• Journal of applied mathematics & informatics
• /
• v.39 no.1_2
• /
• pp.197-214
• /
• 2021

In this paper, we have studied dynamics of fractional order mathematical model of malaria transmission for two groups of human population say semi-immune and non-immune along with growing stages of mosquito vector. The present fractional order mathematical model is the extension of integer order mathematical model proposed by Ousmane Koutou et al. For this study, Atangana-Baleanu fractional order derivative in Caputo sense has been implemented. In the view of memory effect of fractional derivative, this model has been found more realistic than integer order model of malaria and helps to understand dynamical behaviour of malaria epidemic in depth. We have analysed the proposed model for two precisely defined set of parameters and initial value conditions. The uniqueness and existence of present model has been proved by Lipschitz conditions and fixed point theorem. Generalised Euler method is used to analyse numerical results. It is observed that this model is more dynamic as we have considered all classes of human population and mosquito vector to analyse the dynamics of malaria.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1471-1493
• /
• 2022

The goal of this paper is to establish the boundedness of bilinear Calderón-Zygmund operator BT and its commutator [b₁, b₂, BT] which is generated by b₁, b₂ ∈ BMO(ℝⁿ) (or ${\dot{\Lambda}}_{\alpha}$(ℝⁿ)) and the BT on generalized variable exponent Morrey spaces 𝓛^p(·),𝜑(ℝⁿ). Under assumption that the functions 𝜑₁ and 𝜑₂ satisfy certain conditions, the authors proved that the BT is bounded from product of spaces 𝓛^{p₁(·),𝜑₁}(ℝⁿ)×𝓛^{p₂(·),𝜑₂}(ℝⁿ) into space 𝓛^p(·),𝜑(ℝⁿ). Furthermore, the boundedness of commutator [b₁, b₂, BT] on spaces L^p(·)(ℝⁿ) and on spaces 𝓛^p(·),𝜑(ℝⁿ) is also established.

• Journal of the Korean Mathematical Society
• /
• v.57 no.3
• /
• pp.747-775
• /
• 2020

In this work we investigate the nonlocal elliptic equation with critical Hardy-Sobolev exponents as follows, $$(P)\;\{(-{\Delta}_p)^su={\lambda}{\mid}u{\mid}^{q-2}u+{\frac{{\mid}u{\mid}^{p{^*_s}(t)-2}u}{{\mid}x{\mid}^t}}{\hspace{10}}in\;{\Omega},\\u=0{\hspace{217}}in\;{\mathbb{R}}^N{\backslash}{\Omega},$$ where Ω ⊂ ℝ^N is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < t < sp < N, 1 < q < p < p^∗_s where $p^*_s={\frac{N_p}{N-sp}}$, $p^*_s(t)={\frac{p(N-t)}{N-sp}}$, are the fractional critical Sobolev and Hardy-Sobolev exponents respectively. The fractional p-laplacian (-∆_p)^su with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by $\displaystyle(-{\Delta}_p)^su(x)=2{\lim_{{\epsilon}{\searrow}0}}\int{_{{\mathbb{R}}^N{\backslash}{B_{\epsilon}}}}\;\frac{{\mid}u(x)-u(y){\mid}^{p-2}(u(x)-u(y))}{{\mid}x-y{\mid}^{N+ps}}dy$, x ∈ ℝ^N. The main goal of this work is to show how the usual variational methods and some analysis techniques can be extended to deal with nonlocal problems involving Sobolev and Hardy nonlinearities. We also prove that for some α ∈ (0, 1), the weak solution to the problem (P) is in C^1,α(${\bar{\Omega}}$).

• KDI Journal of Economic Policy
• /
• v.12 no.1
• /
• pp.111-125
• /
• 1990

For the last several years, considerable criticism has been leveled against Korea's exchange rate management. While Korea was designated a currency manipulator by the U.S., domestically it is often complained that the won/dollar rate did not adequately reflect changes in Korea's export competitiveness and fluctuations in the exchange rates of major currencies. In view of this situation, Korea changed its exchange regime at the beginning of March this year from the dual currency basket system to a more flexible one, called a "market average rate regime". Under this new regime, the won rate is determined in the exchange market based upon the supply of and demand for foreign exchange and is allowed to freely fluctuate each day within a + 0.4 % range. This paper, first, seeks to evaluate Korea's exchange rate management under the dual basket regime of the 1980s, and then to construct an optimal currency basket for the won which could provide a proper indicator for exchange market intervention under the new market average rate regime. The analysis of fluctuations in the real effective exchange rate (REER) of the won indicates that the won rates in the 1980s failed not only to offset changes in relative prices between home and trading partner countries, but also to properly respond to variations in major exchange rates as further evidenced by sizable fluctuations in the nominal effective rates of the won. In other words, the currency basket regime which was adopted in 1980 for the stabilization of the REER of the won has not been operated properly, mainly because authorities often resorted to policy considerations in determining the won's rate. In the second part of the paper, an optimal currency basket for Korea is constructed, designed to minimize the fluctuations in the REER of the won without including policy considerations as a factor. It is recognized, however, that both domestic and foreign price data are not available immediately for the calculation of the REER. For this problem, the approach suggested by Lipschitz (1980) is followed, in which optimal weights for currencies in the basket are determined based upon the past correlation between price and exchange rates. When the optimal basket is applied to Korea since the mid-80s, it is found that the REER of the won could have been much more stable than it actually was. We also argue for the use of variable weights rather than fixed ones, which would be determined by the changing relationship between exchange rates and relative prices. The optimal basket, and the optimal basket exchange rate based on that basket, could provide an important medium- or long-term reference for proper exchange market intervention under the market average rate regime, together with other factors, such as developments in the current account balance and changes in productivity.

• Journal of Korea Multimedia Society
• /
• v.16 no.3
• /
• pp.318-329
• /
• 2013

This paper proposes a DNA watermarking method for the privacy protection and the prevention of illegal copy. The proposed method allocates codons to random circular angles by using random mapping table and selects triplet codons for embedding target with the help of the Lipschitz regularity value of local modulus maxima of codon circular angles. Then the watermark is embedded into circular angles of triplet codons without changing the codes of amino acids in a DNA. The length and location of target triplet codons depend on the random mapping table for 64 codons that includes start and stop codons. This table is used as the watermark key and can be applied on any codon sequence regardless of the length of sequence. If this table is unknown, it is very difficult to detect the length and location of them for extracting the watermark. We evaluated our method and DNA-crypt watermarking of Heider method on the condition of similar capacity. From evaluation results, we verified that our method has lower base changing rate than DNA-crypt and has lower bit error rate on point mutation and insertions/deletions than DNA-crypt. Furthermore, we verified that the entropy of random mapping table and the locaton of triplet codons is high, meaning that the watermark security has high level.

• Geophysics and Geophysical Exploration
• /
• v.26 no.2
• /
• pp.77-83
• /
• 2023

In this study, the expressions of magnetic vector and magnetic gradient tensor due to an elliptical cylinder were derived. Igneous intrusions and kimberlite structures are often shaped like elliptical cylinders with axial symmetry and different radii in the strike and perpendicular directions. The expressions of magnetic fields due to this elliptical cylinder were derived from the Poisson relation, which includes the direction of magnetization in the gravity gradient tensor. The magnetic gradient tensor due to an elliptical cylinder is derived by differentiating the magnetic fields. This method involves obtaining a total of 10 triple derivative functions acquired by differentiating the gravitational potential of the elliptical cylinder three times in each axis direction. As the order of differentiation and integration can be exchanged, the magnetic gradient tensor was derived by differentiating the gravitational potential of the elliptical cylinder three times in each direction, followed by integration in the depth direction. The remaining double integration was converted to a complex line integral along the closed boundary curve of the elliptical cylinder in the complex plane. The expressions of the magnetic field and magnetic gradient tensor derived from the complex line integral in the complex plane were shown to be perfectly consistent with those of the circular cylinder derived by the Lipschitz-Hankel integral.

• Geophysics and Geophysical Exploration
• /
• v.27 no.2
• /
• pp.108-118
• /
• 2024

In this study, expressions for the magnetic field and magnetic gradient tensor due to an elliptical disk were derived. Igneous intrusions and kimberlite structures often have elliptical cylinders with axial symmetry and elliptical cross sections. An elliptical cylinder with varying cross-sectional areas was approximated using stacks of elliptical disks. The magnetic fields of elliptical disks were derived using the Poisson relation, which includes the direction of magnetization in the gravity gradient tensor, as described in a previous study (Rim, 2024). The magnetic gradient tensor due to an elliptical disk is derived by differentiating the magnetic fields, which is equivalent to obtaining ten triple-derivative functions acquired by differentiating the gravitational potential of the elliptical disk three times in each axis direction. Because it is possible to exchange the order of differentiation, the magnetic gradient tensor is derived by differentiating the gravitational potential of the elliptical disk three times, which is then converted into a complex line integral along the closed boundary curve of the elliptical disk in the complex plane. The expressions for the magnetic field and magnetic gradient tensor derived from a complex line integral in complex plane are perfectly consistent with those of the circular disk derived from the Lipschitz-Hankel integral.