• 대한수학회지
• /
• 제34권4호
• /
• pp.871-894
• /
• 1997

For a lifted nontrivial additive character $\lambda'$ and a multiplicative character $\chi$ of the finite field with $q^2$ elements, the 'Gauss' sums $\Sigma\lambda'$(tr $\omega$) over $\omega$ $\in$ SU(2n + 1, $q^2$) and $\Sigma\chi$(det $\omega$)$\lambda'$(tr $\omega$) over $\omega$ $\in$ U(2n + 1, $q^2$) are considered. We show that the first sum is a polynomial in q with coefficients involving certain new exponential sums and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums and the average (over all multiplicative characters of order dividing q-1) of the usual Gauss sums. As a consequence we can determine certain 'generalized Kloosterman sum over nonsingular Hermitian matrices' which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.

• Journal of electromagnetic engineering and science
• /
• 제9권3호
• /
• pp.124-129
• /
• 2009

Although the maximum sum-rate capacity of multiple-input multiple output(MIMO) broadcast channels(BCs) can be achieved by dirty-paper coding(DPC), the results were obtained without fairness considerations in uncorrelated MIMO channels. In this paper, we propose new multiuser scheduling algorithms, which find a best user set for approaching the maximum sum-rate capacity while maintaining fairness among users. We analyze the performance of the proposed algorithms using zero-forcing dirty paper coding(ZF-DPC) in the correlated MIMO BCs for throughput and delay fairness, respectively. Numerical results demonstrate that a large time window can reduce the average throughput difference between users, but it increases head-of-line(HOL) delay jitters in the case of delay fairness.

• 대한수학회보
• /
• 제48권6호
• /
• pp.1137-1146
• /
• 2011

Let {$X_i$, $i{\geq}1$} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote $S_n={\sum}_{i=1}^n\;X_i$, $M_n=max_{1{\leq}i{\leq}n}\;{\mid}S_i{\mid}$ and $V_n^2={\sum}_{i=1}^n\;X_i^2$. Then for d > -1, we showed that under some regularity conditions, $$\lim_{{\varepsilon}{\searrow}0}{\varepsilon}^2^{d+1}\sum_{n=1}^{\infty}\frac{(loglogn)^d}{nlogn}I\{M_n/V_n{\geq}\sqrt{2loglogn}({\varepsilon}+{\alpha}_n)\}=\frac{2}{\sqrt{\pi}(1+d)}{\Gamma}(d+3/2)\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^{2d+2}}\;a.s.$$ holds in this paper, where If g denotes the indicator function.

• 한국심리학회지 : 문화 및 사회문제
• /
• 제28권3호
• /
• pp.307-329
• /
• 2022

본 연구는 대인 간 관용과 불관용을 구분하여 관용과 불관용에 영향을 미치는 요인을 탐색하고자 하였다. 구체적으로 인구통계학적 변인, 사회적 바람직성, 공감(인지적 공감, 정서적 공감), 타인을 향한 자비불안, 사회신뢰, 제로섬 신념이 관용과 불관용을 예측하는지를 알아보고자 하였다. 연구대상은 전국에 거주하는 성인 445명(남성 218명, 여성 227명)으로 온라인 설문조사를 통해 자료를 얻었다. 자료분석은 인구통계학적 변인과 사회적 바람직성의 영향을 통제하기 위해 위계적 회귀분석 방법을 사용하였다. 연구결과, 관용을 유의하게 예측하는 것은 성별, 주관적 사회경제적지위, 사회적 바람직성, 인지적 공감, 사회신뢰로 나타났고, 불관용은 사회적 바람직성, 타인을 향한 자비불안, 제로섬 신념이 유의하게 예측하는 것으로 나타났다. 이를 통해 관용과 불관용의 개념이 구분되며, 각각을 예측하는 요인도 다르다는 것을 확인할 수 있었다. 따라서 관용을 높이기 위한 개입과 불관용을 낮추기 위한 개입방안을 함께 모색함으로써 다문화·다양성 사회에서 현실적인 공존방안을 마련해나갈 필요가 있을 것이다.

• Journal of Communications and Networks
• /
• 제18권5호
• /
• pp.688-698
• /
• 2016

In this paper, we investigate the achievable sum rate and energy efficiency of downlink massive multiple-input multiple-output antenna systems with zero-forcing precoding, by taking into account the randomness of user locations. Specifically, we propose two types of non-uniform user distributions, namely, center-intensive user distribution and edge-intensive user distribution. Based on these user distributions, we derive novel tight lower and upper bounds on the average sum rate. In addition, the impact of user distributions on the optimal number of users maximizing the sum rate is characterized. Moreover, by adopting a realistic power consumption model which accounts for the transmit power, circuit power and signal processing power, the energy efficiency of the system is studied. In particular, closed-form solutions for the key system parameters, such as the number of antennas and the optimal transmit signal-to-noise ratio maximizing the energy efficiency, are obtained. The findings of the paper suggest that user distribution has a significant impact on the system performance: for instance, the highest average sum rate is achieved with the center-intensive user distribution, while the lowest average sum rate is obtained with the edge-intensive user distribution. Also, more users can be served with the center-intensive user distribution.

• 대한수학회지
• /
• 제47권2호
• /
• pp.263-275
• /
• 2010

Let {$X_n;n\;\geq\;1$} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set $S_n\;=\;{\sum}^n_{k=1}X_k$, $M_n\;=\;max_{k{\leq}n}|S_k|$, $n\;{\geq}\;1$. Suppose $\sigma^2\;=\;EX^2_1+2{\sum}^\infty_{k=2}EX_1X_k$ (0 < $\sigma$ < $\infty$). We prove that for any b > -1/2, if $E|X|^{2+\delta}$(0<$\delta$$\leq$1), then $$lim\limits_{\varepsilon\searrow0}\varepsilon^{2b+1}\sum^{\infty}_{n=1}\frac{(loglogn)^{b-1/2}}{n^{3/2}logn}E\{M_n-\sigma\varepsilon\sqrt{2nloglogn}\}_+=\frac{2^{-1/2-b}{\sigma}E|N|^{2(b+1)}}{(b+1)(2b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2(b+1)}}$$ and for any b > -1/2, $$lim\limits_{\varepsilon\nearrow\infty}\varepsilon^{-2(b+1)}\sum^{\infty}_{n=1}\frac{(loglogn)^b}{n^{3/2}logn}E\{\sigma\varepsilon\sqrt{\frac{\pi^2n}{8loglogn}}-M_n\}_+=\frac{\Gamma(b+1/2)}{\sqrt{2}(b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2b+2'}}$$, where $\Gamma(\cdot)$ is the Gamma function and N stands for the standard normal random variable.

• 호남수학학술지
• /
• 제11권1호
• /
• pp.15-19
• /
• 1989

A conjecture of E. T. H. Wang asserts that if every diagonal disjoint from m mutually disjoint zero diagonals of $A{\in}{\Omega}_n$ has a constant sum, then all entries off the m zero diagonals are equal to l/(n-m). E. T. H. Wang proved the conjecture for m=0, 1, n-2 and n-1. In the present paper, it is proved that the conjecture holds true for m=2.

• 호남수학학술지
• /
• 제27권2호
• /
• pp.301-315
• /
• 2005

Let $\{A_u,\;u=0,\;1,\;2,\;{\cdots}\}$ be a sequence of coefficient matrices such that ${\sum}_{u=0}^{\infty}{\parallel}A_u{\parallel}<{\infty}$ and ${\sum}_{u=0}^{\infty}\;A_u{\neq}O_{m{\times}m}$, where for any $m{\times}m(m{\geq}1)$, matrix $A=(a_{ij})$, ${\parallel}A{\parallel}={\sum}_{i=1}^m{\sum}_{j=1}^m{\mid}a_{ij}{\mid}$ and $O_{m{\times}m}$ denotes the $m{\times}m$ zero matrix. In this paper, a functional central limit theorem is derived for a stationary m-dimensional linear process ${\mathbb{X}}_t$ of the form ${\mathbb{X}_t}={\sum}_{u=0}^{\infty}A_u{\mathbb{Z}_{t-u}}$, where $\{\mathbb{Z}_t,\;t=0,\;{\pm}1,\;{\pm}2,\;{\cdots}\}$ is a stationary sequence of linearly positive quadrant dependent m-dimensional random vectors with $E({\mathbb{Z}_t})={{\mathbb{O}}$ and $E{\parallel}{\mathbb{Z}_t}{\parallel}^2<{\infty}$.

• 호남수학학술지
• /
• 제30권4호
• /
• pp.703-711
• /
• 2008

Let ${{\xi}_k,k{\in}{\mathbb{Z}}}$ be an associated H-valued random variables with $E{\xi}_k$ = 0, $E{\parallel}{\xi}_k{\parallel}$ < ${\infty}$ and $E{\parallel}{\xi}_k{\parallel}^2$ < ${\infty}$ and {$a_k,k{\in}{\mathbb{Z}}$} a sequence of bounded linear operators such that ${\sum}^{\infty}_{j=0}j{\parallel}a_j{\parallel}_{L(H)}$ < ${\infty}$. We define the sationary Hilbert space process $X_k={\sum}^{\infty}_{j=0}a_j{\xi}_{k-j}$ and prove that $n^{-1}{\sum}^n_{k=1}X_k$ converges to zero.

• Journal of applied mathematics & informatics
• /
• 제28권3_4호
• /
• pp.1025-1034
• /
• 2010

Let {$X_n$, $n\;{\in}\;\mathbb{Z}_+^d$} be a field of identically distributed and negatively associated random variables with mean zero and set $S_n\;=\;{\sum}_{k{\leq}n}\;X_k$, $n\;{\in}\;\mathbb{Z}_+^d$, $d\;{\geq}\;2$. We investigate precise asymptotics for ${\sum}_n|n|^{r/p-2}P(|S_n|\;{\geq}\;{\epsilon}|n|^{1/p}$ and ${\sum}_n\;\frac{(\log\;|n|)^{\delta}}{|n|}P(|S_n|\;{\geq}\;{\epsilon}\;\sqrt{|n|\log|n|)}$, ($0\;{\leq}\;{\delta}\;{\leq}\;1$) as ${\epsilon}{\searrow}0$.