• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.231-237
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• 2018

Hardy's inequality is refined non-trivially as the form $${\int_{0}^{{\infty}}}\{{\frac{1}{x}}{\int_{0}^{x}}f(t)dt\}^pdx{\leq}Q_f{\times}({\frac{p}{p-1}})^p{\int_{0}^{x}}f^p(x)dx$$ for some $Q_f:0{\leq}Q_f{\leq}1$. $P{\acute{o}}lya$-Knopp's inequality is also refined by the similar form.

• Nutrition Research and Practice
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• v.6 no.5
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• pp.414-420
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• 2012

Forty guinea pigs were divided into four groups and fed 0.04% cholesterol based control diet, plus 0.05% simvastatin, and statin plus 0.1% CoQ10 or 10% Ardisia Japonica Blume (AJB) leave powder for 4 weeks. Plasma total cholesterol levels decreased significantly in all groups fed the statin-containing diet compared with that in guinea pigs fed the control diet (P < 0.01). Plasma and liver triglycerides decreased significantly in the statin plus CoQ10 group compared with those in the control (both P < 0.05). Maximum platelet aggregation was significantly higher in the statin plus CoQ10 group than that in the other groups (P < 0.05). Na-K ATPase activity increased in the statin group and decreased in the statin plus CoQ10 group (P < 0.01). Na-K co-transport and Na passive transport decreased significantly in the control group compared with those in the other groups (both P < 0.05). Intracellular Na was highest in the statin group and lowest in the statin plus CoQ10 group and was correlated with Na-K ATPase activity. Thiobarbituric acid reactive substance production in platelet-rich plasma and liver tended to decrease in the statin plus CoQ10 group compared with those in the other groups. Plasma glutamic-pyruvic transaminase and glutamic-oxaloacetic transaminase increased significantly in the statin group compared with those in the control (P < 0.05). These result suggest that antioxidant rich AJB did not have positive effects on cardiovascular disease parameters. The statin plus CoQ10 seemed to decrease cholesterol more efficiently than that of statin alone.

• The Journal of Korean Physical Therapy
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• v.14 no.4
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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).

• Journal of Intelligence and Information Systems
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• v.12 no.1
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• pp.107-123
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• 2006

We propose the Generalized Binary Second-order Recurrent Neural Networks(GBSRNNf) being equivalent to regular grammars and ?how the implementation of lexical analyzer recognizing the regular languages by using it. All the equivalent representations of regular grammars can be implemented in circuits by using GSBRNN, since it has binary-valued components and shows the structural relationship of a regular grammar. For a regular grammar with the number of symbols m, the number of terminals p, the number of nonterminals q, and the length of input string k, the size of the corresponding GBSRNN is $O(m(p+q)^2)$ and its parallel processing time is O(k) and its sequential processing time, $O(k(p+q)^2)$.

• Neonatal Medicine
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• v.16 no.1
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• pp.76-80
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• 2009

A male baby with intrauterine growth retardation had a short neck, small hands and feet, hypospadia, both grade I hydronephrosis, type II atrial septal defect, and moderate valvular pulmonary stenosis. The routine chromosome and banding analyses revealed a 46,XY,rec(8)del(8)(p21)dup(8) (q24.1)inv(8)(p21q24.1)pat chromosome constitution. His mother has normal chromosomes, but the father had 46,XY,inv(8)(p21q24.n Also his uncle had an inv(8) chromosome constitution. We used lymphocytes and examined 40 mitotic cells. All mitotic cells showed deletion of 8p21-->pter and duplication of 8q24.1 -->qter. Because Sp21 involves secretion of macrophage and lymphocyte against cancer cells, long-term follow-up for cancer will be needed.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.557-564
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• 2012

This study concerns the existence of positive solution for the following nonlinear system $$\{-div(|x|^{-ap}|{\nabla}u|^{p-2}{\nabla}u)=|x|^{-(a+1)p+c_1}({\alpha}_1f(v)+{\beta}_1h(u)),x{\in}{\Omega},\\-div(|x|^{-bq}|{\nabla}v|q^{-2}{\nabla}v)=|x|^{-(b+1)q+c_2}({\alpha}_2g(u)+{\beta}_2k(v)),x{\in}{\Omega},\\u=v=0,x{\in}{\partial}{\Omega}$$, where ${\Omega}$ is a bounded smooth domain of $\mathbb{R}^N$ with $0{\in}{\Omega}$, 1 < $p,q$ < N, $0{{\leq}}a<\frac{N-p}{p}$, $0{{\leq}}b<\frac{N-q}{q}$ and $c_1$, $c_2$, ${\alpha}_1$, ${\alpha}_2$, ${\beta}_1$, ${\beta}_2$ are positive parameters. Here $f,g,h,k$ : $[0,{\infty}){\rightarrow}[0,{\infty})$ are nondecresing continuous functions and $$\lim_{s{\rightarrow}{\infty}}\frac{f(Ag(s)^{\frac{1}{q-1}})}{s^{p-1}}=0$$ for every A > 0. We discuss the existence of positive solution when $f,g,h$ and $k$ satisfy certain additional conditions. We use the method of sub-super solutions to establish our results.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.373-382
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• 1998

Most of the works in Time Series Analysis are based on the Auto Regressive Integrated Moving Average (ARIMA) models presented by Box and Jeckins(1976). If the data exhibits no ap-parent deviation from stationarity and if it has rapidly decreasing autocorrelation function then a suitable ARIMA(p,q) model is fit to the given data. Selection of the orders of p and q is one of the crucial steps in Time Series Analysis. Most of the methods to determine p and q are based on the autocorrelation function and partial autocor-relation function as suggested by Box and Jenkins (1976). many new techniques have emerged in the literature and it is found that most of them are over very little use in determining the orders of p and q when both of them are non-zero. The Durbin-Levinson algorithm and Innovation algorithm (Brockwell and Davis 1987) are used as recur-sive methods for computing best linear predictors in an ARMA(p,q)model. These algorithms are modified to yield an effective method for ARMA model identification so that the values of order p and q can be determined from them. The new method is developed and its validity and usefulness is illustrated by many theoretical examples. This method can also be applied to an real world data.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.1
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• pp.121-125
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• 2007

Differential cryptanalysis and linear cryptanalysis are the most powerful approaches known for attacking many block ciphers and used to evaluating the security of many block ciphers. So designers have designed secure block ciphers against these cryptanalyses. In this paper, we present new three block cipher structures. And for given r, we prove that differential(linear) probabilities for r-round blockcipher structures are upper bounded by $p^2(q^2),\;2p^2(2q^2)$ if the maximum differential(linear) probability is p(q) and the round function is a bijective function.