Fibonacci Series with Several Parameters

Author(s):  
G. Britto Antony Xavier ◽  
B. Mohan
Keyword(s):  
Author(s):  
A Rakesh Kumar ◽  
Sanjeevikumar Padmanaban ◽  
Partha Sarathi Subudhi ◽  
Frede Blaabjerg ◽  
C Dhanamjayulu

2012 ◽  
Vol 96 (536) ◽  
pp. 213-220
Author(s):  
Harlan J. Brothers

Pascal's triangle is well known for its numerous connections to probability theory [1], combinatorics, Euclidean geometry, fractal geometry, and many number sequences including the Fibonacci series [2,3,4]. It also has a deep connection to the base of natural logarithms, e [5]. This link to e can be used as a springboard for generating a family of related triangles that together create a rich combinatoric object.2. From Pascal to LeibnizIn Brothers [5], the author shows that the growth of Pascal's triangle is related to the limit definition of e.Specifically, we define the sequence sn; as follows [6]:


2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Santiago Tello-Mijares ◽  
Francisco Flores

The identification of pollen in an automated way will accelerate different tasks and applications of palynology to aid in, among others, climate change studies, medical allergies calendar, and forensic science. The aim of this paper is to develop a system that automatically captures a hundred microscopic images of pollen and classifies them into the 12 different species from Lagunera Region, Mexico. Many times, the pollen is overlapping on the microscopic images, which increases the difficulty for its automated identification and classification. This paper focuses on a method to segment the overlapping pollen. First, the proposed method segments the overlapping pollen. Second, the method separates the pollen based on the mean shift process (100% segmentation) and erosion by H-minima based on the Fibonacci series. Thus, pollen is characterized by its shape, color, and texture for training and evaluating the performance of three classification techniques: random tree forest, multilayer perceptron, and Bayes net. Using the newly developed system, we obtained segmentation results of 100% and classification on top of 96.2% and 96.1% in recall and precision using multilayer perceptron in twofold cross validation.


Author(s):  
Louis W. Botsford ◽  
J. Wilson White ◽  
Alan Hastings

This chapter introduces basic concepts in population modeling that will be applied throughout the book. It begins with the oldest example of a population model, the rabbit problem, which was described by Leonardo of Pisa (“Fibonacci”) and whose solution is the Fibonacci series. The chapter then explores what is known about simple models of populations (i.e. those with a single variable such as abundance or biomass). The two major classes are: (1) linear models of exponential (or geometric) growth and (2) models of logistic, density-dependent growth. It covers both discrete time and continuous time versions of each of these. These simple models are then used to illustrate several different population dynamic concepts: dynamic stability, linearizing nonlinear models, calculation of probabilities of extinction, and management of sustainable fisheries. Each of these concepts is discussed further in later chapters, with more complete models.


1960 ◽  
Vol 67 (6) ◽  
pp. 525-532 ◽  
Author(s):  
D. D. Wall
Keyword(s):  

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