Related papers: Fibonacci Numbers, Statistical Convergence and App…
The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive…
In the present paper we will give some new notions, such as {\Delta}-convergence and {\Delta}-Cauchy, by using the {\Delta}-density and investigate their relations. It is important to say that, the results presented in this work generalize…
In part 1 of this paper some linear weighted generalized Fibonacci number summation identities were derived using the fact that the Fibonacci number is the residue of a rational function. In this part, using the same method, some quadratic…
We speculate on the distribution of primes in exponentially growing, linear recurrence sequences $(u_n)_{n\geq 0}$ in the integers. By tweaking a heuristic which is successfully used to predict the number of prime values of polynomials, we…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences and investigate their properties.
It's the age-old recurrence with a twist: sum the last two terms and if the result is composite, divide by its smallest prime divisor to get the next term (e.g., 0, 1, 1, 2, 3, 5, 4, 3, 7, ...). These sequences exhibit pseudo-random…
The method of statistical differentials, which approximates the mean and variance of transformations of random variables is used in many areas of mathematics. This paper will discuss the conditions under which such an approximation will be…
This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability…
In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant…
The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the…
The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximation, results about integral points on algebraic curves and…
In our present investigation we propose to study and develop the I-function of two variables analogous to the I-function of one variable introduced and studied by one of the authors[24]. The conditions for convergence, series…
The Dirichlet forms methods, in order to represent errors and their propagation, are particularly powerful in infinite dimensional problems such as models involving stochastic analysis encountered in finance or physics, cf. [5]. Now, coming…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…
The regularized product of the Fibonacci numbers is evaluated.
A definition for the statistical significance by constructing a correlation between the normal distribution integral probability and the p-value observed in an experiment is proposed, which is suitable for both counting experiment and…