• Journal of Korean Neurosurgical Society
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• 제29권9호
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• pp.1262-1266
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• 2000

Objective : Flat back syndrome constitutes a syndrome complex characterized by the loss of normal lumbar lordosis. Various techniques of correction for flat back syndrome have been reported. Posterior extension osteotomy has certain drawbacks. Forceful hyperextension of the spine may result in vascular complications such as rupture of the aorta or the inferior vena cava and stretching of superior mesenteric artery, and pseudoarthrosis. We describe a rationale and technique of transvertebral posterior extension osteotomy to avoid complications of posterior extension osteotomy and to achieve an correction of 30 degrees of flat back syndrome. Method : A 63-year-old woman with degenerative lumbar kyphosis presented with low back pain, thigh pain, knee pain and walking difficulty. Transpedicular fixation from L1 vertebra to S1 vertebra was accomplished for lumbar degenerative kyphosis. After 6 months, the patient presented with flat back syndrome. A second operation was performed with transvertebral posterior extension osteotomy. Result : With short segemental fusion, early bone fusion and correction of 30 degrees were achieved. Conclusion : Transvertebral posterior extension osteotomy provide an 30-60 degrees of correction of flat back syndrome. This technique is considered to be good method for the revision of lumbar degenerative kyphosis.

• 대한수학회논문집
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• 제35권1호
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• pp.137-149
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• 2020

Let γ⁽ⁿ⁾ ≡ {γ_ij} (0 ≤ i+j ≤ 2n, |i-j| ≤ n) be a sequence in the complex number set ℂ and let E (n) be the Embry truncated moment matrices corresponding from γ⁽ⁿ⁾. For an odd number n, it is known that γ⁽ⁿ⁾ has a rank E (n)-atomic representing measure if and only if E(n) ≥ 0 and E(n) admits a flat extension E(n + 1). In this paper we suggest a related problem: if E(n) is positive and nonsingular, does E(n) have a flat extension E(n + 1)? and give a negative answer in the case of E(3). And we obtain some necessary conditions for positive and nonsingular matrix E (3), and also its sufficient conditions.

• East Asian mathematical journal
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• 제36권1호
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• pp.61-71
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• 2020

Up to the present day, the best solution we can get to the truncated moment problem (TMP) is probably the Flat Extension Theorem. It says that if the corresponding moment matrix of a moment sequence admits a rank-preserving positive extension, then the sequence has a representing measure. However, constructing a flat extension for most higher-order moment sequences cannot be executed easily because it requires to allow many parameters. Recently, the author has considered various decompositions of a moment matrix to find a solution to TMP instead of an extension. Using a new approach with the Hadamard product, the author would like to introduce more techniques related to moment matrix decompositions.

• 대한수학회보
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• 제44권4호
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• pp.589-596
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• 2007

In this paper we prove that the extension of pure injective module is pure injective if and only if the cotorsion envelope and the pure injective envelope of any R-module M are isomorphic over M. And we prove that if the product of pure injective envelopes of flat modules is a pure injective envelope and the product of flat covers is a flat cover, then the product of cotorsion envelopes is a cotorsion envelope.

• 대한수학회지
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• 제42권4호
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• pp.723-747
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• 2005

In this paper, we consider the quartic moment problem suggested by Curto-Fialkow[6]. Given complex numbers $\gamma{\equiv}{\gamma}^{(4)}\;:\;{\gamma00},\;{\gamma01},\;{\gamma10},\;{\gamma01},\;{\gamma11},\;{\gamma20},\;{\gamma03},\;{\gamma12},\;{\gamma21},\;{\gamma30},\;{\gamma04},\;{\gamma13},\;{\gamma22},\;{\gamma31},\;{\gamma40}$, with ${\gamma00},\;>0\;and\;{\gamma}_{ji}={\gamma}_{ij}$ we discuss the conditions for the existence of a positive Borel measure ${\mu}$, supported in the complex plane C such that ${\gamma}_{ij}=\int\;\={z}^i\;z^j\;d{\mu}(0{\leq}i+j{\leq}4)$. We obtain sufficient conditions for flat extension of the quartic moment matrix M(2). Moreover, we examine the existence of flat extensions for nonsingular positive quartic moment matrices M(2).

• 대한수학회보
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• 제61권1호
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• pp.1-12
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• 2024

In this paper, we introduce the notion of Gorenstein (m, n)-flat modules as an extension of (m, n)-flat left R-modules over a ring R, where m and n are two fixed positive integers. We demonstrate that the class of all Gorenstein (m, n)-flat modules forms a Kaplansky class and establish that (𝓖𝓕_m,n(R),𝓖𝓒_m,n(R)) constitutes a hereditary perfect cotorsion pair (where 𝓖𝓕_m,n(R) denotes the class of Gorenstein (m, n)-flat modules and 𝓖𝓒_m,n(R) refers to the class of Gorenstein (m, n)-cotorsion modules) over slightly (m, n)-coherent rings.

• Kyungpook Mathematical Journal
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• 제53권1호
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• pp.25-35
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• 2013

In this paper, we introduce and study the concept of "strongly $t$-linked extensions", which is a stronger version of $t$-linked extensions of integral domains. We show that for an extension of Pr$\ddot{u}$fer $v$-multiplication domains, this concept is equivalent to that of "$w$-faithfully flat".

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2002년도 춘계학술대회 논문집
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• pp.209-214
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• 2002

Mechanical micro-engineering is an easy and cheap way to fabricate micro-structures. If the application of the conventional machining method using flat-end mill becomes available for the micro-manufacturing process, it will be advanced as an extension of the conventional machining process. In this study, micro-grooves cutting using flat-end mill(($\phi$8) was performed. The characteristics on flat-end milling was investigated to improve machinability of micro-grooves. The experiments were performed according to variations of spindle revolution, depth of cut, and feed rate. Machinability through various cutting conditions was evaluated by surface geometry, tool wear, and cutting force. The results show that micro V-grooves of width(pitch) 29${\mu}{\textrm}{m}$ were acquired by flat-end milling. The maximum and minimum roughness of the wall of grooves was 438 and 67nm, respectively

• 대한수학회지
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• 제58권6호
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• pp.1311-1325
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• 2021

One says that a ring homomorphism R → S is Ohm-Rush if extension commutes with arbitrary intersection of ideals, or equivalently if for any element f ∈ S, there is a unique smallest ideal of R whose extension to S contains f, called the content of f. For Noetherian local rings, we analyze whether the completion map is Ohm-Rush. We show that the answer is typically 'yes' in dimension one, but 'no' in higher dimension, and in any case it coincides with the content map having good algebraic properties. We then analyze the question of when the Ohm-Rush property globalizes in faithfully flat modules and algebras over a 1-dimensional Noetherian domain, culminating both in a positive result and a counterexample. Finally, we introduce a notion that we show is strictly between the Ohm-Rush property and the weak content algebra property.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 통신소사이어티 추계학술대회논문집
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• pp.297-301
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• 2003

The binary clipping PW/CDMA system is considered. This system can be constructed with effective cost. leading to reduce the influence of the non-linear amplifier because of converting multi-level signals into constant envelope signals. In addition, the clipping method which is to clip out signal amplitude at some level when multi-level signals are converted into constant envelope signals is used. The multi-level signals are clipped at 1 and -1 to limit the extension of bandwidth and to maintain the bandwidth after clipping. In this paper, the performance of the binary clipping PW/CDMA system with the non-linear amplifier analyzed by simulation over AWGN and flat fading channels respectively. The binary clipping PW/CDMA system with the non-linear amplifier is 2.2dB and 0.9dB better than conventional DS/CDMA system over the flat fading channels when the number of users are 9 and 17 respectively.