• Title/Summary/Keyword: Linear coefficient

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STUDY ON THE PERTURBED PIECEWISE LINEAR SUSPENSION BRIDGE EQUATION WITH VARIABLE COEFFICIENT

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.19 no.2
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    • pp.233-242
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    • 2011
  • We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.

TIME PERIODIC SOLUTIONS TO A HEAT EQUATION WITH LINEAR FORCING AND BOUNDARY CONDITIONS

  • In-Jee Jeong;Sun-Chul Kim
    • Journal of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.465-477
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    • 2023
  • In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.

Experimental assessment for the photon shielding features of silicone rubber reinforced by tellurium borate oxides

  • M. Elsafi;Heba jamal ALasali;Aljawhara H. Almuqrin;K.G. Mahmoud;M.I. Sayyed
    • Nuclear Engineering and Technology
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    • v.55 no.6
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    • pp.2166-2171
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    • 2023
  • In the present study, six silicone rubber doped by tellurium borate oxides were fabricated using the casting method. The densities of the fabricated silicon rubber-doped by tellurium borate oxides samples were measured using the Archimedes Method. Moreover, the linear attenuation coefficient of silicone rubber doped tellurium borate oxides samples was evaluated experimentally using the hyper pure germanium, and the recorded linear attenuation coefficient values were affirmed using the theoretical Phy-X program. The experimental measurements were performed using the narrow beam transmission method with radioactive isotopes Am-241, Cs-137, and Co-60 with energies of 59, 661, 1173, and 1332 keV. The linear attenuation coefficient values showed an enhancement by 4.73 times, 1.20 time, 1.17, time, and 1.17 time, respectively at gamma photon energies of 59, 661, 1173, and 1332 keV, when the TeO2 concentration increased in the fabricated composites from 0 to 50 wt%. The enhancement of the linear attenuation coefficient values has a positive effect on the transmission rate values where the half-value thickness and transmission rate were decreased accompanied by an increase in the RPE.

Testing General Linear Constraints on the Regression Coefficient Vector : A Note

  • Jeong, Ki-Jun
    • Journal of the Korean Statistical Society
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    • v.8 no.2
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    • pp.107-109
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    • 1979
  • Consider a linear model with n observations and k explanatory variables: (1)b $y=X\beta+u, u\simN(0,\sigma^2I_n)$. We assume that the model satisfies the ideal conditions. Consider the general linear constraints on regression coefficient vector: (2) $R\beta=r$, where R and r are known matrices of orders $q\timesk$ and q\times1$ respectively, and the rank of R is $qk+q$.

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Proposal for the Estimation Model of Coefficient of Permeability of Soil Layer using Linear Regression Analysis (단순회귀분석에 의한 토층의 투수계수산정모델 제안)

  • Lee, Moon-Se;Ryu, Je-Cheon;Lim, Heui-Dae;Park, Joo-Whan;Kim, Kyeong-Su
    • The Journal of Engineering Geology
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    • v.18 no.1
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    • pp.27-36
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    • 2008
  • To derive easily the coefficient of permeability from several other soil properties, the estimation model of coefficient of permeability was proposed using linear regression analysis. The coefficient of permeability is one of the major factors to evaluate the soil characteristics. The study area is located in Kangwon-do Pyeongchang-gun Jinbu-Myeon. Soil samples of 45 spots were taken from the study area and various soil tests were carried out in laboratory. After selecting the soil factor influenced by the coefficient of permeability through the correlation analysis, the estimation model of coefficient of permeability was developed using the linear regression analysis between the selected soil factor and the coefficient of permeability from permeability test. Also, the estimation model of coefficient of permeability was compared with the results from permeability test and empirical equation, and the suitability of proposed model was proved. As the result of correlation analysis between various soil factors and the coefficient of permeability using SPSS(statistical package for the social sciences), the largest influence factor of coefficient of permeability were the effective grain size, porosity and dry unit weight. The coefficient of permeability calculated from the proposed model was similar to that resulted from permeability test. Therefore, the proposed model can be used in case of estimating the coefficient of permeability at the same soil condition like study area.

Estimation of Average Roughness Coefficients of Bocheong Stream Basin (보청천 유역의 평균조도계수 산정)

  • Jeon, Min-Woo;Lee, Hyo-Sang;Ahn, Sang-Uk;Cho, Young-Soo;Jeon, Man-Woo
    • Proceedings of the Korea Water Resources Association Conference
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    • 2009.05a
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    • pp.1306-1310
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    • 2009
  • The roughness coefficients were estimated by the Manning's equation for the measured stage and flow velocity of Bocheong stream basin in Kum river. The relationships between the estimated roughness coefficients and the geomorphologic factors were formulated by the linear, logarithmic, exponential and power type function, thereafter correlation equations were presented. The correlation analysis was performed between the measured stream length and the basin area of Bocheong stream basin by the linear, logarithmic, exponential and power type function, and correlation equation for the stream length was given. The roughness coefficient has strong correlationship with stream slope, but low correlation coefficients with stream length and basin area. For the correlationship with the roughness coefficients and the stream slope, the logarithmic type function has the smallest correlation coefficient, on the other hand, the exponential type function has the largest correlation coefficient. For the relationship between the stream length and the basin area, the correlation coefficient of the logarithmic type function shows the smallest value, linear type function shows the largest value.

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Derivation of the Dispersion Coefficient based on the Linear Wave Theory (선형파 이론에 의한 분산계수 유도)

  • 조홍연;정신택
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.12 no.4
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    • pp.190-194
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    • 2000
  • Dispersion coefficient influenced by the wave parameters was derived analytically using the vertical velocity distribution based on linear wave theory. It is the depth- and wave period-averaged value and shows larger values in deep water condition than in shallow water condition. It also shows the general pattern of the dispersion coefficient in the oscillatory flows, i.e. it converges the specific value as the wave period is much larger than the vertical mixing time but it approaches zcro as the wave period is much smaller than the vertical mixing time. The dispersion coefficient derived in the condition of the simple assumption have to be modified in order to consider the shallow water condition or the real condition.

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The Effects of Elastic Modulus Coefficient and Linear Expansion Coefficient of Overhead Conductor on Sag Behavior (가공전선의 이도거동에서 탄성계수와 선팽창계수의 영향)

  • Kim, Byung-Geol;Kim, Shang-Shu;Wang, Yun-Chan
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.21 no.10
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    • pp.954-960
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    • 2008
  • The effects of elastic modulus coefficient and linear expansion coefficient of overhead distribution power line(ACSR $58 mm^2$) on sag behavior in distribution line have been investigated to clarify the difference between specification and experimental level. The elastic modulus coefficients of Al wire and steel wire were $5,182.6 kgf/mm^2,\;18,348.8 kgf/mm^2$, respectively Therefore, the computational composition elastic modulus coefficient of the power line was $7,063.5 kgf/mm^2$, while that of experimentally measured was $7681.1 kgf/mm^2$. As a result, we found that elastic modulus coefficient which was experimentally measured was higher than that of computational by 8.7 %. However, when planner designs the sag of disoibution line, the elastic modulus coefficient of power line $8,400 kgf/mm^2$ should be generally adopted. These two different using values lead to the sag difference of 0.62 m. The other results will be discussed.