presented by fitting the relationship between the cable force error and cable parameters ${\lambda}^2$ and ${\xi}$. A case study on two real cables of the Shanghai Changjiang Bridge shows that employing the method proposed in this paper can increase the accuracy of the determined cable force and reduce the computing time relative to the time required for the finite element model.