Related papers: Properties and applications of some special intege…
The purpose of this paper is to investigate integer sequences with exponent lifting property, a property common in Fibonacci or Lucas sequences.
In this paper we present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were…
In this paper, we investigate some properties of the associated sequence of Daehee and Changhee polynomials. Finally, we give some interesting identities of associated sequence involving some special polynomials.
In this thesis we examined mathematical properties of Fibonacci numbers and applications of this numbers in the nature,geometry and economy.We obtained Golden section and proved some mathematical identities using Golden section. Infinity of…
It is known that for an IP^{*} set A in (\mathbb{N},+) and a sequence \left\langle x_{n}\right\rangle _{n=1}^{\infty} in \mathbb{N}, there exists a sum subsystem \left\langle y_{n}\right\rangle _{n=1}^{\infty} of \left\langle…
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
In this survey of graph polynomials, we emphasize the Tutte polynomial and a selection of closely related graph polynomials. We explore some of the Tutte polynomial's many properties and applications and we use the Tutte polynomial to…
In this note, we present a curious $q$-series identity with applications to certain partitions with bounded part differences.
In the present paper, we investigate some interesting properties including several special polynomials arising from Caputo-fractional derivative. From our investigation, we derive a lot of interesting identities of several special…
One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer…
The paper studies cryptographically useful properties of the sequence of the sizes of Goldbach ellipses. We show that binary subsequences based on this sequence have useful properties. They can be used to generate keys and to provide an…
Sequences of Genocchi numbers of the first and second kind are considered. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these numbers some identities…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
Spinors are used in physics quite extensively. The goal of this study is also the spinor structure lying in the basis of the quaternion algebra. In this paper, first, we have introduced spinors mathematically. Then, we have defined…
The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern…
This paper investigates the randomness and cryptographic properties of the Narayana series modulo p, where p is a prime number. It is shown that the period of the Narayana series modulo p is either p*p+p+1 (or a divisor) or p*p-1 (or a…
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…
In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.