scholarly journals Individual Gap Measures from Generalized Zeckendorf Degompositions

2017 ◽  
Vol 12 (1) ◽  
pp. 27-36 ◽  
Author(s):  
Robert Dorward ◽  
Pari L. Ford ◽  
Eva Fourakis ◽  
Pamela E. Harris ◽  
Steven. J. Miller ◽  
...  
Keyword(s):  
Positive Integer ◽  
Recurrence Relations ◽  
Fibonacci Numbers ◽  
Linear Recurrence ◽  
The Individual ◽  
Geometric Decay ◽  
Almost All ◽  
Zeckendorf’S Theorem ◽  
General Conditions

Abstract Zeckendorf's theorem states that every positive integer can be decomposed uniquely as a sum of nonconsecutive Fibonacci numbers. The distribution of the number of summands converges to a Gaussian, and the individual measures on gajw between summands for m € [Fn,Fn+1) converge to geometric decay for almost all m as n→ ∞. While similar results are known for many other recurrences, previous work focused on proving Gaussianity for the number of summands or the average gap measure. We derive general conditions, which are easily checked, that yield geometric decay in the individual gap measures of generalized Zerkendorf decompositions attached to many linear recurrence relations.

scholarly journals The Proof of a Conjecture on the Density of Sets Related to Divisibility Properties of z(n)

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2912
Author(s):  
Eva Trojovská ◽  
Venkatachalam Kandasamy
Keyword(s):  
Positive Integer ◽  
Fibonacci Numbers ◽  
Fibonacci Sequence ◽  
Natural Density ◽  
Almost All ◽  
Divisibility Properties

Let (Fn)n be the sequence of Fibonacci numbers. The order of appearance (in the Fibonacci sequence) of a positive integer n is defined as z(n)=min{k≥1:n∣Fk}. Very recently, Trojovská and Venkatachalam proved that, for any k≥1, the number z(n) is divisible by 2k, for almost all integers n≥1 (in the sense of natural density). Moreover, they posed a conjecture that implies that the same is true upon replacing 2k by any integer m≥1. In this paper, in particular, we prove this conjecture.

More Power to Fibonacci

2003 ◽  
Vol 87 (509) ◽  
pp. 196-198 ◽  
Author(s):  
Barry Lewis
Keyword(s):  
Recurrence Relations ◽  
Fibonacci Numbers ◽  
Fibonacci Sequence ◽  
Linear Recurrence

You should never judge a book by its title - but I nearly always do. A mathematical colleague recommended a book to me Concrete Mathematics [1]. Just recently, someone else also referred me to the same book. Well a wink’s as good as a nod to a blind man and I now realise what a mistake I’d made; concrete is a conflation of ‘continuous’ and ‘discrete’. Like all good textbooks in mathematics, it distinguishes itself not just by the quality of its contents and presentation, but also by the superb collection of problems that it includes. One such problem - question 58 in Chapter 6 - inspired this article. There was a hint towards a generalised result, but there were no details. It did give a reference, [2, 3], but despite some efforts I found this unobtainable. Hence this article and my attempt to cover the same ground. The question posed in the book is concerned with the linear recurrence relations satisfied by the successive powers of Fibonacci numbers - so we start with the Fibonacci sequence itself.

Adolescent Musicians' Perceptions of Conductors Within Musical Context

2009 ◽  
Vol 57 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Clifford K. Madsen ◽  
John M. Geringer ◽  
Katia Madsen
Keyword(s):  
College Students ◽  
Summer Camp ◽  
The Individual ◽  
Almost All ◽  
Audio Video ◽  
Musical Context

Attention to subtle changes in music, whether inadvertent or purposeful, occupies a great deal of practice and rehearsal time for the performer. Regardless of the extremely subtle acoustic changes that have been found to be perceptible within almost all studies, it is the total overall effect that most occupies the individual listener. This study investigated perception of digitally edited performances of Johann Strauss's Blue Danube Waltz, all performed by the Vienna Philharmonic Orchestra with various conductors across an 18-year period. Two groups of string musicians in grades 7 through 12 participated ( N = 104). One group was an intact class; the second was a group of summer camp students. All participants listened to two conditions: (a) audio only and (b) audio-video combination. Results indicated that there were no significant differences between groups and that no one was able to identify correctly that there were five different conductors in the audio-only condition. Results were much the same as earlier research with college students. In addition, many students indicated that there were differences in the audio portions of the two conditions when in fact there were not.

Justice as Fairness: For Groups?

1975 ◽  
Vol 69 (2) ◽  
pp. 607-614 ◽  
Author(s):  
Vernon Van Dyke
Keyword(s):  
John Rawls ◽  
Homogeneous State ◽  
Dominant Form ◽  
Justice As Fairness ◽  
Theory Of Justice ◽  
Indigenous Groups ◽  
The Social ◽  
Principles Of Justice ◽  
The Individual ◽  
Almost All

In A Theory of Justice, John Rawls assumes that the principles of justice are for individuals in a society, and in general he assumes that the society is an ethnically homogeneous state. He thus follows the tradition associated with the dominant form of the social contract theory, which focuses on the individual and the state. His assumptions neglect the fact that almost all states are ethnically plural or heterogeneous, and that many of them confer special status and rights on ethnic groups as collective entities; for example, many of them confer special status and rights on indigenous groups, on groups disadvantaged by prior discrimination, and on minorities and other groups conceded a right to survive as distinct cultural entities. Status and rights for groups necessarily mean differentiation among individuals depending on their membership; and this in turn means that a theory of justice that focuses on the individual and neglects the group both fails to account for existing practices and fails to give guidance where the practices are at issue.

scholarly journals On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Σn k=0 kW3 k and Σn k=1 kW3− k

2020 ◽  
pp. 37-52 ◽  
Author(s):  
Yuksel Soykan
Keyword(s):  
Recurrence Relations ◽  
Fibonacci Numbers ◽  
Second Order ◽  
Lucas Numbers ◽  
Generalized Fibonacci Numbers ◽  
Special Cases

In this paper, closed forms of the sum formulas Σn k=0 kW3 k and Σn k=1 kW3-k for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery. Our work generalize second order recurrence relations.

scholarly journals The Use of Genotoxicity Endpoints as Biomarkers of Low Dose Radiation Exposure in Interventional Cardiology

2021 ◽  
Vol 9 ◽  
Author(s):  
Martha Habibi ◽  
Panagiotis K. Karyofyllis ◽  
Aggeliki Nikolakopoulou ◽  
Panagiotis Papagiannis ◽  
Pantelis Karaiskos ◽  
...  
Keyword(s):  
Risk Estimation ◽  
Biological Effects ◽  
Interventional Cardiology ◽  
Mean Values ◽  
Individual Level ◽  
Cardiac Procedures ◽  
Before And After ◽  
Radiation Induced ◽  
The Individual ◽  
Almost All

The effect of the reportedly low ionizing radiation doses, such as those very often delivered to patients in interventional cardiology, remains ambiguous. As interventional cardiac procedures may have a significant impact on total collective effective dose, there are radiation protection concerns for patients and physicians regarding potential late health effects. Given that very low doses (<100 mSv) are expected to be delivered during these procedures, the purpose of this study was to assess the potency and suitability of current genotoxicity biomarkers to detect and quantitate biological effects essential for risk estimation in interventional cardiology. Specifically, the biomarkers γ-H2AX foci, dicentric chromosomes, and micronuclei, which underpin radiation-induced DNA damage, were studied in blood lymphocytes of 25 adult patients before and after interventional cardiac procedures. Even though the mean values of all patients as a group for all three endpoints tested show increased yields relative to baseline following medical exposure, our results demonstrate that only the γ-H2AX biomarker enables detection of statistically significant differences at the individual level (p < 0.001) for almost all patients (91%). Furthermore, 24 h after exposure, residual γ-H2AX foci were still detectable in irradiated lymphocytes. Their decline was found to vary significantly among the individuals and the repair kinetics of γ-H2AX foci was found to range from 25 to 95.6% of their maximum values obtained.

scholarly journals Seasonal changes of biological condition and reproductive cycle of hampback shrimp Pandalus hypsinotus (Caridea, Pandalidae) in the Tatar Strait

2021 ◽  
Vol 201 (3) ◽  
pp. 547-560
Author(s):  
D. N. Yuriev ◽  
G. V. Zhukovskaya
Keyword(s):  
Reproductive Cycle ◽  
Japan Sea ◽  
Biological Condition ◽  
Tatar Strait ◽  
Stage Of Development ◽  
Long Time ◽  
Pass Through ◽  
The Individual ◽  
Almost All ◽  
Trawl Catches

Research and commercial trawl catches of humpback shrimp Pandalus hypsinotus from the Tatar Strait (Japan Sea) in 2004–2020 were investigated, with bioanalysis of about 45 thousand specimens. Average timing of group molting, spawning, and eggs laying are determined, terms of gonads and eggs development are estimated. Prespawning and molting of the females occur between January-April, with the peaks in early February and middle February, respectively. All oviparous females have 30–40 days to lay eggs, and molt during 50–55 days; the peak of the eggs laying occurs in late June. The males molt in July-August, afterwards the largest individuals change gender and new intersexes are formed. The males have the second molting in October-December, with the peak in late November. In January, after finish of the males molting, a new annual reproduction cycle starts from the prespawning molting of females. Both vitellogenesis and embryogenesis are observed through the year, though females with developing gonads prevail from August to January (because of a long time span between winter and summer moltings while the egg carrying continued 15 months) but oviparous females — from February to July. The individual reproductive cycle of Pandalus hypsinotus in the Tatar Strait lasts 24 months, with 9 months of vitellogenesis (quick growth of gonads) and 15 months of embryogenesis. During the 2-year reproductive cycle, most of females pass through the following stages: i) gonads development (just after eggs laying) when almost all oviparous females (up to 95 % in May) have green gonads under carapace that corresponds to the stage of development «eggs laid — gonads weakly developed»; ii) summer molting from August when females lose hairs on pleopods and the gonads growth accelerates; iii) respawning in January-March (together with the firstly spawning intersexes, with slight delay of the latter); iv) initial developing of eggs during summer; v) stage of «eyed eggs» from December to March; and vi) eggs laying and molting from late March to late May; then the 2-year reproductive cycle repeats.

scholarly journals Hemoglobin biosynthesis in individual bursts in culture: studies of human umbilical cord blood

Blood ◽  
1979 ◽  
Vol 53 (3) ◽  
pp. 519-522
Author(s):  
K Kidoguchi ◽  
M Ogawa ◽  
JD Karam ◽  
JS McNeil ◽  
MS Fitch
Keyword(s):  
Cord Blood ◽  
Umbilical Cord ◽  
Umbilical Cord Blood ◽  
Methyl Cellulose ◽  
Human Umbilical Cord Blood ◽  
Human Umbilical Cord ◽  
Hemoglobin Biosynthesis ◽  
The Individual ◽  
Gel Isoelectric Focusing ◽  
Almost All

We cultured human umbilical cord blood erythropoietic precursors in methyl cellulose clonal assay and analyzed the synthetic rates of Hb A and Hb F in individual erythropoietic bursts. Hemoglobin was labeled with 14C-amino acids in culture, separated by slab gel isoelectric focusing techniques, and quantitated by fluorographic methods. Almost all bursts exhibited both Hb A and Hb F in varying ratios. Frequencies of the individual bursts differing in percentage Hb F biosynthesis had normal distributions. Natal erythropoietic precursors appeared to be randomly committed to Hb F synthesis.

Sign in / Sign up

Export Citation Format

Share Document