• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1109-1129
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• 2021

This paper considers an anisotropic polytropic infiltration equation with a source term $$u_t={\sum\limits_{i=1}^{N}}{\frac{{\partial}}{{\partial}x_i}}\(a_1(x){\mid}u{\mid}^{{\alpha}_i}{\mid}u_{x_i}{\mid}^{p_i-2}u_{x_i}\)+f(x,t,u)$$, where p_i > 1, α_i > 0, a_i(x) ≥ 0. The existence of weak solution is proved by parabolically regularized method. Based on local integrability $u_{x_i}{\in}W_{loc}^{1,p_i}(\Omega)$, the stability of weak solutions is proved without boundary value condition by the weak characteristic function method. One of the essential characteristics of an anisotropic equation different from an isotropic equation is found originally.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.623-646
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• 2023

In this article, we introduce the hyperbolic space version of a faster iterative algorithm. The proposed iterative algorithm is used to approximate the common fixed point of three multi-valued almost contraction mappings and three multi-valued mappings satisfying condition (E) in hyperbolic spaces. The concepts weak w²-stability involving three multi-valued almost contraction mappings are considered. Several strong and △-convergence theorems of the suggested algorithm are proved in hyperbolic spaces. We provide an example to compare the performance of the proposed method with some well-known methods in the literature.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• Natural Product Sciences
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• v.22 no.1
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• pp.20-24
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• 2016

Pentacyclic triterpenes, mainly, asiatic acid, madecassic acid, asiaticoside, and madecassoside are the active constituents of Centella asiatica. A pentacyclic triterpene enriched C. asiatica extract (PRE) was prepared and standardized to contain a total pentacyclic triterpenes not less than 65% w/w. This work was focused on determination of antiinflammatory, antioxidant, and tyrosinase inhibitory activities of PRE and its stability. The PRE exhibited a satisfactory nitric oxide inhibitory effect, with an $IC_{50}$ value of $64.6{\mu}g/mL$. In addition, the PRE inhibited tyrosinase enzyme activity with an $IC_{50}$ value of $104.8{\mu}g/mL$. In contrast, the PRE possessed only weak antioxidant activity. The PRE was stable over a period of four months when stored as a dried powder but only in a well-closed container protected from light at $4^{\circ}C$. An aqueous alcoholic solution of the PRE was stable at pH values of 5.8 and 7.0, but was not stable at a pH of 8.2. Preparations of the PRE in an aqueous solution should be performed in acidic or neutral conditions.

• Journal of the Korean Vacuum Society
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• v.19 no.1
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• pp.58-65
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• 2010

AlN thin films were deposited on sapphire substrates and ZnO templates by rf-magnetron sputtering. Powder-sintered AlN target was adopted for source material. Thickness of AlN layer was linearly dependent on plasma power from 50 to 110 W, and it decreased slightly when working pressure increased from 3 to 10 mTorr due to short mean free path of source material sputtered from AlN target by Ar working gas. When $N_2$ gas was mixed with Ar, the thickness of AlN layer decreased significantly because of low sputter yield of nitrogen. AlN layer was also deposited on ZnO template. However, it showed weak thermal stability that the interface between AlN and ZnO was deteriorated by rapid thermal annealing treatment above $700^{\circ}C$. In addition, ZnO layer was largely attacked by MOCVD ambient gas of hydrogen and ammonia around $700^{\circ}C$ through inferior AlN layer deposited by sputtering. And AlN layers were fully peeled off above $900^{\circ}C$.

• Korean Journal of Food Science and Technology
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• v.31 no.1
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• pp.83-90
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• 1999

Although the chitosan has many functional properties due to its cationic amino groups, the application of chitosan in foods is limited by its poor water solubility, bitter taste and astringency. This study was conducted to investigate physicochemical and sensory properties of chitosan hydrolysates in various molecular weights obtained by ultrafiltration after enzymatic hydrolysis. As molecular weight decreased, the solubility of chitosan hydrolysates increased, while the viscosity and emulsion stability decreased. High molecular weight chitosan hydrolysates (>30 kDa) exhibited 800% of fat binding capacity, while low molecular weight ones $(3{\sim}30\;kDa)$ showed 500% of fat binding capacity. Water soluble chitosan hydrolysates exhibited no color differences. Freeze-thaw stability of chitosan hydrolysates was good, without variations among fractions. Cholesterol binding capacity of chitosan hydrolysates was changed from 24% to 36% with increasing molecular weights. From sensory evaluation of chitosan hydrolysates, it was found that bitterness, astringency, chemical flavor and fish flavor of chitosan hydrolysates were very weak.

• International Journal of Highway Engineering
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• v.6 no.4 s.22
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• pp.45-53
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• 2004

This study dealt with correlation analysis between deformation strength and rut resistance of asphalt concretes based on binder grade in Superpave specification with changing submerging time. Currently, Mashall mix design is known to have little correlation with rutting related performance. Therefore, some agencies started to use the Superpave method for asphalt mix design. But this method has a weak point in that it can not distinct mechanical property of the asphalt mixtures designed. For solution of these problem, this study used deformation strength, $S_D$, of Kim test which is a new approach under development for finding property which represents rut resistance characteristics of asphalt mixtures under static loading. This study used two aggregates from two regions and five PG asphalt binders. Final rut depth (DR) and dynamic stability (DS) from wheel tracking (WT) test were obtained. and $S_D$ value of the same mixture specimen which was made by gyratory compactor was obtained using loading head [4(1.0)]. Three submerging times 30min, 40min, 50min were used as a test variable at $60^{\circ}C$. Correlation analysis of DR and DS with $S_D$ were performed based on PG grade. It was found out that the $S_D$ has a high correlation with DR and DS of superpave mixtures. The highest $R^2$ was found from the $S_D$ values of 30min. submerged specimen.

• Journal of the Society of Cosmetic Scientists of Korea
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• v.30 no.2
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• pp.181-187
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• 2004

Preparations of mesoporous materials using various templates and their applicability have been intensively investigated for many years. We studied on synthesizing mesoporous Ti02 with pores in which sensitive compounds having weak physico-chemical properties such as thermal or UV irradiation and low solubility in solvent are trapped. Prior to trapping OMC in the pores of mesoporous titania, OMC was nano-emulsified in O/W system using Lecithin. Thereafter the OMC was trapped in the pores of mesoporous titania using sol-gel method. Main focus of this work is to prepare OMC-trapped mesoporous titania and to trace the stability and solubility of nano-emulsified OMC in the pores of mesoporous titania, and compared with that of mesoporous silica. OMC-trapped mesoporous Inorganic-Organic hybrid titania showed higher factors in sun protecting and a skin penetration phenomenon was reduced.