• Geomechanics and Engineering
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• 제28권2호
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• pp.107-116
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• 2022

The steady state of unsaturated soil takes a long time to achieve. The soil seepage behaviours and hydraulic properties depend highly on the wetting/drying rate. It is observed that the soil-water characteristic curve (SWCC) is dependent on the wetting/drying rate, which is known as the dynamic effect. The dynamic effect apparently influences the scanning curves and will substantially affect the seepage behavior. However, the previous models commonly ignore the dynamic effect and cannot quantitatively describe the hysteresis scanning loops under dynamic conditions. In this study, a dynamic hysteresis model for SWCC is proposed considering the dynamic change of contact angle and the moving of the contact line. The drying contact angle under dynamic condition is smaller than that under static condition, while the wetting contact angle under dynamic condition is larger than that under static condition. The dynamic contact angle is expressed as a function of the saturation rate according to the Laplace equation. The model is given by a differential equation, in which the slope of the scanning curve is related to the slope of the boundary curve by means of contact angle. Empirical models can simulate the boundary curves. Given the two boundary curves, the scanning curve can be well predicted. In this model, only two parameters are introduced to describe the dynamic effect. They can be easily obtained from the experiment, which facilitates the calibration of the model. The proposed model is verified by the experimental data recorded in the literature and is proved to be more convenient and effective.

• 충청수학회지
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• 제21권3호
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• pp.321-326
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• 2008

In this note, using the separation theorem for convex sets, we will give a two functions version generalization of Fan's minimax theorem by relaxing the convexlike assumption to the weak convexlike condition.

• 대한수학회논문집
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• 제11권4호
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• pp.895-902
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• 1996

In this paper, we describe the ideal generated by non-empty stable set in a BCI-group as a simple form, and obtain an equivalent condition of prime Z-ideal.

• 충청수학회지
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• 제22권1호
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• pp.11-16
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• 2009

In this paper, using the diagonally $\mathcal{C}$-concave condition, we will prove a functional inequality in a topological space, and as an application, we can obtain a new variational inequality.

• 충청수학회지
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• 제22권2호
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• pp.131-139
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• 2009

As a generalization of a homomorphism of BCK-algebras, the notion of a semi-homomorphism of BCK-algebras is introduced, and its characterization is given. A condition for a semi-homomorphism to be a homomorphism is provided.

• 대한수학회지
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• 제37권4호
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• pp.613-624
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• 2000

We characterize a condition for M to be of weak type ($\Phi$1, $\Phi$2) in terms of Orlicz norms.

• 호남수학학술지
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• 제31권4호
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• pp.489-495
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• 2009

Any BCK-ideal of a d-algebra can be decomposed into the union of some sets. The notion of a complicated d-algebra is introduced and some related properties are obtained.

• 대한수학회지
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• 제35권1호
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• pp.11-21
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• 1998

A condition for a certain maximal operator to be of strong type (p,p) is characterized in terms of Carleson measure.

• East Asian mathematical journal
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• 제38권5호
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• pp.593-601
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• 2022

In this paper, we consider singular 𝜑-Laplacian problems with nonlocal boundary conditions. Using a fixed point index theorem on a suitable cone, the existence results for one or two positive solutions are established under the assumption that the nonlinearity may not satisfy the L¹-Carathéodory condition.

• 충청수학회지
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• 제20권4호
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• pp.551-560
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• 2007

We prove the existence of solutions for the system of the nonlinear biharmonic equations with Dirichlet boundary condition $$\{^{-{\Delta}^2u-c{\Delta}u+{\gamma}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega},\;}_{-{\Delta}^2u-c{\Delta}u+{\delta}(bu^+-av^-)=s{\phi}_1\;in\;{\Omega}}$$, where $u^+$ = max{u, 0}, ${\Delta}^2$ denotes the biharmonic operator and ${\phi}_1$ is the positive eigenfunction of the eigenvalue problem $-{\Delta}$ with Dirichlet boundary condition.