scholarly journals From Fibonacci Sequence to the Golden Ratio

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Alberto Fiorenza ◽  
Giovanni Vincenzi
Keyword(s):  
Characteristic Polynomial ◽  
Golden Ratio ◽  
Fibonacci Sequence ◽  
Maximum Modulus ◽  
Point Of View ◽  
General Point ◽  
Constant Coefficients ◽  
The Difference ◽  
New Perspective

We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive terms of the Fibonacci sequence, and we give an explanation of this property in the framework of the Difference Equations Theory. We show that the Golden ratio coincides with this limit not because it is the root with maximum modulus and multiplicity of the characteristic polynomial, but, from a more general point of view, because it is the root with maximum modulus and multiplicity of a restricted set of roots, which in this special case coincides with the two roots of the characteristic polynomial. This new perspective is the heart of the characterization of the limit of ratio of consecutive terms of all linear homogeneous recurrences with constant coefficients, without any assumption on the roots of the characteristic polynomial, which may be, in particular, also complex and not real.

scholarly journals Grounding semantic transparency in context

Morphology ◽  
2021 ◽  
Author(s):  
Rossella Varvara ◽  
Gabriella Lapesa ◽  
Sebastian Padó
Keyword(s):  
Large Scale ◽  
Point Of View ◽  
Distributional Semantics ◽  
Semantic Transparency ◽  
Inclusion Measure ◽  
The Difference ◽  
Semantic Point ◽  
The Many ◽  
The Relationship

AbstractWe present the results of a large-scale corpus-based comparison of two German event nominalization patterns: deverbal nouns in -ung (e.g., die Evaluierung, ‘the evaluation’) and nominal infinitives (e.g., das Evaluieren, ‘the evaluating’). Among the many available event nominalization patterns for German, we selected these two because they are both highly productive and challenging from the semantic point of view. Both patterns are known to keep a tight relation with the event denoted by the base verb, but with different nuances. Our study targets a better understanding of the differences in their semantic import.The key notion of our comparison is that of semantic transparency, and we propose a usage-based characterization of the relationship between derived nominals and their bases. Using methods from distributional semantics, we bring to bear two concrete measures of transparency which highlight different nuances: the first one, cosine, detects nominalizations which are semantically similar to their bases; the second one, distributional inclusion, detects nominalizations which are used in a subset of the contexts of the base verb. We find that only the inclusion measure helps in characterizing the difference between the two types of nominalizations, in relation with the traditionally considered variable of relative frequency (Hay, 2001). Finally, the distributional analysis allows us to frame our comparison in the broader coordinates of the inflection vs. derivation cline.

scholarly journals Fibonacci, tribonacci, …, hexanacci and parallel “error-free” machine arithmetic

2019 ◽  
Vol 43 (6) ◽  
pp. 1072-1078 ◽  
Author(s):  
V.M. Chernov
Keyword(s):  
Characteristic Polynomial ◽  
Fibonacci Sequence ◽  
Parallel Computations ◽  
New Method ◽  
Direct Sum ◽  
Number Systems ◽  
Residue Number Systems ◽  
Residue Number ◽  
The Difference ◽  
Free Machine

The paper proposes a new method of synthesis of machine arithmetic systems for “error-free” parallel computations. The difference of the proposed approach from calculations in traditional Residue Number Systems (RNS) for the direct sum of rings is the parallelization of calculations in finite reductions of non-quadratic global fields whose elements are represented in number systems generated by sequences of powers of roots of the characteristic polynomial for the n-Fibonacci sequence.

scholarly journals PhiΦBreast & Theory of Spiral Cancer - New Diagnostic Techniques Breast Cancer Detection

2021 ◽  
Author(s):  
Ersilio Trapanese ◽  
Giulio Tarro
Keyword(s):  
Breast Cancer ◽  
Predictive Value ◽  
Golden Ratio ◽  
Fibonacci Sequence ◽  
Diagnostic Technique ◽  
Classification Model ◽  
Predictive Algorithm ◽  
Life Threatening ◽  
Identification And Characterization

Abstract Background Breast cancer today is one of the most aggressive in women and new cases continue to increase worldwide. The incidence of this tumor is kept under control especially by surgery and to reduce mortality we need detect life threatening disease at an earlier stage. We conducted two years a study for the identification and characterization of suspicious breast lesions using a new diagnostic technique applied to ultrasonography and mammography called “PhiΦBreast.” Methods Identification and characterization of category C4-C5 lesions of the breast with high Predictive Positive PPV value, by means of a new innovative method called “PhiΦBreast” using the Golden Ratio (Phi, or Φ 1.618...) Fibonacci sequence and a Predictive Algorithm, applied to the ultrasonography and mammography with subsequent deepening with cytological examination using fine needle aspiration (FNAC), according to evaluation criteria of the Breast Imaging Report Data System (BI-RADS) and the American College of Radiology (ACR). Usefulness of this research is to detect the breast cancer early on with this new diagnostic technique, in addition to develop a classification model of the histological type identified in the section areas and the percentage of probability in relation between the golden spiral and Fibonacci sequence. This amazing intuition gave rise Theory of Spiral Cancer. Results Using Golden Ratio and Fibonacci sequence, applied to ultrasonography and mammography, we have experimented and developed a diagnostic map with characteristics of high probability of identifying suspicious lesions at an early stage. We examined 987 women, 55 lesions detected with PhiΦBreast pattern were classified according to BI-RADS descriptors for US-imaging, including morphologic features that had a high predictive value for the malignancy (p <0.001). This innovative diagnostic tecnique has shown a sensitivity 95%, a specificity 97%, a positive predictive value 97%, a negative predictive value 96%. The discriminating capacity of PhiΦBreast was significantly better than normal ultrasonography (P < 0,05). Furthermore with a predictive algorithm associated with malignant cytology after FNAC, we have classified different types of cancer potentially life threatening for patients. Conclusion PhiΦBreast could be an important new model diagnostic technique to be applied ultrasound and mammography for detection malignant lesions of category C4-C5.

scholarly journals 2D Frequency Domain Fully Focused SAR Processing for High PRF Radar Altimeters

2018 ◽  
Vol 10 (12) ◽  
pp. 1943 ◽  
Author(s):  
Pietro Guccione ◽  
Michele Scagliola ◽  
Davide Giudici
Keyword(s):  
Pulse Repetition Frequency ◽  
Computational Effort ◽  
Point Of View ◽  
Accurate Estimation ◽  
High Pulse ◽  
The Difference ◽  
New Perspective ◽  
Along Track ◽  
Sar Processing ◽  
Orbit Data

Fully-focusing of radar altimeters is a recent concept that has been introduced to allow further improvement of along-track resolution in high pulse repetition frequency (PRF) radar altimeters. The straight potentiality of this new perspective reflects into a more accurate estimation of geophysical parameters in some applications such as sea-ice observation. However, as documented in a recent paper, such capability leaves unsolved the problem of the high computational effort required. In this paper, we face the problem of adapting for altimeters the Omega-Kappa SAR focusing algorithm that is performed in the two-dimensional wavenumber domain, accounting for the difference existing between SAR and altimeter from geometry (looking and swath width) and instrument (echoes are deramped onboard on receiving) point of view. Simulations and an application using in-orbit data show the effectiveness of the proposed approach and the highly reduced computational effort.

Properties of Some Synthetic Rubbers

1943 ◽  
Vol 16 (4) ◽  
pp. 857-862
Author(s):  
L. B. Sebrell ◽  
R. P. Dinsmore
Keyword(s):  
Molecular Structure ◽  
Natural Rubber ◽  
Point Of View ◽  
General Point ◽  
Chain Molecules ◽  
X Ray ◽  
Synthetic Rubber ◽  
The Difference ◽  
Diffraction Patterns ◽  
Long Chain

Abstract X-RAY STRUCTURE OF SYNTHETIC RUBBER In presenting a series of x-ray diagrams of various types of synthetic rubber in comparison with natural rubber, in both the stretched and the unstretched condition, it is our purpose to bring out the fact that the molecular structure of synthetic rubbers is entirely different from that of natural rubber. It is proposed also to review briefly the theories which have been advanced, based on the x-ray analysis of rubber, to account for the elasticity of natural rubber, and to advance the possible reason for the difference shown by the x-ray diagrams of synthetic rubber. At the present time, from the most general point of view, the molecular structure of a rubberlike material is envisaged as a sort of brush-heap structure of entangled long chain molecules. x-Ray diffraction patterns show that, for some rubberlike materials, notable regularities of structure sometimes occur in the tangle of long-chain molecules. It is now realized that these regularities are not essential for rubberlike behavior. Nevertheless their observation and study is important because they afford a unique opportunity for studying the molecular structure of the chains and the molecular rearrangements which occur with the application of stress.

scholarly journals From Fearful to Trustful – How Perceived Risk Dimensions in E-Commerce Differentiate between Consumers

2015 ◽  
Vol 8 (1) ◽  
pp. 45-54
Author(s):  
Patricea Elena Bertea
Keyword(s):  
Perceived Risk ◽  
Online Shopping ◽  
Point Of View ◽  
Ease Of Use ◽  
Perceived Usefulness ◽  
Individual Risk ◽  
Perceived Ease Of Use ◽  
The Difference ◽  
New Perspective ◽  
Risk Dimensions

AbstractThe need to segment the market for e-commerce in terms of risk is without doubt of great importance, from a theoretical, but mainly from a managerial point of view. This is why the present study derives a typology of consumers based on six dimensions of perceived risk in online shopping (product, financial, delivery, privacy, social and psychological) and links the resulting risk profiles to several outcome variables. The study is one of the few that offers a new perspective on perceived risk, identifying a two-factor structure: situational risk and individual risk. These two factors were used in a cluster analysis, where four segments were identified: careful consumers, fearful consumers, suspicious consumers and trustful consumers. To offer valuable information for practitioners, these segments are compared in terms of intentions to buy online, online shopping frequency, trust in e-commerce, perceived ease of use, and perceived usefulness of e-commerce. One interesting finding is that suspicious and trustful consumers do not differ in terms of buying intention, even though the difference between them in terms of perceived risk is significant. Implications and further research directions are identified.

In-Situ Quality Control of the Production of Semiconductor Devices by Microwave Photoconductivity Measurements

1992 ◽  
Vol 269 ◽  
Author(s):  
C. Swiatkowski ◽  
A. Sanders ◽  
M. Kunst ◽  
G. Seidelmann ◽  
C. Haffer ◽  
...  
Keyword(s):  
Quality Control ◽  
Amorphous Silicon ◽  
Semiconductor Devices ◽  
Microwave Frequency ◽  
Point Of View ◽  
General Point ◽  
Frequency Range ◽  
Transient Photoconductivity

ABSTRACTThe application of transient photoconductivity measurements in the microwave frequency range to the characterization of semiconductors and semiconductor devices is analyzed. Quality control and in-situ optimization are discussed from a more general point of view and as a concrete example the optimization of the deposition of amorphous silicon films is presented.

scholarly journals Standards of Classical Architecture Criticism: Between Mathematics and Philosophy

2021 ◽  
Vol 5 (2) ◽  
Author(s):  
Aida Hoteit
Keyword(s):  
Golden Ratio ◽  
Fibonacci Sequence ◽  
Correct Judgment ◽  
Classical Architecture ◽  
Complex Process ◽  
Geographical Environment ◽  
Critical Activity ◽  
The Difference ◽  
Mathematical Evaluation ◽  
Standards Of Beauty

Criticism is an intellectual process that primarily searches for beauty aspects in the works of art, including architecture. This article explores the mathematical and philosophical principles of classical architectural criticism. It is hypothesized that design criteria during the Classic period were clear and specific. The research presents theories of classical art that focus on the process of beauty interpretation. It also assesses the mathematical evaluation of architectural art and beauty through “The Golden Ratio” and “The “Fibonacci Sequence.” Classical philosophy, and its perception of beauty, is discussed as an essential basis in any artistic critical activity. The research asserts that the science of aesthetics is both objective and subjective, which explains the difference in aesthetic evaluation across eras. Objectivity stems from conditions of proportionality that must be met for an architectural art to be aesthetically judged as beautiful. Subjectivity lies in the time and place of the architectural work, whereby tendencies, tastes, and needs related to the human and geographical environment can affect the standards of beauty. This makes the evaluation of beauty in classical architecture a delicate and complex process in which many aspects must be considered to have an objective, fair, and correct judgment. 

scholarly journals PhiΦBreast & theory of spiral cancer new diagnostic techniques for breast cancer detection

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Ersilio Trapanese ◽  
Giulio Tarro
Keyword(s):  
Breast Cancer ◽  
Predictive Value ◽  
Early Stage ◽  
Golden Ratio ◽  
Evaluation Criteria ◽  
Fibonacci Sequence ◽  
Diagnostic Technique ◽  
Predictive Algorithm ◽  
Life Threatening

Abstract Background Today, breast cancer is one of the most aggressive cancers in women and new cases continue to increase worldwide. The incidence of this tumor is kept under control especially with surgery. In order to reduce mortality we need to detect this life threatening disease at an earlier stage. For two years, we have conducted a study for the identification and characterization of suspicious breast lesions using a new diagnostic technique applied to ultrasonography and mammography called “PhiΦBreast.” Methods Identification and characterization of category C4-C5 lesions of the breast with high Predictive Positive PPV value, with a new innovative method called “PhiΦBreast” using the Golden Ratio (Phi, or Φ 1.618...) Fibonacci sequence and a Predictive Algorithm, applied to the ultrasonography and mammography with subsequent deepening with cytological examination using fine needle aspiration (FNAC), according to evaluation criteria of the Breast Imaging Report Data System (BI-RADS) and the American College of Radiology (ACR). Usefulness of this research and the use of this new diagnostic tecnique is to detect the breast cancer in early stage. In addition to develop a classification model of the histological type identified in the section areas and the percentage of probability in relation between the golden spiral and Fibonacci sequence. This amazing intuition and research has given contribution to the new Theory of Spiral Cancer. Results With the use of Golden Ratio and Fibonacci sequence, applied to ultrasonography and mammography, we have experimented and developed a diagnostic map with characteristics of high probability of identifying suspicious lesions at an early stage. We examined 987 women, 55 lesions detected with PhiΦBreast pattern were classified according to BI-RADS descriptors for US-imaging, including morphologic features that had a high predictive value for the malignancy (p <0.001). This innovative diagnostic technique has shown a sensitivity of 95%, a specificity of 97%, a positive predictive value of 97%, and negative predictive value of 96%. The discriminating capacity of PhiΦBreast was significantly better than normal ultrasonography (P < 0,05). Furthermore with a predictive algorithm associated with malignant cytology after FNAC, we have classified different types of potentially life threatening cancers for patients. Conclusion PhiΦBreast could be an important new model diagnostic technique to be applied ultrasound and mammography for detection of malignant lesions of category C4-C5. In diagnostic imaging beyond the identification of a lesion and classification according to the BI-RADS category and the evaluation criteria of the ACR is fundamental to recognize predictively the characteristics of a potentially aggressive tumor. Everything mentioned above, reinforces the concept that the early diagnosis is essential because it allows to remove small tumors and therefore capable of producing more limited metastases than the potential of the most voluminous neoplasm. This way, we could plan an effective cure for the patient. This new model (PhiΦBreast) could represent the cornerstone as an important contribution for early diagnosis of breast cancer.

scholarly journals Is there a Similiarity between Fibonacci Sequence and Euler’s Number with Respect to Quantum Perspective Model?

2021 ◽  
pp. 35-39
Author(s):  
Tahir Ölmez
Keyword(s):  
Golden Ratio ◽  
Fibonacci Sequence ◽  
Point Of View ◽  
Base System ◽  
Fibonacci Series ◽  
Perspective Model ◽  
First Time

According to Quantum Perspective Model, this article studies whether there is a link between the Euler’s numbers and the Fibonacci series. When the digits of the Euler’s number after the comma are converted from decimal(10) number base system to binary(2) number base system, it corresponds to the number in the Fibonacci series.(0,1,1,2,3,5,8,13,21,34,55...)[7].From this point of view, when the first hundred digits of the Euler’s numbers after the comma were calculated, the number "55" (ten times) in the Fibonacci series was found, in particular. Besides, the eleventh number in the Fibonacci series is also "55".In other words, the approximate unchanged numbers of the golden ratio numbers after the comma can be reached for the first time after dividing them from “55” to “34” (1,618). In sum, Euler’s numbers are not only attributed to the Fibonacci series in mathematics, but also attributed to the golden ratio in nature.

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