• Journal of applied mathematics & informatics
• /
• 제36권3_4호
• /
• pp.237-244
• /
• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• Journal of applied mathematics & informatics
• /
• 제35권3_4호
• /
• pp.303-311
• /
• 2017

In this paper we define (p, q)-analogue of Euler zeta function. In order to define (p, q)-analogue of Euler zeta function, we introduce the (p, q)-analogue of Euler numbers and polynomials by generalizing the Euler numbers and polynomials, Carlitz's type q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Euler numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Euler polynomials by using computer.

• 대한수학회지
• /
• 제57권4호
• /
• pp.1019-1030
• /
• 2020

Efficient computation of r-th root in 𝔽_q has many applications in computational number theory and many other related areas. We present a new r-th root formula which generalizes Müller's result on square root, and which provides a possible improvement of the Cipolla-Lehmer type algorithms for general case. More precisely, for given r-th power c ∈ 𝔽_q, we show that there exists α ∈ 𝔽_q^r such that $$Tr{\left(\begin{array}{cccc}{{\alpha}^{{\frac{({\sum}_{i=0}^{r-1}\;q^i)-r}{r^2}}}\atop{\text{ }}}\end{array}\right)}^r=c,$$ where $Tr({\alpha})={\alpha}+{\alpha}^q+{\alpha}^{q^2}+{\cdots}+{\alpha}^{q^{r-1}}$ and α is a root of certain irreducible polynomial of degree r over 𝔽_q.

• Korean Journal of Mathematics
• /
• 제21권4호
• /
• pp.365-374
• /
• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• 호남수학학술지
• /
• 제41권4호
• /
• pp.745-756
• /
• 2019

In this paper, we establish the log convexity and Turán type inequalities of extended (p, q)-beta functions. Likewise, we present the log-convexity, the monotonicity and Turán type inequalities for extended (p, q)-confluent hypergeometric function by utilizing the inequalities of extended (p, q)-beta functions.

• The Korean Journal of Ecology
• /
• 제27권2호
• /
• pp.115-120
• /
• 2004

Coarse woody debris (CWD, $\ge$ 5 cm in maximum diameter) is an important functional component, especially to nutrient cycling in forest ecosystems. To compare mass and nutrient dynamics of CWD in natural oak forests, a two-year study was conducted at Quercus serrata and Q. variabilis stands in Yangpyeong, Kyonggi Province. Total CWD (snag, stump, log and large branch) and annual decomposition mass (Mg/ha) were 1.9 and 0.4 for the Q. serrata stand and 7.5 and 0.5 for the Q. variabilis stand, respectively. Snags covered 72% of total CWD mass for the Q. variabilis stand and 42% for the Q. serrata stand. Most of CWD was classified into decay class 1 for both stands. CWD N and P concentrations for the Q. variabilis stand significantly increased along decay class and sampling time, except for P concentration in 2002. There were no differences in CWD N concentration for the Q. serrata stand along decay class and sampling time. However, CWD P concentration decreased along sampling time. CWD N and P contents (kg/ha) ranged from 3.5∼4.7 and 0.8∼1.3 for the Q. serrata stand to 22.8∼23.6 and 3.7∼4.7 for the Q. variabilis stand. Nitrogen and P inputs (kg/ha/yr) into mineral soil through the CWD decomposition were 0.7 and 0.3 for the Q. serrata stand and 1.6 and 0.3 for the Q. variabilis stand, respectively. The number of CWD and decay rate were main factors influencing the difference in CWD mass and nutrient dynamics between both stands.

• 대한수학회논문집
• /
• 제33권4호
• /
• pp.1141-1158
• /
• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• 디지털산업정보학회논문지
• /
• 제10권3호
• /
• pp.237-247
• /
• 2014

This paper describes a 2D discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the image signal to which it is applied. The tunable Q-factor wavelet transform (TQWT) is a fully-discrete wavelet transform for which the Q-factor, Q, of the underlying wavelet and the asymptotic redundancy (over-sampling rate), r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented. The TQWT can also be used as an easily-invertible discrete approximation of the continuous wavelet transform. The transform is based on a real valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e. g. 3-4 times overcomplete) being sufficient for the analysis/synthesis functions to be well localized. Therefore, This method services good performance in image processing fields.

• 한국의류학회지
• /
• 제15권4호
• /
• pp.367-372
• /
• 1991

In this study, we discussed about the factors effected upon the initial maximum value of heat flux ($q_{max}$). Thermal conductivity, thermal transmittance and surface air cavity of wool fabrics were examind and their correlation to the $q_{max}$ was studied. The factors were examined which had an effect upon the $q_{max}$ of an objective measure of warm/cool feeling. It was simulated by Thermo-Labo apparatures. We selected twenty sorts of pure wool woven fabrics for men's fall -winter cloth (all Wool). The conclusions are as follows; 1. There was not a certain correlation between the $q_{max}$ and the thermal conductivity of wool fabric. 2. When the fabrics touched on the copper plates, the thickness of wool fabric had a negative correlation to the $q_{max}$. The thermal transmittance had a positive correlation. Both of them had a good correlation to the $q_{max}$. 3. As a major factor, the thickness of fabric effected on the $q_{max}$.

• 한국전자파학회논문지
• /
• 제19권4호
• /
• pp.442-450
• /
• 2008

본 논문에서는 직접 변환 방식의 UHF RFID 수신기에서 사용되는 위상 다이버시티의 특성을 분석하고, 태그 변조 방식에 따른 최적의 I/Q 신호 결합 방법을 제시한다. 먼저 위상 다이버시티를 사용하지 않고 단일 채널 수신기를 구성했을 때 송신 신호와 국부발진기 신호 사이의 거리에 따른 위상차에 의해 발생하는 페이딩 특성을 분석하여 위상 다이버시티의 필요성을 보였다. 다음으로 이러한 페이딩 특성에 따른 수신 신호의 감쇄 특성을 극복하기 위한 최적의 I와 Q 채널의 결합 방법을 제안하였다. ASK의 경우, AWGN 환경에서 I와 Q 채널의 전력 평균값이 최적 신호 결합 방법임을 확인하였고, PSK의 경우는 최적 신호 결합 방법으로 arctangent 방법 및 principal component 결합 방법을 제안하였다. 제시된 결합 방법의 성능 비교를 위해 시간 파형 및 심볼 에러확률 성능을 I와 Q 패널 중 최적의 SNR 값을 갖는 패널을 선택하는 선택 다이버시티와 비교하여 분석하였다. 이론 분석 및 시뮬레이션 결과, 제시된 방법이 선택 다이버시티에 비해 최대 3 dB의 SNR 개선 효과를 가짐을 확인하였다.