1,039 Results Found

In the paper, the authors present some symmetric identities involving the Stirling polynomials and higher order Bernoulli polynomials under all permutations in the finite symmetric group of degree n. These identities extend and generalize some known...

Researchers are always inspired to broaden their explorations towards uncertainty theories, owing to their great interest and importance. Soft set theory plays a primary role among all recent uncertainty tools. Though this theory sounds good in all a...

A group signature scheme allows a user to sign a message anonymously on behalf of a group and provides accountability by using an opening authority who can “open” a signature and reveal the signer’s identity. Group signature schemes...

In this paper, we introduce the notion of the semi-symmetric metric connection in the Heisenberg group. Moreover, by using the method of Riemannian approximations, we define the notions of intrinsic curvature for regular curves, the intrinsic geodesi...

The primary objective of this study is the computation of the matching polynomials of a number of symmetric, semisymmetric, double group graphs, and solids in third and higher dimensions. Such computations of matching polynomials are extremely challe...

A non-iterative method for the difference of means is presented to calculate the log-Euclidean distance between a symmetric positive-definite matrix and the mean matrix on the Lie group of symmetric positive-definite matrices. Although affine-invaria...

In respect to the multi-attribute group decision making (MAGDM) problems in which the evaluated value of each attribute is in the form of q-rung orthopair fuzzy numbers (q-ROFNs), a new approach of MAGDM is developed. Firstly, a new aggregation opera...

Aiming at multiple attribute group decision making (MAGDM) problems, especially the attribute values of 2-tuple linguistic numbers and the interrelationships between each attribute needing to be considered, this paper proposes a new method of analysi...

Existing remote sensing scene classification (RSSC) models mainly rely on convolutional neural networks (CNNs) to extract high-level features from remote sensing images, while neglecting the importance of low-level features. To address this, we propo...

A subset S of a group G is symmetric if there is an element g є G such that gS^-1g = S. We study some Ramsey type functions for symmetric subsets in finite Abelian groups.

VB and molecular orbital (MO) models are normally distinguished by the fact the first looks at molecules as a collection of atoms held together by chemical bonds while the latter adopts the view that each molecule should be regarded as an independent...

This paper introduces the concept of symmetric difference operators in terms of overlap and grouping functions, for which the associativity property is not strongly required. These symmetric difference operators are weaker than symmetric difference o...

This paper aims to propose a novel multi-attribute group decision-making (MAGDM) method based on interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs). The IVq-ROFSs have been proved to be effective in handling MAGDM problems, and several novel dec...

We compute the number of symmetric r-colorings and the number of equivalence classes of symmetric r-colorings of the quaternion group.

Let $a\left(n\right)$ be the number of non-isomorphic abelian groups of order n. In this paper, we study a symmetric form of the average value with respect to $a\left(n\right)$ and prove an asymptotic formula. Furthermore, we study an analogue of the well-known Titchmarsh div...

A commuting graph is a graph denoted by $\mathcal{C}(G,X)$ where G is any group and X, a subset of a group G, is a set of vertices for $\mathcal{C}(G,X)$ . Two distinct vertices, $x,y\in X$ , will be connected by an edge if the commutativ...

Most linguistic-based approaches to multi-attribute group decision making (MAGDM) use symmetric, uniformly distributed sets of additive linguistic terms to express the opinions of decision makers. However, in reality, there are also some problems tha...

We discuss a method of analysis of symmetric electromagnetic components with magnetic media based on magnetic group theory. In this description, some of the irreducible corepresentations assume complex values $exp\left(i\theta \right)$ with the real parameter $\mathrm{\&th}$...

To address the high computational and communication overheads and the limited edge security found in many existing batch verification methods for Mobile Edge Computing (MEC), this paper presents a blockchain-based batch authentication and symmetric g...

Some new techniques of aggregating hesitant fuzzy numbers (HFNs) by using monotonic dependent OWA (MDOWA) operators are investigated. By utilizing the score value of HFN, the concepts of hesitant fuzzy configuration vector and hesitant fuzzy hybrid c...

The paper develops applications of symmetric orbit functions, known from irreducible representations of simple Lie groups, in numerical analysis. It is shown that these functions have remarkable properties which yield to cubature formulas, approximat...

Total Coloring of a graph G is a type of graph coloring in which any two adjacent vertices, an edge, and its incident vertices or any two adjacent edges do not receive the same color. The minimum number of colors required for the total coloring of a...

A graph is symmetric if its automorphism group is transitive on the arcs of the graph. Guo et al. determined all of the connected seven-valent symmetric graphs of order $8p$ for each prime p. We shall generalize this result by determining all of the co...

In order to solve multiple-attribute group decision-making (MAGDM) problems under a trapezoid intuitionistic fuzzy linguistic (TIFL) environment and the relationships between multiple input parameters needed, in this paper, we extend the Maclaurin sy...

Recently, symmetry in complex network structures has attracted some research interest. One of the fascinating problems is to give measures of the extent to which the network is symmetric. In this paper, based on the natural action of the automorphism...

Lung cancer is considered to be a significant cause of death in the world, and the timely identification of nodules in the lungs in CT scans is very important to enhance the prognosis of patients. Although the state of the art of nodule delineation u...

We study the group of transformations of ${}_4{F}_3$ hypergeometric functions evaluated at unity with one unit shift in parameters. We reveal the general form of this family of transformations and its group property. Next, we use explicitly known transformat...

This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.

Consumer electronics manufacturers have been incorporating support for 4G/5G communication technologies into many electronic devices. Thus, highly capable Internet of Things (IoT)-ready versions of electronic devices are being purchased which will ev...

A graph is edge-primitive if its automorphism group acts primitively on the edge set of the graph. Edge-primitive graphs form an important subclass of symmetric graphs. In this paper, edge-primitive graphs of order as a product of two distinct primes...

Let G be a group. A k-coloring of G is a surjection $\lambda :G\to \{1,2,\dots ,k\}$. Equivalently, a k-coloring $\lambda$ of G is a partition $\mathcal{P}=\{P_1,P_2,\dots ,P_k\}$ of G into k subsets. If $g\mathcal{P}=\mathcal{P}$ for all g in G, we say that $\lambda$ is perfect. If $h\mathcal{P}=\mathcal{P}$...

We geometrically derive the explicit form of the unitary representation of the Poincaré group for vector-valued wave functions and use it to apply speed-of-light boosts to a simple polarization basis to end up with a Hawton–Baylis photon...

Concrete expanding-plate piles (CEP piles) represent a novel type of variable cross-section concrete cast-in-place pile, wherein one or more bearing plates are added to the pile body to enhance its load-bearing capacity. Compared to traditional unifo...

We report the results of our computations of the spectral polynomials and spectra of a number of graphs possessing automorphism symmetries beyond cubic and icosahedral symmetries. The spectral (characteristic) polynomials are computed in fully expand...

Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on ${\mathbb{R}}^N$ . The Dunkl operators are denoted by $T_j$ for $1\le j\le N$ , and the Laplacian ...

This is mainly a review of an intense 15-year long collaboration between the authors on explicit realisations of compact Lie groups and their applications. Starting with an elementary example, we will illustrate the main idea at the foundation of the...

Traditional electricity networks are replaced by smart grids to increase efficiency at a low cost. Several energy projects in Pakistan have been developed, while others are currently in the planning stages. To assess the performance of the smart grid...

In 2008, Doliskani et al. proposed an ElGamal-style encryption scheme using the symmetric group $S_n$ as mathematical platform. In 2012, an improvement of the cryptosystem’s memory requirements was suggested by Othman. The proposal by Doliskani et...

In this paper, based on the advantages of q-rung orthopair fuzzy sets (q-ROFSs), complex fuzzy sets (CFSs) and cubic sets (CSs), the concept of complex cubic q-rung orthopair fuzzy sets (CCuq-ROFSs) is introduced and their operation rules and propert...

Relations between common information measures include the duality relations based on Möbius inversion on lattices, which are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion). In thi...

The role of substitution boxes is very important in block ciphers. Substitution boxes are utilized to create confusion in the cryptosystem. However, to create both confusion and diffusion in any cryptosystem p-boxes and chaos base substitution boxes...

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many po...

In this paper, we introduce ${\omega }_n$-symmetric polynomials associated with the finite group ${\omega }_n,$ which consists of roots of unity, and groups of permutations acting on the Cartesian product of Banach spaces ${\ell }_1.$ These polynomials extend the...

In general, ethylene/1,3-butadiene copolymerizations provides copolymers possessing both pendant vinyls and vinylenes as olefinic moieties. We, at MCI, studied the substituent effects of C₂-symmetric zirconocene complexes, rac-[Me₂Si(Indenyl’)₂]ZrCl₂...

We consider algebras of polynomials and analytic functions that are invariant with respect to semidirect products of groups of bounded operators on Banach spaces with symmetric bases. In particular, we consider algebras of so-called block-symmetric a...

Hidden corrosion defects can lead to dangerous accidents such as leakage of toxic materials causing extreme environmental and economic consequences. Ultrasonic guided waves showed good potential detecting distributed corrosion in pipeline networks at...

Seven symmetrical azomethines with two imine groups (HC=N) were synthesized by condensation of the benzene-1,4-dicarboxaldehydewith five amines (first group: A1-A5) and of the 2,5-thiophenedicarboxaldehyde with two amines (second group: AT1-AT2). Add...

Structural designers that design buildings use different criteria to select the frames’ materiality and structural solutions. Very often, the primary test is the cost of construction. Sometimes, solutions are determined by the terms of structur...

Let $\mathbb{C}{\mathsf{A}}_n=\mathbb{C}[S_2\wr S_2\wr \cdots \wr S_2]$ be the group algebra of an n-step iterated wreath product. We prove some structural properties of ${\mathsf{A}}_n$ such as their centers, centralizers, and right and double cosets. We apply these results to explicitly...

Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find...