Gaussian Pell Numbers

Gaussian numbers means representation as Complex numbers. In this work, Gaussian Pell numbers are defined from recurrence relation of Pell numbers. Here the recurrence relation on Gaussian Pell number is represented in two dimensional approach. This provides an extension of Pell numbers into the complex plane.

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Shifting perspectives: method, media and the complex image

History and Computing ◽

10.3366/hac.1998.10.1-3.100 ◽

1998 ◽

Vol 10 (1-3) ◽

pp. 100-108 ◽

Cited By ~ 1

Author(s):

Alicia Colson ◽

Ross Parry

Keyword(s):

Image Processing ◽

Three Dimensional ◽

Geographical Location ◽

Spatial Relationship ◽

Two Dimensional ◽

Dimensional Approach ◽

Complex Image ◽

Cultural Resonance

This article argues that the analysis of a threedimensional image demanded a three-dimensional approach. The authors realise that discussions of images and image processing inveterately conceptualise representation as being flat, static, and finite. The authors recognise the need for a fresh acuteness to three-dimensionality as a meaningful – although problematic – element of visual sources. Two dramatically different examples are used to expose the shortcomings of an ingrained two-dimensional approach and to facilitate a demonstration of how modern (digital) techniques could sanction new historical/anthropological perspectives on subjects that have become all too familiar. Each example could not be more different in their temporal and geographical location, their cultural resonance, and their historiography. However, in both these visual spectacles meaning is polysemic. It is dependent upon the viewer's spatial relationship to the artifice as well as the spirito-intellectual viewer within the community. The authors postulate that the multi- faceted and multi-layered arrangement of meaning in a complex image could be assessed by working beyond the limitations of the two-dimensional methodological paradigm and by using methods and media that accommodated this type of interconnectivity and representation.

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EXACT SOLUTION TO THE TWO-DIMENSIONAL APPROACH OF THE REWETTING BY A FALLING FILM

Proceeding of International Heat Transfer Conference 8 ◽

10.1615/ihtc8.1750 ◽

1986 ◽

Cited By ~ 1

Author(s):

Francesco Castiglia ◽

E. Oliveri ◽

S. Taibi ◽

G. Vella

Keyword(s):

Exact Solution ◽

Falling Film ◽

Two Dimensional ◽

Dimensional Approach

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PANEL FLUTTER OF PLATE UNDER SUBSONIC FLOW IN TWO-DIMENSIONAL APPROACH

TsAGI Science Journal ◽

10.1615/tsagiscij.2020034274 ◽

2020 ◽

Vol 51 (1) ◽

pp. 85-98

Author(s):

Vitalii Dmitrievich Chuban

Keyword(s):

Subsonic Flow ◽

Panel Flutter ◽

Two Dimensional ◽

Dimensional Approach

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Winding Numbers, Unwinding Numbers, and the Lambert W Function

Computational Methods and Function Theory ◽

10.1007/s40315-021-00398-1 ◽

2021 ◽

Author(s):

A. F. Beardon

Keyword(s):

Complex Plane ◽

Complex Number ◽

Lambert W Function ◽

Complex Numbers ◽

Winding Number ◽

Line Integral ◽

Complex Functions

AbstractThe unwinding number of a complex number was introduced to process automatic computations involving complex numbers and multi-valued complex functions, and has been successfully applied to computations involving branches of the Lambert W function. In this partly expository note we discuss the unwinding number from a purely topological perspective, and link it to the classical winding number of a curve in the complex plane. We also use the unwinding number to give a representation of the branches $$W_k$$ W k of the Lambert W function as a line integral.

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Evaluation of guide vanes effect over runner Francis turbine sediment erosion using a quasi-two dimensional approach

IOP Conference Series Earth and Environmental Science ◽

10.1088/1755-1315/774/1/012077 ◽

2021 ◽

Vol 774 (1) ◽

pp. 012077

Author(s):

L M Quishpe ◽

E A Valencia ◽

V H Hidalgo ◽

O I Zambrano ◽

E H Cando

Keyword(s):

Francis Turbine ◽

Two Dimensional ◽

Dimensional Approach ◽

Sediment Erosion ◽

Guide Vanes

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Mathematical modelling of straw combustion in a moving bed combustor: A two dimensional approach

Fuel ◽

10.1016/j.fuel.2012.08.017 ◽

2013 ◽

Vol 104 ◽

pp. 351-364 ◽

Cited By ~ 15

Author(s):

Biljana Miljković ◽

Ivan Pešenjanski ◽

Marija Vićević

Keyword(s):

Mathematical Modelling ◽

Two Dimensional ◽

Dimensional Approach ◽

Moving Bed ◽

Straw Combustion

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An exact two-dimensional approach to fiber micro-buckling

International Journal of Solids and Structures ◽

10.1016/0020-7683(87)90103-x ◽

1987 ◽

Vol 23 (9) ◽

pp. 1235-1246 ◽

Cited By ~ 34

Author(s):

Paul S. Steif

Keyword(s):

Two Dimensional ◽

Dimensional Approach

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DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

Modern Physics Letters B ◽

10.1142/s021798490701244x ◽

2007 ◽

Vol 21 (02n03) ◽

pp. 139-154 ◽

Cited By ~ 6

Author(s):

J. H. ASAD

Keyword(s):

Differential Equation ◽

Green’S Function ◽

Recurrence Relation ◽

Green's Function ◽

Two Dimensional ◽

Dimensional Lattice ◽

One Dimensional ◽

The One ◽

Lattice Green's Function ◽

Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

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