• 대한수학회지
• /
• 제39권1호
• /
• pp.51-60
• /
• 2002

Some random fixed point theorems for nonexpansive and *-nonexpansive random operators defined on convex and star-shaped sets in a Frechet space are proved. Our work extends recent results of Beg and Shahzad and Tan and Yaun to noncontinuous multivalued random operators, sets analogue to an earlier result of Itoh and provides a random version of a deterministic fixed point theorem due to Singh and Chen.

• Journal of applied mathematics & informatics
• /
• 제35권1_2호
• /
• pp.147-163
• /
• 2017

In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (MW D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).

• 대한수학회논문집
• /
• 제37권1호
• /
• pp.105-112
• /
• 2022

Let g : X ⟶ Y and f : Y ⟶ Z be two maps between real normed linear spaces. Then f is called generalized isometry or g-isometry if for each x, y ∈ X, ║f(g(x)) - f(g(y))║ = ║g(x) - g(y)║. In this paper, under special hypotheses, we prove that each generalized isometry is affine. Some examples of generalized isometry are given as well.

• Journal of applied mathematics & informatics
• /
• 제41권5호
• /
• pp.937-946
• /
• 2023

In this present work, we inaugurated subclasses of analytic functions which are associated with generalized Mittag Leffler Functions. Inclusion implications and integral preserving properties under the Bernardi integral operator are investigated. Some consequences of these findings are also illustrated.

• 대한수학회지
• /
• 제42권1호
• /
• pp.129-134
• /
• 2005

Lpt X be a reduced Stein space and L a holomorphic line bundle on X. L is spanned by its global sections and the associated holomorphic map $h_L\;:\;X{\to}P(H^0(X, L)^{\ast})$ is an embedding. Choose any locally convex vector topology ${\tau}\;on\;H^0(X, L)^{\ast}$ stronger than the weak-topology. Here we prove that $h_L(X)$ is sequentially closed in $P(H^0(X, L)^{\ast})$ and arithmetically Cohen -Macaulay. i.e. for all integers $k{\ge}1$ the restriction map ${\rho}_k\;:\;H^0(P(H^0(X, L)^{\ast}),\;O_{P(H^0(X, L)^{\ast})}(k)){\to}H^0(h_L(X),O_{hL_(X)}(k)){\cong}H^0(X, L^{\otimes{k}})$ is surjective.

• International Journal of Contents
• /
• 제12권2호
• /
• pp.42-48
• /
• 2016

We present efficient algorithms for computing centroid directions for each of the three types of monotonicity in a polyhedron: strong, weak, and directional monotonicity, which can be used for optimizing directions in many 3D manufacturing processes. Strongly- and directionally-monotone directions are the poles of great circles separating a set of spherical polygons on the unit sphere, the centroids of which are shown to be obtained by applying the previous result for determining the maximum intersection of the set of their dual spherical polygons. Especially in this paper, we focus on developing an efficient method for approximating the weakly-monotone centroid, which is the pole of one of the great circles intersecting a set of spherical polygons on the unit sphere. The original problem is approximately reduced into computing the intersection of great bands for avoiding complicated computational complexity of non-convex objects on the unit sphere, which can be realized with practical linear-time operations.

• East Asian mathematical journal
• /
• 제24권1호
• /
• pp.35-43
• /
• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.

• 한국CDE학회논문집
• /
• 제6권2호
• /
• pp.101-110
• /
• 2001

The maximum intersection of spherical convex polygons are to find spherical regions owned by the maximum number of the polygons, which is applicable for determining the feasibility in manufacturing problems such mould design and numerical controlled machining. In this paper, an efficient method for partitioning a sphere with the polygons into faces is presented for the maximum intersection. The maximum intersection is determined by examining the ownerships of partitioned faces, which represent how many polygons contain the faces. We take the approach of edge-based partition, in which, rather than the ownerships of faces, those of their edges are manipulated as the sphere is partitioned incrementally by each of the polygons. Finally, gathering the split edges with the maximum number of ownerships as the form of discrete data, we approximately obtain the centroids of all solution faces without constructing their boundaries. Our approach is analyzed to have an efficient time complexity Ο(nv), where n and v, respectively, are the numbers of polygons and all vertices. Futhermore, it is practical from the view of implementation since it can compute numerical values robustly and deal with all degenerate cases.

• Journal of Communications and Networks
• /
• 제15권3호
• /
• pp.283-291
• /
• 2013

In this paper, we propose new multiuser detectors (MUDs) based on compressed sensing approaches for the large-scale multiple antenna systems equipped with dozens of low-power antennas. We consider the scenarios where the number of receiver antennas is smaller than the total number of users, but the number of active users is relatively small. This prior information motivates sparsity-embracing MUDs such as sparsity-embracing linear/nonlinear MUDs where the detection of active users and their symbol detection are employed. In addition, sparsity-embracing MUDs with maximum a posteriori probability criterion (MAP-MUDs) are presented. They jointly detect active users and their symbols by exploiting the probability of user activity, and it can be solved efficiently by introducing convex relaxing senses. Furthermore, it is shown that sparsity-embracing MUDs exploiting common users' activity across multiple symbols, i.e., frame-by-frame, can be considered to improve performance. Also, in multiple multiple-input and multiple-output networks with aggressive frequency reuse, we propose the interference cancellation strategy for the proposed sparsity-embracing MUDs. That first cancels out the interference induced by adjacent networks and then recovers the desired users' information by exploiting the low user activity. In simulation studies for binary phase shift keying modulation, numerical evidences establish the effectiveness of our proposed MUDs exploiting low user activity, as compared with the conventional MUD.

• 융합신호처리학회논문지
• /
• 제5권4호
• /
• pp.256-262
• /
• 2004

로봇이 자율주행을 하는데 있어 중요한 요소는 로봇 스스로 위치를 추정하고 동시에 주위 환경에 대한 지도를 작성하는 것이다. 본 논문에서는 어안렌즈를 이용한 비전 기반 위치 추정 및 매핑 알고리즘을 제안한다. 로봇에 어안렌즈가 부착된 카메라를 천정을 바라볼 수 있도록 부착하여 스케일 불변 특징을 갖는 고급의 영상 특징을 구하고, 이 특징들을 맵 빌딩과 위치 추정에 이용하였다. 전처리 과정으로 어안렌즈를 통해 입력된 영상을 카메라 보정을 행하여 축방향 왜곡을 제거하고 레이블링과 컨벡스헐을 이용하여 보정된 영상에서 천정영역과 벽영역으로 분할한다. 최초 맵 빌딩시에는 분할된 영역에 대해 특징점을 구하고 맵 데이터베이스에 저장한다. 맵 빌딩이 종료될 때까지 연속하여 입력되는 영상에 대해 특징점들을 구하고 맵과 매칭되는 점들을 찾고 매칭되지 않은 점들에 대해서는 기존의 맵에 추가하는 과정을 반복한다. 위치 추정은 맵 빌딩 과정과 맵 상에서 로봇의 위치를 찾는데 이용된다. 로봇의 위치에서 구해진 특징점들은 로봇의 실제 위치를 추정하기 위해 기존의 맵과 매칭을 행하고 동시에 기존의 맵 데이터베이스는 갱신된다. 제안한 방법을 적용하면 50㎡의 영역에 대한 맵 빌딩 소요 시간은 2분 이내, 위치 추정시 위치 정확도는 ±13cm, 로봇의 자세에 대한 각도 오차는 ±3도이다.