OOIR: Observatory of International Research

Papers

(The median citation count of Advances in Applied Clifford Algebras is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-11-01 to 2024-11-01.)

Article	Citations
Algorithmically Solving the Tadpole Problem	34
New Applications of Clifford’s Geometric Algebra	25
Geometric Algebra of Singular Ruled Surfaces	22
Some Results for the Two-Sided Quaternionic Gabor Fourier Transform and Quaternionic Gabor Frame Operator	21
Generalized Derivations and Rota-Baxter Operators of $$\varvec{n}$$-ary Hom-Nambu Superalgebras	17
A Quaternion Matrix Equation with Two Different Restrictions	10
Decomposition for a Quaternion Tensor Triplet with Applications	10
Linear Canonical Wavelet Transform in Quaternion Domains	10
Weyl and Majorana Spinors as Pure Goldstone Bosons	10
Quaternion Fourier Transform and Generalized Lipschitz Classes	10
Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra	9
Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense	9
The Sum and the Product of Two Quadratic Matrices: Regular Cases	9
MPCEP-$$*$$CEPMP-Solutions of Some Restricted Quaternion Matrix Equations	8
Multi-modal Medical Image Fusion Based on Geometric Algebra Discrete Cosine Transform	8
Wavelet Transform of Dini Lipschitz Functions on the Quaternion Algebra	7
Investigation of Generalized $$\mathcal {Z}$$- Recurrent Spacetimes and $$f(\mathcal {R},T)$$-Gravity	7
On Structure of Inframonogenic Functions	7
An Introduction to Hyperholomorphic Spectral Theories and Fractional Powers of Vector Operators	7
Basis-free Solution to Sylvester Equation in Clifford Algebra of Arbitrary Dimension	7
A Real Method for Solving Quaternion Matrix Equation $$\mathbf{X}-\mathbf{A}{\hat{\mathbf{X}}}{} \mathbf{B} = \mathbf{C}$$ Based on Semi-Tensor Product of Matrices	7
Quaternionic Linear Canonical Wave Packet Transform	6
Symmetric Functions and 3D Fermion Representation of $$\pmb {W_{1+\infty }}$$ Algebra	6
Classification of Left Octonionic Modules	6
Solvability of New Constrained Quaternion Matrix Approximation Problems Based on Core-EP Inverses	6

Foundations for Strip Adjustment of Airborne Laserscanning Data with Conformal Geometric Algebra	6
Graded Symmetry Groups: Plane and Simple	6
On the Problem of Choosing Subgroups of Clifford Algebras for Applications in Fundamental Physics	5
Weighted Minimization Problems for Quaternion Matrices	5
An All-in-One Geometric Algorithm for Cutting, Tearing, and Drilling Deformable Models	5
The Underlying Fiber Bundle Geometry of the CAM Gauge Model of the Standard Model of Particle Physics: $$\pmb {SU(3)}$$	4
On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb	4
Ternary Clifford Algebras	4
On the Jackson–Stechkin Theorems for the Best Approximations of Functions in Clifford Algebras	4
An Online Calculator for Quantum Computing Operations Based on Geometric Algebra	4
Solving and Algorithm to System of Quaternion Sylvester-Type Matrix Equations with $$*$$-Hermicity	4
Vanishing Vector Rotation in Quadric Geometric Algebra	4
Complete Systems of Beltrami Fields Using Complex Quaternions and Transmutation Theory	4
Deep Learning Gauss–Manin Connections	4
A Multiplication Technique for the Factorization of Bivariate Quaternionic Polynomials	4
On Inner Automorphisms Preserving Fixed Subspaces of Clifford Algebras	4
Adinkras: Graphs of Clifford Algebra Representations, Supersymmetry, and Codes	4
Basis-Free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras	4
Titchmarsh’s Theorem in Clifford Analysis	4
Formalizing Geometric Algebra in Lean	4
A Variation on Uncertainty Principles for Quaternion Linear Canonical Transform	4
Bicomplex Version of Lebesgue’s Dominated Convergence Theorem and Hyperbolic Invariant Measure	4
Energy–Momentum Complex in General Relativity and Gauge Theory	4
On Jordan–Clifford Algebras, Three Fermion Generations with Higgs Fields and a $${{\mathrm {SU}(3) \times \mathrm {SU}(2)_L \times \mathrm {SU}(2)_R \times \mathrm {U}(1)}}$$ Model	4
A Fiber Bundle over the Quaternionic Slice Regular Functions	3
The Fixed Points and Cross-Ratios of Hyperbolic Möbius Transformations in Bicomplex Space	3
Two-Component Spinorial Formalism Using Quaternions for Six-Dimensional Spacetimes	3
Clifford-Valued Stockwell Transform and the Associated Uncertainty Principles	3
Two-sided Clifford-valued Linear Canonical Transform: Properties and Mustard Convolution	3
A Generalised Quaternion and Clifford Algebra Based Mathematical Methodology to Effect Multi-stage Reassembling Transformations in Parallel Robots	3
On Ternary Clifford Algebras on Two Generators Defined by Extra-Special 3-Groups of Order 27	3
Pitt’s Inequality and Logarithmic Uncertainty Principle for the Clifford-Fourier Transform	3
Zeon Matrix Inverses and the Zeon Combinatorial Laplacian	3
Two-State Quantum Systems Revisited: A Clifford Algebra Approach	3
Quaternion Quantum Neural Network for Classification	3
Jackson Theorems for the Quaternion Linear Canonical transform	3
Leibniz Bialgebras, Classical Yang–Baxter Equations and Dynamical Systems	3
One-Dimensional Quaternionic Special Affine Fourier Transform	3
Geometric Algebra Speaks Quantum Esperanto	3
A New Approach to Slice Analysis Via Slice Topology	3
The Explicit Twisted Group Algebra Structure of the Cayley–Dickson Algebra	2
Corner Operators with Symbol Hierarchies	2
Ellipticity of Some Higher Order Conformally Invariant Differential Operators	2
Less is More: Efficient Networked VR Transformation Handling Using Geometric Algebra	2
Special Affine Fourier Transform for Space-Time Algebra Signals in Detail	2
On Some Lie Groups in Degenerate Clifford Geometric Algebras	2
Representations of Extended Carroll Group	2
Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform	2
Biquaternionic Treatment of Inhomogeneous Time-Harmonic Maxwell’s Equations Over Unbounded Domains	2
Beyond the 10-fold Way: 13 Associative $$ {\mathbb Z}_2\times {\mathbb Z}_2$$-Graded Superdivision Algebras	2

On the Mean Ergodic Theorem in Bicomplex Banach Modules	2
A Version of Schwarz Lemma Associated to the k-Cauchy–Fueter Operator	2
Left-Right Symmetric Fermions and Sterile Neutrinos from Complex Split Biquaternions and Bioctonions	2
Ruled Surfaces in Minkowski 3-space and Split Quaternion Operators	2
On Optimal Inequalities for Anti-invariant Riemannian Submersions from Conformal Sasakian Space Forms	2
The Orthogonal Branching Problem for Symplectic Monogenics	2
Binary Encoded Recursive Generation of Quantum Space-Times	2
Geometric Invariant Decomposition of $$\text {SU}(\textbf{3})$$	2
Dynamical Systems of Operators Induced by Scaled Hypercomplex Rings	2
Certain Bases of Polynomials Associated with Entire Functions in Clifford Analysis	2
Dual Hyperquaternion Poincaré Groups	2
The Existence of Cauchy Kernels of Kravchenko-Generalized Dirac Operators	2
Beurling’s Theorem in the Clifford Algebras	2
Propagators Beyond The Standard Model	2
Multilevel Declassification Method for Geographic Vector Field Data: A Geometric Algebra Approach	2
On Elliptic Biquaternion Matrices	2
Exploring Novel Surface Representations via an Experimental Ray-Tracer in CGA	2
Lyapunov Stability: A Geometric Algebra Approach	2
The Atiyah-Singer Index Theorem for a Family of Fractional Dirac Operators on Spin Geometry	2
Extensions and Crossed Modules of $$\varvec{n}$$-Lie–Rinehart Algebras	2
On the Conformal Mappings and the Global Operator G	2
Bicomplex Neural Networks with Hypergeometric Activation Functions	2
Clifford Algebra-Valued Segal–Bargmann Transform and Taylor Isomorphism	1
Repeated Cayley–Dickson Processes and Subalgebras of Dimension 8	1
Clifford Spinors and Root System Induction: $$H_4$$ and the Grand Antiprism	1
Generalizing Classical Clifford Algebras, Graded Clifford Algebras and their Associated Geometry	1
Least-Squares Solutions of Generalized Sylvester-Type Quaternion Matrix Equations	1
Star Product for Para-Grassmann Algebra of Order Two	1
Category Isomorphisms Between Hilbert Spaces Over Octonions and Hilbert Spaces Over Clifford Algebras	1
Concept of s-Numbers in Quaternionic Analysis and Schatten Classes	1
B-Spline Pythagorean Hodograph Curves in Clifford Algebras	1
A New Way to Construct the Riemann Curvature Tensor Using Geometric Algebra and Division Algebraic Structure	1
Hyperquaternion Conformal Groups	1
On Complex Kinematics and Relativity	1
Computational Aspects of Geometric Algebra Products of Two Homogeneous Multivectors	1
Pseudo-inverses Without Matrices	1
On Multi-conditioned Conic Fitting in Geometric Algebra for Conics	1
Isomorphisms of Partial Differential Equations in Clifford Analysis	1
Rock Classification with Features Based on Higher Order Riesz Transform	1
On the Differential Equation of First and Second Order in the Zeon Algebra	1
On the Representations of Clifford and SO(1,9) Algebras for 8-Component Dirac Equation	1
The Study Variety of Conformal Kinematics	1
On the Structure of Ternary Clifford Algebras and Their Irreducible Representations	1
Call for Papers: T.C. Machine-Learning Mathematical Structures	1
Mean Value Theorems for Bicomplex Harmonic Functions	1
Generalized Partial-Slice Monogenic Functions: A Synthesis of Two Function Theories	1
Constructions and $$T^{*}$$-Extensions of 3-BiHom-Lie Superalgebras	1
Rings with Centrally-Extended Higher $$*$$-Derivations	1
Equations Satisfied by the Coordinates of Lipschitzian Elements in Clifford Algebras	1
Biquaternion Extensions of Analytic Functions	1
Inequalities Pertaining to Quaternion Ambiguity Function	1
An Algorithm for the Factorization of Split Quaternion Polynomials	1
The Rules of 4-Dimensional Perspective: How to Implement Lorentz Transformations in Relativistic Visualization	1
Brownian Motion, Martingales and Itô Formula in Clifford Analysis	1
Representations of Quaternion W-MPCEP, W-CEPMP and W-MPCEPMP Inverses	1
Riemann–Hilbert Problems for Axially Symmetric Monogenic Functions in $${\mathbb {R}}^{n+1}$$	1
M, The Power Definition in Geometric Algebra that Unveils the Shortcomings of the Nonsinusoidal Apparent Power S	1
S-Spectrum of Quaternionic Right Linear Bounded Operators	1
The Supergeometric Algebra	1
On Interactions of Quaternionic and Complex Structures of Linear Spaces	1
Blade Products and Angles Between Subspaces	1
Various Characteristic Properties of Lipschitzian Elements in Clifford Algebras	1
Construction of a Few Quantum Mechanical Hamiltonians via Lévy-Leblond Type Linearization: Clifford Momentum, Spinor States and Supersymmetry	1
Necessity of Tensorial Connections for Spinorial Systems	1
Real Spinors and Real Dirac Equation	1
Riemann Boundary Value Problems for Monogenic Functions on the Hyperplane	1
Functional Calculus for Dual Quaternions	1
Clifford Algebraic Approach to the De Donder–Weyl Hamiltonian Theory	1