• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.149-159
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• 2009

In this paper, we introduce some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming, establish dual function and dual problem based on the augmented Lagrangian function, discuss the relationship between the approximate optimal solutions of augmented Lagrangian problem and that of primal problem, obtain approximate KKT necessary optimality condition of the augmented Lagrangian problem, prove that the approximate stationary points of augmented Lagrangian problem converge to that of the original problem. Our results improve and generalize some known results.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.637-647
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• 1999

In this paper, we consider a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition. We shall the stationary solutions ($v^{*}(x),s^{*}$) exist and the Hopf bifurcation occurs at a critical point when s $\in$ (1/3,1).

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.203-216
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• 2023

We consider a bistable attraction-attraction chemotaxis system with global coupling term. The study in this paper asserts that conditions for chemotactic coefficients for attraction and attraction and the global coupling constant to show existence of stationary solutions and Hopf bifurcation in the interfacial problem as the bifurcation parameters vary are obtained analytically.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.3
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• pp.156-164
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• 1999

Two analytical solutions for wave diffraction by a semi-infinite breakwater, which Penney and Price (1952), and Stoker (1957) presented, are rederived. Since in previous works the derivations were skipped or briefly given, in the paper the derivation is brought into focus. Numerical computations of the solutions are presented and solution behavior of Stoker's method due to a number of terms in the series is analyzed.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1365-1388
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• 2019

In this paper we consider a class of nonlinear nonlocal parabolic equations involving p-Laplacian operator where the nonlocal quantity is present in the diffusion coefficient which depends on $L^p$-norm of the gradient and the nonlinear term is of polynomial type. We first prove the existence and uniqueness of weak solutions by combining the compactness method and the monotonicity method. Then we study the existence of global attractors in various spaces for the continuous semigroup generated by the problem. Finally, we investigate the existence and exponential stability of weak stationary solutions to the problem.

• Analytical Science and Technology
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• v.36 no.6
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• pp.259-266
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• 2023

The demand for rare-earth elements (REEs) is increasing owing to their significance as prominent materials in electronics, high-tech industries, geological research, nuclear forensics, and environmental monitoring. In general, the utilization of REEs in various applications requires the use of chromatographic techniques to separate individual elements. However, REEs have similar physicochemical properties, which makes them difficult to separate. Recently, several studies have examined the separation of REEs using LN resin as the stationary phase and aqueous nitric acid and hydrochloric acid solutions as eluents. Using this method, light REEs have been separated using dilute acid solutions as the eluent, whereas heavy REEs are separated using solutions with high acid concentrations. To increase the separation resolution between different REEs, either the column length or resin size is changed. In addition, the suggested methods are implemented to decrease the analysis time. This review presents technical information on the chromatographic separation of REEs using the LN resin and discusses the optimal experimental conditions.

• Journal of the Korean Ceramic Society
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• v.49 no.1
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• pp.56-65
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• 2012

Functional materials are often exposed to high temperatures and inherent temperature gradients. These temperature gradients act as thermodynamic driving forces for the diffusion of mobile components. The detailed consequences of thermodiffusion depend on the boundary conditions of the non-isothermal sample: Once the boundaries of the sample are inert and closed for exchange of the mobile components, thermodiffusion leads to their pile-up in the stationary state (the so called Soret effect). Once the system is open for an exchange of the mobile component, chemical diffusion adds to the Soret effect, and stationary non-zero component fluxes are additionally observed in the stationary state. In this review, the essential aspects of thermodiffusion and Soret effect in inorganic functional materials are briefly summarized and our current practical knowledge is reviewed. Major examples include nonstoichiometric binary compounds (oxides and other chalcogenides) and ternary solid solutions. The potential influence of the Soret effect on the long term stability of high temperature thermoelectrics is briefly discussed. Typical Soret coefficients for nonstoichiometric compounds are found to be of the order of (d${\delta}$/dT) ${\approx}$ 1%/K.

• FOCUS: LIFE SCIENCE
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• no.1
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• pp.6.1-6.9
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• 2024

The document is a white paper on Hydrophilic Interaction Liquid Chromatography (HILIC) analysis method development. HILIC is a type of chromatography that uses an organic/aqueous mobile phase and a polar stationary phase. In HILIC, water is a strong solvent, and unlike in Reversed Phase Liquid Chromatography (RPLC), increasing the proportion of water in the mobile phase reduces the retention time of the analyte. The paper discusses when to consider HILIC analysis methods, the advantages of HILIC, and the challenges often encountered due to the lack of understanding of HILIC mechanisms compared to RPLC. It also provides a systematic flowchart for intelligent solutions for HILIC analysis method development, which includes a three-step approach for chromatography analysis method development. The first step involves gathering as much information as possible about the analyte (e.g., pKa, log P, log D). The second step involves analyzing the sample under different pH conditions using three HILIC columns in either isocratic or gradient mode to identify the suitable column/pH combination for the analyte. The third step involves optimizing the separation by investigating other parameters such as temperature and ionic strength, and assessing the robustness of the method. The paper emphasizes that the selection of the appropriate stationary/mobile phase combination, based on the differences between the HILIC stationary phases and the mobile phase pH, can provide high selectivity in the analysis. This step-by-step approach can help users develop an efficient analysis method.

• Journal of Information Processing Systems
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• v.14 no.2
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• pp.455-468
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• 2018

The concepts of graph theory are applied to model and analyze dynamics of computer networks, biochemical networks and, semantics of social networks. The analysis of dynamics of complex networks is important in order to determine the stability and performance of networked systems. The analysis of non-stationary and nonlinear complex networks requires the applications of ordinary differential equations (ODE). However, the process of resolving input excitation to the dynamic non-stationary networks is difficult without involving external functions. This paper proposes an analytical formulation for generating solutions of nonlinear network ODE systems with functional decomposition. Furthermore, the input excitations are analytically resolved in linearized dynamic networks. The stability condition of dynamic networks is determined. The proposed analytical framework is generalized in nature and does not require any domain or range constraints.

• Journal of computational fluids engineering
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• v.16 no.1
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• pp.90-95
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• 2011

The Navier-Stokes equations are solved to study the flow characteristics of a micro viscous pump. The viscous micropump is consisted of a stationary disk with a spiral shaped channel and a rotating disk. A simple geometrical model for the tip clearance is proposed and validated by comparing computed flow rate with corresponding experimental data. Present numerical solutions show satisfactory agreement with the corresponding experimental data. The tip clearance effect is found to become significant as the rotational speed increases. As the pressure load increases, a reversed flow region is seen to form near the stationary disk. The height of the channel is shown to be optimized in terms of the flow rate for a given rotational speed and pressure load. The optimal height of the channel becomes small as the rotational speed decreases or the pressure load increases. The flow rate of the pump is found to be in proportion to the width of channel.