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Qualified residue difference sets with zero

1998
*
Discrete Mathematics
*

In this paper we point out that if

doi:10.1016/s0012-365x(97)00072-1
fatcat:ei36yebm65gsxdnq3kmrtb7zv4
*zero*is counted as a*residue*then we can obtain further*qualified**residue**difference**sets*for both the biquadratic and the sextic*residues*. ... We previously established that biquadratic*qualified**residue**difference**sets*exist for primes p if and only if p = 16x 2 + 1 and sextic*qualified**residue**difference**sets*exist if and only if p = 108x 2 ... Theorem 3 . 3 If prime p=kn + 1 (k even) then a necessary and sufficient condition for the*set*R*= {O, rl,r2 ..... rk} (nth power*residues*and*zero*) to form a*qualified**residue**difference**set*,*with**qualifier*...##
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An extension for residue difference sets

1997
*
Discrete Mathematics
*

In this paper we extend the idea of

doi:10.1016/s0012-365x(96)00243-9
fatcat:q2ln6s25zzehzb7snilbkboyfq
*residue**difference**sets*,*with*existence theorems being established for certain classes of primes. ... We call R a*qualified**residue**difference**set*if there exists some non-*zero*integer m ¢ R which is such that if we form all the non-*zero**differences*ri-mrj(modp): l<~i,j~k, we obtain every positive integer ... We will refer to this new type of*residue**difference**set*as a*qualified**residue**difference**set*. ...##
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QUALIFIED DIFFERENCE SETS FROM UNIONS OF CYCLOTOMIC CLASSES

2009
*
Bulletin of the Australian Mathematical Society
*

*Qualified*

*difference*

*sets*(QDS) composed of unions of cyclotomic classes are discussed. ... An exhaustive computer search for such QDS and modified QDS that also possess the

*zero*

*residue*has been conducted for all powers n = 4, 6, 8 and 10. ... Acknowledgements The authors would like to thank Dr Shaun Cooper and Professor Ron Evans for their help

*with*this article. ...

##
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Twelfth Power Qualified Residue Difference Sets

2009
*
Integers
*

AbstractQualified

doi:10.1515/integ.2009.032
fatcat:he6qntwyqzbcngakk37frtc4ku
*residue**difference**sets*of power ... We call m a*qualifier*of multiplicity λ for the*set*R. If*zero*is counted as a*residue*we can obtain further*qualified**residue**difference**sets*. ... We call R a*qualified**residue**difference**set*(QRDS) if there exists some non-*zero*integer m / ∈ R which is such that if we form all the non-*zero**differences*r i − mr j (mod p), 1 ≤ i, j ≤ k, we obtain ...##
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An Empirical View on Opportunistic Forwarding Relay Selection Using Contact Records
[chapter]

2012
*
Lecture Notes in Computer Science
*

*zero*. ... Delay Reduced Ratio First, let us look at the average delay reduced ratio of potential relays in

*different*candidate

*sets*. ...

##
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Page 1529 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

1529 1i NUMBER THEORY
modified nth power

*residue**difference**set*(mod p) if there exists an integer A and there exists m (mod p) (m is called a*qualifier*)*with*m ¢ S,, such that the list of*differences*... Similarly, Sg is such a*difference**set*if and only if p = 108x? + 25 for some integer x, where the*qualifiers*are the cubic*residues*not in S¢. ...##
###
Page 90 of British Journal of Clinical Pharmacology Vol. 62, Issue 1
[page]

2006
*
British Journal of Clinical Pharmacology
*

of phase 2/3 studies compared

*with*the more controlled*settings*for phase | studies [17]. ... The*qualified*population pharmacokinetic model was fitted to the combined data*set*and two minor refine- ments were implemented to obtain the final model. ...##
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Lam's power residue addition sets

2011
*
Advances in Applied Mathematics
*

Classical n-th power

doi:10.1016/j.aam.2010.09.008
fatcat:76wesqohu5byrmxyzqhusqp5nm
*residue**difference**sets*modulo p are known to exist for n = 2, 4, 8. ... In 1976, Lam showed that*qualified*n-th power*residue**difference**sets*modulo p exist for n = 2, 4, 6, and he proved their nonexistence for all odd n and for n = 8, 10, 12. ... If m / ∈ H n , we call such an addition*set*a*qualified*power*residue**difference**set*modulo p*with**qualifier*m; cf. [14, 15] . ...##
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Polynomial construction of complex Hadamard matrices with cyclic core

1999
*
Applied Mathematics Letters
*

In conjunction

doi:10.1016/s0893-9659(98)00131-1
fatcat:2wnupxbkkrfmvin3n7e43vcjhe
*with*a certain uniformity property of polynomial coeffÉcients, these conditions yield a simple method by which complex Hadamard matrices*with*cyclic core can be constructed. ... In such cases, a real p-ary linear cyclic error correcting code may be associated*with*the complex Hadamard matrix. ... Ifj is a*residue*in Gf(p), let Aj be the multiplicity of j, as a member of the*set*of elements of V. If j is not such an element, define the multiplicity to be*zero*. ...##
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Lisa Pathfinder: Launch-Minus-7

2015
*
Zenodo
*

Based on the analysis of time series and closer to a seismometer than to a telescope, the science of the top geodesy and free-fall ESA mission of our days shall

doi:10.5281/zenodo.34496
fatcat:dy2uix3ahveihmbuwj3km4z3nm
*qualify*the technology to enable astronomy ... Replace detected force kicks*with**zeros*CheckHistogram Make a histogram of non-*zero*data BuildWindows Build high and low frequency windows based on acceleration data ApplyWindows Apply the windows to ... the chosen telemetry FitContributions Fit*different*signal contributions by minimising PSD ComputeResiduals Compute the*residual*acc noise of TM2 accounting for the*different*contributions Who are you? ...##
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Residue Classes of the PPT Sequence
[article]

2013
*
arXiv
*
pre-print

Primitive Pythagorean triples (PPT) may be put into

arXiv:1305.1900v1
fatcat:yeo7bo625ja6jpvq3e4lik5frq
*different*equivalence classes using*residues**with*respect to primes. ... We show that the probability that the smaller odd number associated*with*the PPT triple is divisible by prime p is 2/(p+1). ...*Residue*Classes We first prove a result on the number a (of the triple a, b, c) of PPTs for it to have*zero**residue**with*respect to mod p. ...##
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Dipole Anisotropy as an Essential Qualifier for the Monopole Component of the Cosmic-Dawn Spectral Signature, and the Potential of Diurnal Pattern for Foreground Estimation
[article]

2018
*
arXiv
*
pre-print

Such dipole

arXiv:1804.07993v2
fatcat:avmtwcclf5e23g6dcvzmc53du4
*qualifier*for the monopole spectrum, when combined*with*reliable foreground estimation, is expected to pave way for in situ validation of spectral signatures from early epochs, important to ... We describe details of such a test, and illustrate its application*with*the help of simulations. ... Fig. 2 . 2 -Expected*set*of*residual*or*difference*spectral profiles across the entire LST range, after subtraction of "all-sky" average spectral profile from the simulated*set*containing the discussed ...##
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Fault Detection and Isolation of a Three-tank System Using Analytical Temporal Redundancy – Parity Space/Relation Based Residual Generation

2020
*
International Journal of Advances in Scientific Research and Engineering
*

It is based on

doi:10.31695/ijasre.2020.33692
fatcat:hxa2cnfqere5tgw4ntej3k23ju
*residual*generation using a parity equations/space approach. The paper further briefly outlines other approaches of model-based*residual*generation. ... These*residuals*were then used to detect whether or not the system is faulty and indicate the location of the fault when it is faulty. ... Such*residual*-*sets*are said to be structured, which thus implies that each*residual*is completely unaffected by a*different*subset of faults. ...##
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Evidence for nonrandom hydrophobicity structures in protein chains

1996
*
Proceedings of the National Academy of Sciences of the United States of America
*

Our results, which

doi:10.1073/pnas.93.18.9533
pmid:8790365
pmcid:PMC38463
fatcat:mqa47ffco5b6daf3xom4hepxlq
*differ*from previous investigations using other methods, might have impact on how permissive*with*respect to sequence specificity the protein folding process is -- only sequences*with*... The results, which are based upon proteins in the SWISS-PROT data base, convincingly show that the amino acid sequences in proteins*differ*from what is expected from random sequences in a statistical significant ... (ii) Sequences*with**different*fractions of hydrophobic*residues*tend to behave in*different*ways. ...##
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Can the ICF osteoarthritis core set represent a future clinical tool in measuring functioning in persons with osteoarthritis undergoing hip and knee joint replacement?

2012
*
Journal of Rehabilitation Medicine
*

, Disability and Health (ICF) osteoarthritis core

doi:10.2340/16501977-1041
pmid:22948262
fatcat:3iikcph3efcinfpujxnzucf6tq
*set*categories in people*with*osteoarthritis undergoing hip and knee arthroplasty. ... Methods: The osteoarthritis core*set*was rated in 316 persons*with*osteoarthritis who were either in the pre-operative or within one year post-operative stage. ... that of the value of*zero**set*for the items. ...
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