• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.401-409
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• 2007

This paper is sequel to [3]. In this paper, we discuss some properties of an algebraic meet-continuous lattice and study a complete lattice which can be embedded into an algebraic meet-continuous lattice.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.05a
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• pp.1103-1104
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• 2012

• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.59-61
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• 1978

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.97-106
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• 2006

The lattice originated from logic, not mathematics. Around 1880, Peirce thought that all the lattices were distributives, however $Schr{\"{o}}der$ corrected the error around 1890. In 1993, Birkhoff used the term lattice for the first time that had a different meaning from today's lattice. This paper introduces Peirce, and studies correlation among atomic lattices, atomistic lattices, J-lattices, strong lattices and distributive lattices.

• Nuclear Engineering and Technology
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• v.55 no.3
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• pp.919-926
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• 2023

To analyze the cause of the destruction of thin, carbon-backed lithium fluoride targets during a measurement of the fusion of ⁷Li and ¹⁷O, we estimate theoretically the lifetimes of carbon and LiF films due to sputtering, thermal evaporation, and lattice damage and compare them with the lifetime observed in the experiment. Sputtering yields and thermal evaporation rates in carbon and LiF films are too low to play significant roles in the destruction of the targets. We estimate the lifetime of the target due to lattice damage of the carbon backing and the LiF film using a previously reported model. In the experiment, elastically scattered target and beam ions were detected by surface silicon barrier (SSB) detectors so that the product of the beam flux and the target density could be monitored during the experiment. The areas of the targets exposed to different beam intensities and fluences were degraded and then perforated, forming holes with a diameter around the beam spot size. Overall, the target thickness tends to decrease linearly as a function of the beam fluence. However, the thickness also exhibits an increasing interval after SSB counts per beam ion decreases linearly, extending the target lifetime. The lifetime of thin LiF film as determined by lattice damage is calculated for the first time using a lattice damage model, and the calculated lifetime agrees well with the observed target lifetime during the experiment. In experiments using a thin LiF target to induce nuclear reactions, this study suggests methods to predict the lifetime of the LiF film and arrange the experimental plan for maximum efficiency.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.511-519
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• 2000

If G is a strict generalized orthomodular lattice and H={I｜I=[0, $\chi$, $\chi$$\in$G}, then H is prime ideal of the Janowitz's hull J(G) of G. If f is the janowitz's embedding, then the set of all commutatiors of f(G) equals the set of all commutators of the Janowitz's hull J(G) of G. Let L be an OML. Then L J(G) for a strict GOML G if and only if ther exists a proper nonprincipal prime ideal G in L.

• Journal of the Korean Magnetics Society
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• v.4 no.1
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• pp.52-55
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• 1994

The proton and deuteron spin-lattice relaxation times, $T_{1}(H)$ and $T_{1}(D)$, have been measured in HD between 30 K and 313 K in the pressure of 0.67 - 1.92 atm. The nuclear magnetic resonance frequencies are respectively 358.012 MHz for a proton and 58.958 MHz for a deuteron. From the measurements of $T_{1}(H)$ and $T_{1}(D)$ the ratio of the correlation times ${\tau}_{1}\;and\;{\tau}_{2}$ that are associated with the molecular angular momentum operators was obtained. The nuclear spin-lattice relaxation time at J = 1 state has been observed to have a temperature dependence being proportional to $T^{0.25}$.

• Proceedings of the PSK Conference
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• 2000.10a
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• pp.146.1-146.1
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• 2000

• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.315-318
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• 2000

In this note we use the Poisson Summation Formula to generalize a result of Harris and Park (1994) on lattice distributions induced by uniform (0,1) random variables to those generated by random variables with step functions as their probability functions.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.5
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• pp.34-42
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• 1993

Due to the low loss, broadband and accurate short time delay properties of optical fiber, it has attracted as a delay medium for high speed and broad-band signal processing. In this paper, we consider the coherent optical fiber filter of lattice structure, which uses coherent light sources and consists of directional couplers and optical fiber delay elements.The differences between the optical fiber filter and the ordinary digital filter are 1) the coupling coefficients of directional couplers are restricted between 0 and 1. 2) the optical signal is divided into ${j\sqrt{a}}and\;{j\sqrt{1-a}}$ at the directional coupler. Considering these restrictions, the design formulae and condition of realibility for optical fiber filter of lattice structure which makes the optimal use of optical signal energy are derived.