THE DEVELOPMENT OF COURSEWARE BASED ON MATHEMATICAL REPRESENTATIONS AND ARGUMENTS IN NUMBER THEORY COURSES by Cita Dwi Rosita

“…Number Theory courses is one of the basic subjects that would be a prerequisite for courses at the next level, such as Linear Algebra, Complex Analysis, Real Analysis, Transformation Geometry, and Algebra Structure. Thus, the student’s understanding about the essential concepts that exist in this course will determine their success in studying subjects that mentioned above. …”
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The role of positivity and causality in interactions involving higher spin by Bert Schroer

“…These principles (and not the imposed gauge symmetry) account also for the Lie-algebra structure of the leading contributions of selfinteracting vector mesons.Second order consistency of selfinteracting vector mesons in SLFT requires the presence of H-particles; this, and not SSB, is the raison d'être for H.The basic conceptual and calculational tool of SLFT is the S-matrix. …”
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The monotone wrapped Fukaya category and the open-closed string map by Ritter, A, Smith, I

“…The module and unital algebra structures, and the generation criterion, also hold for the compact Fukaya category F(E), and also hold for closed monotone symplectic manifolds. …”

Graphical calculi and their conjecture synthesis by Miller-Bakewell, H

“…This work continues the exploration of graphical calculi, inside and outside of the quantum computing setting, by investigating the algebraic structures with which we label diagrams. The initial aim for this was Conjecture Synthesis; the algorithmic process of creating theorems. …”

Dualizable tensor categories by Douglas, C, Schommer-Pries, C, Snyder, N

“…There is furthermore a correspondence between algebraic structures on tensor categories and homotopy fixed point structures, which in turn provide structured field theories; we describe the expected connection between pivotal tensor categories and combed fixed point structures, and between spherical tensor categories and oriented fixed point structures.…”

Dualizable tensor categories by Douglas, CL, Schommer-Pries, C, Snyder, N

“…There is furthermore a correspondence between algebraic structures on tensor categories and homotopy fixed point structures, which in turn provide structured field theories; we describe the expected connection between pivotal tensor categories and combed fixed point structures, and between spherical tensor categories and oriented fixed point structures.…”

On the Hamming Distances of Constacyclic Codes of Length 5<italic>p^S</italic> by Hai Q. Dinh, Xiaoqiang Wang, Jirakom Sirisrisakulchai

“…In this paper, the algebraic structures of constacyclic codes of length <inline-formula> <tex-math notation="LaTeX">$5~p^{s}~(p\neq 5)$ </tex-math></inline-formula> are obtained, which provide all self-dual, self-orthogonal and dual containing codes. …”
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A new method to evaluate regular ternary semigroups in multi-polar fuzzy environment by Shahida Bashir, Ahmad N. Al-Kenani, Maria Arif, Rabia Mazhar

“…There are many algebraic structures which are not closed under binary multiplication that is a reason to study ternary operation of multiplication such as the set of negative integer is closed under the operation of ternary multiplication but not closed for the binary multiplication. …”
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Bidirectional mapping between rhombic triacontahedron and icosahedral hexagonal discrete global grid systems by Xinhai Huang, Jinchi Dai, Jin Ben, Jianbin Zhou, Junjie Ding

“…We established geometric and topological correlations between the RT and icosahedron, abstracted the spatial algebraic structures of hexagonal grids on the two different polygons, and constructed mapping relationships between them. …”
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The Ideal Over Semiring of the Non-Negative Integer by Aisyah Nur Adillah, Fitriana Hasnani, Meryta Febrilian Fatimah, Nikken Prima Puspita

“…Assumed that (S,+,.) is a semiring. Semiring is a algebra structure as a generalization of a ring. A set I⊆S is called an ideal over semiring S if for any α,β∈I, we have α-β∈I and sα=αs∈I for every s in semiring S.  …”
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Distances in zero-divisor and total graphs from commutative rings–A survey by T. Tamizh Chelvam, T. Asir

“…There are so many ways to construct graphs from algebraic structures. Most popular constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite groups and zero-divisor graphs and total graphs from commutative rings. …”
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Self-dual and complementary dual abelian codes over Galois rings by Jitman, Somphong, Ling, San

“…Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, abelian codes over Galois rings are studied in terms of the ideals in the group ring GR(pr,s)[G], where G is a finite abelian group and GR(pr,s) is a Galois ring. …”
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Canonical groups for quantization on the two-dimensional sphere and one-dimensional complex projective space by Ahamad Sumadi, Ahmad Hazazi, Zainuddin, Hishamuddin

“…We explicitly show that the Lie algebra structures of both canonical groups are locally homomorphic. …”
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Determinants of Serum Vitamin D level; A Data Mining Approach by Zahra Amiri, Fahimeh Moafian, Payam Sharifan, Elahe Hasanzadeh, Zahra Khorasanchi, Moniba Bijari, Maryam Mohammadi Bajgiran, Sara saffar soflaei, Susan Darroudi, Hamideh Ghazizadeh, fatemeh rouhi, Fatemeh Mohseni nik, Maryam Tayefi, Samira roohi, Ayad Noor, Abdullah Al yakobi, Mohammed Hadi Lafta Alboresha, Gordon A. Ferns, Habibollah Esmaily, Majid Ghayour-Mobarhan

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Hyers Stability and Multi-Fuzzy Banach Algebra by Parvaneh Lo′lo′, Ehsan Movahednia, Manuel De la Sen

“…In addition, under some conditions on <i>f</i>, the algebra <i>A</i> has multi <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra structure with involution <i>H</i>.…”
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Punctured groups for exotic fusion systems by Ellen Henke, Assaf Libman, Justin Lynd

“…Abstract The transporter systems of Oliver and Ventura and the localities of Chermak are classes of algebraic structures that model the p‐local structures of finite groups. …”
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From Quantum Automorphism of (Directed) Graphs to the Associated Multiplier Hopf Algebras by Farrokh Razavinia, Ghorbanali Haghighatdoost

“…It also concerns quantum linear groups, especially the coordinate ring of <i>M_q</i>(<i>n</i>) and the observation that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">K</mi></semantics></math></inline-formula> [<i>M_q</i>(<i>n</i>)] is a quadratic algebra, and can be equipped with a multiplier Hopf ∗-algebra structure in the sense of quantum permutation groups developed byWang and an observation by Rollier–Vaes. …”
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Floer cohomology in the mirror of the projective plane and a binodal cubic curve by Pascaleff, James Thomas

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A theory of quaternionic algebra, with applications to hypercomplex geometry by Joyce, D

“…So A has a kind of partial algebra structure. It turns out that this structure can be very neatly described using the quaternionic tensor product and AH-morphisms, and that A has the structure of an "H-algebra", a quaternionic analogue of commutative algebra.…”

Sequences and cubes of finite vertices of fuzzy topograpffic topological mapping by Mohd. Yunus, Azrul Azim

“…In this process, geometrical and algebraic structures for some FK; are obtained and proven in this thesis. …”
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