• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.795-814
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• 2021

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: fⁿ + P(f) = R(z)e^α(z) and fⁿ + P_*(f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z) in the complex plane, where P(f) and P_*(f) are differential polynomials in f of degree n - 1 with coefficients being small functions and rational functions respectively, R is a non-vanishing small function of f, α is a nonconstant entire function, p₁, p₂ are non-vanishing rational functions, and α₁, α₂ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when p₁, p₂ are nonzero constants, and deg α₁ = deg α₂ = 1. Our results are improvements and complements of Liao ([9]), and Rong-Xu ([11]), etc., which partially answer a question proposed by Li ([7]).

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.133-147
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• 2024

Let G = (V, E) be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on G $${\Delta}u={\lambda}e^u(e^u-1)^5+4{\pi}\sum_{s=1}^{N}\delta_{ps}$$, where λ > 0, δ_ps is the Dirac mass at the vertex p_s, and p₁, p₂, . . . , p_N are arbitrarily chosen distinct vertices on the graph. We show that there exists a critical value $\hat{\lambda}$ such that when λ > $\hat{\lambda}$, the generalized Chern-Simons equation has at least two solutions, when λ = $\hat{\lambda}$, the generalized Chern-Simons equation has a solution, and when λ < $\hat{\lambda}$, the generalized Chern-Simons equation has no solution.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.745-762
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• 2024

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fⁿ(z) + P_d(z, f) = p₁e^α1z + p₂e^α2z + p₃e^α3z, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, p_j (j = 1, 2, 3) are small meromorphic functions of f and α_j (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on α_j (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.383-395
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• 2010

In the present paper, we construct the traveling wave solutions involving parameters of nonlinear evolution equations in the mathematical physics via the (3+1)- dimensional potential- YTSF equation, the (3+1)- dimensional generalized shallow water equation, the (3+1)- dimensional Kadomtsev- Petviashvili equation, the (3+1)- dimensional modified KdV-Zakharov- Kuznetsev equation and the (3+1)- dimensional Jimbo-Miwa equation by using a simple method which is called the ($\frac{G'}{G}$)- expansion method, where $G\;=\;G(\xi)$ satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the travelling waves. The travelling wave solutions are expressed by hyperbolic, trigonometric and rational functions.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.511-519
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• 2009

A matrix $P{\in}\mathbb{C}^{n{\times}n}$ is called a generalized reflection matrix if $P^*$ = P and $P^2$ = I. An $n{\times}n$ complex matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = -PAP). It is well-known that the reflexive and anti-reflexive matrices with respect to the generalized reflection matrix P have many special properties and widely used in engineering and scientific computations. In this paper, we give new necessary and sufficient conditions for the existence of the reflexive (anti-reflexive) solutions to the linear matrix equation AXB + CY D = E and derive representation of the general reflexive (anti-reflexive) solutions to this matrix equation. By using the obtained results, we investigate the reflexive (anti-reflexive) solutions of some special cases of this matrix equation.

• Bulletin of the Korean Chemical Society
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• v.6 no.1
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• pp.23-29
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• 1985

The charge-transfer complexing properties of 1-methyl nicotinamide (MNA), an acceptor, and adenine, a donor, were investigated in water and SDS micellar solutions in relation to the intramolecular interaction in nicotinamide adenine dinucleotide ($NAD^+$). The spectral and thermodynamic parameters of MNA-indole and methyl viologen-adenine complex formations were determined, and the data were utilized to evaluate the charge-transfer abilities of MNA and adenine. The electron affinity of nicotinamide was estimated to be 0.28 eV from charge-transfer energy $of{\sim}300$ nm for MNA-indole. The large enhancement of MNA-indole complexation in SDS solutions by entropy effect was attributed to hydrophobic nature of indole. The complex between adenine and methyl viologen showed an absorption band peaked near 360 nm. The ionization potential of adenine was evaluated to be 8.28 eV from this. The much smaller enhancement of charge-transfer interaction involving adenine than that of indole in SDS solutions was attributed to weaker hydrophobic nature of the donor. The charge-transfer energy of 4.41 eV (280 nm) was estimated for nicotinamide-adenine complex. The spectral behaviors of $NAD^+$ were accounted to the presence of intramolecular interaction in $NAD^+$, which is only slightly enhanced in SDS solutions. The replacement of nicotinamide-adenine interaction in $NAD^+$ by intermolecular nicotinamide-indole interaction in enzyme bound $NAD^+$, and guiding role of adenine moiety in $NAD^+$ were discussed.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.1019-1043
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• 1998

In this paper we study some asymptotics for solutions of the Ginzburg-Landau equations with Dirichlet boundary conditions. We consider the solutions ( $u_{\in}$, $A_{\in}$) which minimize the Ginzburg-Landau energy functional $E_{\in}$(u, A). We show that the solutions ( $u_{\in$}$ , $A_{\in}$) converge to some ( $u_{*}$, $A_{*}$) in various norms as the coupling parameter $\in$longrightarrow0.ow0.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.11
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• pp.5179-5202
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• 2018

Transmission Control Protocol (TCP) is the most widely used protocol in the cloud data centers today. However, cloud data centers using TCP experience many issues as TCP was designed based on the assumption that it would primarily be used in Wide Area Networks (WANs). One of the major issues with TCP in the cloud data centers is the Incast issue. This issue arises because of the many-to-one communication pattern that commonly exists in the modern cloud data centers. In many-to-one communication pattern, multiple senders simultaneously send data to a single receiver. This causes packet loss at the switch buffer which results in TCP throughput collapse that leads to high Flow Completion Time (FCT). Recently, Software-Defined Networking (SDN) has been used by many researchers to mitigate the Incast issue. In this paper, a detailed survey of various SDN based solutions to the Incast issue is carried out. In this survey, various SDN based solutions are classified into four categories i.e. TCP Receive Window based solutions, Tuning TCP Parameters based solutions, Quick Recovery based solutions and Application Layer based solutions. All the solutions are critically evaluated in terms of their principles, advantages, and shortcomings. Another important feature of this survey is to compare various SDN based solutions with respect to different performance metrics e.g. maximum number of concurrent senders supported, calculation of delay at the controller etc. These performance metrics are important for deployment of any SDN based solution in modern cloud data centers. In addition, future research directions are also discussed in this survey that can be explored to design and develop better SDN based solutions to the Incast issue.

• Korean Journal of Animal Reproduction
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• v.16 no.3
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• pp.269-276
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• 1992

Studies were carried out to find the freezing media which gives no ice crystals in single(glycerol, ethylene glycol, dimethyl sulfoxide(DMSO)) and mixture solutions(glycerol＋propylene glycol, glycerol＋ethylene glycol) of permeable cryoprotectants in vitrification solution and to study effects of VS on the survival of vitrified mouse morulae. The results are summarized as follows: 1. In toxicity test of permeable cryoprotectants, 30% glycerol of single solution showed the highest FDA-score(4.1) in mouse morulae frozen compared among other single solutions. The FDA-score(4.1) of 30% glycerol was higher than 30% ethylene glycol(3.6) and DMSO(1.4( (P<0.05). 2. 20, 30 or 40% single solution of permeable cryoprotectants containing m-PBS with 10% sucrose and 20% BSA was not crystallized during cooling, but crystallized during warming. However, the 30% mixture solution of the two permeable cryoprotectants was not crystallized both during cooling and warming.3. When mouse morulae were frozen in 30% mixture solutions of two permeable cryoprotectants(glycerol and propylene glycol, glycerol and ethylene glycol), highest FDA-score(4.5) was obtained in a mixture solution of 20% glycerol and 10% ethylene glycol(20G10E) than other 30% mixture solutions(10G20E, 15G15E, 20G10P, 15G15P, 10G20P) and there was significant difference between 20G10E and 10G20E(P<0.05).

• Restorative Dentistry and Endodontics
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• v.40 no.4
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• pp.270-275
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• 2015

Objectives: This study examined the color changes of a resin composite with different shades upon exposure to water with different pH. Materials and Methods: Nanohybrid resin composites (Filtek Z350XT, 3M ESPE) with four different shades (A2, A3, B1, and B2) were immersed in water with three different pH (pH 3, 6, and 9) for 14 day. The CIE $L^*a^*b^*$ color coordinates of the specimens were evaluated before and after immersion in the solutions. The color difference (${\Delta}E^*$) and the translucency parameter (TP) were calculated using the color coordinates. Results: ${\Delta}E^*$ ranged from 0.33 to 1.58, and the values were affected significantly by the pH. The specimens immersed in a pH 6 solution showed the highest ${\Delta}E^*$ values (0.87 - 1.58). The specimens with a B1 shade showed the lowest ${\Delta}E^*$ change compared to the other shades. TP ranged from 7.01 to 9.46 depending on the pH and resin shade. The TP difference between before and after immersion in the pH solutions was less than 1.0. Conclusions: The resulting change of color of the tested specimens did not appear to be clinically problematic because the color difference was < 1.6 in the acidic, neutral, and alkaline solutions regardless of the resin shade, i.e., the color change was imperceptible.