• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.125-135
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• 1992

In various viscus flow problems it has been the custom to replace the convective derivative by the ordinary partial derivative in problems for which the data are small. In this paper we consider the Benard Convection problem with small data and compare the solution of this problem (assumed to exist) with that of the linearized system resulting from dropping the nonlinear terms in the expression for the convective derivative. The objective of the present work is to derive an estimate for the error introduced in neglecting the convective inertia terms. In fact, we derive an explicit bound for the L$_{2}$ error. Indeed, if the initial data are O(.epsilon.) where .epsilon. << 1, and the Rayleigh number is sufficiently small, we show that this error is bounded by the product of a term of O(.epsilon.$^{2}$) times a decaying exponential in time. The results of the present paper then give a justification for linearizing the Benard Convection problem. We remark that although our results are derived for classical solutions, extensions to appropriately defined weak solutions are obvious. Throughout this paper we will make use of a comma to denote partial differentiation and adopt the summation convention of summing over repeated indices (in a term of an expression) from one to three. As reference to work of continuous dependence on modelling and initial data, we mention the papers of Payne and Sather [8], Ames [2] Adelson [1], Bennett [3], Payne et al. [9], and Song [11,12,13,14]. Also, a similar analysis of a micropolar fluid problem backward in time (an ill-posed problem) was given by Payne and Straughan [10] and Payne [7].

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.5
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• pp.577-588
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• 2011

This paper provides a novel extended Moving Least Squares(MLS) difference method for the potential problem with weak and strong discontinuities. The conventional MLS difference method is enhanced with jump functions such as step function, wedge function and scissors function to model discontinuities in the solution and the derivative fields. When discretizing the governing equations, additional unknowns are not yielded because the jump functions are decided from the known interface condition. The Poisson type PDE's are discretized by the difference equations constructed on nodes. The system of equations built up by assembling the difference equations are directly solved, which is very efficient. Numerical examples show the excellence of the proposed numerical method. The method is expected to be applied to various discontinuity related problems such as crack problem, moving boundary problem and interaction problems.

• Biomolecules & Therapeutics
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• v.1 no.1
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• pp.20-25
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• 1993

DA-125, a new anthracycline derivative, shows significant anticancer activities. We conducted a study to examine the local irritating effect of DA-125 using mice and rabbits. In the skin test in mice, intradermal injection of 0.4 mg of DA-125, compared to a dosage of 0.2 mg of adriamycin, had weak irritating potentials to induce skin ulceration and erythematous induration. A dosage of 0.6 mg of DA-125 produced similar degree of lesions in perivascular irritation model to that of 0.2 mg of adriamycin, but the healing time was shorter in the case of mice treated with DA-125. In ocular irritation study in rabbit, the highest M.O.I.(mean ocular irritation index) of 0.5% DA-125 solution was 0.67, therefore DA-125 could be considered as a practically non-irritating anticancer agent. These results suggest that substitution of DA-125 for Adriamycin would reduces the possibility of outbreaks of local irritation and the severity of the lesions.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.1-17
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• 2004

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.

• YAKHAK HOEJI
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• v.48 no.1
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• pp.88-92
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• 2004

In this study; a series of 2',4'-doubly branched carbocyclic nucleosides (8,9,10) were synthesized from simple acyclic ketone derivative as starting material. The installation of the 4'-quaternary carbon needed was carried out using a 〔3,3〕-sigmatropic rearrangement. In addition, the introduction of a methyl group in the 2'-position was accomplished by Grig-nard reaction. Bis-vinyl was successfully cyclized using a Grubbs' catalyst II. The natural bases (adenine, cytosine, uracil) were efficiently coupled with the use of a Pd(0) catalyst. Although all the synthesized compounds were assayed against several viruses, only cytosine analogue 9 showed weak antiviral viral activity (EC$_{50}$=45.4 $\mu$M) against CoxB3 virus.s.

• Journal of the Korean Chemical Society
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• v.20 no.4
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• pp.295-298
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• 1976

The fact that a reaction between organothioenamine phosphonate and styrene oxide produces a derivative of cyclopropane has been proved by structural identification. This suggests that an anionic oxygen atom from the ring opening of the styrene oxide by nucleophilic attack of thioenamine phosphonate links to the phosphorous atom to from a betaine as an intermediate which is followed by cleavage of the weak P-C bond. The dextrorotatory optical activity of the product showed that the reaction was under the control of steric stability of the benzyl carbon in styrene which leads to the product through a sterically stable pathway.

• Journal of Communications and Networks
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• v.6 no.2
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• pp.133-146
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• 2004

Recently, many active queue management (AQM) algorithms have been proposed to address the performance degradation. of end-to-end congestion control under tail-drop (TD) queue management at Internet routers. However, these AQM algorithms show performance improvement only for limited network environments, and are insensitive to dynamically changing network situations. In this paper, we propose an adaptive queue management algorithm, called PID-controller, that uses proportional-integral-derivative (PID) feedback control to remedy these weak-Dalles of existing AQM proposals. The PID-controller is able to detect and control congestion adaptively and proactively to dynamically changing network environments using incipient as well as current congestion indications. A simulation study over a wide range of IP traffic conditions shows that PID-controller outperforms other AQM algorithms such as Random Early Detection (RED) [3] and Proportional-Integral (PI) controller [9] in terms of queue length dynamics, packet loss rates, and link utilization.

• Bulletin of the Korean Chemical Society
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• v.30 no.7
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• pp.1553-1558
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• 2009

A series of Eu(III) complexes with various neutral ligands (2,2’:6’,2"-terpyridine (T), diglyme (D), 1N-(2-dimethylamino) ethyl)-1N, 2N, 2N-trimethylethane-1,2-diamine (PT), di-(2-picolyl)-amine derivative (HT), and multidentate terpyridine derivative (DT)) were synthesized to investigate the effect of coordination environment on the sensitized luminescence of Eu(III) complexes. The nine coordination sites of the $Eu^{3+}$ ion are occupied by three bidentate carboxylate moieties and one neutral ligand. The highest emission intensity is obtained for $Eu^{3+}$- $[NA]_3$ (PT), due to the difference in energy transfer efficiency and symmetry of the first coordination sphere of $Eu^{3+}$ ion. But, the lowest emission intensity is obtained for $Eu^{3+}$-$[NA]_3$(T). Terpyridine may not play an important role antenna for photosensitizing $Eu^{3+}$ ion. It could be attributed to the weak spectral overlap integral J value between its phosphorescence band and $Eu^{3+}$ion absorption band. Therefore, different coordination environment of $Ln^{3+}$ ion play an important role in providing sensitization of lanthanide ion emission.

• Food Science and Preservation
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• v.21 no.6
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• pp.838-843
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• 2014

In this study, near-infrared spectroscopy was used to observe the drying non-uniformity of vegetables such as spring onions, onions, and garlic, which are commonly used for seasoning. For the warm-air convection drying method, the vegetables showed drying non-uniformity, which is due to the unevenness of the wind temperature and humidity depending on the height and position of the drying tray. The second derivative spectra between the vegetable samples with different drying degrees were compared. The peak at around 1,390~1,400 nm, which is assigned to weak hydrogen bonds of water, was changed during drying whereas the peak near 1,420 nm, which represents strong hydrogen (H-) bonds of water, was not changed, indicating that water with weak H-bonds evaporates first during drying, and that water with strong H-bonds remains after drying. The hyperspectral NIR imaging technique combined with principal-component analysis made it possible to discriminate the dried vegetables according to their drying degree.

• Korea-Australia Rheology Journal
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• v.18 no.2
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• pp.67-81
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• 2006

Using a strain-controlled rheometer, the dynamic viscoelastic properties of aqueous xanthan gum solutions with different concentrations were measured over a wide range of strain amplitudes and then the linear viscoelastic behavior in small amplitude oscillatory shear flow fields was investigated over a broad range of angular frequencies. In this article, both the strain amplitude and concentration dependencies of dynamic viscoelastic behavior were reported at full length from the experimental data obtained from strain-sweep tests. In addition, the linear viscoelastic behavior was explained in detail and the effects of angular frequency and concentration on this behavior were discussed using the well-known power-law type equations. Finally, a fractional derivative model originally developed by Ma and Barbosa-Canovas (1996) was employed to make a quantitative description of a linear viscoelastic behavior and then the applicability of this model was examined with a brief comment on its limitations. Main findings obtained from this study can be summarized as follows: (1) At strain amplitude range larger than 10%, the storage modulus shows a nonlinear strain-thinning behavior, indicating a decrease in storage modulus as an increase in strain amplitude. (2) At strain amplitude range larger than 80%, the loss modulus exhibits an exceptional nonlinear strain-overshoot behavior, indicating that the loss modulus is first increased up to a certain strain amplitude(${\gamma}_0{\approx}150%$) beyond which followed by a decrease in loss modulus with an increase in strain amplitude. (3) At sufficiently large strain amplitude range (${\gamma}_0>200%$), a viscous behavior becomes superior to an elastic behavior. (4) An ability to flow without fracture at large strain amplitudes is one of the most important differences between typical strong gel systems and concentrated xanthan gum solutions. (5) The linear viscoelastic behavior of concentrated xanthan gum solutions is dominated by an elastic nature rather than a viscous nature and a gel-like structure is present in these systems. (6) As the polymer concentration is increased, xanthan gum solutions become more elastic and can be characterized by a slower relaxation mechanism. (7) Concentrated xanthan gum solutions do not form a chemically cross-linked stable (strong) gel but exhibit a weak gel-like behavior. (8) A fractional derivative model may be an attractive means for predicting a linear viscoelastic behavior of concentrated xanthan gum solutions but classified as a semi-empirical relationship because there exists no real physical meaning for the model parameters.