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Qualified residue difference sets with zero

Derek Jennings, Kevin Byard
1998 Discrete Mathematics  
In this paper we point out that if 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  ... 
doi:10.1016/s0012-365x(97)00072-1 fatcat:ei36yebm65gsxdnq3kmrtb7zv4

An extension for residue difference sets

Derek Jennings, Kevin Byard
1997 Discrete Mathematics  
In this paper we extend the idea of 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.  ... 
doi:10.1016/s0012-365x(96)00243-9 fatcat:q2ln6s25zzehzb7snilbkboyfq


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.  ... 
doi:10.1017/s0004972709000161 fatcat:pm6ocxb2abekzmoauykwzoyrx4

Twelfth Power Qualified Residue Difference Sets

Kevin Byard
2009 Integers  
AbstractQualified 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  ... 
doi:10.1515/integ.2009.032 fatcat:he6qntwyqzbcngakk37frtc4ku

An Empirical View on Opportunistic Forwarding Relay Selection Using Contact Records [chapter]

Jia Jianbin, Chen Yingwen, Xu Ming
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.  ... 
doi:10.1007/978-3-642-35606-3_30 fatcat:ql55efhxczdhliybyopvnwipz4

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.  ... 

Lam's power residue addition sets

Kevin Byard, Ron Evans, Mark Van Veen
2011 Advances in Applied Mathematics  
Classical n-th power 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] .  ... 
doi:10.1016/j.aam.2010.09.008 fatcat:76wesqohu5byrmxyzqhusqp5nm

Polynomial construction of complex Hadamard matrices with cyclic core

C.H. Cooke, I. Heng
1999 Applied Mathematics Letters  
In conjunction 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.  ... 
doi:10.1016/s0893-9659(98)00131-1 fatcat:2wnupxbkkrfmvin3n7e43vcjhe

Lisa Pathfinder: Launch-Minus-7

Michele Armano
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 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?  ... 
doi:10.5281/zenodo.34496 fatcat:dy2uix3ahveihmbuwj3km4z3nm

Residue Classes of the PPT Sequence [article]

Subhash Kak
2013 arXiv   pre-print
Primitive Pythagorean triples (PPT) may be put into 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.  ... 
arXiv:1305.1900v1 fatcat:yeo7bo625ja6jpvq3e4lik5frq

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]

Avinash A. Deshpande
2018 arXiv   pre-print
Such dipole 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  ... 
arXiv:1804.07993v2 fatcat:avmtwcclf5e23g6dcvzmc53du4

Fault Detection and Isolation of a Three-tank System Using Analytical Temporal Redundancy – Parity Space/Relation Based Residual Generation

K. T. Aminu, M. M. Jibril, A. A. Jimoh, S. Mohammed, A. G. Jumba
2020 International Journal of Advances in Scientific Research and Engineering  
It is based on 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.  ... 
doi:10.31695/ijasre.2020.33692 fatcat:hxa2cnfqere5tgw4ntej3k23ju

Evidence for nonrandom hydrophobicity structures in protein chains

A. Irback, C. Peterson, F. Potthast
1996 Proceedings of the National Academy of Sciences of the United States of America  
Our results, which 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.  ... 
doi:10.1073/pnas.93.18.9533 pmid:8790365 pmcid:PMC38463 fatcat:mqa47ffco5b6daf3xom4hepxlq

Can the ICF osteoarthritis core set represent a future clinical tool in measuring functioning in persons with osteoarthritis undergoing hip and knee joint replacement?

M Alviar, J Olver, J Pallant, C Brand, R Steiger, M Pirpiris, A Bucknill, F Khan
2012 Journal of Rehabilitation Medicine  
, Disability and Health (ICF) osteoarthritis core 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.  ... 
doi:10.2340/16501977-1041 pmid:22948262 fatcat:3iikcph3efcinfpujxnzucf6tq
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