The fibonacci sequence is a fascinating mathematical concept with profound significance across various disciplines. Beyond theoretical intrigue, it finds practical applications in art, architecture, nature, and financ...
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The fibonacci sequence is a fascinating mathematical concept with profound significance across various disciplines. Beyond theoretical intrigue, it finds practical applications in art, architecture, nature, and financial markets. The fibonacci sequence, defined by each number is the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8, 13, ... ). This sequence of numbers, often attributed to the 12th century Italian mathematician Leonardo of Pisa, known as fibonacci, has earlier roots in Indian mathematics. Acharya Pingala referenced this sequence in his work centuries before. This paper explores the evolution of the fibonacci sequence and its modern applications, particularly in fractal geometry. We examine Mandelbrot and Julia sets for various functions and study the symmetries of the Mandelbrot and Julia sets obtained using the fibonacci-Mann orbit. Additionally, we investigate the impact of parameter a on the Mandelbrot and Julia sets. To quantify these effects, we employ three measures: Average Escape Time (AET), Non-Escaping Area Index (NAI), and Average Number of Iterations (ANI).
A connection between the Kalman filter and the fibonacci sequence is developed. More precisely it is shown that, for a scalar random walk system in which the two noise sources (process and measurement noise) have equa...
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A connection between the Kalman filter and the fibonacci sequence is developed. More precisely it is shown that, for a scalar random walk system in which the two noise sources (process and measurement noise) have equal variance, the Kalman filter's estimate turns out to be a convex linear combination of the a priori estimate and of the measurements with coefficients suitably related to the fibonacci numbers. It is also shown how, in this case, the steady-state Kalman gain as well as the predicted and filtered covariances are related to the golden ratio phi = (root 5 + 1)/2. Furthermore, it is shown that, for a generic scalar system, there exist values of its key parameters (i.e. system dynamics and ratio of process-to-measurement noise variances) for which the previous connection is preserved. Finally, by exploiting the duality principle between control and estimation, similar connections with the linear quadratic control problem are outlined. (C) 2009 Elsevier B.V. All rights reserved
Let N be the set of positive integers and C be Cantor's ternary set. A function xi : N --> [0, 1] is established by the help of the fibonacci sequence such that , the closure of the set xi(N), is homeomorphic t...
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Let N be the set of positive integers and C be Cantor's ternary set. A function xi : N --> [0, 1] is established by the help of the fibonacci sequence such that <(xi(N))over bar>, the closure of the set xi(N), is homeomorphic to the set C.
This paper is concerned of the fibonacci sequence and the golden ratio in the possibility of predicting the crack propagation of concrete structures subjected to pure tension where it interrelated the effect of the ch...
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This paper is concerned of the fibonacci sequence and the golden ratio in the possibility of predicting the crack propagation of concrete structures subjected to pure tension where it interrelated the effect of the change of dimensions of the reinforced concrete element in the fibonacci sequence to the ratio of cracks transfer lengths and cracks spacing, which appeared in the golden ratio form. A governing differential equation was solved numerically and verified using previous theoretical and experimental researches. Also experimental researches were used to ensure the appearance of golden ratio effect on the cracks behavior.
We proposed a new model of supramolecular DNA structure. Similar to the previously developed by us model of primary DNA structure [11-15], 3D structure of DNA molecule is assembled in accordance to a mathematic rule k...
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We proposed a new model of supramolecular DNA structure. Similar to the previously developed by us model of primary DNA structure [11-15], 3D structure of DNA molecule is assembled in accordance to a mathematic rule known as fibonacci sequence. Unlike primary DNA structure, supramolecular 3D structure is assembled from complex moieties including a regular tetrahedron and a regular octahedron consisting of monomers, elements of the primary DNA structure. The moieties of the supramolecular DNA structure forming fragments of regular spatial lattice are bound via linker (joint) sequences of the DNA chain. The lattice perceives and transmits information signals over a considerable distance without acoustic aberrations. Linker sequences expand conformational space between lattice segments allowing their sliding relative to each other under the action of external forces. In this case, sliding is provided by stretching of the stacked linker sequences.
In this paper the mathematical concept of the fibonacci sequence has been introduced as an accurate and reliable tool to model randomness in a heterogeneous material. It is also argued, that this randomness plays an i...
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In this paper the mathematical concept of the fibonacci sequence has been introduced as an accurate and reliable tool to model randomness in a heterogeneous material. It is also argued, that this randomness plays an important role and can control the response of a heterogeneous material, subjected to dynamic loading, here an elastic wave propagating through the material. A particular dynamic phenomenon, the presence of band gaps, has been analysed. It has been shown that randomness, modelled using the fibonacci sequence, introduced into the material's structure, increases the range of stop band frequencies. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Background Scalp defects commonly occur as a result of tumour excision or trauma. The reconstruction of medium to large defects can be challenging due to the scalp laxity and hair growth pattern. We compare the outcom...
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Background Scalp defects commonly occur as a result of tumour excision or trauma. The reconstruction of medium to large defects can be challenging due to the scalp laxity and hair growth pattern. We compare the outcome of patients who have had snail flap reconstruction in comparison to skin grafts. Methods We conducted a retrospective case study of 45 consecutive patients' over a 3-year period (2016-2018), across three sub-groups, viz. fibonacci sequence flap, split skin graft and full-thickness skin grafts. The sub-cohorts were all matched for age, sex, indications and defect sizes before being analysed in terms of complication rates and wound healing rates over a 4-month period. Results The fibonacci 'snail' flap was found to heal significantly faster than the full-thickness skin graft group and with lower complication rates overall, compared to skin grafts, but the latter outcome did not reach statistical significance. The aesthetic outcome of the fibonacci flap though was superior to skin grafts both in terms of colour and contour match as well as hair restoration. Conclusions The fibonacci 'snail' flap is a sound option for the reconstruction of medium to large size defects of the scalp, even in those with poor performance scores, especially since its lower flap: defect ratio allows it to be performed under local anaesthesia. The advantage of the 'snail' flap over other scalp flaps will be determined in a future comparative study. Level of evidence: Level III, therapeutic study.
In this paper, binary photonic crystal with a quasi-periodic sequence is investigated. A fibonacci sequence of gyroidal graphene and porous silicon terminated by the gyroidal layer is proposed as a refractive index se...
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In this paper, binary photonic crystal with a quasi-periodic sequence is investigated. A fibonacci sequence of gyroidal graphene and porous silicon terminated by the gyroidal layer is proposed as a refractive index sensor. The refractive index or concentration of an analyte can be predicted based on the resonant dip of Tamm plasmon. The excellent optical properties of porous silicon and gyroidal graphene will contribute to enhancing the performance of the proposed sensor. The impact of various geometric parameters is investigated. Compared with the similar structure of periodic photonic crystals, the sensitivity and figure of merit enhanced from 188.8 to 1347.7 THz/RIU (higher 614%) and from 355,384 to 554,405/RIU (higher 56%), respectively. The high-performance results imply that the suggested fibonacci sensor is suitable for gas detection and bio-sensing applications.
This paper presents the equivalence between a fibonacci sequence weighted Successive Approximation Register type A-D converter (SAR ADC) and an SAR ADC based on the golden section search algorithm using the unimodal f...
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ISBN:
(纸本)9781538621592
This paper presents the equivalence between a fibonacci sequence weighted Successive Approximation Register type A-D converter (SAR ADC) and an SAR ADC based on the golden section search algorithm using the unimodal function obtained by the absolute value of the difference between the input voltage and the output of the internal DAC. The golden section search algorithm is used for finding effectively the extreme value of the unimodal function. We have designed an SAR ADC configuration based on this golden section search, and we show that this is equivalent to the fibonacci sequence weighted SAR ADC. We explain their principle, configuration, and operation as well as some simulation results.
This paper demonstrates how a well-known number sequence (the fibonacci numbers) can be generated by a new model of computing called membrane computation. A contribution of this paper is to add a feature to the notati...
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ISBN:
(纸本)1932415041
This paper demonstrates how a well-known number sequence (the fibonacci numbers) can be generated by a new model of computing called membrane computation. A contribution of this paper is to add a feature to the notation describing membrane structure (originally described by Gheorge Paun) called a recursive meta-rule, which defines how new rules are inherited for each new membrane creation. A membrane computer is inspired by the membrane structures of biological cells. The objects within a given membrane may evolve according to a set of rules established for that membrane. Objects can represent, for example, numbers or strings. Typically, the evolution rules are implemented as transformations on string objects. A key feature of the membrane computer is inherent parallelism;distributed operations are performed simultaneously, unless a priority of operations is specified. A membrane computer of the type called a "transition P-system" is used to represent the fibonacci numbers as a sequential evolution of objects.
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