Showing papers on "Fibonacci number published in 2022"
24 Jan 2022
TL;DR: In this article , a comprehensive analysis of this freezing for all discrete subgroups of SU$(2)$ and different classes of asymptotically dense subsets is provided.
Abstract: Efficient discretisations of gauge groups are crucial with the long term perspective of using tensor networks or quantum computers for lattice gauge theory simulations. For any Lie group other than U$(1)$, however, there is no class of asymptotically dense discrete subgroups. Therefore, discretisations limited to subgroups are bound to lead to a freezing of Monte Carlo simulations at weak couplings, necessitating alternative partitionings without a group structure. In this work we provide a comprehensive analysis of this freezing for all discrete subgroups of SU$(2)$ and different classes of asymptotically dense subsets. We find that an appropriate choice of the subset allows unfrozen simulations for arbitrary couplings, though one has to be careful with varying weights of unevenly distributed points. A generalised version of the Fibonacci spiral appears to be particularly efficient and close to optimal.
17 citations
TL;DR: An approach for encrypting medical images that combines scientific computing with cryptography is presented, which uses the Fibonacci Multi Chaos Algorithm to encrypt medical images, making them more secure.
Abstract: At every stage of the digital media transfer, storage, and retrieval process, sensitive images are rendered indecipherable through the use of image encryption. Germany's hospitals have relied on image encryption for years to keep patient data from being accessed by the IT personnel, stolen or left recorded into the network system that could be compromised remotely.
In order to encrypt a file manually, the process is extremely time- and effort-consuming. Automating this process while retaining high security is desirable. In this research, we present an approach for encrypting medical images that combines scientific computing with cryptography.
This algorithm uses the Fibonacci Multi Chaos Algorithm to encrypt medical images, making them more secure. Distinct wavelet transform orthogonal frequency division multiplexing is used to convey picture data in this work, which is a reliable and secure method.
14 citations
TL;DR: In this article , the roots of the Fibonacci polynomials were investigated as complex hyperbolic functions and the relationship between the roots and the modular group, Hecke groups and generalized Heckes with geometric interpretations.
Abstract: In this paper, we investigate Fibonacci polynomials as complex hyperbolic
functions. We examine the roots of these polynomials. Also, we give some
exciting identities about images of the roots of Fibonacci polynomials under
another member of the Fibonacci polynomials class. Finally, we obtain some
excellent relationships between the roots of Fibonacci polynomials and the
modular group, Hecke groups and generalized Hecke groups with geometric
interpretations.
13 citations
TL;DR: In this article , a novel composite based on metal/2D transition metal dichalcogenides (TMDs), namely, platinum/platinum disulfide (Pt/PtS2) composite materials, was introduced for ultra-sensitive greenhouse gas sensors for CO2, N2O, and CH4 gases.
Abstract: Ultra-sensitive greenhouse gas sensors for CO2, N2O, and CH4 gases based on Fano resonance modes have been observed through periodic and quasi-periodic phononic crystal structures. We introduced a novel composite based on metal/2D transition metal dichalcogenides (TMDs), namely; platinum/platinum disulfide (Pt/PtS2) composite materials. Our gas sensors were built based on the periodic and quasi-periodic phononic crystal structures of simple Fibonacci (F(5)) and generalized Fibonacci (FC(7, 1)) quasi-periodic phononic crystal structures. The FC(7, 1) structure represented the highest sensitivity for CO2, N2O, and CH4 gases compared to periodic and F(5) phononic crystal structures. Moreover, very sharp Fano resonance modes were observed for the first time in the investigated gas sensor structures, resulting in high Fano resonance frequency, novel sensitivity, quality factor, and figure of merit values for all gases. The FC(7, 1) quasi-periodic structure introduced the best layer sequences for ultra-sensitive phononic crystal greenhouse gas sensors. The highest sensitivity was introduced by FC(7, 1) quasiperiodic structure for the CH4 with a value of 2.059 (GHz/m.s-1). Further, the temperature effect on the position of Fano resonance modes introduced by FC(7, 1) quasi-periodic PhC gas sensor towards CH4 gas has been introduced in detail. The results show the highest sensitivity at 70 °C with a value of 13.3 (GHz/°C). Moreover, the highest Q and FOM recorded towards CH4 have values of 7809 and 78.1 (m.s-1)-1 respectively at 100 °C.
12 citations
11 citations
TL;DR: The experimental results and security analyses show that the proposed image encryption algorithm not only has high security but also has certain robustness and real-time performance, which is suitable for practical applications.
10 citations
TL;DR: In this article , the authors developed connection formulae between two generalized classes of Fibonacci and Lucas polynomials, and derived new connection coefficients for a specific z. Hypergeometric functions of the kind 2F1(z) are included in all connection coefficients.
Abstract: The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2F1(z) are included in all connection coefficients for a specific z. Several new connection formulae between some famous polynomials, such as Fibonacci, Lucas, Pell, Fermat, Pell–Lucas, and Fermat–Lucas polynomials, are deduced as special cases of the derived connection formulae. Some of the introduced formulae generalize some of those existing in the literature. As two applications of the derived connection formulae, some new formulae linking some celebrated numbers are given and also some newly closed formulae of certain definite weighted integrals are deduced. Based on using the two generalized classes of Fibonacci and Lucas polynomials, some new reduction formulae of certain odd and even radicals are developed.
9 citations
8 citations
TL;DR: In this paper , the multi-channel enhanced absorption properties in graphene monolayer are theoretically studied, and the authors show that three peaks with absorbance above 75% can be achieved, which is attributed to the Tamm plasmon polaritons and multiple photonic stopbands of the Fibonacci dielectric multilayers.
Abstract: The multi-channel enhanced absorption properties in graphene monolayer are theoretically studied. It is realized by inserting a graphene monolayer in a dielectric film, which is sandwiched between a metallic film and a Fibonacci quasiperiodic structure. It is shown that three peaks with absorbance above 75% can be achieved, which is attributed to the Tamm plasmon polaritons and multiple photonic stopbands of the Fibonacci dielectric multilayers. Moreover, the distribution of the normalized electric field intensity is simulated to reveal the physical origin of such multichannel absorption effect. The designed graphene absorber possesses ultra-narrow absorption profiles and performs similar to an antenna. Furthermore, the multichannel absorption performances could be flexibly tuned by changing the angle of the incident and the geometric dimensions. Our results may find potential applications in the design of novel photoelectronic devices.
8 citations
TL;DR: In this paper , the authors discuss the developmental constraints and selective forces that may have favored the selection of phyllotaxis, and argue that a central driver of regular phyllOTaxis may have been limitations in the allocation of founder cells and metabolic resources to the different tissues in the shoot apex.
7 citations
TL;DR: Proven identity of hardware and abstract models suggest that the principles laid down in the organization of AFG and MAFG structures with modules of prime numbers ensure their effective hardware implementation in compliance with all requirements for their statistical characteristics and the possibility of application in cryptographic information security devices.
Abstract: Pseudorandom sequence generation is used in many industries, including cryptographic information security devices, measurement technology, and communication systems. The purpose of the present work is to research additive Fibonacci generators (AFG) and modified AFG (MAFG) with modules p prime numbers, designed primarily for their hardware implementation. The known AFG and MAFG, as with any cryptographic generators of pseudorandom sequences, are used in arguments with tremendous values. At the same time, there are specific difficulties in defining of their statistical characteristics. In this regard, the following research methodologies were used in work: for each variant of AFG and MAFG, two models were created—abstract, which is not directly related to the circuit solution, and hardware, which corresponds to the proposed structure; for relatively small values of arguments, the identity of models was proved; the research of statistical characteristics, with large values of arguments, was carried out using an abstract model and static tests NIST. Proven identity of hardware and abstract models suggest that the principles laid down in the organization of AFG and MAFG structures with modules of prime numbers ensure their effective hardware implementation in compliance with all requirements for their statistical characteristics and the possibility of application in cryptographic information security devices.
TL;DR: In this article , a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of the non-linear Hunter-Saxton equation, which can be solved by any classical method, such as Newton's method.
Abstract: In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of the non-linear Hunter–Saxton equation. Firstly, the operational matrices of integration associated with the Fibonacci wavelets are constructed by following the strategy of Chen and Hsiao. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that can be solved by any classical method, such as Newton’s method. Moreover, the non-linearity arising in the Hunter–Saxton equation is handled by invoking the quasi-linearization technique. To show the efficiency and accuracy of the Fibonacci-wavelet-based numerical technique, the approximate solutions of the non-linear Hunter–Saxton equation with other numerical methods including the Haar wavelet, trigonometric B-spline, and Laguerre wavelet methods are compared. The numerical outcomes demonstrate that the proposed method yields a much more stable solution and a better approximation than the existing ones.
TL;DR: In this paper , all positive integer solutions (m,n,a,k) of the Diophantine equation Fn±a(10m−1)9=k! with 1≤a≤9.
TL;DR: In this paper , the authors performed non-equilibrium molecular dynamics simulations to investigate phonon heat transport in quasiperiodic superlattices of graphene-boron nitride, alternating their domains according to the Thue-Morse and Double-Period sequences.
TL;DR: In this article , the authors give explicit formulas for the Fibonacci triple and the Lucas triple when the number of nonnegative integers is at most 3 and when the largest nonnegative integer can be represented by a linear combination.
Abstract: In this paper we study a certain kind of generalized linear Diophantine problem of Frobenius. Let $ a_1, a_2, \dots, a_l $ be positive integers such that their greatest common divisor is one. For a nonnegative integer $ p $, denote the $ p $-Frobenius number by $ g_p (a_1, a_2, \dots, a_l) $, which is the largest integer that can be represented at most $ p $ ways by a linear combination with nonnegative integer coefficients of $ a_1, a_2, \dots, a_l $. When $ p = 0 $, the $ 0 $-Frobenius number is the classical Frobenius number. When $ l = 2 $, the $ p $-Frobenius number is explicitly given. However, when $ l = 3 $ and even larger, even in special cases, it is not easy to give the Frobenius number explicitly. It is even more difficult when $ p > 0 $, and no specific example has been known. However, very recently, we have succeeded in giving explicit formulas for the case where the sequence is of triangular numbers [1] or of repunits [2] for the case where $ l = 3 $. In this paper, we show the explicit formula for the Fibonacci triple when $ p > 0 $. In addition, we give an explicit formula for the $ p $-Sylvester number, that is, the total number of nonnegative integers that can be represented in at most $ p $ ways. Furthermore, explicit formulas are shown concerning the Lucas triple.
TL;DR: In this article , two special families of bi-univalent functions connected with the activation function were investigated using the Al-Oboudi type operator, and the bounds on initial coefficients and the Fekete-Szego functional were derived.
Abstract: Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions connected with the activation function \(% \phi (s)=\ 2/(1+e^{-s}),\,s\in \mathbb{R}\) and \(k\)-Fibonacci numbers. We derive the bounds on initial coefficients and the Fekete-Szego functional for functions of the type \(g_{\phi }(z)=z+\sum \limits_{j=2}^{\infty }\phi (s)d_{j}z^{j}\) in these introduced families. Furthermore, we present interesting observations of the results investigated.
TL;DR: In this article , a general theory for reflection-induced localised modes in materials that are formed by recursive tiling rules was developed. But the analysis of a material based on the Fibonacci sequence was not considered.
TL;DR: In this article , a transformation between Fibonacci and Galois FSRs is improved based on semi-tensor product (STP) of matrices, which is a primitive building block in stream ciphers.
Abstract: Feedback shift registers (FSRs), which have two configurations: Fibonacci and Galois, are a primitive building block in stream ciphers. In this paper, a transformation between Fibonacci FSRs and Galois FSRs is improved based on semi-tensor product (STP) of matrices. It is verified that a weakly equivalent Galois FSR with fewer stages cannot be found for a Fibonacci FSR with n stages, but not vice versa. Furthermore, for a given Fibonacci FSR with n stages, there are totally (2n−1)!2−1 weakly equivalent Galois FSRs. Additionally, an effective algorithm is developed to reduce the number of variables of the Galois FSRs while keeping it weakly equivalent to the given Fibonacci FSR. Finally, the feasibility of the proposed strategies is demonstrated by numerical examples.
TL;DR: In this paper , a novel class of Fibonacci-based high performance tunable hierarchical waveguides is proposed and special focus is devoted to the design of adaptive-passive control systems for the Bloch wave propagation.
TL;DR: In this paper , the authors proposed quasicrystal materials as a natural platform and showed that they exhibit anyonic behavior that can be used for topological quantum computing, which is the main challenge of quantum computing.
Abstract: The concrete realization of topological quantum computing using low-dimensional quasiparticles, known as anyons, remains one of the important challenges of quantum computing. A topological quantum computing platform promises to deliver more robust qubits with additional hardware-level protection against errors that could lead to the desired large-scale quantum computation. We propose quasicrystal materials as such a natural platform and show that they exhibit anyonic behavior that can be used for topological quantum computing. Different from anyons, quasicrystals are already implemented in laboratories. In particular, we study the correspondence between the fusion Hilbert spaces of the simplest non-abelian anyon, the Fibonacci anyons, and the tiling spaces of the one-dimensional Fibonacci chain and the two-dimensional Penrose tiling quasicrystals. A concrete encoding on these tiling spaces of topological quantum information processing is also presented by making use of inflation and deflation of such tiling spaces. While we outline the theoretical basis for such a platform, details on the physical implementation remain open.
TL;DR: In this paper , a two-variable Vieta-Fibonacci polynomials were constructed and coupled with a matrix collocation method to solve the time-fractional telegraph equations.
Abstract: The vital target of the current work is to construct two-variable Vieta-Fibonacci polynomials which are coupled with a matrix collocation method to solve the time-fractional telegraph equations. The emerged fractional derivative operators in these equations are in the Caputo sense. Telegraph equations arise in the fields of thermodynamics, hydrology, signal analysis, and diffusion process of chemicals. The orthogonality of derivatives of shifted Vieta-Fibonacci polynomials is proved. A bound of the approximation error is ascertained in a Vieta-Fibonacci-weighted Sobolev space that admits increasing the number of terms of the series solution leads to the decrease of the approximation error. The proposed scheme is implemented on four illustrated examples and obtained numerical results are compared with those reported in some existing research works.
TL;DR: In this paper , a trace-map formalism was proposed for the propagation of harmonic axial waves in a class of periodic two-phase phononic rods whose elementary cells are designed adopting the quasicrystalline silver mean Fibonacci substitution rule.
TL;DR: In this paper , the bi-periodic Horadam hybrid numbers were introduced as a new generalization of complex, dual, and hyperbolic numbers and the Binet formula was given.
Abstract: The hybrid numbers were introduced by Ozdemir [9] as a new generalization of complex, dual, and hyperbolic numbers. A hybrid number is defined by $$k=a+bi+c\epsilon +dh$$ , where a, b, c, d are real numbers and $$ i,\epsilon ,h$$ are operators such that $$i^{2}=-1,\epsilon ^{2}=0,h^{2}=1$$ and $$ih=-hi=\epsilon +i$$ . This work is intended as an attempt to introduce the bi-periodic Horadam hybrid numbers which generalize the classical Horadam hybrid numbers. We give the generating function, the Binet formula, and some basic properties of these new hybrid numbers. Also, we investigate some relationships between generalized bi-periodic Fibonacci hybrid numbers and generalized bi-periodic Lucas hybrid numbers.
01 May 2022
TL;DR: This work proposes a novel sketch, PeriodicSketch, aiming to accurately record top-$K$ periodic items, and provides a concrete case: Cache prefetch, which proves that Periodic Sketch can significantly improve the Cache hit ratio.
Abstract: In this paper, we study periodic items in data streams, which refer to those items arriving with a fixed interval. All existing works involving mining periodic patterns does not fit for data stream scenarios. To find periodic items in real time, we propose a novel sketch, PeriodicSketch, aiming to accurately record top-$K$ periodic items. To the best of our knowledge, this is the first work to find periodic items in data streams. Any interval may occur many times, and we use frequency to denote the number of an interval occurred. To pick out periodic items with high frequency, we propose a key technique called Guaranteed Soft Uniform (GSU) replacement strategy. Our theoretical proofs show that when replacement is successful, it is more likely that the new item has a higher frequency than the current smallest frequency; and GSU can ensure that our items in the sketch will approach the true periodic items closer and closer. And as soon as we get all the periodic items, the state would not change worse with high probability. We conduct extensive experiments, and the experimental results show that the Average Absolute Error (AAE) of our sketch using 1/10 memory is around 737 times (up to 2019 times) lower than the baseline solution. Finally, we provide a concrete case: Cache prefetch, which proves that PeriodicSketch can significantly improve the Cache hit ratio. All related codes of PeriodicSketch are open-sourced and available at GitHub [1].
TL;DR: In this article , the authors proposed a bio-inspired design blade profile relying on the Fibonacci spiral, which is repeatedly presented in nature and thus it leads to a bioinspired blade profile.
Abstract: Wind energy is gaining special interest worldwide due to the necessity of reducing pollutant emissions and employ renewable resources. Traditionally, horizontal axis wind turbines have been employed but certain situations require vertical axis wind turbines. With a view to improve the efficiency of a vertical axis wind turbine Savonius type, the present work proposes a bioinspired design blade profile relying on the Fibonacci spiral. This shape is repeatedly presented in nature and thus it leads to a bio-inspired blade profile. A numerical model was carried out and it was found that the Fibonacci shape improves the performance of the original Savonius shape, based on semicircular blade profiles. Particularly, the Fibonacci blade profile increases around 14% the power in comparison with the Savonius blade profile. Besides this comparison between Savonius and Fibonacci, a research study was carried out to improve the efficiency of the Fibonacci turbine. To this end, the effect of several parameters was analyzed: number of blades, aspect ratio, overlap, separation gap, and twist angle. Improvements on the average power greater than 30% were obtained.
TL;DR: In this article , the Fibonacci wavelet collocation method (FWCM) was proposed to extract the numerical solution of linear hyperbolic partial differential equations (HPDEs).