On the 3BD‐closed set <i>B</i><sub>3</sub>({4,5,6})

Ji, Lijun

doi:10.1002/jcd.10067

Cited by 26 publications

(71 citation statements)

References 8 publications

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“…It is proved in Lemma 2.5 that a partitionable candelabra system of type ðg n : 5Þ leads to an LMPðgn þ 5Þ for g ¼ 6; 12: In Sections 3 and 4, we show the existence of partitionable candelabra systems of type ð6 n : 5Þ and type ð12 n : 5Þ; respectively. Such existence is based on the known result of Steiner quadruple systems Sð3; 4; vÞs by Hanani [8] and the recent results of 1-fan Sð3; 4; vÞs and Sð3; f4; 5; 6g; vÞs by Ji [11,12]. In Section 5, we use these partitionable candelabra systems to obtain the main result.…”

Section: Introductionmentioning

confidence: 91%

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Large sets of disjoint packings on 6k+5 points

Cao

Ji²,

Zhu³

2004

Journal of Combinatorial Theory, Series A

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A ð2; 3Þ-packing on X is a pair ðX ; AÞ; where A is a set of 3-subsets (called blocks) of X ; such that any pair of distinct points from X occurs together in at most one block. Its leave is a graph ðX ; EÞ such that E consists of all the pairs which do not appear in any block of A: For a ð6k þ 5Þ-set X a large set of maximum packing, denoted by LMPð6k þ 5Þ; is a set of 6k þ 1 disjoint ð2; 3Þ-packings on X with a cycle of length four as their common leave. Schellenberg and Stinson (J. Combin. Math. Combin. Comput. 5 (1989) 143) first introduced such a large set problem and used it to construct perfect threshold schemes. In this paper, we show that an LMPð6k þ 5Þ exists for any positive integer k: This complete solution is based on the known existence result of Sð3; 4; vÞs by Hanani and that of 1-fan Sð3; 4; vÞs and Sð3; f4; 5; 6g; vÞs by the second author. Partitionable candelabra system also plays an important role together with two special known LMPð6k þ 5Þs for k ¼ 1; 2: r

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Section: Introductionmentioning

confidence: 91%

“…Lemma 3.7 (Ji [12]). There exists an Sð3; f4; 5; 6g; vÞ for any positive integer v 0; 1; 2 ðmod 4Þ and va9; 13: Proof.…”

Section: Constructions For Pcsð6 N : 5þmentioning

confidence: 98%

Large sets of disjoint packings on 6k+5 points

Cao

Ji²,

Zhu³

2004

Journal of Combinatorial Theory, Series A

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“…Below are all blocks of an initial GDD (2,3,15) Developing this initial GDD modulo 15 generates the required 15 pairwise disjoint GDD(2, 3, 15) of type 3 5 and they form a PGDD(3 5 2 1 ).…”

Section: Lemma 33mentioning

confidence: 99%

“…Applying Theorem 5.1 with b = 12 gives the desired design. The input designs GDD(3, 4, 12m ) of type 12 m (m ∈ {4, 5,6,7,9,11,13,15,19,23 For m = 14, there is an inversive plane of order 13, i.e., there is an S (3,14,170). Fix two points x, y.…”

Section: Lemma 54mentioning

confidence: 99%

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A new existence proof for large sets of disjoint Steiner triple systems

Ji¹

2005

Journal of Combinatorial Theory, Series A

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A Steiner triple system of order v (briefly STS(v)) consists of a v-element set X and a collection of 3-element subsets of X, called blocks, such that every pair of distinct points in X is contained in a unique block. A large set of disjoint STS(v) (briefly LSTS(v)) is a partition of all 3-subsets (triples) of X into v − 2 STS(v). In 1983-1984, Lu Jiaxi first proved that there exists an LSTS(v) for any v ≡ 1 or 3 (mod 6) with six possible exceptions and a definite exception v = 7. In 1989, Teirlinck solved the existence of LSTS(v) for the remaining six orders. Since their proof is very complicated, it is much desired to find a simple proof. For this purpose, we give a new proof which is mainly based on the 3-wise balanced designs and partitionable candelabra systems.

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A distance e‐learning platform for signal analysis and measurement using FFT

Chen

Lin

2011

Comp Applic In Engineering

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ABSTRACT:The fast Fourier transform (FFT) and the power spectrum are still powerful tools for analyzing and measuring both stationary and transient signals in power systems. However, the misapplications of FFT can lead to incorrect results caused by some problems such as aliasing effect, spectral leakage, and picket-fence effect. Measurement errors can be efficiently reduced by understanding fundamentals of FFT as well as loading proper windows. This article develops a distance e-learning environment using a graphical programming tool to help electrical students and engineers for enhancing their signal analysis capability via the Internet Explorer (IE). Critical issues pertaining to engineering education, such as programming design of signal analysis, Internet connection, expected learning outcomes, and course evaluation, are discussed in detail.

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On the 3BD‐closed set B₃({4,5,6})

Abstract: Let B 3 ðKÞ ¼ fv

Cited by 26 publications

References 8 publications

Large sets of disjoint packings on 6k+5 points

Large sets of disjoint packings on 6k+5 points

A new existence proof for large sets of disjoint Steiner triple systems

A distance e‐learning platform for signal analysis and measurement using FFT

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On the 3BD‐closed set B3({4,5,6})

Abstract: Let B 3 ðKÞ ¼ fv

Cited by 26 publications

References 8 publications

Large sets of disjoint packings on 6k+5 points

Large sets of disjoint packings on 6k+5 points

A new existence proof for large sets of disjoint Steiner triple systems

A distance e‐learning platform for signal analysis and measurement using FFT

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Product

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On the 3BD‐closed set B₃({4,5,6})