Sets with Several Centers of Symmetry
نویسندگان
چکیده
Let A be a finite subset of the group Z2. Let C = {c0, c1, . . . , cs−1} be a finite set of s distinct points in the plane. For every 0 ≤ i ≤ s− 1, we define Di = {a− a′ : a ∈ A, a′ ∈ A, a + a′ = 2ci} and Rs(A) = |D0 ∪D1 ∪ · · · ∪ Ds−1|. In [1, 2], we found the maximal value of Rs(A) in cases s = 1, s = 2 and s = 3 and studied the structure of A assuming that R3(A) is equal or close to its maximal value. In this paper, we examine the case of s = 4 centers of symmetry and we find the maximal value of R4(A). Moreover, in cases when the maximal value is attained, we will describe the structure of extremal sets.
منابع مشابه
Multimodal medical image fusion based on Yager’s intuitionistic fuzzy sets
The objective of image fusion for medical images is to combine multiple images obtained from various sources into a single image suitable for better diagnosis. Most of the state-of-the-art image fusing technique is based on nonfuzzy sets, and the fused image so obtained lags with complementary information. Intuitionistic fuzzy sets (IFS) are determined to be more suitable for civilian, and medi...
متن کاملNumerical Simulation of Free Surface Flows and Comparison of Symmetry and Real Boundary Conditions at the Free Surface
For implementation
 of the free surface boundary condition, a new subroutine has been introduced to an existing steady 3-D body fitted code. This code was previously written for steady flow simulation in closed ducts. The algorithm used in this subroutine reduces the instability problem according to the free surface wave generation. For code validation, it was applied to two different open c...
متن کاملNumerical Simulation of Free Surface Flows and Comparison of Symmetry and Real Boundary Conditions at the Free Surface
For implementation of the free surface boundary condition, a new subroutine has been introduced to an existing steady 3-D body fitted code. This code was previously written for steady flow simulation in closed ducts. The algorithm used in this subroutine reduces the instability problem according to the free surface wave generation. For code validation, it was applied to two different open cha...
متن کاملA Queuing Model for Stochastic Location-inventory Problem with Waiting Cost Considerations
This paper presents a three-level supply chain model which includes single supplier, several distribution centers and sets of retailers. For this purpose, by adopting the queuing approach, a mixed nonlinear integer programming model is formulated. The proposed model follows minimizing the total cost of the system by determining: 1) the number and location of distribution centers between candida...
متن کاملClustering of Fuzzy Data Sets Based on Particle Swarm Optimization With Fuzzy Cluster Centers
In current study, a particle swarm clustering method is suggested for clustering triangular fuzzy data. This clustering method can find fuzzy cluster centers in the proposed method, where fuzzy cluster centers contain more points from the corresponding cluster, the higher clustering accuracy. Also, triangular fuzzy numbers are utilized to demonstrate uncertain data. To compare triangular fuzzy ...
متن کامل