• Bulletin of the Korean Chemical Society
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• 제26권1호
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• pp.51-56
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• 2005

A PVC membrane electrode for lead ion based on 1-phenyl-2-(2-quinolyl)-1,2-dioxo-2-(4-bromo) phenylhydrazone (PQDBP) as ionophore was demonstrated. The optimum composition of the membrane was 30 wt% poly(vinyl chloride), 60 wt% dibutyl phthalate as a plasticizer, 4 wt% ionophore and 6 wt% sodium tetraphenylborate as additive. The electrode exhibits a Nernstian response (28.7 mV decade$^{-1}$) for Pb$^{2+}$ over a wide concentration range (1.0 ${\times}$ 10$^{-1}$ to 1 ${\times}$ 10$^{-6}$ M) with a detection limit of 6.0 ${\times}$ 10$^{-7}$ M. This sensor has a short response time and can be used for at least 2 months without any divergence in potentials. The proposed electrode could be used in a pH range of 3.0-6.0 and revealed good selectivities for Pb$^{+2}$ over a wide variety of other metal ions. It was successfully applied as an indicator electrode for the potentiometric titration of lead ion with potassium chromate and for the direct determination of lead in mine.

• 대한수학회보
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• 제43권1호
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• pp.225-225
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• 2006

In this note a modification of Proposition 3.10 of [1] is given.

• 호남수학학술지
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• 제42권2호
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• pp.219-234
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• 2020

The fundamental relation on a fuzzy hyperring is defined as the smallest equivalence relation, such that the quotient would be the ring, that is not commutative necessarily. In this paper, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings, where the ring is commutative with respect to both sum and product. With considering this relation on fuzzy hyperring, the set of the quotient is a commutative ring. Also, we introduce fundamental functor between the category of fuzzy hyperrings and category of commutative rings and some related properties. Eventually, we introduce α-part in fuzzy hyperring and determine some necessary and sufficient conditions so that the relation α is transitive.

• 대한수학회보
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• 제50권2호
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• pp.507-524
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• 2013

The notion of $n$-ary algebraic hyperstructures is a generalization of ordinary algebraic hyperstructures. In this paper, we associate an n-ary hypergroupoid (H, $f$) with an ($n+1$)-ary relation ${\rho}_{n+1}$ defined on a non-empty set H. Then, we obtain some basic results in this respect. In particular, we investigate when it is an $n$-ary $H_v$-group, an $n$-ary hypergroup or a join $n$-ary space.

• Communications for Statistical Applications and Methods
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• 제23권1호
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• pp.57-70
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• 2016

Type-II progressive censoring is one of the censoring methods frequently used in clinical studies, reliability trials, quality control of products and industrial experiments. Sometimes in Type-II progressive censoring experiments, the failure rate is low so the waiting time to observe the $m^{th}$ failure will be very long; however, the experimenter may have to terminate the experiment before a predetermined time. In this article, if two generalized types of Type-II progressive censoring are reminded, we then make some changes in the removal method of Type-II progressive censoring such that without reducing the deduction quality, the termination time of the experiment decreases. This can be done with decreasing withdraws throughout the steps of the experiment with a special reasonable method. A simulation study is done and the results are tabulated at the end of this article for a comparison between introduced method and Type-II progressive censoring.

• Korean Journal of Mathematics
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• 제26권2호
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• pp.175-189
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• 2018

In this paper, at first we generalize the notion of algebra over a field. A ${\Gamma}$-algebra is an algebraic structure consisting of a vector space V, a groupoid ${\Gamma}$ together with a map from $V{\times}{\Gamma}{\times}V$ to V. Then, on every associative ${\Gamma}$-algebra V and for every ${\alpha}{{\in}}{\Gamma}$ we construct an ${\alpha}$-Lie algebra. Also, we discuss some properties about ${\Gamma}$-Lie algebras when V and ${\Gamma}$ are the sets of $m{\times}n$ and $n{\times}m$ matrices over a field F respectively. Finally, we define the notions of ${\alpha}$-derivation, ${\alpha}$-representation, ${\alpha}$-nilpotency and prove Engel theorem in this case.

• Fibers and Polymers
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• 제6권2호
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• pp.139-145
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• 2005

The paper reports the physical and mechanical properties of hand-woven carpets, which have been put under static force. Two groups of wool fibres, from two parts of Iran, were prepared to spin pile yams for the carpets. Each group of the fibres included both conventional and tanned wool. Then two yam counts, $N_m$ = 4/2 and 6/2, were spun for two different knot densities. After weaving the carpets, they were put under static force and their thickness variations were measured and plotted against time, in logarithm scale. The resiliency of the carpets piles after eliminating the static force, were measured and plotted against time, in logarithm scale, too. The results were compared to each other and analysed with respect to parameters such as the type and quality of the wool fibres as well as knot density of the carpets.

• 호남수학학술지
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• 제42권4호
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• pp.645-651
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• 2020

The distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism. The strong product G ☒ H of two graphs G and H is the graph with vertex set V (G) × V (H) and edge set {{(x1, x2),(y1, y2)}|xiyi ∈ E(Gi) or xi = yi for each 1 ≤ i ≤ 2.}. In this paper we study the distinguishing number and the distinguishing index of strong product of two graphs. We prove that for every k ≥ 2, the k-th strong power of a connected S-thin graph G has distinguishing index equal two.

• 호남수학학술지
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• 제44권3호
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• pp.402-418
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• 2022

Noise is a fundamental factor to increased validity and regularity of spike propagation and neuronal firing in the nervous system. In this paper, we examine the stochastic version of the Izhikevich-FitzHugh neuron dynamical model. This approach is based on techniques presented by Luo and Guo, which provide a general framework for the bifurcation and stability analysis of two dimensional stochastic dynamical system as an Itô averaging diffusion system. By using largest lyapunov exponent, local and global stability of the stochastic system at the equilibrium point are investigated. We focus on the two kinds of stochastic bifurcations: the P-bifurcation and the D-bifurcations. By use of polar coordinate, Taylor expansion and stochastic averaging method, it is shown that there exists choices of diffusion and drift parameters such that these bifurcations occurs. Finally, numerical simulations in various viewpoints, including phase portrait, evolution in time and probability density, are presented to show the effects of the diffusion and drift coefficients that illustrate our theoretical results.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 12th Asian Congress of Fluid Mechanics
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• pp.32.1-32.1
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• 2008