689 Results Found

Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produ...

Topological indices are numerical parameters used to study the physical and chemical properties of compounds. In quantitative structure–activity relationship QSARs, topological indices correlate the biological activity of compounds with their p...

Using the concepts of q-fractional calculus operator theory, we first define a $(\lambda ,q)$-differintegral operator, and we then use m-fold symmetric functions to discover a new family of bi-close-to-convex functions. First, we estimate the general T...

In this study, we aim to construct a finite set of orthogonal matrix polynomials for the first time, along with their finite orthogonality, matrix differential equation, Rodrigues’ formula, several recurrence relations including three-term rela...

The association of M-polynomial to chemical compounds and chemical networks is a relatively new idea, and it gives good results about the topological indices. These results are then used to correlate the chemical compounds and chemical networks with...

The field of mathematics that studies the relationship between algebraic structures and graphs is known as algebraic graph theory. It incorporates concepts from graph theory, which examines the characteristics and topology of graphs, with those from...

In the current article, making use of certain operator, we initiate and explore a certain family ${\mathcal{W}}_{\Sigma }(\lambda ,\gamma ,\sigma ,\delta ,\alpha ,\beta ,p,q;h)$ of holomorphic and bi-univalent functions in the open unit disk $\mathbb{D}$. We establish upper bou...

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices ar...

The discovery of new nanomaterials adds new dimensions to industry, electronics, and pharmaceutical and biological therapeutics. In this article, we first find closed forms of M-polynomials of polyhex nanotubes. We also compute closed forms of variou...

Topological indices describe mathematical invariants of molecules in mathematical chemistry. M-polynomials of chemical graph theory have freedom about the nature of molecular graphs and they play a role as another topological invariant. Social networ...

A topological index, which is a number, is connected to a graph. It is often used in chemometrics, biomedicine, and bioinformatics to anticipate various physicochemical properties and biological activities of compounds. The purpose of this article is...

In this article, a novel technique to evaluate and compare the neighborhood degree molecular descriptors of two variations of the carbon nanosheet $C_5{C}_7(a,b)$ is presented. The conjugated molecules follow the graph spectral theory, in terms of bonding,...

The main purpose of this article is to derive several convolutions for generalized Bernoulli and Euler–Genocchi polynomials of order $(r,m)$, $B_n^{(r,m)}\left(x\right)$ and $A_n^{(r,m)}\left(x\right)$, respectively. These polynomials have been introduced recently and contain the...

In this paper, we study asymptotic bounds on the m-th derivatives of general algebraic polynomials in weighted Bergman spaces. We consider regions in the complex plane defined by bounded, piecewise, asymptotically conformal curves with strictly posit...

Let $n\ge 1$ be a fixed integer. The main objective of this paper is to compute some topological indices and coindices that are related to the graph complement of the prime ideal sum (PIS) graph of ${\mathbb{Z}}_n$, where $n=p^{\alpha },p^{2}q,p^2{q}^2,pqr,p^{3}q,$$p^{2}qr$, and $pqrs$ f...

In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs J_n,_m for all values of m and n. From the M-polynomial, we recover many degree-based topological indices such as...

In 1997, Sierpinski graphs, $S(n,k)$, were obtained by Klavzar and Milutinovic. The graph $S(1,k)$ represents the complete graph $K_k$ and $S(n,3)$ is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph nam...

The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M‐polynomial of nanotubes produces closed forms of many degree‐based topological indices which are numerical parameters of the structure and,...

Many degree-based topological indices can be obtained from the closed-off M-polynomial of a carbon nanocone. These topological indices are numerical parameters that are associated with a structure and, in combination, determine the properties of the...

Topological indices and connectivity polynomials are invariants of molecular graphs. These invariants have the tendency of predicting the properties of the molecular structures. The honeycomb network structure is an important type of benzene network....

An algebraic graph is defined in terms of graph theory as a graph with related algebraic structures or characteristics. If the vertex set of a graph $\mathcal{G}$ is a group, a ring, or a field, then $\mathcal{G}$ is called an algebraic structure graph. This work uses an al...

A topological index of a graph is a single numeric quantity which relates the chemical structure with its underlying physical and chemical properties. Topological indices of a nanosheet can help us to understand the properties of the material better....

A topological index (TI) is a real number that defines the relationship between a chemical structure and its properties and remains invariant under graph isomorphism. TIs defined for chemical structures are capable of predicting physical properties,...

In the present paper, regular spacelike spatial Minkowski Pythagorean hodograph (MPH) curves are characterized with rational rotation-minimizing frames (RRMFs). We define an Euler–Rodrigues frame (ERF) for MPH curves and by means of this concep...

Carbonallotropes are widely available and can be found in the atmosphere, the earth’s crust, and in living creatures in myriad forms. Allotropes are also used in several fields, including for medicinal and biological applications, due to their...

The subject of convex analysis and integral inequalities represents a comprehensive and absorbing field of research within the field of mathematical interpretation. In recent times, the strategies of convex theory and integral inequalities have becom...

Following the completion of the NIST post-quantum cryptography standardization, Kyber has been adopted as a key encapsulation mechanism (KEM) for quantum-resistant communication. Although lattice-based KEMs provide strong security and efficiency, mos...

The demand for extensive data rates in dense-traffic wireless networks has expanded and needs proper controlling schemes. The fifth generation of mobile communications (5G) will accommodate these massive communications, such as massive Machine Type C...

In the current article, we introduce several new subclasses of m-fold symmetric analytic and bi-univalent functions associated with bounded boundary and bounded radius rotation within the open unit disk $\mathbb{D}.$ Utilizing the Faber polynomial expansion, we...

Special polynomials play an important role in several subjects of mathematics, engineering, and theoretical physics. Many problems arising in mathematics, engineering, and mathematical physics are framed in terms of differential equations. In this pa...

(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅱ) [...]

This paper presents an efficient real-coefficient fitting both Green’s function and its gradient with Fast Fourier Transform (RFGG-FG-FFT) with cube polynomial inter/extrapolation method (CPIE), which is established for the analysis of scatteri...

Many stream ciphers employ linear feedback shift registers (LFSRs) to generate pseudorandom sequences. Many recent LFSRs are defined in $GF\left(2^n\right)$ to take advantage of the n-bit processors, instead of using the classic binary field. In this way, the bit...

We start by an application the of Krein–Milman theorem to the integral representation of completely monotonic functions. Elements of convex optimization are also mentioned. The paper continues with applications of Hahn–Banach-type theorem...

Self-similarity is a common feature among mathematical fractals and various objects of our natural environment. Therefore, escape criteria are used to determine the dynamics of fractal patterns through various iterative techniques. Taking motivation...

The first part of this work provides explicit solutions for two integral equations; both are solved by means of Fourier transform. In the second part of this paper, sufficient conditions for the existence and uniqueness of the solutions satisfying sa...

This paper is devoted to the introduction and systematic study of $(P,Q)$-normal operators in the context of semi-Hilbertian spaces, where P and Q are non-constant complex polynomials in one variable. This class generalizes the well-known notion of pol...

Background: We propose a framework for determining the stage of periodontitis in a personalized medicine context, building on our previously developed model for periodontitis detection. In this study, we improved the earlier model by incorporating ad...

Hilbert proved in 1888 that a positive semi-definite (PSD) homogeneous quartic polynomial of three variables always can be expressed as the sum of squares (SOS) of three quadratic polynomials, and a psd homogeneous quartic polynomial of four variable...

In the intersection of the theories of nonsymmetric Jack polynomials in N variables and representations of the symmetric groups ${\mathcal{S}}_N$ one finds the singular polynomials. For certain values of the parameter $\kappa$ there are Jack polynomia...

The second immanantal polynomial is one of the important directions in algebraic theory. Let $M=\left[m_{ij}\right]$ be an $n\times n$ matrix. The second immanant of matrix M is defined as $d_2\left(M\right)={\sum }_{\sigma \in S_n}\chi \left(\sigma \right){\prod }_{i=1}^n{m}_{i\sigma \left(i\right)}$, where $\chi$ is...

The generalized matrix of a graph G is defined as $M\left(G\right)=A\left(G\right)-tD\left(G\right)$ ($t\in \mathbb{R}$, and $A\left(G\right)$ and $D\left(G\right)$, respectively, denote the adjacency matrix and the degree matrix of G), and the generalized characteristic polynomial of G is merely the characterist...

Finding irreducible polynomials over $\mathbb{Q}$ (or over $\mathbb{Z}$ ) is not always easy. However, it is well-known that the mth cyclotomic polynomials are irreducible over $\mathbb{Q}$ . In this paper, we define the mth modified cyclotomic polynomials and we get...

We report a closed-form formula for the Zhang–Zhang polynomial (also known as ZZ polynomial or Clar covering polynomial) of an important class of elementary peri-condensed benzenoids $Rb\left(n_1,n_2,m_1,m_2\right)$, usually referred to as ribbons. A straightforw...

Multiple zigzag chains $Z\left(m,n\right)$ of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topologica...

This study presents a unified framework for the simultaneous analysis of generalized Fibonacci numbers and their associated polynomial extensions, both of which play a significant role in combinatorial analysis and discrete mathematics. The generaliz...

This article presents a generalization of new classes of degenerated Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi Hermite polynomials of level m. We establish some algebraic and differential properties for generalizations...

We begin with a degree m real homogeneous polynomial in n indeterminants and bound the distance from a given n-dimensional real vector to the real vanishing of the homogeneous polynomial. We then apply these bounds to the real homogeneous polynomial...

The truncated exponential polynomials ${\mathbf{e}}_m\left(x\right)$ (1), their extensions, and certain newly-introduced polynomials which combine the truncated exponential polynomials with other known polynomials have been investigated and applied in various ways. In this p...

In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product ${\displaystyle ⟨f,g⟩=⟨{\mathbf{u}}^{\mathtt{M}},fg⟩+\lambda {\mathcal{T}}^{j}f\left(\alpha \right){\mathcal{T}}^{j}g\left(\alpha \right),}$ where ${\mathbf{u}}^{\mathtt{M}}$ is the Meixner linear operator, $\lambda \in {\mathbb{R}}_{+}$, $j\in \mathbb{N}$,...