This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, ...methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.
Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially ...extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as well
We study the following problem: given a regular symmetric form (linear functional) v, find all the regular symmetric forms u which satisfy the equation . We give the second-order recurrence relation ...of the orthogonal polynomial sequence with respect to u. Moreover, in the case where v is a semi-classical form of class s, we show that u is semi-classical and its class is analyzed in term of the class of v. An example is highlighted.
In this paper we define when a polynomial differential system is orbitally universal and we show the relevance of this notion in the classical center problem, i.e. in the problem of distinguishing ...between a focus and a center.
We prove a new irreducibility result for polynomials over
${\mathbb Q}$
and we use it to construct new infinite families of reciprocal monogenic quintinomials in
${\mathbb Z}x$
of degree
$2^n$
.
Abstract
The connected domination polynomial of a connected graph
G
of order
n
is the polynomial
D
c
G
,
x
=
∑
i
=
γ
c
n
d
c
(
G
,
i
)
x
i
, where
d
c
(
G, i
) is the number of connected dominating ...sets of
G
of cardinality
i
and
γ
c
(G)
is the connected domination number of
G
5. In this paper we find the polynomial
D
c
(
G, x
) for some constructive graphs.
In this paper, we firstly introduce the Gaussian Leonardo polynomial sequences {GLe_n (x)}_(n=0)^∞ and we obtain Binet's formula, generating function of this sequence. Moreover, we define the matrix ...Gl(x) in the form of 3 x 3. Finally, we study on the coding and decoding applications of the Leonardo number by using the Leonardo matrix P.
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