Results 11 to 20 of about 539,388 (277)
Polynomials which take Gaussian integer values at Gaussian integers [PDF]
Journal of Number Theory, 1977 AbstractA factorial set for the Gaussian integers is a set G = {g1, g2 … gn} of Gaussian integers such that G(z) = Πk (z − gk)gk takes Gaussian integer values at Gaussian integers. We characterize factorial sets and give a lower bound for max∥z∥2=nπ ∥ G(z)∥. It is conjectured that there are infinitely many factorial sets.
Douglas Hensley, Hensley, Douglas
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Gaussian Integers and Other Quadratic Integer Rings
, 2021 This thesis deals with quadratic integer rings, in particular the Gaussian integers Z}[i]. Concepts such as quadratic extensions, Euclidean domains and unique factorization domains will be introduced to the reader. The goal of this thesis is to show how a natural generalization of the integers Z, in the form of the Gaussian integers, can be used to ...
Landin, Erik, Hussein, Seif
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Cutting plane methods for general integer programming [PDF]
, 1993 Integer programming (IP) problems are difficult to solve due to the integer restrictions imposed on them. A technique for solving these problems is the cutting plane method.
Mitra, G +5 more
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Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation [PDF]
, 1990 A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear
Hadjiconstantinou, E
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Gaussian process model based predictive control [PDF]
, 2004 Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of non-linear dynamic systems. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack ...
Rasmussen, C.E. +3 more
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Dividing the Topological Charge of a Laguerre–Gaussian Beam by 2 Using an Off-Axis Gaussian Beam
Micromachines, 2022 In optical computing machines, many parameters of light beams can be used as data carriers. If the data are carried by optical vortices, the information can be encoded by the vortex topological charge (TC).
Alexey A. Kovalev +3 more
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Novel Hybrid Public/Private Key Cryptography Based on Perfect Gaussian Integer Sequences
IEEE Access, 2021 This paper proposes a novel hybrid public/private key cryptography scheme based on perfect Gaussian integer sequences (PGISs) of period $N=pq$ . First, a review study of construction degree-4 PGIS is addressed.
Ching-Hsien Hsia +3 more
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Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y
مجلة بغداد للعلوم, 2023 The investigation of determining solutions for the Diophantine equation over the Gaussian integer ring for the specific case of is discussed.
Shahrina Ismail +3 more
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On automatic subsets of the Gaussian integers [PDF]
Indagationes Mathematicae, 2017 Suppose that $a$ and $b$ are multiplicatively independent Gaussian integers, that are both of modulus~$\geq \sqrt 5$. We prove that there exist a $X\subset \mathbb Z[i]$ which is $a$-automatic but not $b$-automatic. This settles a problem of Allouche, Cateland, Gilbert, Peitgen, Shallit, and Skordev.
Bosma, W., Fokkink, R., Krebs, T.
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An objective representation of the Gaussian integers
Journal of Symbolic Computation, 2004 A rig is a ring without negatives. We analyse the free rig on a generator x subject to the equivalence x∼1+x+x2, showing that in it the non-constant polynomials form a ring. This ring can be identified with the Gaussian integers, which thus acquire objective meaning.
Fiore, Marcelo, Leinster, Tom
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