On the Norms of GCD Matrices

Bozkurt, Durmuş; Solak, Süleyman

doi:10.3390/mca7030205

Cited by 4 publications

(4 citation statements)

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“…A divisor d ∈ Z + of n ∈ Z + is said to be a unitary divisor of n and is denoted by d n if (d, n/d) = 1. For example, the unitary divisors of 72 (= 2 3 3 2 ) are 1, 8,9,72. If d n, we also say that n is a unitary multiple of d. The greatest common unitary divisor (GCUD) of m and n exists for all m, n ∈ Z + but, unfortunately, the least common unitary multiple (LCUM) of m and n does not always exist.…”

Section: Unitary Divisors and Convolutionmentioning

confidence: 99%

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Inertia, positive definiteness and ℓ norm of GCD and LCM matrices and their unitary analogs

Haukkanen

Tóth

2018

Linear Algebra and its Applications

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Section: Unitary Divisors and Convolutionmentioning

confidence: 99%

“…Norms of GCD and LCM matrices have not been studied much in the literature. Some results are obtained in [1,2,8,15,16,17,38,39,40,44].…”

Section: ℓ P Normsmentioning

confidence: 99%

Inertia, positive definiteness and ℓ norm of GCD and LCM matrices and their unitary analogs

Haukkanen

Tóth

2018

Linear Algebra and its Applications

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“…Of course, civil penalties under 36.102 are a potentially significant source of revenues for GCDs. 64 The obviously most significant fee structure would be the per acre-foot fees of $1 for agricultural use and $10 for any other use. Yet, these limitations are couched in "not to exceed" language, another restriction on financing possibilities for GCDs.…”

Section: Groundwater Conservation District Finance In Texasmentioning

confidence: 99%

“…Fees set by a district may not unreasonably exceed the cost to the district of performing the administrative function for which the fee is charged.63 This section does not apply to the Edwards Aquifer Authority and certain other districts (see subsection C part iv. and v.) 64. The GCD may rule a penalty of up to $10,000 per day per violation.…”

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confidence: 99%

Groundwater Conservation District Finance in Texas: Results of a Preliminary Study

Porter

2013

Texas Water Journal

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The preferred method of groundwater management in Texas is by locally formed groundwater conservation districts (GCDs). However, not all of Texas groundwater is managed by a district; some areas have not voted to form a GCD. There are 99 GCDs in Texas with 2 pending; only 174 of the 254 counties are covered by a GCD. GCDs are financed by ad valorem taxes, fees, and grants. Not all GCDs have ad valorem tax support. Revenues from the responding GCDs in this study range from $20,000 annually to $2,632,982. Some cannot open their offices daily. All need money for research to determine the actual amount of groundwater in their district, its sources, and its characteristics. Tax rates for the GCDs with ad valorem tax authority in this study run from $.005/$100 valuation to $.035/$100 valuation, meaning a $200,000 home in these districts would pay from $10 to $70 annually, not as much as a few cups of Starbucks coffee cost annually. All Texans agree water is life and groundwater is one of our most precious resources, therefore GCDs deserve more financial resources. The Texas Water Code provides a number of tools for GCDs to finance their operations including ad valorem taxation levies, issuance of bonds, notes, and promulgation of fees to name a few. However, in many of the GCDs who responded to the study, these tools are not practical to use. Since ad valorem taxation and bond authority must be granted by local voter approval, these tools are unavailable in some GCDs as well. Citation: Porter CR Jr. 2013. Groundwater conservation district finance in Texas: results of a preliminary study. Texas Water Journal. 4(1):55-77. Available from: https://doi.org/10.21423/twj.v4i1.6445.

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A note on bounds for norms of the reciprocal LCM matrix

Altınışık¹,

Tuglu²,

Haukkanen³

2004

Mathematical Inequalities &Amp; Applications

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Abstract. Let S = {x 1 , x 2 , . . . , x n } be a set of distinct positive integers and [x i , x j ] denote the least common multiple of x i and x j . The matrix, is called the reciprocal least common multiple (reciprocal LCM) matrix on S. In this paper, we investigate some matrix norms of the reciprocal LCM matrix and one of its generalizations on S = {1, 2, . . . , n} in terms of the Riemann zeta function. (2000): 11C20, 15A36, 15A60, 11A25. Mathematics subject classification

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On the Norms of GCD Matrices

Abstract: In this study, we have established the bounds for the \(\ell_p \) norms and the Euclidean norm of almost GCD Cauchy-Toeplitz, almost GCD Cauchy-Hankel and GCD matrices, respectively.

Cited by 4 publications

References 0 publications

Inertia, positive definiteness and ℓ norm of GCD and LCM matrices and their unitary analogs

Inertia, positive definiteness and ℓ norm of GCD and LCM matrices and their unitary analogs

Groundwater Conservation District Finance in Texas: Results of a Preliminary Study

A note on bounds for norms of the reciprocal LCM matrix

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