scholarly journals CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTION

2018 ◽  
Vol 18 (2) ◽  
pp. 103
Author(s):  
Jullia Titaley ◽  
Tohap Manurung ◽  
Henriette D Titaley
Keyword(s):  
Complex Number ◽  
Complex Dynamics ◽  
Polynomial Function ◽  
Julia Set ◽  
Trigonometric Function ◽  
Quadratic Polynomial ◽  
Cosine Function ◽  
New Class ◽  
Iterated Function ◽  
Iteration Function

CUBIC AND QUADRATIC POLYNOMIAL ON JULIA SET WITH TRIGONOMETRIC FUNCTIONABSTRACTJulia set are defined by iterating a function of a complex number and is generated from the iterated function . We investigate in this paper the complex dynamics of different functions and applied iteration function system to generate an entire new class of julia set. The purpose of this research is to make variation of Cubic and Quadratic polynomial on Julia Set and the two obvious to investigate from julia set are Sine and Cosine function. The results thus obtained are innovative and studies about different behavior of two basic trigonometry.Keywords : Julia Set, trigonometric function, polynomial function  POLINOMIAL  KUBIK DAN KUADRATIK PADA HIMPUNAN JULIA DENGAN FUNGSI TRIGONOMETRI ABSTRAKHimpunan Julia didefiniskan oleh fungsi iterasi dari bilangan kompleks dan dibangkitkan dari fungsi iterasi . Kami melakukan penelitian dalam penulisan ini tentang sistem dinamik kompleks dari fungsi yang berbeda dengan iterasi yang diterapkan untuk menghasilkan kelas baru dari himpunan Julia. Tujuan dari penelitian ini adalah untuk membuah kelas baru himpunan Julia dengan fungsi polinomial kubik dan kuadratik dengan fungsi sinus dan kosinus. Hasil akhir dari penelitian ini ada menemukan inovatif baru dari himpunan Julia dengan menggunakan dua fungsi trigonometri.Kata kunci: Julia set, fungsi trigonometri, fungsi polinomial

scholarly journals Julia Set with Trigonometric Function

2019 ◽  
Vol 8 (2S7) ◽  
pp. 115-119
Keyword(s):  
Complex Number ◽  
Complex Dynamics ◽  
Julia Set ◽  
Julia Sets ◽  
New Class ◽  
Iteration Function ◽  
Cubic Polynomials ◽  
Constant Complex ◽  
Sine And Cosine Functions ◽  
Cosine Functions

Julia sets are generated by initializing a complex number z = x + yi where z is then iterated using the iteration function fc (z)= zn 2 + c, where n indicates the number of iteration and c is a constant complex number. Recently, study of cubic Julia sets was introduced in Noor Orbit (NO) with improved escape criterions for cubic polynomials. In this paper, we investigate the complex dynamics of different functions and apply the iteration function to generate an entire new class of Julia sets. Here, we introduce different types of orbits on cubic Julia sets with trigonometric functions. The two functions to investigate from Julia sets are sine and cosine functions.

scholarly journals Variasi Motif Batik Minahasa Berbasis Julia Set

Jurnal MIPA ◽  
2017 ◽  
Vol 6 (2) ◽  
pp. 81
Author(s):  
Riskika Fauziah Kodri ◽  
Jullia Titaley
Keyword(s):  
Cultural Heritage ◽  
Complex Number ◽  
Julia Set ◽  
Julia Sets ◽  
Complex Numbers ◽  
Self Similarity ◽  
North Sulawesi ◽  
Iterated Function ◽  
Indigenous Land ◽  
Life Philosophies

Batik adalah corak atau gambar (pada kain) yang pengolahannya diproses dengan cara tertentu biasanya dengan menerakan malam yaitu sejenis lilin pada kain. Batik Minahasa merupakan batik yang menggunakan motif tradisional atau ragam hias dari tanah adat Minahasa, Sulawesi Utara, Indonesia. Batik menjadi warisan budaya Indonesia salah satunya karena motif pada batik yang mengandung filosofi kehidupan masyarakat setempat. Variasi motif pola batik minahasa belum terlalu berkembang walaupun telah ada variasi dari penggabungan motif-motif asli batik Minahasa. Matematika memperkenalkan bentuk fraktal yang memiliki sifat keserupaan diri dan banyak dijumpai pada objek di dunia nyata. Julia Set adalah salah satu jenis fraktal yaitu yang berkaitan dengan bilangan kompleks dan dibangkitkan dari fungsi teriterasi . Tujuan penelitian ini adalah membuat variasi batik minahasa berbasis Julia set. Hasil penelitian menunjukkan dengan memilih sebuah bilangan kompleks  tertentu dengan range  dan memberikan bentuk-bentuk Julia set yang menarik. Menggunakan aplikasi basis fraktal, variasi batik minahasa berbasis Julia set dibuat dari ragam hias tradisional Minahasa dan motif Julia set yang dipilih dengan mengatur properti motif yang ada seperti layer layout, banyak iterasi, lebar, panjang, sudut, peningkatan sudut dan lain-lain.Batik is a motif or ornaments (on cloth) which processed in a certain way usually using malam which is some kind of wax to the cloth. Batik Minahasa is batik with traditional motif or ornament from indigenous land of Minahasa, North Sulawesi, Indonesia. One of the reasons batik become the cultural heritage of Indonesia is because of the motif which contained local people’s life philosophies. Motif variation of batik Minahasa has not much developed even though there are variations made by combining the traditional motifs. Mathematics introduces fractal which has self-similarity characteristic in its shapes and Julia Set is one of fractals object that corresponds to complex numbers and is generated from the iterated function . The purpose of this research is to make variations of batik Minahasa based on Julia set. The results show that by selecting a complex number  within a range of  and  give interesting shapes of Julia sets. Using fractal-based applications, variation of batik Minahasa is made from traditional ornament and Julia Set motif which selected and arranging the properties such as layout layers, multiple iterations, width, length, angles, angle increases and more.

scholarly journals The optimal mating distance resulting from heterosis and genetic incompatibility

2018 ◽  
Vol 4 (11) ◽  
pp. eaau5518 ◽  
Author(s):  
Xinzhu Wei ◽  
Jianzhi Zhang
Keyword(s):  
Animal Model ◽  
Genetic Distance ◽  
Polynomial Function ◽  
Genetic Distances ◽  
Quadratic Polynomial ◽  
Model Organisms ◽  
Genetic Incompatibility ◽  
Large Numbers ◽  
Practical Implications

Theory predicts that the fitness of an individual is maximized when the genetic distance between its parents (i.e., mating distance) is neither too small nor too large. However, decades of research have generally failed to validate this prediction or identify the optimal mating distance (OMD). Respectively analyzing large numbers of crosses of fungal, plant, and animal model organisms, we indeed find the hybrid phenotypic value a humped quadratic polynomial function of the mating distance for the vast majority of fitness-related traits examined, with different traits of the same species exhibiting similar OMDs. OMDs are generally slightly greater than the nucleotide diversities of the species concerned but smaller than the observed maximal intraspecific genetic distances. Hence, the benefit of heterosis is at least partially offset by the harm of genetic incompatibility even within species. These results have multiple theoretical and practical implications for speciation, conservation, and agriculture.

scholarly journals Integrability Formulas. Part II

2010 ◽  
Vol 18 (2) ◽  
pp. 129-141
Author(s):  
Bo Li ◽  
Na Ma ◽  
Xiquan Liang
Keyword(s):  
Polynomial Function ◽  
Trigonometric Function ◽  
Composite Functions

Integrability Formulas. Part II In this article, we give several differentiation and integrability formulas of special and composite functions including trigonometric function, and polynomial function.

A Robust and Efficient Method of Designing Piles for Landslide Stabilization

2020 ◽  
Vol 26 (4) ◽  
pp. 481-492
Author(s):  
Yang Yu ◽  
Xingmin Li ◽  
Xiaohua Pan ◽  
Qing Lü
Keyword(s):  
Efficient Method ◽  
Large Scale ◽  
Polynomial Function ◽  
Design Method ◽  
Quadratic Polynomial ◽  
Soil Parameters ◽  
Stabilizing Piles ◽  
Geotechnical Design ◽  
The Mean ◽  
Landslide Stabilization

ABSTRACT Stabilizing pile is a widely used method to reduce the development of large-scale landslides. Optimizing the pile geometry is a great challenge in the design of stabilizing piles with the purpose of cost-effectiveness, especially for soil strength parameters with large uncertainty. The objective of this study is to propose a robust and efficient method of designing piles for landslide stabilization with the consideration of the safety of slope, uncertainty of soil parameters, and cost of stabilizing piles. A new response surface, which incorporates soil parameters and stabilizing force into a quadratic polynomial function, is first proposed. Unknown coefficients of the quadratic polynomial function are solved with a numerical method at typical sampling points. Based on the solved quadratic polynomial function, the mean and standard deviation of factor of safety (FOS) of the pile-stabilized slope as well as the signal-to-noise factor are then calculated in order to evaluate the design robustness. A framework based on the concept of robust geotechnical design is presented, and its feasibility is illustrated by two cases of soil slopes. The results indicate that the proposed robust geotechnical design method could be used to optimize the design of landslide-stabilizing piles.

Knaster-like continua and complex dynamics

1993 ◽  
Vol 13 (4) ◽  
pp. 627-634 ◽  
Author(s):  
Robert L. Devaney
Keyword(s):  
Complex Dynamics ◽  
Julia Set ◽  
Dynamical Behavior ◽  
Invariant Sets ◽  
Entire Plane ◽  
Limit Sets

AbstractIn this paper we discuss the topology and dynamics ofEλ(z) = λezwhen λ is real and λ > 1/e. It is known that the Julia set ofEλis the entire plane in this case. Our goal is to show that there are certain natural invariant subsets forEλwhich are topologically Knaster-like continua. Moreover, the dynamical behavior on these invariant sets is quite tame. We show that the only trivial kinds of α- and ω-limit sets are possible.

Meromorphic multifunctions in complex dynamics

1992 ◽  
Vol 12 (1) ◽  
pp. 39-52 ◽  
Author(s):  
L. Baribeau ◽  
T. J. Ransford
Keyword(s):  
Critical Points ◽  
Complex Dynamics ◽  
Julia Set ◽  
Kleinian Groups ◽  
Rational Maps ◽  
Analytic Family ◽  
Limit Sets ◽  
Upper Semicontinuous ◽  
Open Set ◽  
Similar Vein

AbstractLet {RA} be an analytic family of rational maps and denote by j(λ) the Julia set of Rλ. We prove that the upper semicontinuous regularization j(λ) of j(λ) (which coincides with j(λ) for all λ in a dense open set) is a meromorphic multifunction, and give applications that illustrate the instability of Julia sets. In a similar vein, we also consider forward orbits of critical points and limit sets of Kleinian groups.

ACCOUNTING FOR COVARIANCES AMONG TEST DAY MILK YIELDS IN DAIRY COWS

1987 ◽  
Vol 67 (3) ◽  
pp. 637-644 ◽  
Author(s):  
T. E. ALI ◽  
L. R. SCHAEFFER
Keyword(s):  
Regression Model ◽  
Gamma Function ◽  
Polynomial Function ◽  
Genetic Correlations ◽  
Quadratic Polynomial ◽  
Holstein Friesian ◽  
Lactation Curve ◽  
Observation Vector ◽  
Daily Milk ◽  
Friesian Cows

Daily milk weights from 1006 lactations on 775 Holstein-Friesian cows in 42 herds and monthly test-day weights from 102 540 lactations on 73 717 cows in 17 481 herd-year-seasons were used to study the influence of covariances among milk weighings within a lactation on three models for describing the shape of the lactation curve for individual cows. The models included a gamma function, an inverse quadratic polynomial function, and a regression model of yields on day in lactation (linear and quadratic) and on log of 305 divided by day in lactation (linear and quadratic). For each model, several variance-covariance matrices of the observation vector were used. Models were compared on the basis of squared deviations of predicted versus actual milk weights and on the correlation between predicted and actual weights through the lactation averaged over cows. Better predictions were observed when covariances among test-day yields were ignored while models could be ranked regression model, gamma function, and inverse quadratic polynomial function in order of best to worst. Heritability estimates for the parameters of the various models and for 305-d milk yield ranged from 0.11 to 0.30. Genetic correlations were estimated and predictions of correlated responses in 305-d yield from selecting on various combinations of parameters from each method were computed. The best combination of parameters of the gamma function gave a relative efficiency of 74.7% as compared to selection for 305-d yield alone. Key words: Lactation curves, covariances, Holsteins

A reconstruction theorem for complex polynomials

2015 ◽  
Vol 26 (09) ◽  
pp. 1550073 ◽  
Author(s):  
Luka Boc Thaler
Keyword(s):  
Real Axis ◽  
Ergodic Theory ◽  
Complex Dynamics ◽  
Julia Set ◽  
Complex Polynomials ◽  
Analogous Statement ◽  
The Real ◽  
Ergodic Properties ◽  
Reconstruction Theorem ◽  
Exceptional Polynomials

Recently Takens' Reconstruction Theorem was studied in the complex analytic setting by Fornæss and Peters [Complex dynamics with focus on the real part, to appear in Ergodic Theory Dynam. Syst.]. They studied the real orbits of complex polynomials, and proved that for non-exceptional polynomials ergodic properties such as measure theoretic entropy are carried over to the real orbits mapping. Here we show that the result from [Complex dynamics with focus on the real part, to appear in Ergodic Theory Dynam. Syst.] also holds for exceptional polynomials, unless the Julia set is entirely contained in an invariant vertical line, in which case the entropy is 0. In [The reconstruction theorem for endomorphisms, Bull. Braz. Math. Soc. (N.S.) 33(2) (2002) 231–262.] Takens proved a reconstruction theorem for endomorphisms. In this case the reconstruction map is not necessarily an embedding, but the information of the reconstruction map is sufficient to recover the (2m + 1) th image of the original map. Our main result shows an analogous statement for the iteration of generic complex polynomials and the projection onto the real axis.

scholarly journals Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure

2012 ◽  
Vol 154 (2) ◽  
pp. 325-349 ◽  
Author(s):  
G. C. BOORE ◽  
K. J. FALCONER
Keyword(s):  
Directed Graph ◽  
Hausdorff Measure ◽  
Iterated Function Systems ◽  
New Class ◽  
Iterated Function ◽  
Separation Conditions

AbstractFor directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known.

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