• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.405-426
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• 2014

The concept of interval-valued (${\alpha},{\beta}$)-fuzzy ideals, interval-valued (${\alpha},{\beta}$)-fuzzy generalized bi-ideals are introduced in LA-semigroups, using the ideas of belonging and quasi-coincidence of an interval-valued fuzzy point with an interval-valued fuzzy set and some related properties are investigated. We define the lower and upper parts of interval-valued fuzzy subsets of an LA-semigroup. Regular LA-semigroups are characterized by the properties of the lower part of interval-valued (${\in},{\in}{\vee}q$)-fuzzy left ideals, interval-valued (${\in},{\in}{\vee}q$)-fuzzy quasi-ideals and interval-valued (${\in},{\in}{\vee}q$)-fuzzy generalized bi-ideals. Main Facts.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.721-727
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• 2008

Let $W_{\alpha}$ be a weighted shift with positive weight sequence ${\alpha}=\{\alpha_i\}_{i=0}^{\infty}$. The semi-cubical hyponormality of $W_{\alpha}$ is introduced and some flatness properties of $W_{\alpha}$ are discussed in this note. In particular, it is proved that if ${\alpha}_n={\alpha}_{n+1}$ for some $n{\geq}1$, ${{\alpha}_{n+k}}={\alpha}_n$ for all $k{\geq}1$.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.293-314
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• 2009

The notions of pre-local function, semi-local functions and ${\alpha}$-local functions with respect to a topology and an ideal are introduced, and several properties are investigated. Also, the concept of $P-\mathcal{I}$-open sets and $P-\mathcal{I}$-closed sets in ideal topological spaces are discussed. Relations between $\mathcal{I}$-open sets and $P-\mathcal{I}$-open sets are provided, and several properties related to $P-\mathcal{I}$-open sets, pre-local functions, semi-local functions and ${\alpha}$-local functions with respect to a topology and an ideal are investigated.

• Preventive Nutrition and Food Science
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• v.3 no.1
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• pp.48-55
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• 1998

An acute ethanol load(50mmol/kg , i.p) resulted in an increase in peroxidation and a decrease in the levels of $\alpha$-tocopherol and ascorbate in rat cerebellum. Pretreatement with allopurinol(146$\mu$mol/kg, i.p) prevented the ethnol-induced increment in lipid peroxidation and decrease in $\alpha$-tocopherol content. However, the decrease of ascorbate was of greater magnitude when allopurinol was associated with ethanol. These results suggested that allopurinol. besides its action as a radical scavenger and xanthine oxidase inhibitor, might favor the regeneration of $\alpha$-tocopherol antioxidant acitviity was studied using ${\gamma}$-radiolysis in aerated ethanolic solutions. Even though allopurinol did not react by itself with $\alpha$-hydroxyethyl-peroxyl radicals [H3C-CH(OH)OO] , it enhance the $\alpha$-hydroxyethyl-peroxyl radical scavenging properties of $\alpha$tocopherol. The regeneration of $\alpha$-tocopherol from the $\alpha$-hydroxyethyl-peroxyl radical scavenging properties of $\alpha$-tocophero. The regeneration of $\alpha$-tocopherol from the $\alpha$-tocopherol radical by ascorbate remained as efficient in the presence of allopurinol as in its absence. The effects of allopurinol on the Vitamin E oxidation-reduction mechanism could be involoved in the beneficial effectof allopurinol on the biological cellular damages linked to free radical reactions.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.217-227
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• 2016

Let X be a nonempty set, and let $\mathfrak{F}=\{Y_i:i{\in}I\}$ be a family of nonempty subsets of X with the properties that $X={\bigcup}_{i{\in}I}Y_i$, and $Y_i{\cap}Y_j={\emptyset}$ for all $i,j{\in}I$ with $i{\neq}j$. Let ${\emptyset}{\neq}J{\subseteq}I$, and let $T^{(J)}_{\mathfrak{F}}(X)=\{{\alpha}{\in}T(X):{\forall}i{\in}I{\exists}_j{\in}J,Y_i{\alpha}{\subseteq}Y_j\}$. Then $T^{(J)}_{\mathfrak{F}}(X)$ is a subsemigroup of the semigroup $T(X,Y^{(J)})$ of functions on X having ranges contained in $Y^{(J)}$, where $Y^{(J)}:={\bigcup}_{i{\in}J}Y_i$. For each ${\alpha}{\in}T^{(J)}_{\mathfrak{F}}(X)$, let ${\chi}^{({\alpha})}:I{\rightarrow}J$ be defined by $i{\chi}^{({\alpha})}=j{\Leftrightarrow}Y_i{\alpha}{\subseteq}Y_j$. Next, we define two congruence relations ${\chi}$ and $\widetilde{\chi}$ on $T^{(J)}_{\mathfrak{F}}(X)$ as follows: $({\alpha},{\beta}){\in}{\chi}{\Leftrightarrow}{\chi}^{({\alpha})}={\chi}^{({\beta})}$ and $({\alpha},{\beta}){\in}\widetilde{\chi}{\Leftrightarrow}{\chi}^{({\alpha})}{\mid}_J={\chi}^{({\alpha})}{\mid}_J$. We begin this paper by studying the regularity of the quotient semigroups $T^{(J)}_{\mathfrak{F}}(X)/{\chi}$ and $T^{(J)}_{\mathfrak{F}}(X)/{\widetilde{\chi}}$, and the semigroup $T^{(J)}_{\mathfrak{F}}(X)$. For each ${\alpha}{\in}T_{\mathfrak{F}}(X):=T^{(I)}_{\mathfrak{F}}(X)$, we see that the equivalence class [${\alpha}$] of ${\alpha}$ under ${\chi}$ is a subsemigroup of $T_{\mathfrak{F}}(X)$ if and only if ${\chi}^{({\alpha})}$ is an idempotent element in the full transformation semigroup T(I). Let $I_{\mathfrak{F}}(X)$, $S_{\mathfrak{F}}(X)$ and $B_{\mathfrak{F}}(X)$ be the sets of functions in $T_{\mathfrak{F}}(X)$ such that ${\chi}^{({\alpha})}$ is injective, surjective and bijective respectively. We end this paper by investigating the regularity of the subsemigroups [${\alpha}$], $I_{\mathfrak{F}}(X)$, $S_{\mathfrak{F}}(X)$ and $B_{\mathfrak{F}}(X)$ of $T_{\mathfrak{F}}(X)$.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.02a
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• pp.265-265
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• 2013

We have investigated the influences of dangling bonds generated by alpha particle irradiation on friction and adhesion properties of graphene. Single layer of graphene grown with chemical vapor deposition on copper foil was irradiated by the alpha beam with the average energy of 3.04 MeV and the irradiation dosing between $1{\times}10^{14}$ and $1{\times}10^{15}$/$cm^3$. Raman spectroscopic showed that the ${\pi}$ electron states below Fermi level arises and the $I_D$/$I_G$ increases as increasing the dosing of alpha particle irradiation. The core level X-ray photoelectron (XPS) revealed that these defects represent the creation of various carbon-related defects and dangling bond. The nanoscale tribological properties were investigated with atomic force microscopy in ultrahigh vacuum. The friction appeared to increase remarkably as increasing the amount of dosing, indicating that the dangling bonds on graphene layers enhances the energy dissipations in friction. This trend can be explained by the additional channel of energy dissipation by dangling bond or O- and H- terminated clusters created by alpha particle irradiation.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.83-93
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• 2009

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy $\alpha$-I-open and r-fuzzy $\beta$-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy $\alpha$-I-openness (r-fuzzy pre-I-openness) sets regardless the fuzzy ideal topological space in Sostak sense. Moreover, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal $\alpha$-continuity, and obtain several characterization and some properties of these functions. Also, we investigate their relationship with other types of function.

• Journal of Powder Materials
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• v.5 no.1
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• pp.15-21
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• 1998

The effect of $\alpha$/$\beta$ phase on the mechanical properties and contact damage of silicon nitrides $Si_3N_4$) was investigated. Silicon nitride materials were prepared from two starting powders, at selective increasing hot-pressing temperatures to coarsen the microstructures: (i) from relatively coarse $\alpha$-phase powder, essentially equiaxed $\alpha$-$Si_3N_4$ grains, with limited, slow transformation to $\beta$-$Si_3N_4$ grain; (ii) from relatively fine $\alpha$-phase powder, a more rapid transformation to $\beta$-$Si_3N_4$, with attendant grain elongation. The resulting micro-structure thereby provided a spectrum of $\alpha$/$\beta$ phase ratios, grain sizes, and grain shapes. Fracture strength, hardness, and toughness were measured, and contact damage and strength degradation after indentation were investigated by Hertzian indentation using spherical indenter. A brittle to ductile transition in $Si_3N_4$ depended on $\alpha$/$\beta$ phase ratio as well as grain size. Silicon nitride with elongated $\beta$ grains showed a superior, contact damage resistance.

• Textile Coloration and Finishing
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• v.9 no.6
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• pp.18-25
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• 1997

The change of crystalline structure and mechanical properties of i-PP films which had before isothermally annealed at various temperature and times have been studied. The following results were abtain The crystallinity and crystallite size of the samples showed increasing above the annealing temperature of 13$0^{\circ}C$ and these are equilibrated after an annealing time of 30min. When the crystalline form was at annealling condition were below 13$0^{\circ}C$, 2min, subsequently achieving an $\alpha$, $\beta$ mixing form and at 13$0^{\circ}C$, 10min, the crystalline form entered an $\alpha$ form transition. It is achieved a typical $\alpha$ form at 15$0^{\circ}C$. The value of T'm was increasing until 13$0^{\circ}C$ but it was not founded at 15$0^{\circ}C$. The slopes which represented crystalline form in an Avrami plot differed from each other within the range of this experiment.

• East Asian mathematical journal
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• v.19 no.2
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• pp.241-249
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• 2003

In [11] the feeble continuity is introduced and then the weak and strong forms of feeble(or, equivalently $\alpha$-continuity) continuity are studied. In this note, we introduce a type of function called a slightly $\alpha$-continuous function and study several properties of it