• Korean Journal of Logic
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• v.8 no.2
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• pp.59-84
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• 2005

Adams' Thesis, or the so-called equation Pr$(A{\rightarrow}C)$ = Pr(C|A) seems to express a correct relationship between the probabilities of conditionals and conditional probabilities. But D. K. Lewis has proved the remarkable fact that probabilities of conditionals are not conditional probabilities. In this paper 1 present a version of Lewis' triviality results and give an explanation why probabilities of conditionals are not conditional probabilities. A conditional probability of C given A has a peculiar properly in that its probability is insulated from not-A facts: the only thing relevant is the proportion of ways in which A is true which are also ways for C to be true. This peculiarity of conditional probability seems to put the great obstacle in the way of attempting to find a proposition such that its probability of being true systematically coincides with conditional probability of something else.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.3
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• pp.32-41
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• 2008

In this paper, we describe the synthesis of robust and non-fragile $H^{\infty}$ state feedback controllers for linear systems with affine parameter uncertain tracking servo system of blu-ray disc drive, as well as static state feedback controller with polytopic uncertainty Similarity any other control system, the objective of the track-following system design for optical disc drives is to construct the system with better performance and robustness against modeling uncertainties and various disturbances. Also, the obtained condition can be rewritten as parameterized linear matrix inequalities(PLMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. We show that the resulting controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system in spite of controller gain variations within a resulted polytopic region.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.3
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• pp.183-190
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• 2002

This paper describes the synthesis of robust and non-fragile H$\infty$ state feedback controllers for linear varying systems with affine parameter uncertainties, and static state feedback controller with structured uncertainty. The sufficient condition of controller existence, the design method of robust and non-fragile H$\infty$ static state feedback controller, and the set of controllers which satisfies non-fragility are presented. The obtained condition can be rewritten as parameterized Linear Matrix Inequalities(PLMls), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. However, in contrast to LMIs, PLMIs feasibility problems involve infinitely many LMIs hence are inherently difficult to solve numerically. Therefore PLMls are transformed into standard LMI problems using relaxation techniques relying on separated convexity concepts. We show that the resulting controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system in spite of controller gain variations within a degree.

• Explosives and Blasting
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• v.21 no.3
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• pp.23-35
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• 2003

An analytical diffusion model for flood routing with backwater effects and lateral flows is developed. The basic diffusion equation is linearized about an average depth of (H + h), and is solved using the boundary conditons which take into account the effects of backwater and lateral flows. Scouring phenomenon around pier which affects on the support function of pier and the stabilization if river bed is a complex problem depending on flow properties and river bed state as well as pier geometry. therefore, there is no uniting theory at present which would enable the designer to estimate, with confidence, the depth of scour at bridge piers. The various methods used in erosion control are collectively called upstream engineering, HEC-RAS Model, underwater blasting. They consist of reforestation, check-dam construction, planting of burned-over areas, contour plowing and regulation of crop and grazing practices. Also included are measures for proper treatment of high embankments and cuts and stabilization of streambanks by planting or by revetment construction. One phase of reforestation that may be applied near a reservoir is planting of vegetation screens. Such screens, planted on the flats adjacent to the normal stream channel at the head of a reservoir, reduce the velocity of silt-laden storm inflows that inundate these areas. This stilling action causes extensive deposition to occur before the silt reaches the main cavity of the reservoir.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.1-10
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• 2008

In this paper, we investigate the part dealing with algebra in Hong Gil Ju's GiHaSinSul to analyze his algebraic structure. The book consists of three parts. In the first part SangChuEokSan, he just renames Die jie hu zheng(疊借互徵) in Shu li jing yun to SangChuEokSan and adds a few examples. In the second part GaeBangMongGu, he obtains the following identities: $$n^2=n(n-1)+n=2S_{n-1}^1+S_n^0;\;n^3=n(n-1)(n+1)+n=6S_{n-1}^2+S_n^0$$; $$n^4=(n-1)n^2(n+1)+n(n-1)+n=12T_{n-1}^2+2S_{n-1}^1+S_n^0$$; $$n^5=2\sum_{k=1}^{n-1}5S_k^1(1+S_k^1)+S_n^0$$ where $S_n^0=n,\;S_n^{m+1}={\sum}_{k=1}^nS_k^m,\;T_n^1={\sum}_{k=1}^nk^2,\;and\;T_n^2={\sum}_{k=1}^nT_k^1$, and then applies these identities to find the nth roots $(2{\leq}n{\leq}5)$. Finally in JabSwoeSuCho, he introduces the quotient ring Z/(9) of the ring Z of integers to solve a system of congruence equations and also establishes a geometric procedure to obtain golden sections from a given one.

• Journal of the Mineralogical Society of Korea
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• v.20 no.3
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• pp.193-201
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• 2007

We used $^6Li$ and $^7Li$ MAS NMR to investigate the fate and local environments of Li in the interlayer of clay minerals such as hectorite, Woming-montmorillonite, beidellite, and lepidollite at room and high ($250^{\circ}C$) temperature. Although $^6Li$ NMR spectra show narrower peaks than those of $^7Li$ NMR, S/N ratio is low and there are no obvious differences in chemical shifts suggesting that it is difficult to apply $^6Li$ NMR to have information on the local environments of Li in the clay interlayers. $^7Li$ NMR spectra, however, show changes in the peak width and quadrupole patterns providing information on the local environments of Li in the interlayer even though changes in the chemical shift are not observed. In montmorillonite, two different local environments of Li are observed; one has a narrow peak with typical quadrupole patterns whereas another has a broad peak without those of the patterns. Changes in the peak width is also observed from broad to narrow in the $^7Li$ NMR spectra for beidellite but not for hectorite at high temperature. Our results suggest that the peak width change in the broad peak is attributed to the coordination changes in the water molecules around Li which is tightly bonded on the basal oxygen of Si tetrahedra as inner-sphere complexes. The narrow peak in montmorillnoite can be assigned to the Li bended as outer-sphere complexes.