• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.167-181
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• 2009

Based on Ricatti equation $XA^{-1}X=B$ for two (positive invertible) operators A and B which has the geometric mean $A{\sharp}B$ as its solution, we consider a cubic equation $X(A{\sharp}B)^{-1}X(A{\sharp}B)^{-1}X=C$ for A, B and C. The solution X = $(A{\sharp}B){\sharp}_{\frac{1}{3}}C$ is a candidate of the geometric mean of the three operators. However, this solution is not invariant under permutation unlike the geometric mean of two operators. To supply the lack of the property, we adopt a limiting process due to Ando-Li-Mathias. We define reasonable geometric means of k operators for all integers $k{\geq}2$ by induction. For three positive operators, in particular, we define the weighted geometric mean as an extension of that of two operators.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.3
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• pp.69-75
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• 2000

The object of the research is to estimate for pearlite structure of quenched carbon steels. The effects of temperature on physical properties metallic structures and the latent heat by phase transformation were considered. In this study a set of constitutive equations relevant to the analysis of thermo-elasto plastic materials with pearlite phase transformation during quenching process way presented on the basis of continuum thermo-dynamics. The iso-thermal transformation curve of the SM50C was formlated by cubic spline curve. The formulated equations of evolution in pearlite transformation was used for structure analysis. The volume fraction of pearlite was obtained from the results of calculated metallic structure by Finite element equation.

• Structural Engineering and Mechanics
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• v.75 no.1
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• pp.87-100
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• 2020

The present paper investigates the combination resonance behavior of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal and external functionally graded stiffeners under two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. With regard to classical plate theory of shells, von-Kármán equation and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The combination resonance is obtained by using the multiple scales method. Finally, the influences of the stiffeners angles, foundation type, the nonlinear elastic foundation coefficients, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

• Smart Structures and Systems
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• v.26 no.3
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• pp.361-371
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• 2020

Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integral-differential equation. The von Kármán geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined.

• Transactions of the Korean Society of Automotive Engineers
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• v.13 no.4
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• pp.105-112
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• 2005

Analyses of dynamic models which were one and two degrees of freedom, and had the nonlinear springs and dampings with certain polynomial functions were performed from SIMULINK in MATLAB. Those consisted of 12 programs and were built on the basis of the preceding programs fur the linear dynamic simulations. However the programs for the nonlinear simulations were quite different from those f3r the linear ones, and showed the results of the analyses in real time with animating. It was found that the programs would help us to solve any kind of nonlinear dynamic simulation with one and two degrees of freedom. Especially, the simulations for 1 DOF system with cubic nonlinear spring farce showed the results for Duffing's equation, of which phenomena were jump-up and jump-down. It will be applied to the dynamic simulation of the car seat vibration with a passenger, of which model has the equivalent nonlinear springs and is two degrees of freedom.

• Korean Journal of Hydrosciences
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• v.5
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• pp.85-97
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• 1994

A hybrid finite difference method for the longitudinal dispersion equation, which is based on combining the Holly-Preissmann scheme with fifth-degree Hermite interpolating polynomial and the generalized Crank-Nicholson scheme, is described and comparatively evaluated with other characteristics-based numerical methods. Longitudinal dispersion of an instantaneously-loaded pollutant source is simulated, and computational results are compared with the exact solution. The present method is free from wiggles regardless of the Courant number, and exactly reproduces the location of the peak concentration. Overall accuracy of the computation increases for smaller value of the weighting factor, $\theta$of the model. Larger values of $\theta$ overestimates the peak concentration. Smaller Courant number yields better accuracy, in general, but the sensitivity is very low, especially when the value of $\theta$ is small. From comparisons with the hybrid method using cubic interpolating polynomial and with splitoperator methods, the present method shows the best performance in reproducing the exact solution as the advection becomes more dominant.

• Steel and Composite Structures
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• v.42 no.4
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• pp.477-487
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• 2022

The shear stiffness of headed-stud shear connectors has no unified definition due to the nonlinear characteristics of its load-slip relationship. A unified framework was firstly adopted to develop a general expression of shear load-slip equation for headed-stud shear connectors varying in a large parameter range based on both force and energy balance. The pre- and post-yield shear stiffness were then determined through bilinear idealization of proposed shear load-slip equation. An updated and carefully selected push-out test database of 157 stud shear connectors, conducting on studs 13~30mm in diameter and on concretes 30~180 MPa in cubic compressive strength, was used for model regression and sensitivity analysis of shear stiffness. An empirical calculation model was also established for the stud shear stiffness. Compared with the previous models through statistical analysis, the proposed model demonstrates a better performance to predict the shear load-slip response and stiffness of the stud shear connectors.

• Journal for History of Mathematics
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• v.36 no.1
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• pp.1-17
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• 2023

Paper folding is a versatile tool that can be used not only as a mathematical model for analyzing the geometric properties of plane and spatial figures but also as a visual method for finding the real roots of polynomial equations. The historical evolution of origami's geometric and algebraic techniques has led to the discovery of definitions and properties that can enhance one's cognitive understanding of mathematical concepts and generate mathematical interest and motivation on an emotional level. This paper aims to examine the history of origami geometry, the utilization of origami for solving polynomial equations, and the process of determining the real roots of quadratic, cubic, and quartic equations through origami techniques.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.32 no.3
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• pp.266-272
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• 1996

The distribution and abundance of fish in the Cheju southeastern area was studied by the combined hydroacoustic and bottom trawl surveys in April 1994 and in July 1995, respectively. The main purpose of these investigations was to provide the basic data for this management and the biomass estimation of commercially important demersal fish stocks in this area. The hydroacoustic surveys were performed by using a 50 kHz scientific echo sounder system with a microcomputer-based echo integrator. Acoustical measurements of fish abundance and distribution were conducted along the cruise tracks of research vessel and during all trawl hauls by continuous echo sounding. The average weight-normalized target strength for demersal fish aggregations was derived from the relationship between the mean volume backscattering strength for the depth strata of trawl hauls and the weight per cubic meter of trawl catches. The geographical distribution of fish stocks in the 1994 survey area was investigated in relation to oceanographic conditions. The results obtained can be summarized as follows: 1. From the 1994 and 1995 survey data, the relationship between the mean volume backscattering strength (, dB) for the depth strata of trawl hauls and the weight (W, kg/$m^3$) per cubic meter of trawl catches was expressed by the following equation = - 32.8+ lOlog(W) The average weighted-target strength value at 50 kHz derived from this equation was .. 32.8 dB/kg. 2. In 1994 and 1995, both surveys showed a trend of decreasing fish abundance toward the southern area of the Cheju Island with high densities offish along the west coast ofth.e Tsushima Island. The highest demersal concentrations in the southern area of the CheJu Island appeared in bottom waters colder than $12^{\circ}C.$. . 3. From the results of combined bottom trawl and hydroacoustic surveys, the estunated fish densities in the southeastern area of the Cheju Island were 1.5488 x $10^-4$kg/$m^3$ in the 1994 surveyand 1.9498 x $10^-4$kg/$m^3$ in the 1995 survey, respectively.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.28 no.3
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• pp.118-122
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• 2018

Ceria ($CeO_2$) is a rare earth oxide, which has been widely investigated to improve the property. It is important to increase the surface area of $CeO_2$, because high surface area of $CeO_2$ can improve the catalytic ability. $CeO_2$ nanoparticles were synthesized by a solvothermal process. A discussion on the influence of solvent ratio and precursors on $CeO_2$ nanoparticles was performed. The size and degree of the agglomeration of the synthesized $CeO_2$ could be tuned by controlling those parameters. The average size and distribution of prepared $CeO_2$ powders was in the range of 3 to 13 nm and narrow, respectively. The XRD pattern showed that the synthesized $CeO_2$ powders were crystalline with cubic phase of $CeO_2$. The average particle size was calculated by Scherrer equation and FE-TEM images. The morphology of the synthesized $CeO_2$ particle was objected using FE-TEM and FE-SEM. Specific surface area of the synthesized $CeO_2$ was determined using BET (Brunauer-Emmett-Teller) equation.