• Korean Journal of Mathematics
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• 제26권2호
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• pp.175-189
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• 2018

In this paper, at first we generalize the notion of algebra over a field. A ${\Gamma}$-algebra is an algebraic structure consisting of a vector space V, a groupoid ${\Gamma}$ together with a map from $V{\times}{\Gamma}{\times}V$ to V. Then, on every associative ${\Gamma}$-algebra V and for every ${\alpha}{{\in}}{\Gamma}$ we construct an ${\alpha}$-Lie algebra. Also, we discuss some properties about ${\Gamma}$-Lie algebras when V and ${\Gamma}$ are the sets of $m{\times}n$ and $n{\times}m$ matrices over a field F respectively. Finally, we define the notions of ${\alpha}$-derivation, ${\alpha}$-representation, ${\alpha}$-nilpotency and prove Engel theorem in this case.

• 대한수학회지
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• 제41권6호
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• pp.945-955
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• 2004

In this paper, we establish a number system in $R^n$ which arises from a Haar wavelet basis in connection with decompositions of certain Cuntz algebra representations on $L^2$( $R^n$). Number systems in $R^n$ are also of independent interest [9]. We study radix-representations of $\chi$ $\in$ $R^n$: $\chi$:$\alpha$$_{ι}$ $\alpha$$_{ι-1}$…$\alpha$$_1$$\alpha$$_{0}$ ㆍ$\alpha$$_{-1}$ $\alpha$$_{-2}$ … as $\chi$= $M^{ι}$$\alpha$$_{ι}$ $\alpha$＋…M$\alpha$$_1$＋$\alpha$$_{0}$ ＋ $M^{-1}$ $\alpha$$_{-1}$ ＋ $M^{-2}$ $\alpha$$_{-2}$ ＋… where each $\alpha$$_{k}$ $\in$ D, and D is some specified digit set. Our analysis uses iteration techniques of a number-theoretic flavor. The view-point is a dual one which we term fractals in the large vs. fractals in the small,illustrating the number theory of integral lattice points vs. fractions.s vs. fractions.

• 정보과학회 논문지
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• 제44권3호
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• pp.295-305
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• 2017

얼굴 외형은 조명의 영향을 크게 받기 때문에 조명 변화는 얼굴 인식 시스템의 성능을 저하시키는 요인 중 하나이다. 본 논문에서는 non-alpha Weberface(non-alpha WF)와 히스토그램 평활화를 결합하여 조명 변화에 강건한 얼굴 표현 방법을 제안한다. 먼저, 입력 얼굴 영상에 대해 명암 대비 조절 파라미터를 적용하지 않은 non-alpha WF를 생성한다. 이후, non-alpha WF의 히스토그램 분포를 전역적으로 균일하게 하고 명암 대비를 향상시키기 위해 히스토그램 평활화를 수행한다. 제안하는 방법을 통해 전처리된 얼굴 영상으로부터 저차원 판별 특징을 추출하기 위해 $(2D)^2PCA$를 적용한다. Extended Yale B 및 CMU PIE 얼굴 데이터베이스에 대해 실험한 결과, 제안하는 방법으로 각각 93.31%와 97.25%의 평균 인식률을 얻었다. 또한, 제안하는 방법은 기존 WF뿐만 아니라 여러 조명 처리 방법들과 비교하여 향상된 인식 성능을 보였다.

• 호남수학학술지
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• 제33권4호
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• pp.519-527
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• 2011

Recently, the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$ are introduced in [3]: In this paper we give some interesting p-adic integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$. From those integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$.

• 대한수학회지
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• 제50권1호
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• pp.61-80
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• 2013

In this paper, we study ${\alpha}$-completely positive maps between locally $C^*$-algebras. As a generalization of a completely positive map, an ${\alpha}$-completely positive map produces a Krein space with indefinite metric, which is useful for the study of massless or gauge fields. We construct a KSGNS type representation associated to an ${\alpha}$-completely positive map of a locally $C^*$-algebra on a Krein locally $C^*$-module. Using this construction, we establish the Radon-Nikod$\acute{y}$m type theorem for ${\alpha}$-completely positive maps on locally $C^*$-algebras. As an application, we study an extremal problem in the partially ordered cone of ${\alpha}$-completely positive maps on a locally $C^*$-algebra.

• 대한수학회지
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• 제36권1호
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• pp.97-107
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• 1999

Given a C-dynamical system (A, G, $\alpha$) with a locally compact group G, two kinds of C-algebras are made from it, called the full C-crossed product and the reduced C-crossed product. In this paper, we extend the theory of the classical C-crossed product to the C-dynamical system (A, G, $\alpha$) with a left-cancellative semigroup M with unit. We construct a new C-algebra A $\alpha$rM, the reduced crossed product of A by the semigroup M under the action $\alpha$ and investigate some properties of A $\alpha$rM.

• East Asian mathematical journal
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• 제5권2호
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• pp.135-150
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• 1989

In this paper, we define new classes $S*({\alpha},{\beta},{\gamma})$ and $C*({\alpha},{\beta},{\gamma})$ of T, the class of analytic and univalent functions with negative coefficients. We have sharp results concerning coefficients, distortion of functions belonging to these classes along with a. representation formular for the function in $S*({\alpha},{\beta},{\gamma})$ and $C*({\alpha},{\beta},{\gamma})$. Furthermore, we improve the results of Libera for the class of starlike functions having negative coefficients.

• Korean Journal of Mathematics
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• 제12권2호
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• pp.107-115
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• 2004

In this paper, the new subclass denoted by $S_p({\alpha},{\beta},{\xi},{\gamma})$ of $p$-valent holomorphic functions has been introduced and investigate the several properties of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$. In particular we have obtained integral representation for mappings in the class $S_p({\alpha},{\beta},{\xi},{\gamma})$) and determined closed convex hulls and their extreme points of the class $S_p({\alpha},{\beta},{\xi},{\gamma})$.

• 대한수학회보
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• 제37권1호
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• pp.135-152
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• 2000

For a linear operator Q from $R^{d}\; into\; R^{d},\; {\alpha}\;>0\; and\ 0-semi-stability and the operater semi-stability of probability measures on $R^{d}$ are defined. Characterization of $(Q,b,{\alpha})$-semi-stable Gaussian distribution is obtained and the relationship between the class of $(Q,b,{\alpha})$-semi-stable non-Gaussian distributions and that of operator semistable distributions is discussed.

• 대한수학회보
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• 제33권2호
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• pp.303-310
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• 1996

The Gottlieb group of a compact connected ANR X, G(X), consists of all $\alpha \in \prod_{1}(X)$ such that there is an associated map $A : S^1 \times X \to X$ and a homotopy commutative diagram $$ S^1 \times X \longrightarrow^A X $$ $$incl \uparrow \nearrow \alpha \vee id $$ $$ S^1 \vee X $$.