• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.465-472
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• 2008

For a nonnegative real matrix A of rank 1, A can be factored as $ab^t$ for some vectors a and b. The perimeter of A is the number of nonzero entries in both a and b. If B is a matrix of rank k, then B is the sum of k matrices of rank 1. The perimeter of B is the minimum of the sums of perimeters of k matrices of rank 1, where the minimum is taken over all possible rank-1 decompositions of B. In this paper, we obtain characterizations of the linear operators which preserve perimeters 2 and k for some $k\geq4$. That is, a linear operator T preserves perimeters 2 and $k(\geq4)$ if and only if it has the form T(A) = UAV or T(A) = $UA^tV$ with some invertible matrices U and V.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.1-20
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• 2020

A simple but elegant result of Rival states that every sublattice L of a finite distributive lattice 𝒫 can be constructed from 𝒫 by removing a particular family 𝒥_L of its irreducible intervals. Applying this in the case that 𝒫 is a product of a finite set 𝒞 of chains, we get a one-to-one correspondence L ↦ 𝒟_𝒫(L) between the sublattices of 𝒫 and the preorders spanned by a canonical sublattice 𝒞^⋄ of 𝒫. We then show that L is a tight sublattice of the product of chains 𝒫 if and only if 𝒟_𝒫(L) is asymmetric. This yields a one-to-one correspondence between the tight sublattices of 𝒫 and the posets spanned by its poset J(𝒫) of non-zero join-irreducible elements. With this we recover and extend, among other classical results, the correspondence derived from results of Birkhoff and Dilworth, between the tight embeddings of a finite distributive lattice L into products of chains, and the chain decompositions of its poset J(L) of non-zero join-irreducible elements.

• Bulletin of the Korean Chemical Society
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• v.6 no.5
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• pp.284-287
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• 1985

Cyanoisopropyl radical derived from azobisisobutyronitrile (AIBN) by either thermolysis or photolysis reacts with oxygen to give cyanoisopropylperoxy radical which then was converted to acetone and cyano radical and/or acetyl cyanide and methyl radical. Of these products, acetone formed was quantitatively determined by the addition of thianthrene cation radical perchlorate to the reaction mixture. The results showed that 55.7 mmol, 16.9 mmol, and 16.0 mmol of acetone were formed for 7 hours from 1 mol of AIBN at $82{\pm}1^{\circ}C$ in acetonitrile, carbon tetrachloride, and benzene, respectively. However, 22.2 mmol of acetone was formed from photolysis of 1 mmol of AIBN in acetonitrile. The value decreased to 13.2 mmol by bubbling argon into the solvent prior to photolysis.

• Communications for Statistical Applications and Methods
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• v.24 no.1
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• pp.81-96
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• 2017

Cumulative logit random effects models are typically used to analyze longitudinal ordinal data. The random effects covariance matrix is used in the models to demonstrate both subject-specific and time variations. The covariance matrix may also be homogeneous; however, the structure of the covariance matrix is assumed to be homoscedastic and restricted because the matrix is high-dimensional and should be positive definite. To satisfy these restrictions two Cholesky decomposition methods were proposed in linear (mixed) models for the random effects precision matrix and the random effects covariance matrix, respectively: modified Cholesky and moving average Cholesky decompositions. In this paper, we use these two methods to model the random effects precision matrix and the random effects covariance matrix in cumulative logit random effects models for longitudinal ordinal data. The methods are illustrated by a lung cancer data set.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-69
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• 2023

Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝⁿ → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

• Bulletin of the Korean Chemical Society
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• v.10 no.3
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• pp.262-269
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• 1989

The gas phase thermal decomposition of 1-bromo-3-chloropropane in the presence of radical inhibitor was studied by using the conventional static system. The mechanism of unimolecular elimination channel is shown below. [...] In this scheme, the total molecular dissociation rate constant, ($k_1\;+\;k_2$), for the decomposition of $BrCH_2CH_2CH_2Cl$ was determined by pyrolyzing the $BrCH_2CH_2CH_2Cl$ in the temperature range of $380-420^{\circ}C$ and in the pressure range of 10∼100 torr. To obtain $k_3\;and\;k_4,\;and\;to\;obtain\;k_1\;and\;k_2$ independently, the thermal decompositions of allyl chloride and allyl bromide were also studied. The Arrhenius parameters for each step are as follows; $log\;A_{\infty}\;=\;14.20(sec^{-1}),\;E_a$ = 56.10(kcal/mol) for reaction path 1; $log\;A_{\infty}\;=\;12.54(sec^{-1}),\;E_a$ = 49.75(kcal/mol) for reaction path 2; $log\;A_{\infty}\;=\;13.41(sec^{-1}),\;E_a$ = 50.04(kcal/mol) for reaction path 3; $log\;A_{\infty}\;=\;12.43(sec^{-1}),\;E_a$ = 52.78(kcal/mol) for reaction path 4; Finally, the experimentally observed pressure dependence of the rate constants in each step is compared with the theoretically predicted values that are obtained by the RRKM calculations.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.945-955
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• 2004

In this paper, we establish a number system in $R^n$ which arises from a Haar wavelet basis in connection with decompositions of certain Cuntz algebra representations on $L^2$( $R^n$). Number systems in $R^n$ are also of independent interest [9]. We study radix-representations of $\chi$ $\in$ $R^n$: $\chi$:$\alpha$$_{ι}$ $\alpha$$_{ι-1}$…$\alpha$$_1$$\alpha$$_{0}$ ㆍ$\alpha$$_{-1}$ $\alpha$$_{-2}$ … as $\chi$= $M^{ι}$$\alpha$$_{ι}$ $\alpha$＋…M$\alpha$$_1$＋$\alpha$$_{0}$ ＋ $M^{-1}$ $\alpha$$_{-1}$ ＋ $M^{-2}$ $\alpha$$_{-2}$ ＋… where each $\alpha$$_{k}$ $\in$ D, and D is some specified digit set. Our analysis uses iteration techniques of a number-theoretic flavor. The view-point is a dual one which we term fractals in the large vs. fractals in the small,illustrating the number theory of integral lattice points vs. fractions.s vs. fractions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.4
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• pp.387-397
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• 1992

The spatial domain design of 2-dimensional separable denominator digital filters(SDDF) based on the reduced dimensional decomposition can be realized when the given 2-D impulse response specifications are decomposed into a pair of 1-D specifications via singular value decompositions(SVD). Because of use of the balaned approximation and equivalent transform as 1-D design algorithm, 2-D design algorithm retains the advantage that is numerically stable and can minimize quantization errors. In this paper in order to analyze and reduce these errors, minimum comfficient quantization realization is directly derived from impulse response specification. And using the equivalent trans form relation between mininum coefficient quantization error and minimum roundoff error realizations, we optimally realize a SDDF. This algorithm is analyzed by the simulation, which shows that it is superior to direct or balanced realization in quantization errors.

• Journal of the Korean Chemical Society
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• v.54 no.1
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• pp.43-48
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• 2010

Polyamide derived from azo compound of o-amino phenol coupled with acetyl acetone, maleic anhydride acid and p-phenylene diamine were prepared. The prepared polyamide (PA) was refluxed with metal salts of transition metal ions include, $Co^{+2},\;Cr^{+2},\;Ni^{+2},\;Cu^{+2},\;Zn^{+2},\;Cd^{+2}$ and $Fe^{+3}$ in dimethyl formamide (DMF) in different molar ratios. These complexes were characterized and identified by elemental and thermal analysis, IR, 1H NMR spectra. The data showed that PA ligand coordinates with metal ions in abidentate manner through donating N=N and O-H groups. The metal ions are surrounded by coordinated water molecules and anions to establish the geometrical structure of the complexes. The thermal analysis degradation at different temperatures explained the weight loss of hydrated water and the decompositions of complexes until a constant weight loss of metal oxides is obtained.

• Korean Journal of Computational Design and Engineering
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• v.9 no.1
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• pp.44-50
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• 2004

Mechanical parts are often grouped into part families based on the similarity of their shapes, to support efficient manufacturing process planning and design modification. The 2-part sequence papers present similarity assessment techniques to support part family classification for machined parts. These exploit the multiple feature decompositions obtained by the feature recognition method using convex decomposition. Convex decomposition provides a hierarchical volumetric representation of a part, organized in an outside-in hierarchy. It provides local accessibility directions, which supports abstract and qualitative similarity assessment. It is converted to a Form Feature Decomposition (FFD), which represents a part using form features intrinsic to the shape of the part. This supports abstract and qualitative similarity assessment using positive feature volumes. FFD is converted to Negative Feature Decomposition (NFD), which represents a part as a base component and negative machining features. This supports a detailed, quantitative similarity assessment technique that measures the similarity between machined parts and associated machining processes implied by two parts' NFDs. Features of the NFD are organized into branch groups to capture the NFD hierarchy and feature interrelations. Branch groups of two parts' NFDs are matched to obtain pairs, and then features within each pair of branch groups are compared, exploiting feature type, size, machining direction, and other information relevant to machining processes. This paper, the first one of the two companion papers, describes the similarity assessment methods using convex decomposition and FFD.