• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.21-36
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• 2024

In this paper, we study the existence of solutions for hybrid fractional differential equations with p-Laplacian operator involving fractional Caputo derivative of arbitrary order. This work can be seen as an extension of earlier research conducted on hybrid differential equations. Notably, the extension encompasses both the fractional aspect and the inclusion of the p-Laplacian operator. We build our analysis on a hybrid fixed point theorem originally established by Dhage. In addition, an example is provided to demonstrate the effectiveness of the main results.

• Journal of the Society of Cosmetic Scientists of Korea
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• v.25 no.1
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• pp.120-136
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• 1999

A newly synthesized polyhydroxy aromatic compound(LG 106w) has good skin lightening effect. Inclusion complexation of LG 106w with $\beta$-cyclodextrin and its hydroxypropyl and dimethyl derivatives was studied by the solubility method, scanning electron microscopy and differential thermal analysis. A relationship between host and guest was clearly reflected in the magnitude of the stability constant(DM-$\beta$> HP-$\beta$>$\beta$ -cyclodextrin). Formulation problems, which resulted from its very low solubility in aqueous solution, were resolved by the inclusion formation. LG 106W from inclusions is much more water-soluble than pure one. The improvement of pH and temperature stability correlated with the increased solubility was also observed. Inclusion complex of LG 106w had similar activity to pure LG 106w on the inhibition of melanin synthesis in B-16 melanoma cell but showed lower irritation on cultured cell test in vitro. According to the results, cyclodextrins might be one of the reliable candidates for improving the availability of LG 106w.

• YAKHAK HOEJI
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• v.39 no.2
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• pp.175-184
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• 1995

The interaction of omeprazole(OMP) with $\gamma$-cyclodextrin($\gamma$-CyD) was investigated by solubility study and the complexation was confirmed by means of UV/VIS spectrophotometer, circular dichroism, differential scanning calorimeter, and $^{1}$H nuclear magnetic resonance spectra. The stability, dissolution rate, and partition coefficient of the complex were measured. The results present that the benzimidazole moiety and a part of pyridine ring containing sulfur atom of OMP might be included into the cavity of $\gamma$-CyD and the formation type of inclusion complex appeared to be B$_{s}$. The stoichiometric ratio of OMP to $\gamma$-CyD in the complex was found to be 1:1 and the stability constant of the complex found to be 97.1 M$^{-1}$. And the dissolution rate of OMP was markedly increased by inclusion complex formation with $\gamma$-CyD, and so it was above 90% in 5 min. from solid complex. Oil to water partition coefficient of OMP-$\gamma$-CyD complex was 60, which is significantly higher than that of OMP itself, 36.4. The degradation rate constant of OMP were greater than OMP-$\gamma$-CyD complex in aqueous solutions of various pHs, and the half lives of OMP and OMP-$\gamma$-CyD at pH 9 were 279.2 and 509.9 days, respectively, showing that the complex was more stable than OMP, therefore it was thought that OMP was stabilized by inclusion formation with $\gamma$-CyD.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.379-385
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• 2008

Making use of a linear operator, we introduce certain subclass of meromorphically univalent functions in the punctured unit disk and study its properties including some inclusion results, coefficient and distortion problems. Our result generalize many results known in the literature.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.137-147
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• 2020

In this paper, we introduce two subclasses of analytic and Spiral-like functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.57-64
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• 2021

In this paper we deal with the embedding inclusions on the fractional Orlicz-Sobolev spaces which are crucial roles for studying the theories of the partial differential equations. We get some properties and theories of the embedding inclusions on the fractional Orlicz-Sobolev spaces.

• Journal of Pharmaceutical Investigation
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• v.20 no.3
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• pp.153-159
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• 1990

To increase the solubility of fentiazac which is used widely as a non-steroidal antiinflammatory drug, its inclusion complex and suppositories were prepared and studied. Inclusion complexes of fentiazac with ${\beta}-cyclodertin$ $({\beta}-CyD)$ were prepared by four diffrent methods; coprecipitation method, kneading method, solvent evaporation method, freeze drying method. Suppositories of $fentiazac/{\beta}-CyD$ with PEG 1500 and Witepsol H-15 were prepared by solvent evaporation method and freeze drying method. Inclusion complex formation of fentiazac with ${\beta}-CyD$ was ascertained by powder X-ray diffractometry, differential scanning calorimetry and IR spectroscopy. The dissolution rate of fentiazac from the inclusion complex increased in distilled water and KP 2nd disintegration test fluids (pH 6.8) but extemly decreased in KP 1st disintegration test fluid (pH 1.2). Inclusion complexes prepared by freeze drying method and solvent evaporation method were similar. Freeze drying method seemed to be suitable for preparation of complex with most higher dissolution rate but coprecipitation method seemed not to be suitable. The dissolution rate of fentiazac increased markedly by ${\beta}-CyD$ complexation. The release rates of suppositories increased in the following order. Complex prepared by freeze dying method in PEG 1500 > complex prepared by solvent evaporation method in PEG 1500 > fentiazac in PEG 1500 > complex prepared by freeze dying method in Witepsol H-15 > complex prepared by solvent evaporation method in Witepsol H-15 > fentiazac in Witepsol H-15.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.7
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• pp.2931-2938
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• 2011

Effective thermal conductivity of three-phase composites, consisting of matrix and two kinds of spherical inclusions, has been derived as an explicit form by extending modified Eshelby model (MEM) for two-phase composites. The present results are compared with those by differential effective medium model (DEMM), which are also compared with the experimental results of two- and three-phase composites in the literatures to be validated. For two-phase composites, the results by MEM are better than those by DEMM for the inclusion volume fraction smaller than 0.5. Comparisons between the results by two models and experimental results have been made for three-phase composite, resulting in that MEM predicts better than DEMM for smaller volume fraction of the inclusion having larger inclusion-to-matrix thermal conductivity ratio, but DEMM predicts better as its volume fraction increases. It has been observed through parametric study that its volume fraction is the critical factor affecting the deviation of predictions by the two models. The results by them show a good agreement with the three-phase composite proposed by Molina et al..

• Coupled systems mechanics
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• v.3 no.3
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• pp.291-304
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• 2014

Paper discusess a dynamic engineering problem of a mass attached to a pendulum sliding along a cable. In this problem the pendulum mass and the cable are coupled together in a model described by a system of differential algebraic equations (DAE). In the paper we have presented formulation of the system of differential equations that models the problem and determination of the initial conditions. The developed model is general in a sense of free choice of support location, elastic cable properties, pendulum length and inclusion of braking forces. Examples illustrate and validate the model.

• Steel and Composite Structures
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• v.3 no.3
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• pp.169-184
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• 2003

This paper presents a generic modelling of composite steel-concrete beams with elastic shear connection. It builds on the well-known seminal technique of Newmark, Siess and Viest, in order to formulate the partial interaction formulation for solution under a variety of end conditions, and lends itself well for modification to enable direct quantification of effects such as shrinkage, creep, and limited shear connection slip capacity. This application is possible because the governing differential equations are set up and solved in a fashion whereby inclusion of the kinematic and static end conditions merely requires a statement of the appropriate constants of integration that are generated in the solution of the linear differential equations. The method is applied in the paper for the solution of the well-studied behaviour of simply supported beams with partial interaction, as well as to provide solutions for a beam encastr$\acute{e}$ at its ends, and for a propped cantilever.