• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.229-243
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• 2019

We use the so-called pseudoinversion of degenerate metrics technique on foliated compact null hypersurface, $M^{n+1}$, in Lorentzian manifold ${\overline{M}}^{n+2}$, to derive an integral formula involving the r-th order mean curvatures of its foliations, ${\mathcal{F}}^n$. We apply our formula to minimal foliations, showing that, under certain geometric conditions, they are isomorphic to n-dimensional spheres. We also use the formula to deduce expressions for total mean curvatures of such foliations.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.773-793
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• 2001

The explicit expressions for the 2n+1 primitive idempotents in R/sub pⁿ/ = F[x]/< x/sup pⁿ/ -1>, where F is the field of prime power order q and the multiplicative order of q modulo pⁿ is ø(pⁿ)/2(n≥1 and p is an odd prime), are obtained. An algorithm for computing the generating polynomials of the minimal QR cyclic codes of length pⁿ, generated by these primitive idempotents, is given and hence some bounds on the minimum distance of some QR codes of prime length over GF(q)(q=2, 3, ...) are obtained.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.359-368
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• 2018

In this paper, we investigate quasi-cyclic codes over the ring $R={\mathbb{F}}_2+v{\mathbb{F}}_2$, where $v^2=v$. We investigate the structure of generators for one-generator quasi-cyclic codes over R and their minimal spanning sets. Moreover, we find the rank and a lower bound on minimum distances of free quasi-cyclic codes over R. Further, we find a relationship between cyclic codes over a different ring and quasi-cyclic codes of index 2 over R.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.419-424
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• 2011

Let D be an integral domain, Spec(D) the set of prime ideals of D, and X a subspace of the Zariski topology on Spec(D). We show that X is compact if and only if given any ideal I of D with $I{\nsubseteq}P$ for all $P{\in}X$, there exists a finitely generated idea $J{\subseteq}I$ such that $J{\nsubseteq}P$ for all $P{\in}X$. We also prove that if D = ${\cap}_{P{\in}X}D_P$ and if * is the star-operation on D induced by X, then X is compact if and only if * $_f$-Max(D) ${\subseteq}$X. As a corollary, we have that t-Max(D) is compact and that ${\mathcal{P}}$(D) = {P${\in}$ Spec(D)$|$P is minimal over (a : b) for some a, b${\in}$D} is compact if and only if t-Max(D) ${\subseteq}\;{\mathcal{P}}$(D).

• Phonetics and Speech Sciences
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• v.2 no.4
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• pp.67-74
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• 2010

The purpose of this study was to explore the cross-linguistic difference in the spectral movement pattern of American English and Korean vowels. Eight American vowels /a/, /e/, /$\varepsilon$/, /i/, /I/, /o/, /u/, and /$\mho$/, and five Korean vowels, /a/, /e/, /i/, /o/ and /u/ in a fricative-vowel environment produced by adult speakers of each language were analyzed. The spectral movement patterns of the first two formant frequency values were measured and analyzed. The results showed that Korean vowels had minimal spectral movement, both in F1 and F2 values, as compared to American English vowels. Moreover, no consistent direction of movement was found in the three corner Korean vowels, while American English vowels showed consistent direction of movement for each vowel of the same phonemic category.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.361-368
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• 2011

In this paper, we construct a cover ($\mathcal{L}(X)$, $c_X$) of a space X such that for any cloz-cover (Y, f) of X, there is a covering map g : $Y{\longrightarrow}\mathcal{L}(X)$ with $c_X{\circ}g=f$. Using this, we show that every Tychonoff space X has a minimal cloz-cover ($E_{cc}(X)$, $z_X$) and that for a strongly zero-dimensional space X, ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$ if and only if $E_{cc}(X)$ is $z^{\sharp}$-embedded in $E_{cc}({\beta}X)$.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.475-484
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• 2023

Let R be a commutative ring with identity. In this paper, we characterize the prime submodules of a free R-module F of finite rank with at most n generators, when R is a GCD domain. Also, we show that if R is a Bézout domain, then every prime submodule with n generators is the row space of a prime matrix. Finally, we study the existence of primary decomposition of a submodule of F over a Bézout domain and characterize the minimal primary decomposition of this submodule.

• Korean Journal of Radiology
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• v.25 no.8
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• pp.742-748
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• 2024

Objective: ¹⁸F-N-(2-(Diethylamino)ethyl)-5-(2-(2-(2-fluoroethoxy)ethoxy)ethoxy) picolinamide (¹⁸F-PFPN) is a novel positron emission tomography (PET) probe designed to specifically targets melanin. This study aimed to evaluate the diagnostic feasibility of ¹⁸F-PFPN in patients with ocular or orbital melanoma. Materials and Methods: Three patients with pathologically confirmed ocular or orbital melanoma (one male, two females; age 41-59 years) were retrospectively reviewed. Each patient underwent comprehensive ¹⁸F-PFPN and ¹⁸F-fluorodeoxyglucose (¹⁸F-FDG) PET scans. The maximum standardized uptake value (SUV_max) of the lesion and the interference caused by background tissue were compared between ¹⁸F-PFPN and ¹⁸F-FDG PET imaging. In addition, the effect of intrinsic pigments in the uvea and retina on the interpretation of the results was examined. The contralateral non-tumorous eye of each patient served as a control. Results: All primary tumors (3/3) were detected using ¹⁸F-PFPN PET, while only two primary tumors were detected using ¹⁸F-FDG PET. Within each lesion, the SUV_max of ¹⁸F-PFPN was 2.6 to 8.3 times higher than that of ¹⁸F-FDG. Regarding the quality of PET imaging, the physiological uptake of ¹⁸F-FDG PET in the brain and periocular tissues limited the imaging of tumors. However, ¹⁸F-PFPN PET minimized this interference. Notably, intrinsic pigments in the uvea and retina did not cause abnormal concentrations of ¹⁸F-PFPN, as no anomalous uptake of ¹⁸F-PFPN was detected in the healthy contralateral eyes. Conclusion: Compared to ¹⁸F-FDG, ¹⁸F-PFPN demonstrated higher detection rates for ocular and orbital melanomas with minimal interference from surrounding tissues. This suggests that ¹⁸F-PFPN could be a promising clinical diagnostic tool for distinguishing malignant melanoma from benign pigmentation in ocular and orbital melanomas.

• The korean journal of orthodontics
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• v.48 no.5
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• pp.304-315
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• 2018

Objective: The purpose of this study was to analyze initial displacement and stress distribution of the maxillofacial complex during dentoskeletal maxillary protraction with various appliance designs placed on the palatal region by using three-dimensional finite element analysis. Methods: Six models of maxillary protraction were developed: conventional facemask (Type A), facemask with dentoskeletal hybrid anchorage (Type B), facemask with a palatal plate (Type C), intraoral traction using a Class III palatal plate (Type D), facemask with a palatal plate combined with rapid maxillary expansion (RME; Type E), and Class III palatal plate intraoral traction with RME (Type F). In Types A, B, C, and D, maxillary protraction alone was performed, whereas in Types E and F, transverse expansion was performed simultaneously with maxillary protraction. Results: Type C displayed the greatest amount of anterior dentoskeletal displacement in the sagittal plane. Types A and B resulted in similar amounts of anterior displacement of all the maxillofacial landmarks. Type D showed little movement, but Type E with expansion and the palatal plate displayed a larger range of movement of the maxillofacial landmarks in all directions. Conclusions: The palatal plate served as an effective skeletal anchor for use with the facemask in maxillary protraction. In contrast, the intraoral use of Class III palatal plates showed minimal skeletal and dental effects in maxillary protraction. In addition, palatal expansion with the protraction force showed minimal effect on the forward movement of the maxillary complex.