• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.23-34
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• 2019

In this paper, we first define generalizations of Pell and Pell-Lucas sequences by the recurrence relations $$p_n=2ap_{n-1}+(b-a^2)p_{n-2}\;and\;q_n=2aq_{n-1}+(b-a^2)q_{n-2}$$ with initial conditions $p_0=0$, $p_1=1$, and $p_0=2$, $p_1=2a$, respectively. We give generating functions and Binet's formulas for these sequences. Also, we obtain some identities of these sequences.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.35-56
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• 2015

In this paper, we classify all nonconstant smooth CR maps from a sphere $S_{n,1}{\subset}\mathbb{C}^n$ with n > 3 to the Shilov boundary $S_{p,q}{\subset}\mathbb{C}^{p{\times}q}$ of a bounded symmetric domain of Cartan type I under the condition that p - q < 3n - 4. We show that they are either linear maps up to automorphisms of $S_{n,1}$ and $S_{p,q}$ or D'Angelo maps. This is the first classification of CR maps into the Shilov boundary of bounded symmetric domains other than sphere that includes nonlinear maps.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권2호
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• pp.127-137
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• 2007

The classical Bohr's inequality states that $|z+w|^2{\leq}p|z|^2+q|w|^2$ for all $z,\;w{\in}\mathbb{C}$ and all p, q>1 with $\frac{1}{p}+\frac{1}{q}=1$. In this paper, Bohr's inequality is generalized to the setting of n-inner product spaces for all positive conjugate exponents $p,\;q{\in}\mathbb{R}$. In. In particular, the parallelogram law is recovered and an interesting operator inequality is obtained.

• 대한수학회지
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• 제59권3호
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• pp.621-634
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• 2022

The scaled inverse of a nonzero element a(x) ∈ ℤ[x]/f(x), where f(x) is an irreducible polynomial over ℤ, is the element b(x) ∈ ℤ[x]/f(x) such that a(x)b(x) = c (mod f(x)) for the smallest possible positive integer scale c. In this paper, we investigate the scaled inverse of (xⁱ - x^j) modulo cyclotomic polynomial of the form Φ_p^s (x) or Φ_p^sq^t (x), where p, q are primes with p < q and s, t are positive integers. Our main results are that the coefficient size of the scaled inverse of (xⁱ - x^j) is bounded by p - 1 with the scale p modulo Φ_p^s (x), and is bounded by q - 1 with the scale not greater than q modulo Φ_p^sq^t (x). Previously, the analogous result on cyclotomic polynomials of the form Φ_2ⁿ (x) gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of {x^k}_k∈ℤ in ℤ[x]/Φ_pq(x) which might be of independent interest.

• 한국조경학회지
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• 제21권2호
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• pp.50-67
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• 1993

This study analyzed the distribution and structure of the vegetation landscape in Naejangsan National Park. The plant distribution was investigated using a field survey. There were 72 sites sampled using the clumpled sampling method. The data derived from the investigation was analyzed using the quantitative analysis of Bray-Curtis method. The analysis was performed by the classification of TWINSPAN. The ordination of DCA and RA was used for the species composition and successional trends. The results are as follows; 1. Quercus. serrata-Q. variabilis community as 21.76(16.49$\textrm{km}^2$), was the largest community in the actual vegetation of the Naejangsan National Park. The degree of green naturality index 8 area covered 64.8% of the study area and the index 6 area did 16%. 2. Classified by the ordination of DCA and environmental variables, such as the plant community was divided into seven groups according to the altitude and forming groups; Chamaecy Paris. pisifera-P.densiflora community, P.densiflora community, Q.variailis community, T.nuciofera-A.palmatum community. 3. Ther species diversity and evenness indices of C.pisifera-P.densiflora community, P.densiflora community appeared low but C.laxiflora communitywhich was the most stable community in the study area. 4. The similarity indices between Q.variabilis community and Q.serrata-Q.variabilis community were calculated 58.84%, but those between other communities were comparatively low level. 5. The successional trends of DBH class seem to be from C. pisifera-P.densiflora community, P.densiflora community to Quercus species community and from Q.variabilis community, Q.serrata-Q.variabilis community to Carpinus species community. 6. Results suggested that the successional trends in Naejangsan National Park; P.densiflora community\longrightarrowQ.variablilis community, Q.serrata-Q.variabilis community\longrightarrowC.laxiflora community in sequence.

• 한국환경생태학회지
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• 제26권1호
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• pp.74-81
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• 2012

상록활엽수인 가시나무와 낙엽활엽수인 상수리나무 낙엽의 분해율 및 분해과정에 따른 영양염류의 함량 변화를 파악하기 위해 2008년 12월 공주의 상수리나무군락에 낙엽주머니를 설치하고 2009년 3월부터 2010년 12월까지 3개월 간격으로 낙엽주머니를 수거하여 분해율, 분해상수(k), 그리고 분해과정에 따른 C/N비, C/P비의 변화와 영양염류의 동태를 조사하였다. 24개월경과 후 상수리나무 낙엽과 가시나무 낙엽의 잔존률은 각각 $46.3{\pm}5.4%$와 $37.8{\pm}2.5%$로 가시나무 낙엽의 분해가 상수리나무 낙엽의 분해보다 빠르게 진행되는 것으로 나타났다. 24개월경과 후 상수리나무 낙엽과 가시나무 낙엽의 분해상수(k)는 각각 0.38과 0.49로 가시나무 낙엽의 분해상수가 높게 나타났다. 상수리나무 낙엽의 분해과정에 따른 C/N. C/P 비율은 초기에 각각 46.8, 270.9 이었으나 24개월경과 후에는 각각 22.5와 104.2로 점차 감소하였으며, 가시나무 낙엽의 경우 초기 C/N, C/P 비율은 각각 22.4와 41.7로 나타났고, 24개월경과 후에는 각각 16.7와 89.9로 나타났다. 낙엽의 초기 N, P, K, Ca, Mg 함량은 상수리나무 낙엽에서 각각 8.31, 0.44, 4.18, 9.38, 1.37 mg/g, 가시나무 낙엽에서 각각 19.88, 2.73, 7.06, 8.24, 2.61 mg/g으로 가시나무 낙엽의 질소와 인의 함량이 상수리나무 낙엽에 비해 현저히 높았다. 24개월경과 후 N, P, K, Ca, Mg의 잔존률은 상수리나무 낙엽에서 각각 100.91, 114.75, 32.99, 50.63, 15.51% 이었고, 가시나무 낙엽에서 각각 43.22, 11.35, 12.98, 82.22, 44.23% 로 조사기간 동안에 상수리나무 낙엽에서는 질소와 인의 부동화가, 가시나무 낙엽에서는 질소와 인의 무기화가 진행되었다.

• The Journal of Korean Physical Therapy
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• 제14권4호
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• pp.342-366
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• 2002

An excessive Q-angle has been implicated in the development of knee injuries by altering the lower-extremity locomotion kinematics. The purpose of this study was measured the Q-angle and the CTA when the foot moves pronation and supination of the foot in the standing status. The participants of this examination were 60 adult(30 men and 30 women) who had no orthopaedic and neurological impairment, aged between 20 and 40years. The foot tilt(FT 1)is made of acrylic plate and the slope of the suface is altered as $0^{\circ}$, pronation ($10^{\circ},20^{\circ},30^{\circ}$)and supination($10^{\circ},20^{\circ},30^{\circ}$). The results were as follows : 1. The result about the left/right Q-angle and the left/right CAT There was no statistical significant difference between the left and the right side of the Q-angle with different position of the foot(P > 0.05). While significant difference in the left CTA at the $0^{\circ}$, pronation($10^{\circ},20^{\circ},30^{\circ}$) and supination($10^{\circ},20^{\circ}$) has been observed(P < 0.05). 2. The result about the Q-angle and the CTA between male and female There was significant difference in the Q-angle between male and female with different position of the foot(P < 0.05). while significant different in the right CTA at the $0^{\circ}$ pronation ($20^{\circ}$)(P < 0.05), no significant difference in the left CTA have been observed(P > 0.05). 3. The result about correlation between the left/right Q-angle and the left/right CAT There was statistical significant positive correlation between the left/right Q-angle and the left/right CAT with the different position of the foot(P < 0.01).

• Progress in Superconductivity
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• 제9권1호
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• pp.29-34
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• 2007

The baseline selection is the first and important step to analyze magnetocardiography (MCG) parameters. There are no difficulties to select the baseline between P- and Q-wave peak (P-Q interval) of MCG wave recorded from healthy subjects because the P-Q intervals of the healthy subjects do not much vary. However, patients with ischemic heart disease often show an unstable P-Q interval which does not seem to be appropriate for the baseline. In this case, T-P interval is alternatively recommended for the baseline. However, there has been no study on the difference made by the baseline selection. In this study, we studied the effect of the different baseline selection. MCG data were analyzed from twenty healthy subjects and twenty one patients whose baselines were alternatively selected in the T-P interval for their inappropriate P-Q interval. Paired T-test was used to compare two set of data. Fifteen parameters derived from the R-wave peak, the T-wave peak, and the period, $T_{max/3}{\sim}T_{max}$ were compared for the different baseline selection. As a result, most parameters did not show significant differences (p>0.05) except few parameters. Therefore, there will be no significant differences if anyone of two intervals were selected for the MCG baseline. However, for the consistent analysis, P-Q interval is strongly recommended for the baseline correction.

• 수산해양기술연구
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• 제20권2호
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• pp.65-71
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• 1984

저예망어구에서 어구제작시의 망지배치와 그 결과 예망중에 얻어지는 망구형상의 관계를 구명하기 위한 시도로서 4폭짜리 자루그물을 단순화시켜서 두께 0.15mm의 비닐막으로 원추형의 자루그물 모형을 만들어 실험, 분석하였다. 이때, 자루그물에 연결되는 날개그물 대신 4개의 지지줄을 망입구에 연결하여 유수중에 모형을 지지시키고, 망입구에서의 지지점 간격을 조절하여 자루그물 각폭의 배치면적비를 윗판 및 밑판의 가로폭 p와 양옆판의 세로높이 q 사이의 비 q/p로서 나타내고, 이 q/p를 변화시키므로서 얻어지는 유수중의 망구형상을 망고 h와 망폭 w의 비 h/w로서 나타내어 q/p와 h/w의 관계를 검토하였다. 그 결과 1) 유수중의 망구형상은 q/p가 작을수록 망고가 높아지고 q/p값이 증가하면 h/w값은 반대로 작아져서 이들 q/p와 h/w 사이에서는 h/w=k 하(1) e 상(k) 2 상(q/p)+C (k 하(1), k 하(2), C는 계수)의 관계가 성립함을 실험식으로서 나타내었다.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.435-457
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• 2013

Using the Lukasiewicz 3-valued implication operator, the notion of an (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring is introduced, where ${\alpha},{\beta}{\in}\{{\in},q,{\in}{\wedge}q,{\in}{\vee}q\}$. We define intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of a hemiring R and investigate their various properties. We characterize intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) and (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring R by its level sets. We establish that an intuitionistic fuzzy set A of a hemiring R is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$)-intuitionistic fuzzy left (right) $h$-ideal of R if and only if A is an intuitionistic fuzzy left (right) $h$-ideal with thresholds (0, 1) (or (0, 0.5) or (0.5, 1)) of R respectively. It is also shown that A is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$))-intuitionistic fuzzy left (right) $h$-ideal if and only if for any $p{\in}$ (0, 1] (or $p{\in}$ (0, 0.5] or $p{\in}$ (0.5, 1] ), $A_p$ is a fuzzy left (right) $h$-ideal. Finally, we prove that an intuitionistic fuzzy set A of a hemiring R is an intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of R if and only if for any $p{\in}(s,t]$, the cut set $A_p$ is a fuzzy left (right) $h$-ideal of R.