Size of k-uniform hypergraph with diameter d

Miao-lin, YE

doi:10.1016/s0012-365x(02)00593-9

Cited by 5 publications

(4 citation statements)

References 2 publications

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“…In Section 3, through combination with the idea of Siriwong et al [9] and the idea presented in Section 2, we choose another ideal I of D that enables us to construct the k-partite σ-zero-divisor hypergraph of D I with the integer σ ≥ k. Moreover, we determine its diameter and minimum length of all cycles or girth. For the definition of diameter and cycles in a hypergraph, we refer to [19,20], respectively.…”

Section: Introductionmentioning

confidence: 99%

k-Zero-Divisor and Ideal-Based k-Zero-Divisor Hypergraphs of Some Commutative Rings

Siriwong

Boonklurb

2021

Symmetry

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Let R be a commutative ring with nonzero identity and k≥2 be a fixed integer. The k-zero-divisor hypergraph Hk(R) of R consists of the vertex set Z(R,k), the set of all k-zero-divisors of R, and the hyperedges of the form {a1,a2,a3,⋯,ak}, where a1,a2,a3,⋯,ak are k distinct elements in Z(R,k), which means (i) a1a2a3⋯ak=0 and (ii) the products of all elements of any (k−1) subsets of {a1,a2,a3,⋯,ak} are nonzero. This paper provides two commutative rings so that one of them induces a family of complete k-zero-divisor hypergraphs, while another induces a family of k-partite σ-zero-divisor hypergraphs, which illustrates unbalanced or asymmetric structure. Moreover, the diameter and the minimum length of all cycles or girth of the family of k-partite σ-zero-divisor hypergraphs are determined. In addition to a k-zero-divisor hypergraph, we provide the definition of an ideal-based k-zero-divisor hypergraph and some basic results on these hypergraphs concerning a complete k-partite k-uniform hypergraph, a complete k-uniform hypergraph, and a clique.

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Section: Introductionmentioning

confidence: 99%

k-Zero-Divisor and Ideal-Based k-Zero-Divisor Hypergraphs of Some Commutative Rings

Siriwong

Boonklurb

2021

Symmetry

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“…Oxidised pellets, possessing good mechanical and metallurgical properties, are high quality burdens for blast furnace ironmaking 1,2 However, with the rapid development of the iron and steel industries, magnetite resources are becoming scarce.…”

Section: Introductionmentioning

confidence: 99%

Oxidising roasting behaviours of anthracite containing haematite pellets

Tang

Zhang

et al. 2013

Ironmaking & Steelmaking

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In this investigation, the roasting features of haematite pellets to which a small amount of anthracite was added and the effects of carbon on the induration behaviours of the pellets were studied. The results indicate that the suitable dosage of pulverised anthracite is 1?0-1?5%. During the roasting, part of the original haematite grains in the pellets are reduced to magnetite, and some original haematite grains are decomposed into magnetite. Then, the newborn magnetite is oxidised to secondary haematite, which is beneficial to the recrystallisation of Fe 2 O 3 in the fired pellets. Therefore, adding a certain proportion of anthracite is an effective way to improve the roasting strength of haematite pellets, as well as to reduce the roasting temperature and the total energy consumption of the pellet production. IntroductionOxidised pellets, possessing good mechanical and metallurgical properties, are high quality burdens for blast furnace ironmaking. 1,2 However, with the rapid development of the iron and steel industries, magnetite resources are becoming scarce. Thus, it is imperative to make good use of haematite resources to produce pellets. 3 Imported haematite concentrate is of high iron grade, low gangue content and fine granularity. 4 However, the high quality finished pellets from haematite concentrates require a higher roasting temperature and narrower firing temperature range (1300-1350uC), and the fired strength is relatively lower than that of magnetite pellets. 5,6 Hence, how to solve the problems of oxidised pellets prepared from haematite concentrates becomes very important. Much research has been conducted on oxidised pellets prepared from mixed haematite-magnetite concentrates, 4,6,7 where it has been shown that roasting temperature can be reduced and fired strength improved. However, to ensure adequate strength for blast furnace use, magnetite needs to exceed 20%. 7,8 Practical results for adding a certain proportion of solid fuel to haematite concentrates show that the pellet strength is increased, energy consumption is reduced and the pellet metallurgical properties are improved. 9,10 However, before the oil crisis of 1973, because of their low price and easy use, oil and natural gas were widely used as fuels, and the practice of adding solid fuel in haematite pellets had not been well developed. 9 Since the oil crisis, the price of oil has soared and far exceeds that of solid fuel, and much research on carbon containing pellet preparation has been conducted. 9,11,12 However, most of the research has focused on energy saving, and few studies have been designed to reveal the induration mechanisms of carbon containing haematite pellets.In the last 20 years, some investigations on carbon containing haematite pellets have been carried out in China; 13-17 however, most of the research was directed towards the preparation of reduced pellets for non-blast furnace ironmaking. 18 With the increasing requirement for Blast Furnace (BF) fuel economy, adding solid fuel to pellets as an energy saving measu...

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“…Oxidised pellets are increasingly used in ironmaking burdens resulting from the high total iron content, symmetrical granularity, good mechanical strength and superior reducibility. [1][2][3][4] With the rapid development of the Chinese iron and steel industry, the demand for acid oxidised pellets has increased significantly and the domestic pellet industry is a developing opportunity. 5 However, this increase in pellet use has resulted in material shortages and how to make best use of iron ore resources both at home and abroad is increasingly studied.…”

Section: Introductionmentioning

confidence: 99%

Induration mechanisms of oxidised pellets prepared from mixed magnetite–haematite concentrates

Zhang

et al. 2009

Ironmaking & Steelmaking

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The crystallisation behaviour of Fe 2 O 3 during preheating and roasting of pellets made from mixed magnetite-haematite (M-H) concentrates has been studied. The results indicate that the strength of pellets is mainly provided by the crystalline connections between Fe 2 O 3 particles during preheating. This occurs because the activity of Fe 2 O 3 from secondary haematite (SH) (oxidised from magnetite concentrate, SH) is higher than from original haematite (OH). In the roasting process, when temperature is lower than 1250uC, the strength is mainly provided by the development, connection and growth of Fe 2 O 3 crystalline grains from SH. Only if the temperature exceeds 1280uC does Fe 2 O 3 recrystallisation in OH grains develop well with the iron ore particles in the pellets fully connected, so increasing pellet strength.

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Size of k-uniform hypergraph with diameter d

Cited by 5 publications

References 2 publications

k-Zero-Divisor and Ideal-Based k-Zero-Divisor Hypergraphs of Some Commutative Rings

k-Zero-Divisor and Ideal-Based k-Zero-Divisor Hypergraphs of Some Commutative Rings

Oxidising roasting behaviours of anthracite containing haematite pellets

Induration mechanisms of oxidised pellets prepared from mixed magnetite–haematite concentrates

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