scholarly journals Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment

2016 ◽  
Vol 3 (5) ◽  
pp. 160091 ◽  
Author(s):  
Jonathan Swinton ◽  
Erinma Ochu ◽  

This citizen science study evaluates the occurrence of Fibonacci structure in the spirals of sunflower ( Helianthus annuus ) seedheads. This phenomenon has competing biomathematical explanations, and our core premise is that observation of both Fibonacci and non-Fibonacci structure is informative for challenging such models. We collected data on 657 sunflowers. In our most reliable data subset, we evaluated 768 clockwise or anticlockwise parastichy numbers of which 565 were Fibonacci numbers, and a further 67 had Fibonacci structure of a predefined type. We also found more complex Fibonacci structures not previously reported in sunflowers. This is the third, and largest, study in the literature, although the first with explicit and independently checkable inclusion and analysis criteria and fully accessible data. This study systematically reports for the first time, to the best of our knowledge, seedheads without Fibonacci structure. Some of these are approximately Fibonacci, and we found in particular that parastichy numbers equal to one less than a Fibonacci number were present significantly more often than those one more than a Fibonacci number. An unexpected further result of this study was the existence of quasi-regular heads, in which no parastichy number could be definitively assigned.

2021 ◽  
Author(s):  
Pedro M. Martin‐Sanchez ◽  
Eva‐Lena F. Estensmo ◽  
Luis N. Morgado ◽  
Sundy Maurice ◽  
Ingeborg B. Engh ◽  
...  

1989 ◽  
Vol 26 (3) ◽  
pp. 591-605 ◽  
Author(s):  
David J. Mossman ◽  
Craig H. Place

Vertebrate trace fossils are reported for the first time from red beds near the top of megacyclic sequence II at Prim Point in southwestern Prince Edward Island. They occur as casts of tetrapod trackways. The ichnocoenose also includes a rich invertebrate ichnofauna. The trackmakers thrived in an area of sparse vegetation and occupied out-of-channel river sediments, most likely crevasse-splay deposits.Amphisauropus latus, represented by three trackways, has been previously reported from Germany, Poland, and Czechoslovakia. It is here interpreted as the track of a cotylosaur. It occurs together with the track of Gilmoreichnus kablikae, which is either a captorhinomorph or possibly a juvenile pelycosaur. These facilitate the assignment of a late Early Permian (late Autunian) age to the strata. The third set of footprints, those of a small herbivorous pelycosaur, compare most closely with Ichniotherium willsi, known hitherto from the Keele beds (latest Stephanian) of the English Midlands.This ichnocoenose occurs in a plate-tectonically rafted segment of crust stratigraphically equivalent to the same association of ichnofauna in the English Midlands and central Europe. The community occupied piedmont-valley-flat red beds within the molasse facies of Variscan uplands.


Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 962
Author(s):  
Eva Trojovská  ◽  
Pavel Trojovský

Let (tn(r))n≥0 be the sequence of the generalized Fibonacci number of order r, which is defined by the recurrence tn(r)=tn−1(r)+⋯+tn−r(r) for n≥r, with initial values t0(r)=0 and ti(r)=1, for all 1≤i≤r. In 2002, Grossman and Luca searched for terms of the sequence (tn(2))n, which are expressible as a sum of factorials. In this paper, we continue this program by proving that, for any ℓ≥1, there exists an effectively computable constant C=C(ℓ)>0 (only depending on ℓ), such that, if (m,n,r) is a solution of tm(r)=n!+(n+1)!+⋯+(n+ℓ)!, with r even, then max{m,n,r}<C. As an application, we solve the previous equation for all 1≤ℓ≤5.


1995 ◽  
Vol 400 ◽  
Author(s):  
R.T. Malkhassian

AbstractA new technology for obtainment of amorphous single-component metals is presented.For the first time the reduction of molybdenum oxide with formation of its amorphous phase is realized in conditions of a given quantum-chemical technology by means of vibrationally excited to the third quantum level hydrogen molecules with 1.5 ± 0.2 eV energy. The evidences of formation of this nonequilibrium amorphous phase are presented along with certain physicochemical properties of the obtained amorphous molybdenum.A model is proposed for the origin of amorphous phase under the influence of nonequilibrium quantum-chemical technology.


2021 ◽  
Vol 66 (1) ◽  
pp. 329-343
Author(s):  
Liudmyla Shapovalova ◽  
Іryna Romaniuk ◽  
Marianna Chernyavska ◽  
Svitlana Shchelkanova

"In the article under consideration are the ways of symphony genre transformation in the early works of Valentin Silvestrov (Ukraine). For the first time, the First, Second, Third, and Fourth symphonies by the genius composers of the 20th century are analyzed as a certain stylistic system. These compositions are endowed with the features of avant-garde poetics, and as a subject of musicological reflection, they are associated with a rethinking of the semantic paradigm of the genre. V. Silvestrov's early symphonies stand out from the classical practice of European symphonies. Scientific awareness of their phenomenal nature necessitated a methodological choice aimed at the most accurate identification of the philosophical concept of the new sound universum of V. Silvestrov's music. Deep correlation of the image of a human being as a factor of the symphony poetics (the influence of philosophical concepts of human ontology in the 20th century with the transformation of the genre canon) is considered. This refers to the nonmusical dimension of the genre semantics. The study of V. Silvestrov's early symphonies reveal a new philosophy of music through gradual movement – modulation: from the neo-baroque First Symphony and ""cosmic pastorals"" Musica Mundana of the Second Symphony through the history anthropologisation in the Third Symphony ""Eschatology"" to the monodrama Musica Humana in the Fourth Symphony. The dichotomy of Musica Mundana – Musica Humana is not accidental: in V. Silvestrov's creative method, remains relevant, which is confirmed by the dramaturgy of his latest work – the Ninth symphony (2019). Keywords: V. Silvestrov's early symphonies, evolution of style, worldview, Musica Mundana, monodrama. "


2021 ◽  
pp. 1-22
Author(s):  
Tofigh Maboudi ◽  
Ghazal P. Nadi ◽  
Todd A. Eisenstadt

Abstract Since the third wave of democracy, term limits have become a popular fixture of most constitutions intended to constrain the executive. Yet, recent constitutional reforms around the world show that presidents seeking re-election sometimes overturn the entire constitutional order to extend their power. What is the impact of these constitutional manipulations on the longevity of the executive in office? Using survival analysis of all political leaders and national constitutions from 1875 to 2015, this article demonstrates, for the first time, that when ‘authoritarian-aspiring’ presidents remove constitutional term limits, they increase their stay in office by more than 40%. Our findings contrast with a widely held position in the comparative authoritarian literature suggesting that dictators survive longer under institutional constraints. On the contrary, we argue that by removing constitutional barriers, rulers consolidate more power at the expense of their most ambitious allies and can stay in power longer.


Author(s):  
Т.А. Богумил

В статье предлагается концепция жизни и творческого роста В.М. Шукшина сквозь призму тезаурусного и кластерного подходов. Объяснительными «персональными моделями» для интерпретации биографического текста писателя являются кластеры Мартина Идена, Гамлета и Степана Разина. Ранее биографы и литературоведы указывали на важность этих персон для Шукшина, но разрозненно. Впервые предпринята попытка свести указанные персональные модели воедино, в целостный сюжет становления писателя в пространстве культуры. На разных этапах эволюции автора доминирует одна из указанных моделей, последовательно сменяя друг друга, но не вытесняя, а «внахлест». Ранний этап творчества, ориентированный на стратегию Мартина Идена, является попыткой «вписаться» в наличный культурный мейнстрим. Выражено это в следовании поэтике соцреализма. Второй этап подспудно начинается с реабилитации отца Шукшина в 1956 года, когда актуализируется «гамлетовский комплекс», проявляющийся в чувстве вины перед отцом, через стратегию утаивания подлинного «я», мотивы чудаковатости. Третий этап связан с личностью реального исторического лица, Степана Разина, и выражается в открытом протесте против власти. Все важные для В.М. Шукшина поведенческие модели объединены мотивом одинокого противостояния враждебному социуму и имеют трагический финал, что обусловило ранний уход писателя и порождение мифов о насильственном характере его смерти. В.М. Шукшин одновременно был фигурой неординарной и типичной, что позволило его биографии стать «персональной моделью» для последующих авторов, выходцев из сельской глубинки. The article proposes the concept of life and creative growth of V.M. Shukshin through the prism of the thesaurus and cluster approach. The explanatory "personal models" for interpreting the biographical text of the writer are clusters of Martin Eden, Hamlet and Stepan Razin. Earlier, biographers and literary critics pointed out the importance of these people for Shukshin, but it was scattered. For the first time, an attempt was made to bring these personal models together into an integral plot of the formation of the writer in the space of culture. At different stages of the writer’s evolution, one of these models dominates, successively replacing each other, but not crowding out, but “overlapping”. The early stage of creativity, focused on Martin Eden’s strategy, is an attempt to “fit in” the current cultural mainstream. This is expressed in following the poetics of socialist realism. The second stage implicitly begins with the rehabilitation of Shukshin’s father in 1956, when the “Hamletian complex” is actualized. It is manifested in a sense of guilt towards his father, the strategy of concealing the true “I”, eccentricities. The third stage is connected with the personality of a real historical person, Stepan Razin, and is expressed in an open protest against the authorities. All important for V.M. Shukshin's behavioral models are united by the motive of a lonely confrontation with a hostile society and have a tragic ending, which led to the early departure of the writer and the generation of myths about the violent nature of his death. V.M. Shukshin was an extraordinary and typical figure at the same time. That allowed his biography to become a “personal model” for subsequent authors who came from the rural outback.


Author(s):  
L. G. Vakulenko ◽  
◽  
O. D. Nikolenko ◽  
D. A. Novikov ◽  
P. A. Yan ◽  
...  

A comprehensive study of the composition of sand and silt deposits of the Yu1 horizon of the Vasyuganskaya Formation upper part of the Verkh-Tarskoye oil field has been carried out. Associations of authigenic minerals have been determined in their cement, among which the calcite is the most widespread. According to petrographic parameters, three generations of calcite have been identified for which detailed isotopicgeochemical and ultramicroscopic studies were carried out for the first time. Wide and multi directional changes in the isotopic composition of carbon and oxygen and in the chemical composition of carbonate minerals were recorded, they indicate significant variations in the conditions of diagenesis and catagenesis, primarily temperature, and different sources of CO2. Significant variations in the isotopic composition of formation waters and its relationship with the isotopic composition of carbonates have been established. Thus, a narrow interval of close δ13C values was revealed, amounting to –10.5 to –9.1 ‰ in the formation waters of group II, and from –10.7 to –9.1 ‰ in calcites of the third generation. The source of CO2 in this system should be considered a carbon dioxide, which is formed in the process of metamorphism of carbonate rocks of the Paleozoic age.


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