• Korean Journal of Mathematics
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• v.27 no.3
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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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• v.3 no.2
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• pp.35-61
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• 1978

To find out the power tiller's travel and tractive characteristics on the general slope land, the tractive p:nver transmitting system was divided into the internal an,~ external power transmission systems. The performance of power tiller's engine which is the initial unit of internal transmission system was tested. In addition, the mathematical model for the tractive force of driving wheel which is the initial unit of external transmission system, was derived by energy and force balance. An analytical solution of performed for tractive forces was determined by use of the model through the digital computer programme. To justify the reliability of the theoretical value, the draft force was measured by the strain gauge system on the general slope land and compared with theoretical values. The results of the analytical and experimental performance of power tiller on the field may be summarized as follows; (1) The mathematical equation of rolIing resistance was derived as $$Rh=\frac {W_z-AC \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\] sin\theta_1}} {tan\phi \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]+\frac{tan\theta_1}{1}$$ and angle of rolling resistance as $$\theta _1 - tan^1\[ \frac {2T(AcrS_0 - T)+\sqrt (T-AcrS_0)^2(2T)^2-4(T^2-W_2^2r^2)\times (T-AcrS_0)^2 W_z^2r^2S_0^2tan^2\phi} {2(T^2-W_z^2r^2)S_0tan\phi}\] $$and the equation of frft force was derived as$$P=(AC+Rtan\phi)\[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]cos\phi_1 \ulcorner \frac {W_z \ulcorner{AC\[ [1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]sin\phi_1 {tan\phi[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\]+ \frac {tan\phi_1} { 1} \ulcorner W_1sin\alpha $$The slip coefficient K in these equations was fitted to approximately 1. 5 on the level lands and 2 on the slope land. (2) The coefficient of rolling resistance Rn was increased with increasing slip percent 5 and did not influenced by the angle of slope land. The angle of rolling resistance Ol was increasing sinkage Z of driving wheel. The value of Ol was found to be within the limits of Ol =2\ulcorner "'16\ulcorner. (3) The vertical weight transfered to power tiller on general slope land can be estim ated by use of th~ derived equation: $$R_pz= \frac {\sum_{i=1}^{4}{W_i}} {l_T} { (l_T-l) cos\alpha cos\beta \ulcorner \bar(h) sin \alpha - W_1 cos\alpha cos\beta$$The vertical transfer weight $R_pz$ was decreased with increasing the angle of slope land. The ratio of weight difference of right and left driving wheel on slop eland,$\lambda= \frac { {W_L_Z} - {W_R_Z}} {W_Z} $, was increased from ,$\lambda$=0 to$\lambda$=0.4 with increasing the angle of side slope land ($\beta = 0^\circ~20^\circ) (4) In case of no draft resistance, the difference between the travelling velocities on the level and the slope land was very small to give 0.5m/sec, in which the travelling velocity on the general slope land was decreased in curvilinear trend as the draft load increased. The decreasing rate of travelling velocity by the increase of side slope angle was less than that by the increase of hill slope angle a, (5) Rate of side slip by the side slope angle was defined as $ S_r=\frac {S_s}{l_s} \times$ 100( %), and the rate of side slip of the low travelling velocity was larger than that of the high travelling velocity. (6) Draft forces of power tiller did not affect by the angular velocity of driving wheel, and maximum draft coefficient occurred at slip percent of S=60% and the maximum draft power efficiency occurred at slip percent of S=30%. The maximum draft coefficient occurred at slip percent of S=60% on the side slope land, and the draft coefficent was nearly constant regardless of the side slope angle on the hill slope land. The maximum draft coefficient occurred at slip perecent of S=65% and it was decreased with increasing hill slope angle $\alpha$. The maximum draft power efficiency occurred at S=30 % on the general slope land. Therefore, it would be reasonable to have the draft operation at slip percent of S=30% on the general slope land. (7) The portions of the power supplied by the engine of the power tiller which were used as the source of draft power were 46.7% on the concrete road, 26.7% on the level land, and 13~20%; on the general slope land ($\alpha = O~ 15^\circ ,\beta = 0 ~ 10^\circ$) , respectively. Therefore, it may be desirable to develope the new mechanism of the external pO'wer transmitting system for the general slope land to improved its performance.l slope land to improved its performance.

• Journal of Biosystems Engineering
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• v.3 no.2
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• pp.34-34
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• 1978

To find out the power tiller's travel and tractive characteristics on the general slope land, the tractive p:nver transmitting system was divided into the internal an,~ external power transmission systems. The performance of power tiller's engine which is the initial unit of internal transmission system was tested. In addition, the mathematical model for the tractive force of driving wheel which is the initial unit of external transmission system, was derived by energy and force balance. An analytical solution of performed for tractive forces was determined by use of the model through the digital computer programme. To justify the reliability of the theoretical value, the draft force was measured by the strain gauge system on the general slope land and compared with theoretical values. The results of the analytical and experimental performance of power tiller on the field may be summarized as follows; (1) The mathematical equation of rolIing resistance was derived as $$Rh=\frac {W_z-AC \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\] sin\theta_1}} {tan\phi \[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]+\frac{tan\theta_1}{1}$$ and angle of rolling resistance as $$\theta _1 - tan^1\[ \frac {2T(AcrS_0 - T)+\sqrt (T-AcrS_0)^2(2T)^2-4(T^2-W_2^2r^2)\times (T-AcrS_0)^2 W_z^2r^2S_0^2tan^2\phi} {2(T^2-W_z^2r^2)S_0tan\phi}\] $$and the equation of frft force was derived as$$P=(AC+Rtan\phi)\[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]cos\phi_1 ? \frac {W_z ?{AC\[ [1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\)\]sin\phi_1 {tan\phi[1+ \frac{sl}{K} \(\varrho ^{-\frac{sl}{K}-1\]+ \frac {tan\phi_1} { 1} ? W_1sin\alpha $$The slip coefficient K in these equations was fitted to approximately 1. 5 on the level lands and 2 on the slope land. (2) The coefficient of rolling resistance Rn was increased with increasing slip percent 5 and did not influenced by the angle of slope land. The angle of rolling resistance Ol was increasing sinkage Z of driving wheel. The value of Ol was found to be within the limits of Ol =2? "'16?. (3) The vertical weight transfered to power tiller on general slope land can be estim ated by use of th~ derived equation: $$R_pz= \frac {\sum_{i=1}^{4}{W_i}} {l_T} { (l_T-l) cos\alpha cos\beta ? \bar(h) sin \alpha - W_1 cos\alpha cos\beta$$The vertical transfer weight $R_pz$ was decreased with increasing the angle of slope land. The ratio of weight difference of right and left driving wheel on slop eland,$\lambda= \frac { {W_L_Z} - {W_R_Z}} {W_Z} $, was increased from ,$\lambda$=0 to$\lambda$=0.4 with increasing the angle of side slope land ($\beta = 0^\circ~20^\circ) (4) In case of no draft resistance, the difference between the travelling velocities on the level and the slope land was very small to give 0.5m/sec, in which the travelling velocity on the general slope land was decreased in curvilinear trend as the draft load increased. The decreasing rate of travelling velocity by the increase of side slope angle was less than that by the increase of hill slope angle a, (5) Rate of side slip by the side slope angle was defined as $ S_r=\frac {S_s}{l_s} \times$ 100( %), and the rate of side slip of the low travelling velocity was larger than that of the high travelling velocity. (6) Draft forces of power tiller did not affect by the angular velocity of driving wheel, and maximum draft coefficient occurred at slip percent of S=60% and the maximum draft power efficiency occurred at slip percent of S=30%. The maximum draft coefficient occurred at slip percent of S=60% on the side slope land, and the draft coefficent was nearly constant regardless of the side slope angle on the hill slope land. The maximum draft coefficient occurred at slip perecent of S=65% and it was decreased with increasing hill slope angle $\alpha$. The maximum draft power efficiency occurred at S=30 % on the general slope land. Therefore, it would be reasonable to have the draft operation at slip percent of S=30% on the general slope land. (7) The portions of the power supplied by the engine of the power tiller which were used as the source of draft power were 46.7% on the concrete road, 26.7% on the level land, and 13~20%; on the general slope land ($\alpha = O~ 15^\circ ,\beta = 0 ~ 10^\circ$) , respectively. Therefore, it may be desirable to develope the new mechanism of the external pO'wer transmitting system for the general slope land to improved its performance.

• Journal of Korean Neurosurgical Society
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• v.64 no.6
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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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• v.60 no.5
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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.

• Asian Journal of Turfgrass Science
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• v.10 no.1
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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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• v.53 no.6
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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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• v.43 no.2
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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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• v.47 no.3
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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 ${\Delta}({\alpha},{\beta}){\leq}1$.

• The Journal of Engineering Geology
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• v.15 no.1
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• pp.9-17
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• 2005

A set of soil samples were picked up from a failed slope formed by rainfall in limestone zone in Jangseong-gun, Jeonnam, Korea, to find out its physical and mechanical characteristics for this study, and variation of safety factor depending on slope inclination was defined by analysing slope stability affected by rainfall. Decomposed limestone soil in the research area is composed of quartz, orthoclase, gibbsite, geothite, etc., with specific gravity of 2.73, and this soil is included in SC by unified soil classification system. Calcium ingredient decreased remarkably during weathering at its mother rock. Coefficient of permeability is 2.56×10/sup -4/ cm/ sec, similar to its value of silty clay. Cohesion decreases remarkably from 3.0 t/ ㎡ to 0.72 t/ ㎡, and Φ value of internal friction angle tends to decrease as it turns to be saturated soil from partial saturated soil in the shear test. To analyze slope stability affected by rainfall, it is reasonable to seek seepage depth with reference to rainfall＊ intensity. In the slope stability analysis, when the seepage depth is the larger, its safety factor is the less, which makes the slope unstable. Comparing with minimum safety factor, 1.5 of cut slope in consideration of the seep-age line, safety factor is found to be satisfactory only when inclination of cut slope of decomposed limestone soil is more than 1：1.2 slope at least considering rainfall. It is also found that decrease of cohesion has great effect on decline of safety factor of slope while partial saturated soil turns to be saturated soil.