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Cyclic Resultants [article]

Christopher J. Hillar
2005 arXiv   pre-print
We characterize polynomials having the same set of nonzero cyclic resultants.  ...  Finally, we discuss how our results yield algorithms for explicit reconstruction of polynomials from their cyclic resultants.  ...  Cyclic Resultants and Rational Functions We begin with some preliminaries concerning cyclic resultants.  ... 
arXiv:math/0401220v3 fatcat:kya5gg4i5veibnraufc6ac5zye

Cyclic resultants

Christopher J. Hillar
2005 Journal of symbolic computation  
We characterize polynomials having the same set of nonzero cyclic resultants.  ...  Finally, we discuss how our results yield algorithms for explicit reconstruction of polynomials from their cyclic resultants.  ...  Cyclic resultants and rational functions We begin with some preliminaries concerning cyclic resultants.  ... 
doi:10.1016/j.jsc.2005.01.001 fatcat:osxcipynlnhgfphudlu5jrafzq

Polynomial recurrences and cyclic resultants [article]

Christopher J. Hillar, Lionel Levine
2006 arXiv   pre-print
The m-th cyclic resultant of f is r_m = Res(f,x^m-1).  ...  In addition, we show that cyclic resultants satisfy a polynomial recurrence of length d+1.  ...  The sequence {r n } n≥1 of cyclic resultants of f obeys a polynomial recurrence of length d + 1.  ... 
arXiv:math/0411414v4 fatcat:o2lzlj23nreanbcc6uzhvetq64

A classification result and contact structures in oriented cyclic orbifold [article]

Saibal Ganguli
2015 arXiv   pre-print
In course of proving the above results we prove a classification result for compact oriented cyclic-3 orbifolds which has not been seen by us in literature before.  ...  We prove every oriented compact cyclic 3-orbifold has a contact structure.  ...  The resulting space has a cyclic orbifold structure. 6. Contact orbifold Definition 6.1.  ... 
arXiv:1503.05645v7 fatcat:zizpj3alezgu3fgf625qq5sfdu

Exceptional units and cyclic resultants

C. L. Stewart
2012 Acta Arithmetica  
Hillar and Levine [8] proved that a generic monic polynomial f is determined by its first 2 d+1 cyclic resultants and conjectured that the first d + 1 cyclic resultants suffice to determine f.  ...  Hillar [7] , and later Bézivin [2, 3] , studied the general case and characterized polynomials f and g in C[x] which generate the same sequence of non-zero cyclic resultants.  ... 
doi:10.4064/aa155-4-5 fatcat:vxnws7ne3jb5pgkzfyhkkwg4ze

Polynomial recurrences and cyclic resultants

Christopher J. Hillar, Lionel Levine
2006 Proceedings of the American Mathematical Society  
The m-th cyclic resultant of f is A generic monic polynomial is determined by its full sequence of cyclic resultants; however, the known techniques proving this result give no effective computational bounds  ...  In addition, we show that cyclic resultants satisfy a polynomial recurrence of length d + 1.  ...  The sequence {r n } n≥1 of cyclic resultants of f obeys a polynomial recurrence of length d + 1.  ... 
doi:10.1090/s0002-9939-06-08672-2 fatcat:navbx5cxjfemddbjeq4zd3wfsq

CYCLICALLY PRESENTED GROUPS AND RESULTANTS

J. E. CREMONA, M. EDJVET
2010 International journal of algebra and computation  
The following corollary to the results of Cyclically Presented Groups and Resultants 419 Sec. 3 confirms this for l ≤ 15 and 6 ≤ n ≤ 100.  ...  Now the automorphism θ of F n defined above induces an automorphism of G n (w), and the resulting split extension H n (w), of G n (w) by the cyclic group of order n, has a presentation H n (w) = x, t |  ...  The results are given in Table 4 .  ... 
doi:10.1142/s0218196710005777 fatcat:fsr6yktaj5gczgmiaxtmfywrri

Planck 2013 results support the cyclic universe

Jean-Luc Lehners, Paul J. Steinhardt
2013 Physical Review D  
We show that results from the Planck satellite reported in 2013 are consistent with the simplest cyclic models for natural parameter ranges i.e., order unity dimensionless coefficients, assuming the standard  ...  With improved precision, forthcoming results from Planck and other experiments should be able to test the parameter ranges by confirming or refuting the core predictions - i.e., no observable primordial  ...  LD14438 R E V I E W C O P Y N O T F O R D I S T R I B U T I O N Planck2013 results support the cyclic universe The recent results by the Planck satellite have been presented as supporting the predictions  ... 
doi:10.1103/physrevd.87.123533 fatcat:vllunuhyerfldpo3ewhpueeahy

Some results on quasi-cyclic codes

C.L. Chen, W.W. Peterson, E.J. Weldon
1969 Information and Control  
The last result is a proof that there exist very long quasicyclic codes which meet the Gilbert bound.  ...  These quasicyclic codes are closely related in structure to cyclic codes although they are not nearly as well understood.  ...  Many of the more elementary results for cyclic codes have quasicyclic analogs, and it would appear that several decoding techniques suited to short cyclic codes can be used for short quasicyclic codes.  ... 
doi:10.1016/s0019-9958(69)90497-5 fatcat:t7ljngviirhdffcw3ez72wpyga

Results On Cyclic Signal Processing Systems

P.P. Vaidyanathan
1998 Zenodo  
CYCLIC STATE-SPACE DESCRIPTIONS Consider a cyclic LTI structure with N cyclic delay elements (e.g., N = L − 1 and N = 1 in Figs. 1 and 2, respectively).  ...  The quantity W k L is interpreted as a unit of "cyclic-delay", and is used in structures representing cyclic systems.  ... 
doi:10.5281/zenodo.36884 fatcat:6jz7jrausjgwzb6syjxcjzhnri

Exact results on linear response of cyclic molecular aggregates [article]

A.V.Ilinskaia, K.N.Ilinski, G.V.Kalinin, V.V.Melezhik, A.S.Stepanenko
1995 arXiv   pre-print
The exact results for characteristics of the response are obtained. In particular, we calculate time-dependent two-point correlation functions at finite temperature for the cyclic 1-D XY-model.  ...  Basing on the picture of Frenkel excitons in molecular crystals described by the XY-model we consider the linear response of linear cyclic aggregates at finite temperature.  ...  The conclusion completes the paper with a discussion of the resulting formulae for characteristics of the linear response for the cyclic J-aggregates.  ... 
arXiv:cond-mat/9509040v2 fatcat:r56dsp6thrftjakkwhg74o4vbe

Some Results on Cyclic Interval Edge Colorings of Graphs [article]

Armen S. Asratian, Carl Johan Casselgren, Petros A. Petrosyan
2017 arXiv   pre-print
Some results are obtained for (a,b)-biregular graphs, that is, bipartite graphs with the vertices in one part all having degree a and the vertices in the other part all having degree b; it has been conjectured  ...  that all these have cyclic interval colorings.  ...  The resulting coloring is a cyclic interval 5-coloring.  ... 
arXiv:1606.09389v2 fatcat:a5pjmipz2zft3kdh4iwvuknque

New cyclic voltammetry method for examining phase transitions: Simulated results

I. Abou Hamad, D.T. Robb, P.A. Rikvold
2007 Journal of Electroanalytical Chemistry  
We propose a new experimental technique for cyclic voltammetry, based on the first-order reversal curve (FORC) method for analysis of systems undergoing hysteresis.  ...  Experimental data for EC-FORC analysis could easily be obtained by simple reprogramming of a potentiostat designed for conventional cyclic-voltammetry experiments.  ...  The method is thus a simple generalization of the standard cyclic voltammetry (CV) method, in which the negative return potential is decreased for each cycle.  ... 
doi:10.1016/j.jelechem.2006.10.037 fatcat:4e4hg4znonadlf5wefaxbjl7ke

Further results on the global cyclicity index of graphs [article]

Yujun Yang
2013 arXiv   pre-print
In this paper, by utilizing techniques from graph theory, electrical network theory and real analysis, we obtain some further results on this new cyclicity measure, including the strictly monotone increasing  ...  property, some lower and upper bounds, and some Nordhuas-Gaddum-type results.  ...  In this section, we will consider Nordhaus-Gaddum-type results for the global cyclicity index. There is only one connected graph P 4 on 4 vertices with the connected complement P 4 = P 4 .  ... 
arXiv:1303.0369v1 fatcat:dg4pvgplbjeqlie2aeriyqa5ii

A Further Result on the Cyclic Subspace

Huailei Wang
2014 Advances in Linear Algebra and Matrix Theory  
By this result, a new approach of proof is found for the fact that a square matrix with only one eigenvalue and one-dimensional eigenspace is similar to a Jordan block matrix.  ...  Based on the geometric theories of vector space, a Cross-Identity theorem is proved for the relationship between the power kernels and power images of linear map Α Ι − λ on its cyclic subspace.  ...  Now, it is ready to present some further results for a cyclic space as follows.  ... 
doi:10.4236/alamt.2014.42007 fatcat:mvuwsuftw5aa5ngb7kajy2dwfm
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