• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.311-326
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• 2011

In this paper, we adopt discontinuous Galerkin methods with penalty terms namely symmetric interior penalty Galerkin methods, to solve nonlinear viscoelasticity type equations. We construct finite element spaces and define an appropriate projection of u and prove its optimal convergence. We construct extrapolated fully discrete discontinuous Galerkin approximations for the viscoelasticity type equation and prove ${\ell}^{\infty}(L^2)$ optimal error estimates in both spatial direction and temporal direction.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.271-277
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• 2010

We prove the global (in time) vorticity existence for the 2-D Euler equations of a perfect incompressible fluid in $B^0_{{\infty},1}({\mathbb{R}}^2){\cap}L^p({\mathbb{R}}^2)$ with 1 < p < 2. Moreover, we prove that the particle trajectory map X(x, t) satisfies the following estimate: for some positive constant C $${\parallel}X^{\pm1}(\cdot,\;t)-id(\cdot){\parallel}_{B^1_{\infty,1}}{\leq}Ce^{e^{Ct}}$$, where id represents the identity map on ${\mathbb{R}}^2$.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• East Asian mathematical journal
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• v.35 no.1
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• pp.1-7
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• 2019

We consider the initial value problem of the Schrodinger equation for an interesting Cauchy-Euler type operator ${\mathfrak{R}}$ on ${\mathbb{C}}^n$ that is an analogue of the harmonic oscillator in ${\mathbb{R}}^n$. We get an appropriate $L^1-L^{\infty}$ dispersive estimate for the solution of the initial value problem.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.163-174
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• 1999

The purpose of this paper is to obtain the solution of Fredholm-Volterra integral equation with singular kernel in the space $L_2(-1, 1)\times C(0,T), 0 \leq t \leq T< \infty$, under certain conditions,. The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrices. Also the error estimate is computed and some numerical examples are computed using the MathCad package.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1043-1057
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• 2000

This paper is devoted to the investigation of mixed Fourier-Bessel transformation (※Equations, See Full-text) We apply the method of [6] which provides the estimate for weighted L(sub)$\infty$-norm of the spherical mean of │f│$^2$ via its weighted L$_1$-norm (generally it is wrong without the requirement of the non-negativity of f). We prove that in the case of Fourier-Bessel transformatin the mentioned method provides (in dependence on the relation between the dimension of the space of non-special variables n and the length of multiindex ν) similar estimates for weighted spherical means of │f│$^2$, the allowed powers of weights are also defined by multiindex ν. Further those estimates are applied to partial differential equations with singular Bessel operators with respect to y$_1$, …, y(sub)m and we obtain the corresponding estimates for solutions of the mentioned equations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.169-180
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• 2009

A discontinuous Galerkin method with interior penalty terms is presented for linear Sobolev equation. On appropriate finite element spaces, we apply a symmetric interior penalty Galerkin method to formulate semidiscrete approximate solutions. To deal with a damping term $\nabla{\cdot}({\nabla}u_t)$ included in Sobolev equations, which is the distinct character compared to parabolic differential equations, we choose special test functions. A priori error estimate for the semidiscrete time scheme is analyzed and an optimal $L^\infty(L^2)$ error estimation is derived.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.50 no.4
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• pp.583-594
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• 2014

This study was performed to estimate biomass and provide management guidance through population ecological characteristics, including growth parameters, instantaneous coefficients of natural and fishing mortalities, and age at first capture of the starry flounder, Platichthys stellatus and olive flounder, Paralichthys olivaceus of Korea. For describing growth of this species, a von Bertalanffy growth model was adopted. The von Bertalanffy growth parameters estimated from a non-linear regression for starry flounder were $L_{{\infty}}=48.25cm$, K=0.16/yr, and $t_0=-1.48$, respectively and those for olive flounder were $L_{{\infty}}=86.46cm$, K=0.26/yr, and $t_0=-0.29$, respectively. Biomass of Platichthys stellatus was estimated by direct biomass estimation method was 2.6 M/T, that was estimated by indirect method was 13.4 M/Tt. Those of Paralichthys olivaceus were estimated as 10.1 M/T, 19.3 M/T, respectively. An yield per recruit analysis showed that the current yield per recruit on Platichthys stellatus was about 48.2 g with F=0.646/yr and the age at first capture ($t_c$) 1.35yr, that on Paralichthys olivaceus was about 167.6 g with F=1.121/yr and the age at first capture ($t_c$) 1yr.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.23-38
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• 2004

We consider finite element methods applied to a class of quasi parabolic integro-differential equations in $R^d$. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results are demonstrated in $W^{1,p}(\Omega)\;and\;L_p(\Omega)$, for $2\;{\leq}p\;<\;{\infty}$.

• Korean Journal of Ecology and Environment
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• v.43 no.1
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• pp.82-90
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• 2010

The ecological characteristics of the Korean Aucha perch, Coreoperca herzi, were determined in order to estimate stock of the mid-upper system of the Seomjin River. The age was determined by counting the otolith annuli. The oldest fish observed in this study was 5 years old. Relationships between body length (BL) and body weight (BW) were $BW=0.0195BL^{3.08}$ ($R^2=0.966$) (p<0.01). Relationships between the otolith radius (R) and body length (BL) were BL=3.882R+1.66 ($R^2=0.944$). The von Bertalanffy growth parameters estimated from a non-linear regression method were $L_{\infty}=19.68\;cm$, $W_{\infty}=188.64\;g$, $K=0.17\;year^{-1}$ and $t_0=-1.46$ year. Therefore, growth in length of the fish was expressed by the von Bertalanffy's growth equation as $L_t=19.68$ ($1-e^{-0.17(t+1.46)}$) ($R^2=0.997$). The annual survival rate (S) was estimated to be $0.666\;year^{-1}$. The instantaneous coefficient of natural mortality (M) of estimated from the Zhang and Megrey method was $0.346\;year^{-1}$, and instantaneous coefficient of fishing mortality (F) was calculated $0.061\;year^{-1}$. From the estimates of survival rate (S), the instantaneous coefficient of total mortality(Z) was estimated to be $0.407\;year^{-1}$.