• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권4호
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• pp.55-68
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• 2007

First-order least-squares method of a distributed optimal control problem for the incompressible Navier-Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing velocity-flux variables and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $L^2$ norm of the residual equations of the system. The optimal error estimates for least-squares finite element approximations are obtained.

• 대한수학회지
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• 제46권5호
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• pp.1007-1025
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• 2009

First-order least-squares method of a distributed optimal control problem for the incompressible Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing the vorticity and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $H^{-1}$ and $L^2$ norms of the residual equations of the system. Finite element approximations are studied and optimal error estimates are obtained. Resulting linear system of the optimality system is symmetric and positive definite. The V-cycle multigrid method is applied to the system to test computational efficiency.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2006년도 추계학술대회 학술발표 논문집 제16권 제2호
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• pp.293-296
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• 2006

This paper presents new sufficient conditions to an intelligent digital redesign (IDR). The purpose of the IDR is to effectively convert an existing continuous-time fuzzy controller to an equivalent sampled-data fuzzy controller in the sense of the state-matching. The state-matching error between the closed-loop trajectories is carefully analyzed using the integral quadratic functional approach. The problem of designing the sampled-data fuzzy controller to minimize the state-matching error as well as to guarantee the stability is formulated and solved as the convex optimization problem with linear matrix inequality (LMI) constraints.

• International journal of advanced smart convergence
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• 제9권4호
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• pp.101-105
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• 2020

In this study, we are going to discuss the role of sound, which exists as the background of a movie scene, and the relationship between seeing and hearing. In order to analyze the form in which the scene and sound are matched, the visual content of the image must be analyzed first. In this study, we analyzed Stanley Kubrick's film . Generally, there are both visual and auditory features in the scene of the movie. In some cases, the sound is emphasized more than the scene, and the scene is emphasized more than the sound. In particular, the sound in movies enables a wider imagination and a three-dimensional experience. Images and sounds will have different meanings and effects depending on the purpose of use. By analyzing the correlation between visual scene and auditory sound based on the role sound plays in the film in this study, we would like to confirm that sound is one essential element that has the role of equivalent and independent expression, not the role of assisting images.

• 식품과학과 산업
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• 제52권4호
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• pp.387-400
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• 2019

Fat replacers are divided into three categories. These include carbohydrate-based, protein-based and fat-based replacers. Carbohydrate-based replacers occupy half of the fat replacers market. The main ingredients of carbohydrate-based are gums, starch, modified starch, cellulose and fiber. The functional properties of fat replacers are to retain moisture, to retard staling, to provide mouthfeel and texture, to emulsify, to stabilize emulsion, and to reduce fat. Using these functionalities, fat replacers are used in various foods such as baked goods, salad dressing, sauces, meat products, dairy products, frying foods, bakery, and confectionery. Success factors of fat replacers in the market are sensory equivalent, texture and safety as food ingredients.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.839-853
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• 2022

We define the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property in terms of the topology of the phase space. Secondly we define these notions in terms of the compatible uniformity of the phase space. When the phase space is a compact Hausdorff space, we establish the equivalence of the corresponding definitions of the topological approach and the uniformity approach. In case the phase space is a compact metric space, the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property defined in terms of topology and uniformity are equivalent to their respective standard definitions.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.83-98
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• 2024

In this paper, we investigate the existence and uniqueness of solutions to a new class of integro-differential equation boundary value problems (BVPs) with ㄒ-Hilfer operator. Our problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed points coincide with the solutions to the given problem. Using Banach's and Schauder's fixed point techniques, the uniqueness and existence result for the given problem are demonstrated. The stability results for solutions of the given problem are also discussed. In the end. One example is provided to demonstrate the obtained results

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.989-1004
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• 2023

In this paper, we are motivated to evaluate and investigate the necessary conditions for the fractional Volterra Fredholm integro-differential equation involving the ς-Hilfer fractional derivative. The given problem is converted into an equivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence and uniqueness results for the given problem are derived by applying Krasnoselskii and Banach fixed point theorems respectively. Furthermore, we investigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.501-515
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• 2024

The primary focus of this paper is to thoroughly examine and analyze a coupled system by a Hilfer-Hadamard-type fractional differential equation with coupled boundary conditions. To achieve this, we introduce an operator that possesses fixed points corresponding to the solutions of the problem, effectively transforming the given system into an equivalent fixed-point problem. The necessary conditions for the existence and uniqueness of solutions for the system are established using Banach's fixed point theorem and Schaefer's fixed point theorem. An illustrate example is presented to demonstrate the effectiveness of the developed controllability results.

• 한국자기공명학회논문지
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• 제28권3호
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• pp.15-19
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• 2024

1,1'-carbonyldiimidazole (CDI) is a versatile reagent that can be used for synthesizing a variety of organic compounds containing carbonyl functional groups. The reactivity of CDI with two ortho-substituted anilines was tested and characterized with analytic techniques such as NMR, IR, and ESIMS. A reaction of CDI with two equivalents of disubstituted aniline (N¹,N¹-diethylbenzene-1,2-diamine) formed a urea compound, 1,3-bis(2-(diethylamino)phenyl)urea (1). On the other hand, a reaction with one equivalent of mono-substituted aniline (tert-butyl (2-aminophenyl)carbamate) formed a substituted benzimidazolone, tert-butyl 2-oxo-2,3-dihydro-1H-benzo[d]imidazole-1-carboxylate (2). These results demonstrated that a singly substituted aniline prefers an intramolecular ring formation while an N,N-doubly-substituted aniline prefers a urea formation.