• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.171-180
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• 1998

In this paper we analyze the convergence of the semidis-crete solution of the Roseneau equation. We introduce the auxiliary projection of the solution and derive the optimal convergence of the semidiscrete solution as well as the auxiliary projection in L2 normed space.

• Journal of Microbiology and Biotechnology
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• 제27권3호
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• pp.598-609
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• 2017

Pediococcus pentosaceus ID-7 was isolated from kimchi, a Korean fermented food, and it showed high activity for lactose hydrolysis. The ${\beta}$-galactosidase of P. pentosaceus ID-7 belongs to the GH2 group, which is composed of two distinct proteins. The heterodimeric LacLM type of ${\beta}$-galactosidase found in P. pentosaceus ID-7 consists of two genes partially overlapped, lacL and lacM encoding LacL (72.2 kDa) and LacM (35.4 kDa). In this study, Escherichia coli MM294 was used for the production of LacL, LacM, and LacLM. These three types of recombinant proteins were expressed, purified, and characterized. The specific activities of LacLM and LacL were 339 and 31 U/mg, respectively. However, activity was not detected with LacM alone. The optimal pH of LacLM and LacL was pH 7.5 and pH 7.0, and the optimal temperature of LacLM and LacL was $40^{\circ}C$ and $50^{\circ}C$, respectively. The optimal temperature changes indicate that LacLM is able to achieve higher activity at a relatively lower temperature. LacLM was strongly activated by $Mg^{2+}$, $Mn^{2+}$, and $Zn^{2+}$, which was not true for LacL. Consistent with this, EDTA strongly inactivated LacLM and LacL, but the presence of reducing agents did not dramatically alter the activity. Taken together, multiple alignment of amino acid sequences and phylogenetic analysis results of LacL and LacM of P. pentosaceus ID-7 suggest the evolution of LacL into LacLM and that the use of divalent metal ions results in higher activity.

• Journal of the Korean Statistical Society
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• 제21권2호
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• pp.153-166
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• 1992

Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $\hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $\Vert \hat{T}_n - T(f) \Vert_2$ be the usual $L_2$ norm of the restriction of $\hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $\Vert \hat{T}_n - T(f) \Vert_2$ is discussed.

• 한국환경과학회지
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• 제31권8호
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• pp.715-725
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• 2022

Lactic Acid Bacteria (LAB) are among the representative probiotics that have been used for a long time in fermented food. Although there are many studies on detecting the radical scavenging activity of LAB, few studies have been conducted on the environmental factors that improve scavenging activity. This study investigated the environmental factors affecting the DPPH radical scavenging and various antioxidant activities of Kimchi-derived Lactobacillus plantarum K-21 with antihypertensive and radical scavenging activities. The optimal conditions for scavenging DPPH radicals were glucose 2%, bactopeptone 0.5%, Tween 80 0.05%, L-cysteine 0.05%, and an initial pH 6.5 at 35℃. Under optimal conditions, the DPPH radical scavenging activity was 94.8±2.2%, which was 1.5 times higher than that of the basic medium. In addition, L. plantarum K-21 had other antioxidant activities; ABTS radical scavenging (93.6±1.5%), hydroxyl radical scavenging (8.5±0.9%), metal chelating (65.9±0.5%), NO scavenging (53.1±19%), SOD-like (25.1±1.5%), and reducing power (11.7±1.4%) activities were detected. Therefore, L. plantarum K-21 may act not only as a starter for lactic acid-fermented foods with improved functionality but also as a drug for various diseases caused by oxidative stress.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.17-30
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• 1997

In this work we approximate the solution of initialboun-dary value problem using a Galerkin-finite element method for the spatial discretization and Implicit Runge-Kutta method for the spatial discretization and implicit Runge-Kutta methods for the time stepping. To deal with the nonlinear term f(x, t, u), we introduce the well-known extrapolation sheme which was used widely to prove the convergence in $L_2$-norm. We present computational results showing that the optimal order of convergence arising under $L_2$-norm will be preserved in $L_{\infty}$-norm.

• 한국산업융합학회 논문집
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• 제19권2호
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• pp.50-61
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• 2016

This study proposes a new approach to control the nozzle pressure of homogenizer in refrigerator foam system in the 900L class. Generally, dynamic characteristics of the hydraulic nozzle system is highly nonlinear due to uncertain parameters, and it is very difficult to control of hydraulic dynamics. Firstly, it has been performed to derive a real-time control algorithm based on the mathematical model of hydraulic cylinder, and to estimate the values of the unknown parameter in the hydraulic system. Secondly, the feedback controller was designed to implement the optimal pressure control of the hydraulic nozzle system. Finally the control performance was illustrated by simulation.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.707-719
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• 2014

In this paper, we investigate a variational discretization approximation of elliptic optimal control problems with control constraints. The state and the co-state are approximated by piecewise linear functions, while the control is not directly discretized. By using some proper intermediate variables, we derive a second-order convergence in $L^2$-norm and superconvergence between the numerical solution and elliptic projection of the exact solution in $H^1$-norm or the gradient of the exact solution and recovery gradient in $L^2$-norm. Then we construct a posteriori error estimates by using the superconvergence results and do some numerical experiments to confirm our theoretical results.

• 한국산업융합학회 논문집
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• 제22권2호
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• pp.191-199
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• 2019

In this paper, dissimilar friction welding were produced using 15 mm diameter solid bar in chrome molybedenum steel(SCM440) to stainless steel(STS316L) to investigate their mechanical properties. Consequently, optimal welding conditions were n=2000 rpm, HP=70 MPa, UP=140 MPa, HT=10 sec and UT=10 sec when the metal loss(Mo) is 8.6 mm. In addition, an acoustic emission technique was applied to evaluate the optimal friction welding condition. AE parameters including the cumulative count, amplitude and energy showed a various changes according to the friction condition. A continuous type waveforms and low frequency spectrum was presented in friction time. On the other hand, a burst type waveform and high frequency spectrum was exhibited in pressing time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.25-37
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• 2001

We consider the finite element method applied to nonlinear Sobolev equation with smooth data and demonstrate for arbitrary order ($k{\geq}2$) finite element spaces the optimal rate of convergence in $L_{\infty}\;W^{1,{\infty}}({\Omega})$ and $L_{\infty}(L_{\infty}({\Omega}))$ (quasi-optimal for k = 1). In other words, the nonlinear Sobolev equation can be approximated equally well as its linear counterpart. Furthermore, we also obtain superconvergence results in $L_{\infty}(W^{1,{\infty}}({\Omega}))$ for the difference between the approximate solution and the generalized elliptic projection of the exact solution.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.19-34
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• 2016

In this paper, we present a split least-squares characteristic mixed finite element method(MFEM) to get the approximate solutions of the convection dominated Sobolev equations. First, to manage both convection term and time derivative term efficiently, we apply a least-squares characteristic MFEM to get the system of equations in the primal unknown and the flux unknown. Then, we obtain a split least-squares characteristic MFEM to convert the coupled system in two unknowns derived from the least-squares characteristic MFEM into two uncoupled systems in the unknowns. We theoretically prove that the approximations constructed by the split least-squares characteristic MFEM converge with the optimal order in L² and H¹ normed spaces for the primal unknown and with the optimal order in L² normed space for the flux unknown. And we provide some numerical results to confirm the validity of our theoretical results.