• Korean Journal of Mathematics
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• 제27권3호
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• pp.723-734
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• 2019

We study the negative trinomial table T' of $(x^2+x+1)^{-n}$ and its t/u-slope diagonals for any t, u > 0. We investigate recurrence formula of the t/u-slope diagonal sums of T' and find interrelationships with t/u-slope diagonal sums of the trinomial table T.

• Journal of Biosystems Engineering
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• 제3권2호
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• pp.35-61
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• 1978

동력경운깅가 일반 경사지에서 견인주행하는 경우 견인주행성능과 주행특성을 구명하기 위하여 토양의 종류 및 상태는 일정하게 하고 지면의 기하학적 조건과 견인주행속도 및 견인하중을 변수로 하여 외부동력전달계의 시점인 좌우차륜과 토양간에 발생하는 차륜구동력 및 굴름정항과 Engine에서 구동륜까지 내부전달계를 통하여 전달된 동력의 이론치와 실험치와의 부합여부를 검정하고 부가적으로 동력경운기가 경사지기계화의 동력기로써의 가능성여부와 문제점을 찾으려한다.

• Journal of Biosystems Engineering
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• 제3권2호
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• pp.34-34
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• 1978

동력경운깅가 일반 경사지에서 견인주행하는 경우 견인주행성능과 주행특성을 구명하기 위하여 토양의 종류 및 상태는 일정하게 하고 지면의 기하학적 조건과 견인주행속도 및 견인하중을 변수로 하여 외부동력전달계의 시점인 좌우차륜과 토양간에 발생하는 차륜구동력 및 굴름정항과 Engine에서 구동륜까지 내부전달계를 통하여 전달된 동력의 이론치와 실험치와의 부합여부를 검정하고 부가적으로 동력경운기가 경사지기계화의 동력기로써의 가능성여부와 문제점을 찾으려한다.

• Journal of Korean Neurosurgical Society
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• 제64권6호
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• pp.913-921
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• 2021

Objective : Accurate measurement of T1 slope (a component of T1s minus cervical lordosis [CL]) is often constrained by anatomical limitations. In this situation, efforts should be made to find the exact meaning of T1s-CL and whether there are any alternatives to it. Methods : We enrolled 117 patients who received two-level anterior cervical discectomy and fusion (ACDF). Occipital slope, C2 slope (C2s), C7 slope (C7s), T1, O-C2 angle (O-C2A), C2-7 angle (C2-7A), O-C7 angle (O-C7A), T1s-CL, C7-T1 angle (C7-T1A), and C2-7 sagittal vertical axis were measured. We determined 16° (T1s-CL) as the reference point for dividing subjects into the mismatch group and the balance group, and a comparative analysis was performed. Results : The mean value of C7-T1A was constantly maintained within 2.6° peri-operatively. In addition, C2s and T1s-CL showed the same absolute change (Δ|0.8|°). The mean values of T1s-CL of the mismatch and balance groups were 23.0° and 7.6°, respectively. The five factors with the largest differences between the two groups were as follows : C2s (Δ13.3°), T1s-CL (Δ15.4°), O-C2A (Δ8.7°), C2-7A (Δ14.7°), and segmental angle (Δ7.9°) before surgery. Only four factors showed statistically significant change between the two groups after ACDF : T1s-CL (Δ4.0° vs. Δ0.2°), C2s (Δ3.2° vs. Δ0.7°), O-C2A (Δ2.6° vs. Δ1.3°), C2-7A (Δ6.3° vs. Δ1.3°). A very strong correlation between T1s-CL and C2s was also found (r=|0.88-0.96|). Conclusion : C2s itself may be the essential key to represent T1s-CL. The amounts and directions of change of these two factors (T1s-CL and C2s) were also almost identical. The above phenomenon was re-confirmed once again through the correlation analysis.

• Journal of Korean Neurosurgical Society
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• 제60권5호
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• pp.577-583
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• 2017

Objective : Laminoplasty is an effective surgical method for treating cervical degenerative disease. However, postoperative complications such as kyphosis, restriction of neck motion, and instability are often reported. Despite sufficient preoperative lordosis, this procedure often aggravates the lordotic curve of the cervical spine and straightens cervical alignment. Hence, it is important to examine preoperative risk factors associated with postoperative kyphotic alignment changes. Our study aimed to investigate preoperative radiologic parameters associated with kyphotic deformity post laminoplasty. Methods : We retrospectively reviewed the medical records of 49 patients who underwent open door laminoplasty for cervical spondylotic myelopathy (CSM) or ossification of the posterior longitudinal ligament (OPLL) at Pusan National University Yangsan Hospital between January 2011 and December 2015. Inclusion criteria were as follows : 1) preoperative diagnosis of OPLL or CSM, 2) no previous history of cervical spinal surgery, cervical trauma, tumor, or infection, 3) minimum of one-year follow-up post laminoplasty with proper radiologic examinations performed in outpatient clinics, and 4) cases showing C7 and T1 vertebral body in the preoperative cervical sagittal plane. The radiologic parameters examined included C2-C7 Cobb angles, T1 slope, C2-C7 sagittal vertical axis (SVA), range of motion (ROM) from C2-C7, segmental instability, and T2 signal change observed on magnetic resonance imaging (MRI). Clinical factors examined included preoperative modified Japanese Orthopedic Association scores, disease classification, duration of symptoms, and the range of operation levels. Results : Mean preoperative sagittal alignment was $13.01^{\circ}$ lordotic; $6.94^{\circ}$ lordotic postoperatively. Percentage of postoperative kyphosis was 80%. Patients were subdivided into two groups according to postoperative Cobb angle change; a control group (n=22) and kyphotic group (n=27). The kyphotic group consisted of patients with more than $5^{\circ}$ kyphotic angle change postoperatively. There were no differences in age, sex, C2-C7 Cobb angle, T1 slope, C2-C7 SVA, ROM from C2-C7, segmental instability, or T2 signal change. Multiple regression analysis revealed T1 slope had a strong relationship with postoperative cervical kyphosis. Likewise, correlation analysis revealed there was a statistical significance between T1 slope and postoperative Cobb angle change (p=0.035), and that there was a statistically significant relationship between T1 slope and C2-C7 SVA (p=0.001). Patients with higher preoperative T1 slope demonstrated loss of lordotic curvature postoperatively. Conclusion : Laminoplasty has a high probability of aggravating sagittal balance of the cervical spine. T1 slope is a good predictor of postoperative kyphotic changes of the cervical spine. Similarly, T1 slope is strongly correlated with C2-C7 SVA.

• 아시안잔디학회지
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• 제10권1호
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• pp.41-47
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• 1996

The theory of slope erosion is developed along similar lines to the theory of heat flow in solid added to the correcting factor. if slope erosion in the forest and grassland proceeds according to the hypothesis, it is $\delta$y $\delta^2$y = k $\delta^2$y $\delta$$X^2$+f(s b. t) where 5 is internal properties of slope soil and b is biota on slope. When the variables of the equation of slope erosion are x = -λ the initial elevation=-f(λ), x=λ, x==a, the steady value of the initial elevation=y, and dy dx x=0> =O(t>o), respectively, the houndary condition due to the solution of the equation of slope erosion is y= 2 √$\pi$kt [∫a o λe $(X-λ)^2$4kt dλ- ∫ao- $(x+λ)^2$4kt dλ] + ∫∫∫ f (s.b. t)dtdbds

• Journal of Korean Neurosurgical Society
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• 제53권6호
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• pp.356-369
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• 2013

Objective : We performed a retrospective analysis of medical records and radiographic images of patients who never underwent spinal treatment including diagnosis. The objective of this study is to explain the biomechanical and physiologic characteristics of cervical alignment related to thoracic inlet angle including T1 slope changes in each individual. Methods : We reviewed the cervical CT radiographs of 80 patients who visited ENT outpatient clinic without any symptom, diagnosis and treatment of cervical spine from January 2011 to September 2012. All targeted people were randomized without any prejudice. We assessed the data-T1 slope, Cobb's angle C2-7, neck tilt, sagittal vertical axis (SVA) C2-7 and thoracic inlet angle by the CT radiographs. Results : The relationships between each value were analyzed and we concluded that Cobb's angle C2-7 gets higher as the T1 slope gets higher, while the SVA C2-7 value decreases. Conclusion : We propose that the T1 slope is background information in deciding how much angle can be made in the cervical spinal angle of surgical lordotic curvature, especially severe cervical deformity.

• Journal of Ecology and Environment
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• 제43권2호
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• pp.161-182
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• 2019

Quantifying the amount of carbon pools in forest ecosystems enables to understand about various carbon pools in the forest ecosystem. Therefore, this study was conducted in the Chilimo dry afromontane forest to estimate the amount of carbon stored. The natural forest was stratified into three forest patches based on species composition, diversity, and structure. A total of 50 permanent sample plots of 20 m × 20 m (400 ㎡ ) each were established, laid out on transects of altitudinal gradients with a distance of 100 m between plots. The plots were measured twice in 2012 and 2017. Tree, deadwood, mineral soil, forest floor, and stump data were collected in the main plots, while shrubs, saplings, herbaceous plants, and seedling data were sampled inside subplots. Soil organic carbon (SOC %) was analyzed following Walkely, while Black's procedure and bulk density were estimated following the procedure of Blake (Methods of soil analysis, 1965). Aboveground biomass was calculated using the equation of Chave et al. (Glob Chang Biol_20:3177-3190, 2014). Data analysis was made using RStudio software. To analyze equality of means, we used ANOVA for multiple comparisons among elevation classes at α = 0.05. The aboveground carbon of the natural forest ranged from 148.30 ± 115.02 for high altitude to 100.14 ± 39.93 for middle altitude, was highest at 151.35 ± 108.98 t C ha^-1 for gentle slope, and was lowest at 88.01 ± 49.72 t C ha^-1 for middle slope. The mean stump carbon density 2.33 ± 1.64 t C ha^-1 was the highest for the middle slope, and 1.68 ± 1.21 t C ha^-1 was the lowest for the steep slope range. The highest 1.44 ± 2.21 t C ha^-1 deadwood carbon density was found under the middle slope range, and the lowest 0.21 ± 0.20 t C ha^-1 was found under the lowest slope range. The SOCD up to 1 m depth was highest at 295.96 ± 80.45 t C ha^-1 under the middle altitudinal gradient; however, it was lowest at 206.40 ± 65.59 t C ha^-1 under the lower altitudinal gradient. The mean ecosystem carbon stock density of the sampled plots in natural forests ranged from 221.89 to 819.44 t C ha^-1. There was a temporal variation in carbon pools along environmental and social factors. The highest carbon pool was contributed by SOC. We recommend forest carbon-related awareness creation for local people, and promotion of the local knowledge can be regarded as a possible option for sustainable forest management.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.335-340
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• 2007

Let M be a hyperbolic 3-manifold such that ${\partial}M$ has at least two boundary tori ${\partial}_oM$ and ${\partial}_1M$. Suppose that M contains an essential orientable surface P of genus $g$ with one outer boundary component ${\partial}_oP$, lying in ${\partial}_oM$ and having slope ${\lambda}$ in ${\partial}_oM$, and $p$ inner boundary components ${\partial}_iP$, $i=1$, ${\cdots}$, $p$, each having slope ${\alpha}$ in ${\partial}_1M$. Let ${\beta}$ be a slope in ${\partial}_1M$ and suppose that $M({\beta})$ is toroidal. Let $\hat{T}$ be a minimal essential torus in $M({\beta})$, which means that $\hat{T}$ is pierced a minimal number of times by the core of the ${\beta}$-Dehn filling, among all essential tori in $M({\beta})$. Let $T=\hat{T}{\cap}M$ and denote by $t$ the number of components of ${\partial}T$. In this paper we prove: (i) if $t{\geq}3$, then ${\Delta}({\alpha},{\beta}){\leq}6+\frac{10g-5}{p}$, (ii) If $t=2$, then ${\Delta}({\alpha},{\beta}){\leq}13+\frac{24g-12}{p}$, (iii) If $t=1$, then ${\Delta}({\alpha},{\beta}){\leq}1$.

• 지질공학
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• 제15권1호
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• pp.9-17
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• 2005

본 연구는 전라남도 장성군 일대의 석회암지대에서 강우로 인해 파괴된 절개사면을 대상으로 시료를 채취하여 물리적ㆍ역학적 특성을 파악하고 강우로 인한 사면 안정 해석을 통해 사면구배의 변화에 따른 안전율의 변화를 규명하였다. 연구지역 석회암 풍화토는 석영, 정장석, 깁사이트, 침철석 등으로 구성되어 있고 비중은 2.73, 통일분류상 SC에 해당되며 모암에서 풍화가 진행되면서 칼슘성분이 현저하게 감소하였다. 투수계 수는 2.56×10/sup -4/ cm/ sec 로서 실트 성 점토의 투수계수와 비슷한 값을 보였고 전단시험결과 불포화토에서 포화토로 변할수록 점착력은 3.0 t/㎡에서 0.72 t/㎡로 현저하게 줄어들며 내부마찰각 Φ 값도 감소하는 경향을 보였다. 강우로 인한 사면안정 해석시 강우강도를 고려한 침투심도를 구하는 것이 합리적이며 사면안정해석결과 침투심도가 클수록 사면의 안전율은 낮아져서 불안정하게 되고 침윤선을 고려한 절토사면의 최소안전율 1.5와 비교 시 강우를 고려한 석회암 풍화토의 절토사면 구배는 1 ： 1.2이상 되어야 안전율을 만족하는 것으로 나타났다. 또한, 불포화토에서 포화토로 변할수록 점착력의 감소는 사면의 안전율감소에 많은 영향을 미침을 알 수 있었다.