57 Results Found

We consider a non-abelian leakage-free qudit system that consists of two qubits each composed of three anyons. For this system, we need to have a non-abelian four dimensional unitary representation of the braid group $B_6$ to obtain a totally l...

Representations of braid group $B_n$ on $n\ge 2$ strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group $V{B}_n$ on $n\ge 2$ strands is an ex...

In this note, we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order) reproduces the...

In this paper, by introducing an isomorphism from the Mihailova subgroup of $F_2\times F_2$ to the Mihailova subgroups of a braid group, we give an explicit presentation of Mihailova subgroups of a braid group. Hence, in a braid group, there are some Mih...

In this paper we present a detailed study of bonded knots and their related structures, integrating recent developments into a single framework. Bonded knots are classical knots endowed with embedded bonding arcs modeling physical or chemical bonds....

A new kind of quantum gates, higher braiding gates, as matrix solutions of the polyadic braid equations (different from the generalized Yang–Baxter equations) is introduced. Such gates lead to another special multiqubit entanglement that can speed up...

For a group $\pi$ with unit e, we introduce and study the notion of a $\pi$-graded Hopf algebra. Then we introduce and construct a new braided monoidal category ${}_H^{H_e}{\mathcal{YD}}_{\pi }$ over a $\pi$-graded Hopf algebra H. We introduce the notion of a $\pi$-double centr...

The source of cancerous mutations and the relationship to telomeres is explained in an alternative way. We define the smallest subunit in the genetic code as a loop braid group element. The loop braid group is suitable to be defined as a configuratio...

We give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use th...

A research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings and braided group st...

The present article reviews the multiple applications of group theory to the symmetry problems in physics. In classical physics, this concerns primarily relativity: Euclidean, Galilean, and Einsteinian (special). Going over to quantum mechanics, we f...

Let H be a crossed group-cograded Hopf quasigroup. We first introduce the notion of p-Yetter–Drinfeld quasimodule over H. If the antipode of H is bijective, we show that the category $YDQ\left(H\right)$ of Yetter–Drinfeld quasimodules over H is a cros...

We introduce and study a large class of coalgebras (possibly (non)coassociative) with group-algebraic structures Hopf (non)coassociative group-algebras. Hopf (non)coassociative group-algebras provide a unifying framework for classical Hopf algebras a...

Image encryption is crucial for ensuring the confidentiality and integrity of digital images, preventing unauthorized access and alterations. However, existing encryption algorithms often involve complex mathematical operations or require specialized...

In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being locked in...

In this paper, we present two different ways for computing the Kauffman bracket skein module of $S^1\times S^2$, $\mathrm{KBSM}\left(S^1\times S^2\right)$, via braids. We first extend the universal Kauffman bracket type invariant V for knots and links in the Solid Torus ST, which...

We show that, generically, finding the k-th root of a braid is very fast. More precisely, we provide an algorithm which, given a braid x on n strands and canonical length l, and an integer $k>1$ , computes a k-th root of x, if it exists, or...

Given the Yetter–Drinfeld category over any quasigroup and a braided Hopf coquasigroup in this category, we first mainly study the Radford’s biproduct corresponding to this braided Hopf coquasigroup. Then, we investigate Sweedler’s...

We generalize orbifold models for chords and voice leading to incorporate loudness, allowing for the modeling of resting voices, which are used frequently by composers and arrangers across genres. In our generalized setting (strictly speaking, that o...

In general, the braid structures in a topological space can be classified into algebraic forms and geometric forms. This paper investigates the properties of a braid structure involving 2-simplices and a set of directed braid-paths in view of algebra...

Carbon fiber is mainly distributed in the shape of short fibers and continuous fiber bundles as the reinforcing phase in metal matrix composites, and it is seldom studied as braided rope shaped to reinforce the matrix. For this paper, the pretreatmen...

This paper proposes a new research method for braided river sedimentation on the beach shore based on the action of tidal currents. This study conducts a statistical analysis of the length and width of a single braided river and channel bar sand body...

We recently classified baryonic matter in the ground and first excited states thanks to the discrete group of braids inherent to $SU{\left(2\right)}_2$ Ising anyons. Remarkably, the braids of $SU{\left(2\right)}_4$ anyons allow the neutrino mixing matrix to be generated with an acc...

In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston’s geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement $C\left(K\right)$...

In order to identify the degree of water flooding in a reservoir and to discover any remaining oil-enriched areas, in this paper, a systematic study on the water flooding of cores in obturated coring wells is carried out. With observations and testin...

Extending Eilenberg–Mac Lane’s cohomology of abelian groups, a cohomology theory is introduced for commutative monoids. The cohomology groups in this theory agree with the pre-existing ones by Grillet in low dimensions, but they differ beyond dimensi...

This paper investigates quantum contextuality, a central nonclassical aspect of quantum mechanics, by employing the algebraic and topological structures of modular tensor categories. The analysis establishes that braid group representations construct...

The fundamental group ${\pi }_1\left(L\right)$ of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states...

Khovanov homology is a categorication of the Jones polynomial. It consists of graded chain complexes which, up to chain homotopy, are link invariants, and whose graded Euler characteristic is equal to the Jones polynomial of the link. In this article...

(i) Objective: The present study aimed to compare the electrochemical corrosion resistance of six different types of fixed lingual retainer wires used as fixed retention appliances in an in vitro study. (ii) Methods: In the study, two different Ringe...

Algebraic structures in which the property of commutativity is substituted by the mediality property are introduced. We consider (associative) graded algebras and instead of almost commutativity (generalized commutativity or $\epsilon$-commutativity), we intr...

Novel chitosan (CS)-coated poly(l-lactic acid) (PLA) fibers (CS–PLA) were prepared by reaction of an alkali and CS under heat treatment without a chemical binder. These treatments induced hydrolysis on the PLA surface, formation of ionic bonds betwee...

The composite group investigates endlessly the features of natural fiber/thermoplastic matrix composite materials to improve recyclability, use of renewable sources, and reduce material costs. In this context, the development and use of biodegradable...

The Kitaev chain model exhibits topological order that manifests as topological degeneracy, Majorana edge modes and $Z_2$ topological invariant of the bulk spectrum. This model can be obtained from a transverse field Ising model(TFIM) using the Jordan–W...

The problem with composite rebars in the civil engineering industry is often described as the material’s brittleness while overloaded. To overcome this drawback, researchers pay attention to the pseudo-ductility effect. The paper presents four-point...

The aim of the study was to analyze retention protocols and materials for fixed retainers used by clinicians providing orthodontic treatment in Poland. The survey was carried out from February to April 2021. The questionnaire was designed using the G...

Haruki Murakami’s Hard-Boiled Wonderland and the End of the World portrays a world where the “shadow”, the seat of memory, desire, and volition, is surgically removed, leaving behind a perfectly fluent but phenomenologically empty s...

The discharge of aquaculture wastewater and the excessive selenium in aquaculture effluent caused by selenium addition to aquatic feed are posing a serious risk for the marine environment. In this study, batch tests were carried out to investigate th...

Using scaffolds is a promising alternative to current methods of treatment for ruptures of tendons and ligaments. However, scaffolds are subject to a wide range of challenges, including mechanical, degradation, process-related and biological requirem...

This paper reports on the Walnut Digital Signature Algorithm (WalnutDSA), which is an asymmetric signature scheme recently presented for standardization at the NIST call for post-quantum cryptographic constructions. WalnutDSA is a group theoretical c...

A generalization of the famous Dirac belt trick opens up the way to a haptic model for quantum phases of fermions and bosons in Hilbert space based on knot theory. We introduce a simple paper strip model as an aid for visualization of the quantum pha...

The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C. N. Yang, and in statistical mechanics, in R. J. Baxter’s work. Later, it turned out that this equation plays a crucial role in: quantum groups, knot t...

We find that the whole set of known baryons of spin parity $J^P={{\displaystyle \frac{1}{2}}}^{+}$ (the ground state) and $J^P={{\displaystyle \frac{3}{2}}}^{+}$ (the first excited state) is organized in multiplets which may efficiently be encoded by the multiplets of conjugacy classes in the small finite group $G=($...

The present field and petrographic investigations of the Tortonian to Gelasian Siwalik Group in the core of the Hazara-Kashmir Syntaxis have been carried out to comprehend the middle stage Himalayan orogeny that resulted from the collision of Indian...

Background: Fixed retainers assist in maintaining the outcomes of orthodontic treatment. Fixed retention may be affected by bruxism. Objective: Evaluate two adhesives (an ormocer and a flowable composite) used for fixed orthodontic retention in simul...

Hopf algebras, as a crucial generalization of groups, have a very symmetric structure and have been playing a prominent role in mathematical physics. In this paper, let H be a dual quasi-Hopf algebra which is a more general Hopf algebra structure. A....

The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal dev...

The volcanic activity of the Xiong’er Group and its concomitant sedimentation are related to the stretching–breakup of the Columbia supercontinent. The Dagushi Formation overlies the Paleoproterozoic Shuangfang Formation with an angular u...

Objective: Comparison of the results of stent-assisted coiling (SAC) with braided stents (BS), flow diverters (FD), and laser-cut stents (LCS) to determine the relative flow-diverting capacity of BS (Leo baby and Accero). Methods: Saccular intracrani...

The framework plan for kindergartens in Norway emphasizes knowledge of Indigenous Sámi culture among the core values of pedagogical practice. Preservice students in early childhood teacher education (ECTE) are thus obliged to learn about S&aac...