scholarly journals Logarithmic Spirals and Right-angled Triangles

2020 ◽  
Author(s):  
Rahul Gohil
Keyword(s):  
Linear Combination ◽  
Fibonacci Numbers ◽  
Discrete Form ◽  
Recurrent Functions ◽  
Logarithmic Spirals ◽  
Special Arrangement

This article presents some recurrent functions which we can use to make Right-angledTriangles and through their special arrangement we can obtain logarithmic spirals,and their discrete form. The recurrent functions are obtained through recurrencerelations which can be expressed as a linear combination of fibonacci numbers.

scholarly journals Summing a Family of Generalized Pell Numbers

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Helmut Prodinger
Keyword(s):  
Linear Combination ◽  
Computer Algebra ◽  
Generating Functions ◽  
Fibonacci Numbers ◽  
Partial Sums ◽  
Pell Numbers ◽  
New Family ◽  
Binet Formula

AbstractA new family of generalized Pell numbers was recently introduced and studied by Bród ([2]). These numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power P lnis expressed as a linear combination of Pmn. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter R = 2r, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.

scholarly journals Triple sums including Fibonacci numbers with three binomial coefficients

2021 ◽  
Vol 27 (1) ◽  
pp. 188-197
Author(s):  
Funda Taşdemir ◽  
Keyword(s):  
Linear Combination ◽  
Fibonacci Numbers ◽  
Binomial Coefficients ◽  
Lucas Numbers ◽  
Fibonacci And Lucas Numbers

In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial coefficients. We chose the indices of Fibonacci numbers as linear combination of the summation indices. Moreover, various types of alternating analogues of them whose powers depend on the index or indices are computed. These sums are evaluated in nice multiplication forms in terms of Fibonacci and Lucas numbers.

scholarly journals How to sum powers of balancing numbers efficiently

2021 ◽  
Vol 27 (1) ◽  
pp. 134-137
Author(s):  
Helmut Prodinger ◽  
Keyword(s):  
Linear Combination ◽  
Fibonacci Numbers ◽  
Partial Sums ◽  
Balancing Numbers ◽  
Binet Formula

Balancing numbers possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of balancing numbers can be summed explicitly. For this, as a first step, a power B_n^l is expressed as a linear combination of B_{mn}.

Architecture of the Official Spaces of Selected Residences in Nea Paphos, Cyprus

2020 ◽  
pp. 87-105 ◽  
Author(s):  
Aleksandra Brzozowska-Jawornicka
Keyword(s):  
Social Status ◽  
Roman Period ◽  
The Social ◽  
Public Areas ◽  
Special Arrangement

This paper deals with public areas in ancient residences. These zones, emphasising the social status of the owners of the houses, are analysed in several large residences erected in the Graeco-Roman Period in Nea Paphos, Cyprus: the ‘Hellenistic’ House, the Villa of Theseus, and the House of Aion. Particularly, the special arrangement of the layout and the architectural decoration of three major public zones were studied: the entrance, the main courtyard, and the main room.

Recognition by Linear Combination of Models

1989 ◽  
Author(s):  
Shimon Ullman ◽  
Ronen Basri
Keyword(s):  
Linear Combination

scholarly journals An Accurate Reconstruction of CMB E Mode Signal over Large Angular Scales using Prior Information of CMB Covariance Matrix in ILC Algorithm

2020 ◽  
Author(s):  
Ujjal Purkayastha ◽  
Vipin Sudevan ◽  
Rajib Saha
Keyword(s):  
Power Spectrum ◽  
Linear Combination ◽  
Covariance Matrix ◽  
Large Scale ◽  
Prior Information ◽  
Future Generation ◽  
Temperature Anisotropy ◽  
Satellite Mission ◽  
Angular Power Spectrum ◽  
Accurate Reconstruction

Abstract Recently, the internal-linear-combination (ILC) method was investigated extensively in the context of reconstruction of Cosmic Microwave Background (CMB) temperature anisotropy signal using observations obtained by WMAP and Planck satellite missions. In this article, we, for the first time, apply the ILC method to reconstruct the large scale CMB E mode polarization signal, which could probe the ionization history, using simulated observations of 15 frequency CMB polarization maps of future generation Cosmic Origin Explorer (COrE) satellite mission. We find that the clean power spectra, from the usual ILC, are strongly biased due to non zero CMB-foregrounds chance correlations. In order to address the issues of bias and errors we extend and improve the usual ILC method for CMB E mode reconstruction by incorporating prior information of theoretical E mode angular power spectrum while estimating the weights for linear combination of input maps (Sudevan & Saha 2018b). Using the E mode covariance matrix effectively suppresses the CMB-foreground chance correlation power leading to an accurate reconstruction of cleaned CMB E mode map and its angular power spectrum. We compare the performance of the usual ILC and the new method over large angular scales and show that the later produces significantly statistically improved results than the former. The new E mode CMB angular power spectrum contains neither any significant negative bias at the low multipoles nor any positive foreground bias at relatively higher mutlipoles. The error estimates of the cleaned spectrum agree very well with the cosmic variance induced error.

scholarly journals Single Neuronal Dynamical System in Self-Feedbacked Hopfield Networks and Its Application in Image Encryption

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 456
Author(s):  
Xitong Xu ◽  
Shengbo Chen
Keyword(s):  
Dynamical System ◽  
Image Encryption ◽  
Chaotic Dynamic ◽  
Security Analysis ◽  
High Sensitivity ◽  
Hopfield Network ◽  
Complex Structures ◽  
Hopfield Networks ◽  
Discrete Form ◽  
Chaotic Parameter

Image encryption is a confidential strategy to keep the information in digital images from being leaked. Due to excellent chaotic dynamic behavior, self-feedbacked Hopfield networks have been used to design image ciphers. However, Self-feedbacked Hopfield networks have complex structures, large computational amount and fixed parameters; these properties limit the application of them. In this paper, a single neuronal dynamical system in self-feedbacked Hopfield network is unveiled. The discrete form of single neuronal dynamical system is derived from a self-feedbacked Hopfield network. Chaotic performance evaluation indicates that the system has good complexity, high sensitivity, and a large chaotic parameter range. The system is also incorporated into a framework to improve its chaotic performance. The result shows the system is well adapted to this type of framework, which means that there is a lot of room for improvement in the system. To investigate its applications in image encryption, an image encryption scheme is then designed. Simulation results and security analysis indicate that the proposed scheme is highly resistant to various attacks and competitive with some exiting schemes.

scholarly journals Partially constrained internal linear combination: A method for low-noise CMB foreground mitigation

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
Y. Sultan Abylkairov ◽  
Omar Darwish ◽  
J. Colin Hill ◽  
Blake D. Sherwin
Keyword(s):  
Linear Combination ◽  
Low Noise
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