The maximum, supremum, and spectrum for critical set sizes in (0,1)‐matrices

Cavenagh, Nicholas J.; Wright, Liam K.

doi:10.1002/jcd.21660

Cited by 3 publications

(3 citation statements)

References 6 publications

(18 reference statements)

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“…The optimum values for the mass ratio ϕ cannot be obtained using Eqs (8) and (10). To overcome this problem, we use the Taylor series of those equations with respect to the parameter ϕ of order n as follows (see references [24,30]), https://doi.org/10.1371/journal.pone.0228955.g008…”

Section: Pressure Control By Reining Mass Ratiomentioning

confidence: 99%

“…In statistics, a confidence interval (CI) is a type of interval estimate, computed from the statistics of the observed data, that might contain the true value of an unknown parameter [28][29][30]. Therefore, the confidence interval for the optimum values of the pressure P is defined as ½min P 0 ; � P optimal ; max P 0 ; � P optimal Þ, where min P 0 ; � P optimal and max P 0 ; � P optimal are given by,…”

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confidence: 99%

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Controlling the pressure of hydrogen-natural gas mixture in an inclined pipeline

Chaharborj

Amin

2020

PLoS ONE

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This paper discusses the optimal control of pressure using the zero-gradient control (ZGC) approach. It is applied for the first time in the study to control the optimal pressure of hydrogen natural gas mixture in an inclined pipeline. The solution to the flow problem is first validated with existing results using the Taylor series approximation, regression analysis and the Runge-Kutta method combined. The optimal pressure is then determined using ZGC where the optimal set points are calculated without having to solve the non-linear system of equations associated with the standard optimization problem. It is shown that the mass ratio is the more effective parameter compared to the initial pressure in controlling the maximum variation of pressure in a gas pipeline. OPEN ACCESSCitation: Chaharborj SS, Amin N (2020) Controlling the pressure of hydrogen-natural gas mixture in an inclined pipeline. PLoS ONE 15(2): e0228955.

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Section: Pressure Control By Reining Mass Ratiomentioning

confidence: 99%

mentioning

confidence: 99%

Controlling the pressure of hydrogen-natural gas mixture in an inclined pipeline

Chaharborj

Amin

2020

PLoS ONE

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“…Cavenagh and Wright [4] studied critical sets, that is, defining sets which are minimal in the sense that the removal of any element destroys the property of being a defining set. They showed that the complement of a critical set is itself a defining set.…”

Section: Introductionmentioning

confidence: 99%

Most binary matrices have no small defining set

Bodkin,

Liebenau,

Wanless

2019

Preprint

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Consider a matrix M chosen uniformly at random from a class of m × n matrices of zeros and ones with prescribed row and column sums. A partially filled matrix D is a defining set for M if M is the unique member of its class that contains the entries in D. The size of a defining set is the number of filled entries. A critical set is a defining set for which the removal of any entry stops it being a defining set.For some small fixed ε > 0, we assume that n m = o(n 1+ε ), and that λ 1/2, where λ is the proportion of entries of M that equal 1. We also assume that the row sums of M do not vary by more than O(n 1/2+ε ), and that the column sums do not vary by more than O(m 1/2+ε ). Under these assumptions we show that M almost surely has no defining set of size less than λmn − O(m 7/4+ε ). It follows that M almost surely has no critical set of size more than (1 − λ)mn + O(m 7/4+ε ). Our results generalise a theorem of Cavenagh and Ramadurai, who examined the case when λ = 1/2 and n = m = 2 k for an integer k.

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