• Honam Mathematical Journal
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• v.44 no.4
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• pp.572-593
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• 2022

Crime committed by civilians and criminals using legal and illegal firearms and conversion of legal firearms into illegal ones has become a common practice around the world. As a result, policies to control civilian gun ownership have been debated in several countries. The issue arose because the linkages between firearm-related mortality, weapon accessibility, and violent crime data can imply diverse options for addressing criminality. In this paper, we have projected a mathematical model in terms of the Caputo fractional derivative to address the issues viz. input of legal guns, crime committed by legal and illegal guns, and strict government policies to monitor the license of legal guns, strict action against violent crime. The boundedness, existence and uniqueness of solutions and the stability of points of equilibrium are examined. It is observed that violent crime increases with the increase of crime committed by illegal guns, crime committed by legal guns and, decreases with the increase of legal guns, the deterrent effect of civilian gun ownership, and action of law against crime. Further, legal guns increase with the increase of the limitation of trade of illegal guns and decrease with the increase of conversion of legal guns into illegal guns and increase of the growth rate of illegal guns. Again, as crime is committed by legal guns also, the policy of illegal gun control does not assure a crime-free society. Weak gun control can lead to a society with less crime. Theoretical aspects are numerically verified in the present work.

• Biomolecules & Therapeutics
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• v.5 no.1
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• pp.74-81
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• 1997

DA-5018(N-(3-(3, 4-dimethylphenyl)propyl)-4-(2-aminoethoxy)-3-methoxyphenylacetamide) is a new capsaicin derivative under development as topical analgesic agent. The general pharmacological properties of DA-5018 on central nervous, cardiovascular, gastrointestinal and other organ systems were studied in experimental animals. DA-5018 cream (0.3%) had no effects on behavior, hexobarbital-induced sleeping time, body temperature, spontaneous activity, blood pressure, heart rate, intestinal charcoal propulsion, urine volume and electrolyte excretion even at a high dose of 2000 mg/kg in rats. In addition, DA-5Ol8 cream had little skin irritation compared to Zostrix-HP (capsaicin, 0.075%) cream in rabbits. In isolated guinea pig tissue studies, DA-5018 increased the contractility of trachea and ileum and also increased sinus rate of atrium in a range of 10^{-8}-10^{-5}$$ M, but its efficacy as a agonist was weak. These results suggest that DA-5018 cream might be used topically without serious side effects.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.781-793
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• 2016

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

• Natural Product Sciences
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• v.21 no.4
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• pp.293-296
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• 2015

A new L-isoascorbic acid derivative epi-leptosphaerin (1) and two known compounds leptosphaerin (2), and verongamine (3) were isolated from sponges of the orders Verongida and Thorectidae. Compounds 1 and 2 are most likely of sponge-associated fungal origin. In the present study, isolated compounds were investigated for their inhibition of soluble epoxide hydrolase (sEH), which is considered a promising target for the management of pain, inflammation, and comorbidities associated with diabetes. Compound 3, verongamine, displayed weak inhibitory activity against sEH with an $IC_{50}$ value $51.5{\pm}1.0{\mu}M$.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.117-123
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• 2012

We provide a convergence analysis of Newton's method for set valued maps under center H$\ddot{o}$lder continuity conditions on the Fr$\acute{e}$chet derivative of the operator involved. This approach extends the applicability of earlier works [4,5,7].

• Journal of Power Electronics
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• v.18 no.6
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• pp.1780-1790
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• 2018

Voltage feed-forward control (VFFC) is widely used in LCL-type grid-tied inverters due to its advantages in terms of disturbance rejection performance and fast dynamic response. However, VFFC may worsen the stability of inverters under weak grid conditions. It is revealed in this paper that a large phase-lag in the low-frequency range is introduced by VFFC, which reduces the phase margin significantly and leads to instability. To address this problem, a novel virtual-impedance-based control, where a phase-lead is introduced into the low-frequency area to compensate for the phase lag caused by VFFC, is proposed to improve system stability. The proposed control is realized with a high-pass filter, without high-order-derivative components. It features easy implementation and good noise immunity. A detailed design procedure for the virtual impedance control is presented. Both theoretical analysis and experimental results verify the effectiveness of the control proposed.

• Advances in Traditional Medicine
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• v.5 no.4
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• pp.283-293
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• 2005

Our previous study showed that a novel synthetic shikonin derivative, 6-(1-hydroxyimino-4-methylpentyl)5,8-dimethyoxy 1,4-naphthoquinone S-52 (DMNQ S-52) induced apoptosis. In the present study, we investigated its anti-metastatic activities as compared with shikonin because DMNQ S-52 was synthesized for overcoming weak points of shikonin such as high toxicity, low solubility and deleterious effects. DMNQ S-52 showed the weaker cytotoxicity $(IC_{50};\;12.3{\pm}1.6\;{\mu}M)$ against Lewis lung carcinoma (LLC) cells than that of shikonin $(IC_{50};\;4.2{\pm}1.1\;{\mu}M)$. DMNQ S-52, at non-toxic concentrations $(less\;than\;10\;{\mu}M)$, significantly inhibited the invasion and migration of LLC cells. DMNQ S-52 also significantly inhibited the production of MMP-9, MTl-MMP and uPAR. Moreover, daily i.p. administration of DMNQ S-52 at dose of 5 mg/kg in mice resulted in a potent inhibition of the primary tumor size of LLC in the lung as well as the metastasis of lymph nodes. These findings suggest that the DMNQ S-52 has therapeutic potential to inhibit metastasis via inhibition of MMP family and uPA/plasminogen system.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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• 2001.06a
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• pp.1515-1515
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• 2001

Retrogradation of starch is one of important quality indexes for food based on starch such as rice. Therefore, in this research, possibility of near infrared spectroscopy to determine the degree of the retrogradation was examined. The degree of the retrogradation was indicated as the degree of geratinization analyzed by BAP(-amylase-pullulanase) method. 20 samples which have a wide range of the degree of the retrogradation were prepared and the NIR spectra of the samples were measured in reflectance mode with the NIR Systems 6500. In the correlation plots calculated from the 2nd derivative values of the MSC treated spectra and the degree of the geratinization, the major negative peaks of 1544 nm and 2258 nm, and the major positive peaks of 1460 nm, 1602 nm, 1766 nm and 2136 nm could be observed, indicating that NIR absorption at the positive peak wavelengths became strong while the absorption at the negative peak wavelengths became weak as the degree of the retrogradation increased. Because there is negative correlation between the degree of the retrogradation and the degree of the geratinization. As a result of MLR using the 2nd derivative values of the MSC treated spectra and the degree of the geratinization, good calibration equation which include 2258 nm as the first wavelength and 1764 nm as the second one could be obtained, indicating that NIR spectroscopy has a possibility to detect the retrogradation of starch. In order to find the assignment of the bands observed in the correlation plots, further study may be needed.

• Proceedings of the Korean Society of Near Infrared Spectroscopy Conference
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• 2001.06a
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• pp.1283-1283
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• 2001

NIR spectroscopy has been used extensively to investigate the structure of water, alcohol and other self-associate molecules because the frequencies of NIR bands due to OH and NH groups strength of hydrogen bonds. We have studied the structure of water -methanol mixtures by use of NIR spectroscopy. Strong features in the 7200-6300 $cm^{-1}$ / region consist of a number of overlapped bands due to the combination of OH antisymmetric and symmetric stretching modes of water and the first overtone of the OH stretching modes of free and hydrogen bonded methanol, while weak fratures in the 6000-5800 cm-1 region are ascribed to the first overtones of $CH_3$ stretching modes of methanol. We will focus the discussion on the $CH_3$ stretching bands. They seem to show a significant shift is not clear from the spectra shown in figure 1(a). Figure 1(b) depicts the second derivative in the 6000-5700 $cm^{-1}$ / region. Now, it is clear from the second derivative that there are two major bands near 5950 and 5900 $cm^{-1}$ / and that they do show a shift be about 30 $cm^{-1}$ / Why do the $CH_3$ bands show the shift with increasing concentration of methanol\ulcorner Probably, the CH, group interacts directly with OH groups of water. The results in figure 1(b) demonstrate the usefulness of the second derivative in resolution enhancement as well as the potential of NIR spectroscopy in the studies of molecular interactions.(Figure omitted).