• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.427-430
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• 2009

In this paper we introduce the intermediate differential of a Lipschitz map from a Banach space to another Banach space and prove that every locally Lipschitz function f defined on an open subset ${\Omega}$ of a superreflexive real Banach space X to a finite dimensional Banach space Y is uniformly intermediate differentiable at every point ${\Omega}/A$, where A is a ${\sigma}$-lower porous set.

• Advances in nano research
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• v.7 no.1
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• pp.25-38
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• 2019

This research is aimed at studying the asymmetric thermal buckling of porous functionally graded (FG) annular nanoplates resting on an elastic substrate which are made of two different sets of porous distribution, based on nonlocal elasticity theory. Porosity-dependent properties of inhomogeneous nanoplates are supposed to vary through the thickness direction and are defined via a modified power law function in which the porosities with even and uneven type are approximated. In this model, three types of thermal loading, i.e., uniform temperature rise, linear temperature distribution and heat conduction across the thickness direction are considered. Based on Hamilton's principle and the adjacent equilibrium criterion, the stability equations of nanoporous annular plates on elastic substrate are obtained. Afterwards, an analytical solution procedure is established to achieve the critical buckling temperatures of annular nanoplates with porosities under different loading conditions. Detailed numerical studies are performed to demonstrate the influences of the porosity volume fraction, various thermal loading, material gradation, nonlocal parameter for higher modes, elastic substrate coefficients and geometrical dimensions on the critical buckling temperatures of a nanoporous annular plate. Also, it is discussed that because of present of thermal moment at the boundary conditions, porous nanoplate with simply supported boundary condition doesn't buckle.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.157-178
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• 2019

The present correspondence is conveyed on to consider the fascinating and novel characteristics of radiative hydromagnetic convective flow of a chemically reacting fluid over an exponentially accelerated inclined porous plate. Exact solutions for the fluid velocity, temperature and species concentration, under Boussinesq approximation, are obtained in closed form by the two term perturbation technique. The interesting parts of thermal dispersing outcomes are accounted in this correspondence. Graphical evaluation is appeared to depict the trademark direct of introduced parameters on non dimensional velocity, temperature and concentration profiles. Also, the numerical assortment for skin friction coefficient, Nusselt number and Sherwood number is examined through tables. The certification of current examination is confirmed by making an examination with past revelations available in composing, which sets a benchmark for utilization of computational approach.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.225-238
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• 2020

This work treats the axisymmetric buckling of functionally graded (FG) porous annular/circular nanoplates based on modified couple stress theory (MCST). The nanoplate is located at the elastic medium which is simulated by Kerr foundation with two spring and one shear layer. The material properties of the porous FG nanostructure are assumed to vary through the nanoplate thickness based on power-law rule. Based on two variables refined plate theory, the governing equations are derived by utilizing Hamilton's principle. Applying generalized differential quadrature method (GDQM), the buckling load of the annular/circular nanoplates is obtained for different boundary conditions. The influences of different involved parameters such as boundary conditions, Kerr medium, material length scale parameter, geometrical parameters of the nanoplate, FG power index and porosity are demonstrated on the nonlinear buckling load of the annular/circular nanoplates. The results indicate that with increasing the porosity of the nanoplate, the nonlinear buckling load is decreased. In addition, with increasing the material length scale parameter to thickness ratio, the effect of spring constant of Kerr foundation on the buckling load becomes more prominent. The present results are compared with those available in the literature to validate the accuracy and reliability. A good agreement is observed between the two sets of the results.

• Proceedings of the Korean Vacuum Society Conference
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• 2015.08a
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• pp.59.1-59.1
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• 2015

In the Linford group at Brigham Young University we have recently developed three new sets of materials for three different areas of separations science: thin layer chromatography (TLC), high performance liquid chromatography (HPLC), and solid phase microextraction (SPME). First, via microfabrication we have grown patterned carbon nanotube (CNT) forests on planar substrates that we have infiltrated with inorganic materials such as silicon nitride. The coatings on the CNTs are conformal and typically deposited in a process like low pressure chemical vapor deposition. The resulting materials have high surface areas, are porous, and function as effective separation devices, where separations on our new TLC plates are typically significantly faster than on conventional devices. Second, we used the layer-by-layer (electrostatically driven) deposition of poly (allylamine) and nanodiamond onto carbonized poly (divinylbenzene) microspheres to create superficially porous particles for HPLC. Many interesting classes of molecules have been separated with these particles, including various cannabinoids, pesticides, tricyclic antidepressants, etc. Third, we have developed new materials for SPME by sputtering silicon onto cylindrical fiber substrates in a way that creates shadowing of the incoming flux so that materials with high porosity are obtained. These materials are currently outperforming their commercial counterparts. Throughout this work, the new materials we have made have been characterized by X-ray photoelectron spectroscopy, time-of-flight secondary ion mass spectrometry, scanning electron microscopy, transmission electron microscopy, etc.

• The Journal of Engineering Research
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• v.6 no.1
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• pp.161-168
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• 2004

In the present study, a simple method was successfully used for hydroxyapatite coatings on Ti-6AL-4V substrates deposited by using a sol-gel derived precursor. Prior to hydroxyapatite coating the samples were micropolished (0.1 micron) and divided into three sets. The first set, were the micropolished samples kept as such. The second set were coated with titania sol and the third set was treated with 5M NaOH. After three repetitions of hydroxyapatite coating procedures on each set and heat treatment at $600^{\circ}C$, the formation of hydroxyapatite has been confirmed by XRD analyses and the substrate material was found to be oxidized with negligible amount of CaO in the coating. The SEM studies revealed surface morphology. Hydroxyapatite, calcined at $600^{\circ}C$, displaying a porous structure arisen from heating of the bulk

• Journal of Technologic Dentistry
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• v.26 no.1
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• pp.139-144
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• 2004

In the present study, a simple method was successfully used for hydroxyapatite coatings on Ti-6Al-4V substrates deposited by using a sol-gel derived precursor. Prior to hydroxyapatite coating the samples were micropolished (0.1 micron) and divided into three sets. The first set,were the micropolished samples kept as such. The second set were coated with titania sol and the third set was treated with 5M NaOH. After three repetitions of hydroxyapatite coating procedures on each set and heat treatment at 600 $^{\circ}\Delta C$, the formation of hydroxyapatite has been confirmed by XRD analyses and the substrate material was found to be oxidized with negligible amount of CaO in the coating. The SEM studies revealed surface morphology. Hydroxyapatite, calcined at 600$^{\circ}\Delta C$, displaying a porous structure arisen from heating of the bulk. But, it is very meaningful in trying to approach morale management plans with an object of dental technicians. It is necessary that dental technicians should make efforts to control themselves.

• Journal of Environmental Science International
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• v.5 no.1
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• pp.61-69
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• 1996

The combined wastewater of municipal landfill leachate and municipal sewage was treated using several sets of bench-scale aerated circulating system including porous media. Investigated items in this experiment were the dominant protozoa and metazoa in this system, the variation of microfauna relationship between operating condition and dominant genera. Also considered the factors determining dominant genera and their role. The outcome of this research is as follows; 1. Aspidisca, Vorticella, Truhellophyllum, Lecane, Philodina, Cyclops were mainly appeared prior to combinding leachate, while Trachelocerca, Bodo, Glaucoma were the dominant genera after combinding leachate. 2. As to metazoa, Nematode and Philodina were not influenced by 5oA leachate mixing ratio, meanwhile Crustacea has high sensitivity for increased leachate mixing ratio and it was not appeared in 5% leachate mixing ratio. 3. The appropriate treatability could'nt be expected at the above 10% leachate mixing ratio. Especially, in the condition of 20% leachate mixing ratio, all of the microfauna were affected damage seriously on their existence. Meanwhile hydraulic retention time, substrate loading rate and slut자e production rate didn't give notable influence on increasing the number of microfauna. 4. As to protozoa, saprozoic and holozoic species were appeared commonly and polysaprobic species were dominent. 5. Filamentous organsms were nearly not affected by leachate mixing. It seems that they could live without any trouble at the 10% leachate mixing ratio, if the substrate is sufficient. 6. Diversity of microfauna had a reducing trernd as the sewage was mixed with leachate.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.16 no.5
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• pp.385-389
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• 2003

There are four main components of the CMP process: polishing pad, slurry, elastic supporter, and pad conditioner. The polishing pad is an essential component to the reproducibility of polishing uniformity in CMP process. However, the polishing pad in recently using metal CMP raised the several points of high cost caused by the increase of cycle time and the many usage of slurry. It is necessary to develop the novel polishing pad which would lead the cost reduction by the higher pad life-cycle, minimized cycle time and lower slurry usage. The characteristics of polishing pad were studied on the effects of different sets of the Polishing pad, which can be applied to metal chemical mechanical polishing process for global planarization of multilevel interconnection structure. The main purpose of this experiment is cost reduction by the increase of pad life-time, the decrease of cycle time and the lower usage of slurry through the specific hard porous structured pad design. It is confirmed that the novel polishing pad made the slurry usage decrease to 60% as well as the pad life-time increase twice with the 25% improvement of removal rate. The polishing time could be decreased and it also helped the cycle time to diminish. It can be expected that this results will help both the process throughput and the device yield to be improved.