Results 221 to 230 of about 165,995,511 (248)

Zero Divisor Graph for the Ring of Gaussian Integers Modulo n

Communications in Algebra, 2008
This article studies the zero divisor graph for the ring of Gaussian integers modulo n, Γ (ℤ n [i]). For each positive integer n, the number of vertices, the diameter, the girth and the case when the dominating number is 1 or 2 is found. Complete characterizations, in terms of n, are given of the cases in which Γ (ℤ n [i]) is complete, complete ...
Emad Abu Osba, Salah Al-Addasi, Nafiz Abu Jaradeh   +2 more
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A systolic discrete Fourier transform using residue number systems over the ring of Gaussian integers

ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005
A VLSI implementation of a bit-serial systolic architecture for a DFT processor has been developed which performs residue number system (RNS) processing over the ring of Gaussian integers. An architecture for a 128-point DFT using the chirp z-transform algorithm is described, and its use in an R2FFT architecture to obtain a 16,384-point transform is ...
John J. Vaccaro, Bruce L. Johnson, Carol L. Nowacki   +2 more
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FACTORIZATION IN THE RING OF ARITHMETIC FUNCTIONS ON GAUSSIAN INTEGERS

JP Journal of Algebra, Number Theory and Applications
In this paper, we investigate the multiplicative structure of the ring of complex valued arithmetic functions defined on the ring of Gaussian integers, and show that this ring is a unique factorization domain.
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Divisor Functions in the Ring of Gaussian Integers Weighted by the Generalized Klosterman Sum

Lithuanian Mathematical Journal, 2001
In the ring \(R\) of Gaussian integers let \(\tau_{a,b,c}(\omega)\) denote the number of factorizations of \(\omega \in R\) in the form \(\omega = \omega_1^a \omega_2^b \omega_3^c\), where \(a,b,c\) are natural numbers. The author constructs an asymptotic formula for the sum \[ \sum_{N (\omega) \leq x} \tau_{1,b,c}(\omega) K_{1,b,c}(\gamma; \omega,1,1),
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Quasi-perfect geometrically uniform codes derived from graphs over Gaussian integer rings

2010 IEEE International Symposium on Information Theory, 2010
In this paper we present a generalization of the perfect codes derived from the quotient rings of Gaussian integers. We call this class of codes quasi-perfect, which in addition to preserving the property of being geometrically uniform codes they are able to correct more error patterns than the perfect codes.
Cátia Regina de Oliveira Quilles Queiroz, Reginaldo Palazzo Júnior   +1 more
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Testing a polynomial for zeros inside the unit-circle over the ring of Gaussian integers

2006 IEEE International Symposium on Circuits and Systems, 2006
The paper considers a Gaussian-integer preserving (GIP) form for the author's method to test whether a polynomial with complex coefficients has its zeros inside the unit-circle (is 'stable'). The GIP property describes the fact that for a polynomial with Gaussian integer (i.e.
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Residue classes euclidean ring over integral domain of gaussian integers

i-manager’s Journal on Mathematics
Z√i = {m + in: m, n ∈ Z} is an integral domain under the addition defined by (m1+in1) ⊕ (m2+in2) = (m1+nm2) + i(n1+nn2) and multiplication defined by (m1+in1) ʘ (m2+in2) = (m1m2+n(-n1n2)) + i(m1n2+nn1m2). Taking nth - degree polynomials taking coefficients from the integral domain of Gaussian integers and using the residue classes modulo n operation on
L. Sujatha, Rao T. Srinivasa
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General Kloosterman sums over ring of Gaussian integers

2020
?????????????????????? ???????? ?????????????????????? K(m,n;k;q) ?????? Z ?????????????? S. Kanemitsu, Y. Tanigawa, Yi. Yuan, Zhang Wenpeng ?? ???? ?????????????????????? ???????????????? D. H. Lehmer. ?? ?????? ???????????? ???????????????? ?????????????? ???????????? K(??,??;k;??) ?????? Z[i]. ?????????? ???????????????????? ???????? K??(??,??;h,q;k)
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Nature of Graphs of Commutative Ring of Gaussian Integer modulo n under x3 - 1 mapping

2021
© 2021. All Rights Reserved.The aim of the present paper is to observe the structures of digraphs derived from the mappings f1: Zn[i] Zn[i] defined by f1 (x) = x3 — 1 whose vertex is Zn[i] = {a + bi: a, b (Formula presented) Zn} and for which there is a directed edge from x (Formula presented) Zn[i] to y (Formula presented) Zn[i] if and only if x3 — 1 =
Qayyum, Kishmala, Cancan, Murat, Nazeer, Saima, Khalaf, Abdul Jalil M.   +3 more
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Finding Factors of Factor Rings over the Gaussian Integers

The American Mathematical Monthly, 2005
Greg Dresden, Wayne M. Dymàcek
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