• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.277-283
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• 1992

Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

• Journal of Veterinary Science
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• v.21 no.5
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• pp.69.1-69.11
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• 2020

Background: An inappropriate Q angle may affect the biomechanics of the canine patellofemoral joint. Objectives: The purpose of this study was to evaluate the effects of changes in quadriceps angle (Q angle) on patellofemoral joint pressure distribution in dogs. Methods: Eight stifles were positioned at 45, 60, 75, 90, 105, and 120° of flexion in vitro, and 30% body weight was applied through the quadriceps. Patellofemoral contact pressure distribution was mapped and quantified using pressure-sensitive film. For the pressure area, mean pressure, peak pressure, medial peak pressure, and lateral peak pressure, differences between groups according to conditions for changing the Q angle were statistically compared. Results: Increases of 10° of the Q angle result in increases in the pressure area (P = 0.04), mean pressure (P = 0.003), peak pressure, and medial peak pressure (P ≤ 0.01). Increasing the Q angle by 20° increases the pressure area (P = 0.021), mean pressure (P ≤ 0.001), peak pressure (P ≤ 0.01), and medial peak pressure (P ≤ 0.01) significantly, and shows higher mean (P ≤ 0.001) and peak pressures than increasing by 10°. Decreasing the Q angle increases the mean pressure (P = 0.013), peak pressure, and lateral peak pressure (P ≤ 0.001). Conclusions: Both increases and decreases in the Q angle were associated with increased peak patellofemoral pressure, which could contribute to the overloading of the cartilage. Therefore, the abnormal Q angle should be corrected to the physiologically normal value during patellar luxation repair and overcorrection should be avoided.

• Journal of the Korean Data and Information Science Society
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• v.18 no.1
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• pp.211-218
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• 2007

Nonlinear ARMA model $X_n\;=\;h(X_{n-1},{\cdots},X_{n-p},e_{n-1},{\cdots},e_{n-p})+e_n$ is considered and easy-to-check sufficient condition for strict stationarity of {$X_n$} without some irreducibility or continuity assumption is given. Threshold ARMA(p, q) and momentum threshold ARMA(p, q) models are examined as special cases.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.469-479
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• 2003

Let B be the open unit ball in $C^{n}$ and ${\mu}_{q}$(q > -1) the Lebesgue measure such that ${\mu}_{q}$(B) ＝ 1. Let ${L_{a,q}}^2$ be the subspace of ${L^2(B,D{\mu}_q)$ consisting of analytic functions, and let $\overline{{L_{a,q}}^2}$ be the subspace of ${L^2(B,D{\mu}_q)$) consisting of conjugate analytic functions. Let $\bar{P}$ be the orthogonal projection from ${L^2(B,D{\mu}_q)$ into $\overline{{L_{a,q}}^2}$. The little Hankel operator ${h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}$ is defined by ${h_{\varphi}}^{q}(\cdot)\;=\;{\bar{P}}({\varphi}{\cdot})$. In this paper, we will find the necessary and sufficient condition that the little Hankel operator ${h_{\varphi}}^{q}$ is bounded(or compact).

• Journal of Genetic Medicine
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• v.7 no.1
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• pp.78-81
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• 2010

Pericentric inversion is not rare in humans and is usually benign. However, pericentric inversion can lead to production of an unbalanced recombinant and might be a cause of repetitive pregnancy loss. Pericentric inversion of chromosome 22 is rare and only a few cases have been reported. We report a case of inv(22)(p13q12) carrier who had history of repetitive pregnancy loss including three spontaneous abortions and one fetal hydrops in which the chromosomal complement was rec(22)dup(22q) inv(22)(p13q12)mat. The maternal inv(22) and fetal rec(22) were confirmed by fluorescence in situ hybridization using region-specific probes (TUPLE1 on 22q11.2 and ARSA on 22q13). Because the identification of inv(22) or rec(22) in conventional karyotyping might be easily overlooked, great attention and additional molecular tests are required for accurate diagnosis of inv(22) and rec(22).

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.53-63
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• 2005

Let R be a ring R and ${\sigma}$ be an endomorphism of R. R is called ${\sigma}$-rigid (resp. reduced) if $a{\sigma}r(a) = 0 (resp{\cdot}a^2 = 0)$ for any $a{\in}R$ implies a = 0. An ideal I of R is called a ${\sigma}$-ideal if ${\sigma}(I){\subseteq}I$. R is called ${\sigma}$-quasi-Baer (resp. right (or left) ${\sigma}$-p.q.-Baer) if the right annihilator of every ${\sigma}$-ideal (resp. right (or left) principal ${\sigma}$-ideal) of R is generated by an idempotent of R. In this paper, a skew polynomial ring A = R[$x;{\sigma}$] of a ring R is investigated as follows: For a ${\sigma}$-rigid ring R, (1) R is ${\sigma}$-quasi-Baer if and only if A is quasi-Baer if and only if A is $\={\sigma}$-quasi-Baer for every extended endomorphism $\={\sigma}$ on A of ${\sigma}$ (2) R is right ${\sigma}$-p.q.-Baer if and only if R is ${\sigma}$-p.q.-Baer if and only if A is right p.q.-Baer if and only if A is p.q.-Baer if and only if A is $\={\sigma}$-p.q.-Baer if and only if A is right $\={\sigma}$-p.q.-Baer for every extended endomorphism $\={\sigma}$ on A of ${\sigma}$.

• The Korean Journal of Ecology
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• v.27 no.2
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• pp.87-92
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• 2004

Soil respiration rate was measured from March to November 2003 using the KOH absorption method in Pinus densiflora, Quercus variabilis, Platycarya strobilacea stands in Jinju, Gyeongnam Province. Throughout the study period, average soil temperature and moisture content were 16.2$^{\circ}C$, 25.1% for P. densiflora stand, 17.1$^{\circ}C$, 24.3% for Q. variabilis stand, and 17.6$^{\circ}C$, 25.1% for P. strobilacea stand, respectively. The seasonal fluctuations of soil respiration rate increasing in summer and decreasing in winter, which there were strong positive correlations of soil respiration and soil temperature in all study stands. However, there were no significant correlations between soil moisture and soil respiration. Soil respiration rates throughout the study period ranged from 0.12 to 0.77 for P. densiflora stand, 0.23 to 1.37 for Q. valiabilis stand, and 0.30 to 1.47 g $CO_2\cdotm^{-2}\cdothr^{ -1}$ for P. strobilacea stand, respectively. Mean soil respiration rates in P. densiflora, Q. variabilis, P. strobilacea stands were 0.43, 0.80, and 0.90 g $CO_2\cdotm^{-2}\cdothr^{ -1}$, respectively. The Q$_{10}$ values were 2.38 for P. densiflora stand, 2.11 for Q. variabilis stand, and 2.07 for P. strobilacea stand. Annual total soil respiration was 24 for P. densiflora stand, 49.3 for Q. variabilis stand, and 55.3 t $CO_2\cdotha^{-1}\cdotyr^{ -1}$ for P. strobilacea stand, respectively.y.

• Journal of Nutrition and Health
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• v.38 no.7
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• pp.570-577
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• 2005

The purpose of this study was to investigate the effect of bone mineral density on life styles, dietary habits and nutrient intakes among the male college students. The subjects were divided into four groups; $Q_1$ (calcaneus BMD < 25 percentile, n = 117), $Q_2$ (25 percentile $\le$ calcaneus BMD < 50 percentile, n = 118), $Q_3$ (50 percentile $\le$ calcaneus BMD < 75 percentile, n = 118) $Q_4$ (calcaneus BMD $\ge$ 75 percentile, n = 116). And they were asked about general characteristics, life style, dietary habit, and nutrient intake using questionnaire and 24-hr recall method. They were measured the bone mineral density of calcaneus using quantitative ultrasound. The average age of the subjects of the study was 23.0 yews and the average height, weight, and BMI were 174.7 cm, 69.0 kg, $22.5 kg/m^2$. The bone mineral density in calcaneus was $0.43 g/cm^2$ in $Q_1,\;0.50 g/cm^2$ in $Q_2,\;0.56 g/cm^2$ in $Q_3$, and $0.69 g/cm^2$ in $Q_4$ (p < 0.001). The results showed that $Q_1$ tended to have irregular exercise compared to the other three groups. Compared with $Q_1$ and $Q_2$, the frequency of skipping breakfast was lower in $Q_3$ and $Q_4$. Also the results showed that the $Q_4$ was significantly more often to drink coffee compared with the other three groups (p < 0.01). The mean daily energy intake was 2210.6 kcal ($88.4\%$ of RDA). The intake of energy, vitamin $B_2$, calcium, and zinc did not meet the Korean RDA. Also the $Q_2$consumed significantly lower intakes of protein (p < 0.05) and plant protein (p < 0.05) compared to the $Q_3$ and $Q_4$. The $Q_1$ and $Q_2$ consumed significantly lower intakes of vitamin $B_2$ (p < 0.01) compared to the $Q_3$ and $Q_4$. In conclusion, male student in lower bone mineral density appeared to have unhealthy life styles and dietary habits in terms of irregular exercise, high frequency of skipping breakfast and lower intakes of protein, vitamin $B_2$ showing a strong need proper education on meal practices and exercise habits for the bone health.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.1-12
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• 2007

In this paper, we consider the q-Volkenborn integral of uniformly differentiable functions on the p-adic integer ring. By using this integral, we obtain the generating functions of twisted q-generalized Bernoulli numbers and polynomials. We find some properties of these numbers and polynomials.

• Journal of the Korean Mathematical Society
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• v.8 no.1
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• pp.25-30
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• 1971

Put ($$^*$$) $$G[x,y]={\sum}\limits^{p+q=n}_{p,q=0}[-n]_{p+q}c_{p,q}x^py^q$$, where $[{\lambda}]_m$ is the Pocbhammer symbol and the $c_{p,q}$ are arbitrary constants. Making use of the specialized forms of some of his earlier results (see [8] and [9] the author derives here bilateral generating functions of the type ($$^{**}$$) $${\sum}\limits^{\infty}_{n=0}{\frac{[\lambda]_n}{n!}}_2F_1[\array{{\rho}-n,\;{\alpha};\\{\lambda}+{\rho};}x]\;G[y,z]t^n$$ where ${\alpha}$, ${\rho}$ and ${\lambda}$ are arbitrary complex numbers. In particular, it is shown that when G[y, z] is a double hypergeometric polynomial, the right-band member of ($^{**}$) belongs to a class of general triple hypergeometric functions introduced by the author [7]. An interesting special case of ($^{**}$) when ${\rho}=-m,\;m$ being a nonnegative integer, yields a class of bilateral generating functions for the Jacobi polynomials $\{P_n{^{{\alpha},{\beta}}}(x)\}$ in the form ($$^{***}$$) $${\sum\limits^{\infty}_{n=0}}\(\array{m+n\\n}\)P{^{({\alpha}-n,{\beta}-n)}_{m+n}(x)\;G[y,z]{\frac{t^n}{n!}}$$, which provides a unification of several known results. Further extensions of ($^{**}$) and ($^{***}$) with G[y, z] replaced by an analogous multiple sum $H\[y_1,{\cdots},y_m\]$ are also discussed.