• 호남수학학술지
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• 제30권2호
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• pp.335-341
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• 2008

In this paper, we use the convexity of distance function between geodesics in a singular Hadamard space to generalize Hadamard-Cartan theorem for 2-dimensional metric spaces. We also determine a neighborhood of a closed geodesic where no other closed geodesic exists in a complete space of nonpositive curvature.

• Journal of electromagnetic engineering and science
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• 제7권1호
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• pp.17-27
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• 2007

Jacket matrices which are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^+=nI_n$ where $A^+$ is the transpose matrix of elements inverse of A,i.e., $A^+=(a_{kj}^-)$, was introduced by Lee in 1984 and are used for signal processing and coding theory, which generalized the Hadamard matrices and Center Weighted Hadamard matrices. In this paper, some properties and constructions of Jacket matrices are extensively investigated and small orders of Jacket matrices are characterized, also present the full rate and the 1/2 code rate complex orthogonal space time code with full diversity.

• 한국통신학회논문지
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• 제34권7C호
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• pp.635-639
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• 2009

본 논문에서는 행벡터의 집합이 이진 벡터합 연산에 관해 닫혀있는 모든 하다마드 (Hadmard) 행렬들은 서로 동치(equivalent) 임융 증명한다. 이를 이용하면, 최대길이 수열로부터 생성된 순회 (cyclic) 하다마드 행렬과 크로네커 (Kronecker) 곱에 의해 생성된 월쉬-하다마드 (Walsh-Hadamard) 행렬이 동치임을 간단히 보일 수 있다.

• 대한수학회지
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• 제38권6호
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• 대한수학회논문집
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• 제31권3호
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• pp.483-493
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• 2016

In this paper, we study and prove common fixed point theorems for N generalized I-asymptotically nonexpansive mappings in a Hadamard space.

• 대한수학회지
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• 제59권3호
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• pp.549-570
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• 2022

In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.

• 대한수학회지
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• 제43권3호
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• pp.579-591
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• 2006

In this paper we obtain a sufficient and necessary condition for an analytic function f on the unit ball B with Hadamard gaps, that is, for $f(z)\;=\;{\sum}^{\infty}_{k=1}\;P_{nk}(z)$ (the homogeneous polynomial expansion of f) satisfying $n_{k+1}/n_{k}{\ge}{\lambda}>1$ for all $k\;{\in}\;N$, to belong to the weighted Bergman space $$A^p_{\alpha}(B)\;=\;\{f{\mid}{\int}_{B}{\mid}f(z){\mid}^{p}(1-{\mid}z{\mid}^2)^{\alpha}dV(z) < {\infty},\;f{\in}H(B)\}$$. We find a growth estimate for the integral mean $$\({\int}_{{\partial}B}{\mid}f(r{\zeta}){\mid}^pd{\sigma}({\zeta})\)^{1/p}$$, and an estimate for the point evaluations in this class of functions. Similar results on the mixed norm space $H_{p,q,{\alpha}$(B) and weighted Bergman space on polydisc $A^p_{^{\to}_{\alpha}}(U^n)$ are also given.

• Journal of Communications and Networks
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• 제12권3호
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• pp.240-245
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• 2010

Jacket matrices, motivated by the complex Hadamard matrix, have played important roles in signal processing, communications, image compression, cryptography, etc. In this paper, we suggest a novel approach to design a simple class of space-time block codes (STBCs) to reduce its peak-to-average power ratio. The proposed code provides coding gain due to the characteristics of the complex Hadamard matrix, which is a special case of Jacket matrices. Also, it can achieve full rate and full diversity with the simple decoding. Simulations show the good performance of the proposed codes in terms of symbol error rate. For generality, a kind of quasi-orthogonal STBC may be similarly designed with the improved performance.

• 한국인터넷방송통신학회논문지
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• 제16권6호
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• pp.319-327
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• 2016

본 논문에서는 나무나 염소 뿔처럼 대부분의 동식물이 대칭임을 살펴본다. 또한 DNA를 가지고 있는 인간의 신체 역시 대칭이다. 피보나치수열, 식물의 나선, 동물의 대수 나선에서 볼 수 있는 것은 대칭이다. 해바라기 꽃은 원형이다. 원(元)은 원점을 중심으로 회전을 해도 모양이 꼭 같으므로 회전대칭이다. 공간상의 회전변환을 넘어서, 시간 공간의 대칭적 변환으로 일반화하면 아인슈타인의 특수상대성 이론이 시공간 변환관계이다. 동식물의 나선은 좌우 나선들이 대칭을 이루며 그 속에는 element-wise inverse가 존재한다. Hadamard 행렬 중 가운데 하중 값을 2로 준 것은 자연대수의 밑 2와 같고, 나선 행렬은 Symmetric하며 역행렬은 element-wise inverse이다.

• Journal of information and communication convergence engineering
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• 제20권1호
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• pp.1-7
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• 2022

Herein, a new space-time block coding technique is proposed for a MIMO 2 × 2 multiple-input multiple output (MIMO) system to minimize the bit error rate (BER) in Rayleigh fading channels with reduced decoding complexity using ZF and MMSE linear detection techniques. The main objective is to improve the service quality of wireless communication systems and optimize the number of antennas used in base stations and terminals. The idea is to exploit the correlation product technique between both information symbols to transmit per space-time block code and their own orthogonal Walsh-Hadamard sequences to ensure orthogonality between both symbol vectors and create a full-rate orthogonal STBC code. Using 16 quadrature amplitude modulation and the quasi-static Rayleigh channel model in the MATLAB environment, the simulation results show that the proposed space-time block code performs better than the Alamouti code in terms of BER performance in the 2 × 2 MIMO system for both cases of linear decoding ZF and MMSE.