scholarly journals Fibonacci Graphs

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1383 ◽  
Author(s):  
Aysun Yurttas Gunes ◽  
Sadik Delen ◽  
Musa Demirci ◽  
Ahmet Sinan Cevik ◽  
Ismail Naci Cangul
Keyword(s):  
Social Sciences ◽  
Graph Theory ◽  
Degree Sequence ◽  
Golden Ratio ◽  
Fibonacci Numbers ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Apart from its applications in Chemistry, Biology, Physics, Social Sciences, Anthropology, etc., there are close relations between graph theory and other areas of Mathematics. Fibonacci numbers are of utmost interest due to their relation with the golden ratio and also due to many applications in different areas from Biology, Architecture, Anatomy to Finance. In this paper, we define Fibonacci graphs as graphs having degree sequence consisting of n consecutive Fibonacci numbers and use the invariant Ω to obtain some more information on these graphs. We give the necessary and sufficient conditions for the realizability of a set D of n successive Fibonacci numbers for every n and also list all possible realizations called Fibonacci graphs for 1≤n≤4.

Aggregation Bias and the Analysis of Necessary and Sufficient Conditions in fsQCA

2016 ◽  
Vol 46 (2) ◽  
pp. 242-251 ◽  
Author(s):  
Bear F. Braumoeller
Keyword(s):  
Social Sciences ◽  
Comparative Analysis ◽  
Qualitative Comparative Analysis ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Aggregation Bias ◽  
Data Sets ◽  
The Social ◽  
Necessary And Sufficient ◽  
Causal Complexity

Fuzzy-set qualitative comparative analysis (fsQCA) has become one of the most prominent methods in the social sciences for capturing causal complexity, especially for scholars with small- and medium- N data sets. This research note explores two key assumptions in fsQCA’s methodology for testing for necessary and sufficient conditions—the cumulation assumption and the triangular data assumption—and argues that, in combination, they produce a form of aggregation bias that has not been recognized in the fsQCA literature. It also offers a straightforward test to help researchers answer the question of whether their findings are plausibly the result of aggregation bias.

Connectability-Based Controllability of Large Scale Nonlinear Dynamic Thermal Systems

2009 ◽  
Author(s):  
Rahmat Shoureshi ◽  
Virdi Permana
Keyword(s):  
Graph Theory ◽  
Nonlinear Systems ◽  
Lie Algebra ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Rank Condition ◽  
Thermal Systems ◽  
Necessary And Sufficient ◽  
Controllability And Observability

A new approach using graph-theory to determine the controllability and observability of large scale nonlinear dynamic thermal systems is presented. The novelty of this method is in adapting graph theory for a nonlinear class and establishing graphic conditions that describe the necessary and sufficient conditions for a class of nonlinear systems to be controllable and observable which is equivalent to the analytical method of Lie algebra rank condition. Graph theory of directed graph (digraph) is utilized to model the system and its adaptation to nonlinear problems is defined. The necessary and sufficient conditions for controllability are investigated through the structural property of a digraph called connectability. In comparison to the Lie Algebra, this approach has proven to be easier, from a computational point of view, thus it is found to be useful when dealing with large scale systems. This paper presents the problem statement, properties of structured system, and analytical method of Lie algebra rank condition for controllability and observability of bilinear systems. The main results of graphical approach which describe the necessary and sufficient conditions for controllability of nonlinear systems are presented and applied to the problem of a coupled two heat exchangers, connected in an arbitrary fashion.

Eco-Holonic as a Framework for the Design of Sustainable Autopoietic Cyberphysical Systems

2021 ◽  
pp. 1-37
Author(s):  
María Jesús Ávila-Gutiérrez ◽  
Francisco Aguayo-González
Keyword(s):  
Social Sciences ◽  
Systems Theory ◽  
Circular Economy ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Living Systems ◽  
Cyberphysical Systems ◽  
The Social ◽  
New Perspective ◽  
Necessary And Sufficient

The concept of autopoiesis created by scientists Maturana and Varela to specify the necessary and sufficient conditions of living systems has been strongly criticized by different authors. In spite of the constant attempts to introduce it to the sciences in general, it has only managed to be partially installed, although very strongly, in the social sciences. This chapter will seek to clarify what kind of problems the concept of autopoiesis presents and, in accordance with this, will present a new perspective. The concept of autopoiesis will be analyzed, placing it within the systems theory, critically evaluated, and its deficiencies made evident. Based on this, the concept of interpoiesis for the resolution of the deficiencies presented in the autopoiesis will be presented in order to install this new concept in the discussion. Finally, the concept will be evaluated from the Holonic paradigm shortened a case of application for business from the circular economy.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

On the domain of Riesz mean in the space Ls

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 925-940 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Double Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Double Sequences ◽  
Riesz Mean ◽  
Double Sequence Space ◽  
Necessary And Sufficient ◽  
Barrelled Space

Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls) as the domain of four dimensional Riesz mean Rqt in the space Ls of absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for 0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p, bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls) : Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 < s < 1 and 1 ? s < 1 together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.

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