• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.729-737
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• 2008

In this paper we characterize multi-Jensen functions f : $V^n\;{\rightarrow}\;W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$) such that the Jensen difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;f(x)\;-\;f(y)$$ (respectively, the Pexider difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;g(x)\;-\;h(y))$$ takes values in a countable subgroup of $\mathbb{R}$.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.739-748
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• 2008

In this paper, we obtain the general solution of a generalized cubic functional equation, the Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a generalized cubic functional equation $$4f(\sum_{j=1}^{n-1}\;x_j\;+\;mx_n)\;+\;4f(\sum_{j=1}^{n-1}\;x_j+mx_n\;x_j\;-\;mx_n}\;+\;m^2\sum_{j=1}^{n-1}\;(f(2x_j)\;=\;8f(\sum_{j=1}^{n-1}\;x_j)\;+\;4m^2{\sum_{j=1}^{n-1}}\;\(f(x_j+x_n)\;+\;f(x_j-x_n)\)$$ for a positive integer $m\;{\geq}\;1$.

• Proceedings of the Korea Multimedia Society Conference
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• 2000.11a
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• pp.45-48
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• 2000

본 논문은 현재 고성능 가역압축 부호화의 표준이 되는 JPEG-LS의 예측오차에 대한 확률분포를 결정하는 컨텍스트 모델링(context modelling)에서 컨텍스트 정수의 결정 방법에 관해 기술한다. 먼저, 압축률 향상을 위해 낮은 대비(low contrast)를 적용하는 전처리 과정을 도입한다. 둘째로, 낮은 복잡도(low complexity)를 위해 주목화소와 주변화소 사이의 차분을 양자화하고, 그 값 Q$_1$,Q$_2$, Q$_3$로부터 컨텍스트 정수(Q)의 결정을 위해 우선 순위를 정한 후, 3차원 가상좌표 위로의 할당을 고려한다. 또한, 제안 방법과 JPEG-LS의 near-lossless부분을 비교하여, 다양한 영상에 대하여 적용시켜 본 결과, 제안한 방법의 압축률과 손실이득이 훨씬 좋음을 보인다.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.5-16
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• 2009

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability for a following functional equation $$\sum\limits_{i=1}^mf(x_i+\frac{1}{m}\sum\limits_{{i=1\atop j{\neq}i}\.}^mx_j)+f(\frac{1}{m}\sum\limits_{i=1}^mx_i)=2f(\sum\limits_{i=1}^mx_i)$$ for a fixed positive integer m with $m\;{\geq}\;2$. This is applied to investigate derivations and their stability on proper Lie $CQ^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.2C
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• pp.153-157
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• 2009

In this paper, for even integer N, we propose a new construction method of quaternary low correlation zone(LCZ) sequence set from a binary LCZ sequence set with parameters (N,M,L,$\varepsilon$). Proposed method applies the inverse gray mapping from Krone and Sarwate to binary LCZ sequences and their phase shifts. The only needed condition of binary LCZ sequence set used in this construction is even period.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.43-55
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• 2022

Let R be a *-ring and n ≥ 1 be an integer. The objective of this paper is to introduce the notion of n-skew centralizing maps on *-rings, and investigate the impact of these maps. In particular, we describe the structure of prime rings with involution '*' such that _*[x, d(x)]_n ∈ Z(R) for all x ∈ R (for n = 1, 2), where d : R → R is a nonzero derivation of R. Among other related results, we also provide two examples to prove that the assumed restrictions on our main results are not superfluous.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.709-717
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• 2022

The objective of this research is to prove that an additive mapping T : R → R is a left as well as right centralizer on R if it satisfies any one of the following identities: (i) T(xⁿyⁿ + yⁿxⁿ) = T(xⁿ)yⁿ + yⁿT(xⁿ) (ii) 2T(xⁿyⁿ) = T(xⁿ)yⁿ + yⁿT(xⁿ) for each x, y ∈ R, where n ≥ 1 is a fixed integer and R is any n!-torsion free semiprime ring. In addition, we talk over above identities in the setting of *-ring(ring with involution).

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.13 no.1
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• pp.42-47
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• 2020

In OFDM-based very high-speed communication systems, FFT/IFFT processor should have several properties of low-area and low-power consumption as well as high throughput and low processing latency. Thus, radix-2k MDF (multipath delay feedback) architectures by adopting pipeline and parallel processing are suitable. In MDF architecture, the feedback memory which increases in proportion to the input signal word-length has a large area and power consumption. This paper presents a feedback memory size reduction method of radix-22 MDF IFFT processor for OFDM applications. The proposed method focuses on reducing the feedback memory size in the first two stages of MDF architectures since the first two stages occupy about 75% of the total feedback memory. In OFDM transmissions, IFFT input signals are composed of modulated data and pilot, null signals. In order to reduce the IFFT input word-length, the integer mapping which generates mapped data composed of two signed integer corresponding to modulated data and pilot/null signals is proposed. By simulation, it is shown that the proposed method has achieved a feedback memory reduction up to 39% compared to conventional approach.

• The Journal of Korean Medicine Ophthalmology and Otolaryngology and Dermatology
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• v.13 no.2
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• pp.200-210
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• 2000

objective to ascertain whether the concept of the therapeutic side is associated with changes in the blind sport mapping that represents the brain function. design Physiological blind spot maps were used as an integer of brain activity before and after acupuncture needling on the meridian point Hapkok(合谷) and Techung(太衝) in the unilateral side decided by double-blind controlled study(20 subjects). setting outpatient clinic participants: adult volunteers intervention twenty subjects were divided into two comparative groups and underwent specific acupuncture therapy on the unilateral side. Blinded examiners obtained reproducible pre and post-acupuncture cortical maps, which were subjected to statistical analysis. main outcome measures Brain activity was demonstrated by reproducible circumferential measurements of cortical hemispheric blind spot maps before and after acupuncture on the unilateral side. in case of acupuncture needling on the ipsilateral side of an enlarged side of bilnd spot, there were reduction of blind spot in 7 cases of 10 subjects, and enlargement in 3 cases. in case of acupuncture needling on the contralateral side of the enlarged side of blind spot, there were enlargement of blind spot in 6 cases of 10 subjects, and reduction in 4 cases. results the significant changes in the blind spots before and after acupuncture were observed Acupuncture needlings on the ipsilateral or contralateral side of an enlarged cortical map were associated with the concept of the therapeutic side traditionally accepted in the oriental medical society. Acupuncture needling on the ipsilateral side of an enlarged blind spot map is associated with the reduction of map, and increaed contralateral cortical activity. Acupuncture needling on the side opposite an enlarged blind spot map is associated with the enlargement of map, and decreased cortical activity. conclusion Reproducible maps of cortical responses can be used to measure the neurological consequences of acupuncture needling. Acupuncture can affect the somatic sensory informations that reach to the contralateral thalamus, and so affect thalamic integration. we found that acupuncture therapy may be associated with an increase or a decrease in brain function depending on the side of acupuncture needling. thus, the traditional concept of the contralateral therapeutic theory in acupuncture approach has the clinical significance in the view of brain function.

• ETRI Journal
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• v.42 no.4
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• pp.619-632
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• 2020

Highly dispersive S-boxes are desirable in cryptosystems as nonlinear confusion sublayers for resisting modern attacks. For a near optimal cryptosystem resistant to modern cryptanalysis, a highly nonlinear and low differential probability (DP) value is required. We propose a method based on a piecewise linear chaotic map (PWLCM) with optimization conditions. Thus, the linear propagation of information in a cryptosystem appearing as a high DP during differential cryptanalysis of an S-box is minimized. While mapping from the chaotic trajectory to integer domain, a randomness test is performed that justifies the nonlinear behavior of the highly dispersive and nonlinear chaotic S-box. The proposed scheme is vetted using well-established cryptographic performance criteria. The proposed S-box meets the cryptographic performance criteria and further minimizes the differential propagation justified by the low DP value. The suitability of the proposed S-box is also tested using an image encryption algorithm. Results show that the proposed S-box as a confusion component entails a high level of security and improves resistance against all known attacks.