• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.233-247
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• 2022

This manuscript addressed, the existence and uniqueness result for random impulsive stochastic functional differential equations with finite time delays. The study of random impulsive stochastic system is a new area of research. We interpret the meaning of a stochastic derivative and how it differs from the classical derivative. We prove the existence and uniqueness of mild solutions to the equations by using the successive approximation method. We conclude the article with some interesting future extension. This work extends the work of [18, 12, 20]. Finally, an example is given to illustrate the theoretical result.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1725-1739
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• 2016

Abstract. Numerical solutions for the evolutionary space fractional order differential equations are considered. A predictor corrector method is applied in order to obtain numerical solutions for the equation without solving nonlinear systems iteratively at every time step. Theoretical error estimates are performed and computational results are given to show the theoretical results.

• The Korean Journal of Financial Management
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• v.26 no.4
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• pp.63-81
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• 2009

This paper empirically examines the relation between stock volatility and volatilities of macroeconomic variables and financial derivative trading. Previous studies have shown that stock volatility has been much greater than volatilities of macroeconomic variables, and their explanatory powers are too weak to confirm hypothesized theoretical relation between stock volatility and macroeconomic volatilities. The test for the relation using Korean data since 1980 verified such a finding. It is argued that this may have been the result from omitting the influence of financial activities on stock volatility. In particular, this paper demonstrates that, by including the volatility of financial derivative trading, stock volatility-macroeconomic volatility relation can not only be explained better, but also the hypothesized significance of macroeconomic volatilities can be restored.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• Wind and Structures
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• v.22 no.3
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• pp.273-290
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• 2016

The flutter derivatives of bridge decks can be efficiently identified using the experimentally and/or numerically coupled forced vibration method. This paper addresses the issue of inherent requirement for adopting different frequencies of three modes in this method. The aerostatic force components and the inertia of force and moment are mathematically proved to exert no influence on identification results if the signal length (t) is integer (n=1,2,3...) times of the least common multiple (T) of three modal periods. It is one important contribution to flutter derivatives identification theory and engineering practice in this study. Therefore, it is unnecessary to worry about the determination accuracy of aerostatic force and inertia of force and moment. The influences of signal length, amplitude, and frequency ratio on flutter derivative are thoroughly investigated using a bridge example. If the signal length t is too short, the extraction results may be completely wrong, and particular attention should be paid to this issue. The signal length t=nT ($n{\geq}5$) is strongly recommended for improving parameter identification accuracy. The proposed viewpoints and conclusions are of great significance for better understanding the essences of flutter derivative identification through coupled forced vibration method.

• Journal of Pharmaceutical Investigation
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• v.29 no.3
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• pp.205-210
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• 1999

To formulate the parenteral delivery of a new cephalosporin derivative, 7-${\beta}$-[(2)-2-(2-arninothiazol-4-yl)-2methoxyiminoacetamido]- 3- [(2,3-cyclopenteno-4-carbamoyl-l-pyridinium)methyl]- 3-cephem-4-carboxylate sulfate( CKD604), the stability and solubility of CKD-604 in various aqueous media were investigated. The degradation kinetics of CKD-604 in aqueous solutions (ionic strength 0.1, pH 1-8) were studied at $37^{\circ}C$. The observed degradation rates followed pseudo first order kinetics. The pH-rate profile exhibited a minimum degradation rate at pH 5. The Arrhenius activation energy was 14.2 kcal/mol in pH 5 buffer solution. Excellent agreement between the cephalosporins' theoretical pH-rate profile and the experimental data indicated that the degradation pathway of CKD-604 could be predicted according to the general pathway of cephalosporins. The solubility of CKD-604 was 8.16 mg/ml at $25^{\circ}C$. To enhance the solubility and adjust the suitable pH, CKD-604 was solubilized by using sodium ascorbate, ascorbic acid and urea. The compositions were obtained to satisfy optimum pH and concentration, and the total amount of additives was several times of the active ingredient, CKD-604.

• 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.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.1-14
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• 2008

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and $Gr\ddot{u}nwald$-Letnikov(G-L) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.203-224
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• 2014

We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Fredholm-Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• Wind and Structures
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• v.7 no.3
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• pp.173-186
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• 2004

Flutter derivatives provide the basis of predicting the critical wind speed in flutter and buffeting analysis of long-span cable-supported bridges. In this paper, one popular stochastic system identification technique, covariance-driven Stochastic Subspace Identification(SSI in short), is firstly presented for estimation of the flutter derivatives of bridge decks from their random responses in turbulent flow. Secondly, wind tunnel tests of a streamlined thin plate model and a ${\Pi}$ type blunt bridge section model are conducted in turbulent flow and the flutter derivatives are determined by SSI. The flutter derivatives of the thin plate model identified by SSI are very comparable to those identified by the unifying least-square method and Theodorson's theoretical values. As to the ${\Pi}$ type section model, the effect of turbulence on aerodynamic damping seems to be somewhat notable, therefore perhaps the wind tunnel tests for flutter derivative estimation of those models with similar blunt sections should be conducted in turbulent flow.