• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.565-571
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• 2006

In this paper, we present the explicit formula of the generalized inverse $A^{(2)}_{T,S}$, and we apply this result to solve restricted linear equation $Ax+y=b$, $x{\in}T$, $y{\in}S$ and $Ax+By=b$, $x{\in}T$, $y{\in}S$.

• Tunnel and Underground Space
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• v.13 no.3
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• pp.169-179
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• 2003

Anisotropic shear strength of rock joints is studied based on the artificially fractured specimens using experimental and analytical methods. Series of direct shear tests are performed to obtain the strength, stiffness and friction angle of joints under various low normal stresses and shearing directions. The results of shear strength and stiffness show anisotropic value according to shearing direction under low normal stress specially less than 2.45 MPa. But, the effect of joint roughness on strength decreases with increasing normal stress. To estimate more effectively the peak shear strength under low normal stress, the modified Barton's equation is suggested.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1011-1020
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• 2008

The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, $R(X){\subset}T$, $N(X){\supset}\tilde{S}$. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for $A_{T,S}^{(2)}$ A and $AA_{T,S}^{(2)}$ are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.191-202
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• 2007

By using the weighted averaging techniques, we establish oscillation criteria for the second order damped quasilinear elliptic differential equation $$\sum_{i,j=1}^{N}D_i(a_{ij}(x){\parallel}Dy{\parallel}^{p-2}D_jy)+{\langle}b(x),\;{\parallel}Dy{\parallel}^{p-2}Dy{\rangle}+c(x)f(y)=0,\;p>1$$. The obtained theorems include and improve some existing ones for the undamped halflinear partial differential equation and the semilinear elliptic equation.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.113-123
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• 2006

The arches may buckle in a symmetrical snap-through mode or in an asymmetry bifurcation mode if the load reaches a certain value. Each bifurcation curve develops as pressure increases. The governing equation is derived according to the bending theory. The balance of forces provides a nonlinear equilibrium equation. Bifurcation theory near trivial solution of the equation is developed, and the buckling pressures are investigated for various spring constants and opening angles.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.853-865
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• 2019

In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $${\Delta}_Vu+cu^{\alpha}=0$$, where c, ${\alpha}$ are two real constants and $c{\neq}0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-${\acute{E}}mery$ Ricci curvature bounded from below, which generalize some results of [8].

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.837-848
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• 2024

It is shown in [1] that the Cauchy problem for the Fornberg-Whitham equation is well-posed in C¹(ℝ) and the data-to-solution map is Hölder continuous from C^α to C([0, T]; C^α) with α ∈ [0, 1). In this short paper, we further show that the data-to-solution map of the Fornberg-Whitham equation is not uniformly continuous on the initial data in C¹(ℝ).

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.315-335
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• 2023

Limited studies are available on the mathematical estimates of the compressive strength (CS) of glass fiber-embedded polymer (glass-FRP) compressive elements. The present study has endeavored to estimate the CS of glass-FRP normal strength concrete (NSTC) compression elements (glass-FRP-NSTC) employing two various methodologies; mathematical modeling and artificial neural networks (ANNs). The dataset of 288 glass-FRP-NSTC compression elements was constructed from the various testing investigations available in the literature. Diverse equations for CS of glass-FRP-NSTC compression elements suggested in the previous research studies were evaluated employing the constructed dataset to examine their correctness. A new mathematical equation for the CS of glass-FRP-NSTC compression elements was put forwarded employing the procedures of curve-fitting and general regression in MATLAB. The newly suggested ANN equation was calibrated for various hidden layers and neurons to secure the optimized estimates. The suggested equations reported a good correlation among themselves and presented precise estimates compared with the estimates of the equations available in the literature with R²= 0.769, and R² =0.9702 for the mathematical and ANN equations, respectively. The statistical comparison of diverse factors for the estimates of the projected equations also authenticated their high correctness for apprehending the CS of glass-FRP-NSTC compression elements. A broad parametric examination employing the projected ANN equation was also performed to examine the effect of diverse factors of the glass-FRP-NSTC compression elements.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1755-1771
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• 2018

In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and $q{\in}{\mathbb{C}}$ such that 0 < ${\mid}q{\mid}$ < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.