The stability in stock markets is the theme of this work. It has been demonstrated that the random walk theory alone is insufficient to explain the dynamic behavior of asset or stock prices. Deviations from the random...
详细信息
The stability in stock markets is the theme of this work. It has been demonstrated that the random walk theory alone is insufficient to explain the dynamic behavior of asset or stock prices. Deviations from the random walk theory reveal collective behaviors that produce waves and patterns. Research has shown that the fibonacci sequence and the golden ratio emerge in such dynamic systems, representing states of minimal stability. Their sustained stability is ensured by the presence of Landau damping within the system. The complex dynamics of the stock market can be analyzed by considering the exchanged shares as fluctuating and the unexchanged shares as nonfluctuating entities. The traders exhibit a kind of group oscillations that resemble the waves in physical plasma. At steady state, the waves can be expressed by a cosine term, and at the least stable state, the dynamics involves the golden ratio, such that the cosine of 36 degrees is equal to half of the golden ratio. Using the trigonometric cosine formula, it is possible to obtain other angles which are the multiples of 9 degrees. They can be expressed in terms of the golden ratio, and they stand as fibonacci angles. The stabilization is achieved by a mechanism so-called Landau damping, and the waves thus created are called Elliott waves, and they keep the system near the instability border. It was found that these angles appear quite often in the motive and corrective Elliott waves in the weekly price change of crude oil between January 2001 and June 2023. The percent occurrence of these angles increases through oscillations in motive waves with peaks at 18 degrees, 45 degrees and 72 degrees. The corrective wave has a maximum peak at 36 degrees, and the percent occurrence decreases through oscillations having smaller peak values at 54 degrees and 72 degrees. The highest values are such that the motive waves appear at 50% in the bull market, and the corrective waves at 27.8% in the bear market.
This paper presents the design of biosensors utilizing one-dimensional photonic crystals with periodical and fibonacci sequences for measuring glucose concentration in urine, aimed at facilitating continuous blood glu...
详细信息
This paper presents the design of biosensors utilizing one-dimensional photonic crystals with periodical and fibonacci sequences for measuring glucose concentration in urine, aimed at facilitating continuous blood glucose monitoring for diabetic patients. Exploiting Tamm plasmon resonance within a photonic band gap in the medium wave infrared band, the biosensor comprises a configuration with a one-dimensional photonic crystal and an Ag layer deposited on an infrared prism, with a urine sample layer in between. Utilizing the transfer matrix method, the reflection spectra for electromagnetic waves are calculated. The wavelength position of the Tamm plasmon resonant dip is influenced by variations in glucose concentration within the urine sample. This is attributed to the distinct refractive indices exhibited by urine samples with different glucose concentrations. Optimizing biosensor performance under various incident angles involves adjusting the Ag layer and urine sample thicknesses while maintaining excellent linear characteristics. The optimal performance of the biosensor with fibonacci sequence one-dimensional photonic crystal is significantly superior, with a sensitivity of 113,000 nm RIU-1, a figure of merit of 2.05 x 105 RIU-1, and a detection limit of 4.84 x 10-7 RIU. The combination of high performance and a straightforward structure makes the proposed biosensors for detecting urine glucose concentrations promising in biomedical diagnostics.
We study the extended Frobenius problem for sequences of the form {f(a) + f(n)} n ? N, where {f(n)} n ? N is the fibonacci sequence and f(a) is a fibonacci number. As a consequence of this study, we show that the fami...
详细信息
We study the extended Frobenius problem for sequences of the form {f(a) + f(n)} n ? N, where {f(n)} n ? N is the fibonacci sequence and f(a) is a fibonacci number. As a consequence of this study, we show that the family of numerical semigroups associated with these sequences satisfies Wilf's conjecture.
Consider the generalized fibonacci sequence {q(n)}(n-0)(infinity) 0 having initial conditions q(0) = 0;q(1) 1 and recurrence relation q(n) = aq(n-1) + q(n-2) (when n is even) or q(n) = bq(n-1) + q(n-2) (when n is odd)...
详细信息
Consider the generalized fibonacci sequence {q(n)}(n-0)(infinity) 0 having initial conditions q(0) = 0;q(1) 1 and recurrence relation q(n) = aq(n-1) + q(n-2) (when n is even) or q(n) = bq(n-1) + q(n-2) (when n is odd), where a and b are nonzero real numbers. These sequences arise in a natural way in the study of continued fractions of quadratic irrationals and combinatorics on words or dynamical system theory. Some well-known sequences are special cases of this generalization. The fibonacci sequence is a special case of {q(n)} with a = b= 1. Pell's sequence is {q(n)} with a = b= 2 and the k-fibonacci sequence is {q(n)} with a = b= k. In this article, we study numerous new properties of these sequences and investigate a sequence closely related to these sequences which can be regarded as a generalization of Lucas sequence of the first kind. (C) 2010 Elsevier Inc. All rights reserved.
It is well known that the Boolean functions can be represented by two-layer perceptrons, and a part of them, namely separable Boolean functions, can be represented by one-layer perceptrons. How many separable Boolean ...
详细信息
It is well known that the Boolean functions can be represented by two-layer perceptrons, and a part of them, namely separable Boolean functions, can be represented by one-layer perceptrons. How many separable Boolean functions of n variables there are is an open problem. On the other hand, given a n-element set X, how many antichains does P(X) have is also an open problem. This paper established an inequality reflecting the relationship between these two open problems. Second, this paper introduced two classes of Boolean functions which are generalizations of AND-OR functions and OR-AND functions, respectively, and proved that they are all separable and the weights in representing them are exactly terms of corresponding generalized fibonacci sequences. (C) 2000 Elsevier Science Ltd. All rights reserved.
We study the random fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single child, also the number 1. We define the tree recursively in...
详细信息
We study the random fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single child, also the number 1. We define the tree recursively in the following way: if x is the parent of y, then y has two children, namely vertical bar x-y vertical bar and x + y. This tree was studied by Benoit Rittaud [6] who proved that any pair of integers a, b that are coprime occur as a parent-child pair infinitely often. We extend his results by determining the probability that a random infinite walk in this tree contains exactly one pair (1, 1), that being at the root of the tree. Also, we give tight upper and lower bounds on the number of occurrences of any specific coprime pair (a, b) at any given fixed depth in the tree. (C) 2018 Elsevier Inc. All rights reserved.
A new formulation is proposed for the computation of average growth rates of generalized random fibonacci sequences. Based on the new formula, a novel numerical scheme is designed and successfully implemented, and int...
详细信息
A new formulation is proposed for the computation of average growth rates of generalized random fibonacci sequences. Based on the new formula, a novel numerical scheme is designed and successfully implemented, and interesting analytic asymptotic expansions are obtained for several examples.
Let * denote the canonical involution of the group algebra KG induced by the map x bar right arrow x(-1) for x is an element of G. In case K is a real extension of Q, we consider Cayley unitary elements built out of s...
详细信息
Let * denote the canonical involution of the group algebra KG induced by the map x bar right arrow x(-1) for x is an element of G. In case K is a real extension of Q, we consider Cayley unitary elements built out of skew elements k = alpha(x - x(-1)) in KG such that 1 + k is invertible in KG, for alpha is an element of K and x is an element of G. The constructions involve an interesting sequence in the coefficients of (1 + k)(-1) which is the fibonacci sequence when alpha = 1.
Starting from billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in d-dimensional Euclidean space, we introduce a new type of separable integer partition clas...
详细信息
Starting from billiard partitions which arose recently in the description of periodic trajectories of ellipsoidal billiards in d-dimensional Euclidean space, we introduce a new type of separable integer partition classes, called type B. We study the numbers of basis partitions with d parts and relate them to the fibonacci sequence and its natural generalizations. Remarkably, the generating series of basis partitions can be related to the quiver generating series of symmetric quivers corresponding to the framed unknot via knots-quivers correspondence, and to the count of Schr & ouml;der paths.
In this study, we present an investigation of the optical properties and band structures for the conventional and fibonacci photonic crystals (PCs) based on some A5B6C7 ferroelectrics (SbSBr and BiTeCl). Here, we use ...
详细信息
In this study, we present an investigation of the optical properties and band structures for the conventional and fibonacci photonic crystals (PCs) based on some A5B6C7 ferroelectrics (SbSBr and BiTeCl). Here, we use one dimensional SbSBr and BiTeCl based layers in air background. We have theoretically calculated the photonic band structure and transmission spectra of SbSBr and BiTeCl based PC superlattices. The position of minima in the transmission spectrum correlates with the gaps obtained in the calculation. The intensity of the transmission depths is more intense in the case of higher refractive index contrast between the layers. In our simulation, we employed the finite-difference time domain technique and the plane wave expansion method, which implies the solution of Maxwell equations with centered finite-difference expressions for the space and time derivatives.
暂无评论