• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.57-65
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• 1998

An estimation of remainder for Simpson's quadrature formula for differentiable mappings whose derivatives belong to $L_p$-spaces and applications in theory of special means (logarithmic mean, identric mean etc...) are given.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.22 no.2
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• pp.40-45
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• 1986

In this paper, the I-resistance curve of low-carbon steel with 3 mm thickness was investigated for various crack ratios. The experiments were carried out for the center cracked tension (CCT) specimen with about 50 mm width on an instron machine. The plane stress fracture toughness obtained by the Simpson's formula was Ii. = 24.96 kgffmm. Simpson's formula which considers crack growth in obtaining J integral showed more conservative lin than Rice's and Sumpter's. For materials that may be approximated by the Ramberg and Osgood stress strain law, the relevant crack parameters like the J integral, load line displacement are approximately normalized. Crack driving forces in terms of the I integral are computed for low-carbon steel CCT specimen using the above estimation scheme. Comparison of the prediction with actual experimental measurements by Simpson's formula showed good agreement for several different sized specimen.

• Korean Journal of Mathematics
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• v.32 no.3
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• pp.365-379
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• 2024

Researchers continue to explore and introduce new operators, methods, and applications related to fractional integrals and inequalities. In recent years, fractional integrals and inequalities have gained a lot of attention. In this paper, firstly we established the new identity for the case of differentiable function through the fractional operator (Caputo-Fabrizio). By utilizing this novel identity, the obtained results are improved for Simpson second formula-type inequality. Based on this identity the Simpson second formula-type inequality is proved for the s-convex functions. Furthermore, we also include the applications to special means.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.3A
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• pp.251-258
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• 2009

This paper deals with the strongest beams with the solid regular polygon cross-section, whose volumes are always held constant. The differential equation of the elastic deflection curve of such beam subjected to the concentrated and trapezoidal distributed loads are derived and solved by using the double integration method. The Simpson's formula was used to numerically integrate the differential equation. In the numerical examples, the clamped-clamped and clamped-hinged ends are considered as the end constraints and the linear, parabolic and sinusoidal tapers are considered as the shape function of cross sectional depth. As the numerical results, the configurations, i.e. section ratios, of the strongest beams are determined by reading the section ratios from the numerical data obtained in this study, under which static maximum behaviors become to be minimum.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.91-106
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• 2010

This is the study for various methods for getting the volume of frustum of pyramid. This study will first deal with how the formula of getting the volume of frustum of pyramid has been changed in the history of Mathematics. Secondly, based on the study of 'Prasolov' this study will deal with the calculation method for the volume of frustum of pyramid which was written in the 14th question of 'Moscow Papyrus' and search for the rules of solution for frustum of pyramid in the middle school textbooks. Finally, this study will consider various solutions for the volume of frustum of pyramid and its generalization.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.160-183
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• 2023

In the present paper, we prove that our main inequality reduces to some trapezoid and Newton type inequalities for differentiable s-convex functions. These inequalities are established by using the well-known Riemann-Liouville fractional integrals. With the help of special cases of our main results, we also present some new and previously obtained trapezoid and Newton type inequalities.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.3
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• pp.376-385
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• 1987

In this study, the plane stress fracture toughness and Tearing modulus are investigated for various crack ratios using the J integral. To evaluate the J integral and Tearing modulus, both experiments and estimation are used. The thickness of the low carbon steel specimens that is used in the experiments is 3mm. The type of specimen that is considered in the study is center-cracked-tension one. The measurements of crack length are performed by unloading compliance method. In the estimation of crack parameters such as the J integral and load line displacement, the Ramberg and Osgood stress strain law is assumed. Then simple formulas are given for estimating the crack parameters from contained yielding to fully plastic solutions. Obtained results are as follows; (1) When the crack ratio is in the range of 0.500 - 0.701, the plane stress fracture toughness is almost constant regardless of crack ratios. (2) The fracture toughness (J$\_$c/) and Tearing modulus (T) obtained are J$\_$c/=28.51kgf/mm, T=677.7 for base metal, J$\_$c/=31.85kgf/mm, T=742.0 for annealed metal. (3) Simpson's and McCabe's formulas which consider crack growth in estimating J integral are shown more conservative J and lower T than Rice's and Sumpter's. (4) Comparison of the prediction with the actual experimental measurements by Simpson's formula shows good agreement.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.39-53
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• 2014

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

• Korean journal of applied entomology
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• v.30 no.1
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• pp.65-79
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• 1991

In order to investigate the species composition and the colony density of ants in Mt. Namsan, Seoul, 39 quadrats were installed in 13 vegetations, 443 colonies of ants were collected from June, 1989 to October, 1990. As the result, 4 subfamilies, 23 genera, 28 species was confirmed. Among them, Cerapachys humicola $O_{GATA}$ is new to Korean fauna along with the subfamily Cerapachinae. For the species composition of ant communities in each vegetation, Robinia pseudoacacia vegetation(containing 3 subfamilies, 14 genera, 15 species-53.6% of all colonies collected in Mt. Namsan) and Quercus mongolica vegetation (3 subfamiles, 12 genera, 14 species -50%) showed relatively rich composition, while Platunus orientalis vegetation (3 subfamilies, 3 genera, 3 species) showed the simplest composition. Colony density was the highest in Prunus sargentii vegetation (7.875 colony /$m^2$) and the lowest in Platunus orientalis (1.000 colony/$m^2$). The relative density of Paratrechina flavipes proved to be the highest (RD = 0.422) and that of Cerapachys humicola $O_{GATA}$ Massor aciculatus was the lowest (RD = O. 002 respectively). In the analysis of the similarity of ant communities between each vegetation by S¢rensen's coefficient, Prunus sargentii was very similar to Sorbus alnifolia (0.745) and Pinus densiflora (0.736), but had the lowest similarity to Metasequoia glyptostoboides and Chamaecyparis pisifera vegetation (0.164 respectively). Dominance of ants in each vegetation analyzed by Simpson'formula was found to be high in Platunus orientalis ($\lambda$ = 0.393) and Sorbus alnifolia ($\lambda$ = 0.392) and the lowest in Metasequoia glyptostroboides vegetation($\lambda$= 0.067). The analysis of diversity by reverse Simpson's coefficient revealed that it was high in Metasequoia glyptostroboides ($d_s$ = 14.925), Pinus rigida ($d_s$ = 7.874) and was the lowest in Platunus orientalis vegetation ($d_s$ = 2.545). Evenness calculated by using d. and $d_{max}$(maximal diversity) was high in Metasequoia glyptostroboides ($E_s$ = 0.714) and Chamaecyparis pisifera vegetation ($E_s$ = 0.624). On the contrary, Quercus mongo/ica vegetation had the lowest value of evenness ($E_s$ = 0.182).