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 2020-03-01 to 2024-03-01.)

Article	Citations
Algorithmically Solving the Tadpole Problem	27
Some Results for the Two-Sided Quaternionic Gabor Fourier Transform and Quaternionic Gabor Frame Operator	19
Geometric Algebra of Singular Ruled Surfaces	18
New Applications of Clifford’s Geometric Algebra	16
Generalized Derivations and Rota-Baxter Operators of $$\varvec{n}$$-ary Hom-Nambu Superalgebras	16
3-Hom-Lie Algebras Based on $$\sigma $$-Derivation and Involution	15
Heisenberg’s and Hardy’s Uncertainty Principles for Special Relativistic Space-Time Fourier Transformation	11
Weyl and Majorana Spinors as Pure Goldstone Bosons	9
Linear Canonical Wavelet Transform in Quaternion Domains	9
A Quaternion Matrix Equation with Two Different Restrictions	9
Multi-modal Medical Image Fusion Based on Geometric Algebra Discrete Cosine Transform	8
Quaternion Fourier Transform and Generalized Lipschitz Classes	8
Sedeonic Equations in Field Theory	7
MPCEP-$$*$$CEPMP-Solutions of Some Restricted Quaternion Matrix Equations	7
An Introduction to Hyperholomorphic Spectral Theories and Fractional Powers of Vector Operators	7
Split Quaternion-Valued Twin-Multistate Hopfield Neural Networks	7
Basis-free Solution to Sylvester Equation in Clifford Algebra of Arbitrary Dimension	6
Wavelet Transform of Dini Lipschitz Functions on the Quaternion Algebra	6
Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense	6
On Structure of Inframonogenic Functions	6
Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra	6
TbGAL: A Tensor-Based Library for Geometric Algebra	6
Solvability of New Constrained Quaternion Matrix Approximation Problems Based on Core-EP Inverses	6
Symmetric Functions and 3D Fermion Representation of $$\pmb {W_{1+\infty }}$$ Algebra	6
Fractional Clifford–Fourier Transform and its Application	5

An All-in-One Geometric Algorithm for Cutting, Tearing, and Drilling Deformable Models	5
Generalized Fractional Cauchy–Riemann Operator Associated with the Fractional Cauchy–Riemann Operator	5
Classification of Left Octonionic Modules	5
Polynomial Approximation in Quaternionic Bloch and Besov Spaces	5
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	5
Projection Factors and Generalized Real and Complex Pythagorean Theorems	5
Decomposition for a Quaternion Tensor Triplet with Applications	5
The Sum and the Product of Two Quadratic Matrices: Regular Cases	5
Almansi Theorem and Mean Value Formula for Quaternionic Slice-regular Functions	4
Formalizing Geometric Algebra in Lean	4
The Unified Standard Model	4
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
BiHom–Lie Superalgebra Structures and BiHom–Yang–Baxter Equations	4
Some Fundamental Theorems of Functional Analysis with Bicomplex and Hyperbolic Scalars	4
Titchmarsh’s Theorem in Clifford Analysis	4
GAALOPWeb for Matlab: An Easy to Handle Solution for Industrial Geometric Algebra Implementations	4
Investigation of Generalized $$\mathcal {Z}$$- Recurrent Spacetimes and $$f(\mathcal {R},T)$$-Gravity	4
Differential Topological Aspects in Octonionic Monogenic Function Theory	4
Foundations for Strip Adjustment of Airborne Laserscanning Data with Conformal Geometric Algebra	3
Two-Component Spinorial Formalism Using Quaternions for Six-Dimensional Spacetimes	3
On the Jackson–Stechkin Theorems for the Best Approximations of Functions in Clifford Algebras	3
A New Approach to Slice Analysis Via Slice Topology	3
Energy–Momentum Complex in General Relativity and Gauge Theory	3
An Online Calculator for Quantum Computing Operations Based on Geometric Algebra	3
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	3
Deep Learning Gauss–Manin Connections	3
Factorization and Generalized Roots of Dual Complex Matrices with Rodrigues’ Formula	3
A Multiplication Technique for the Factorization of Bivariate Quaternionic Polynomials	3
Ternary Clifford Algebras	3
Hyperbolic Harmonic Functions and Hyperbolic Brownian Motion	3
On the Problem of Choosing Subgroups of Clifford Algebras for Applications in Fundamental Physics	3
Basis-Free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras	3
Complete Systems of Beltrami Fields Using Complex Quaternions and Transmutation Theory	3
One-Dimensional Quaternionic Special Affine Fourier Transform	3
Weighted Minimization Problems for Quaternion Matrices	3
Zeon Matrix Inverses and the Zeon Combinatorial Laplacian	3
On Inner Automorphisms Preserving Fixed Subspaces of Clifford Algebras	3
Adinkras: Graphs of Clifford Algebra Representations, Supersymmetry, and Codes	3
Clifford-Valued Stockwell Transform and the Associated Uncertainty Principles	3
The Octonionic Bergman Kernel for the Half Space	3
A Fiber Bundle over the Quaternionic Slice Regular Functions	3
Less is More: Efficient Networked VR Transformation Handling Using Geometric Algebra	2
Propagators Beyond The Standard Model	2
Jackson Theorems for the Quaternion Linear Canonical transform	2
A Variation on Uncertainty Principles for Quaternion Linear Canonical Transform	2
Multilevel Declassification Method for Geographic Vector Field Data: A Geometric Algebra Approach	2
Octonion Measures for Solutions of PDEs	2
Ruled Surfaces in Minkowski 3-space and Split Quaternion Operators	2
Spacetime Geometry with Geometric Calculus	2

Exploring Novel Surface Representations via an Experimental Ray-Tracer in CGA	2
Vanishing Vector Rotation in Quadric Geometric Algebra	2
Pitt’s Inequality and Logarithmic Uncertainty Principle for the Clifford-Fourier Transform	2
Conformal Mappings Revisited in the Octonions and Clifford Algebras of Arbitrary Dimension	2
On the Conformal Mappings and the Global Operator G	2
Efficient Development of Competitive Mathematica Solutions Based on Geometric Algebra with GAALOPWeb	2
On Elliptic Biquaternion Matrices	2
Representations of Extended Carroll Group	2
A Generalised Quaternion and Clifford Algebra Based Mathematical Methodology to Effect Multi-stage Reassembling Transformations in Parallel Robots	2
Lyapunov Stability: A Geometric Algebra Approach	2
Corner Operators with Symbol Hierarchies	2
Bicomplex Version of Lebesgue’s Dominated Convergence Theorem and Hyperbolic Invariant Measure	2
On Ternary Clifford Algebras on Two Generators Defined by Extra-Special 3-Groups of Order 27	2
The Moore–Penrose Inverse and Singular Value Decomposition of Split Quaternions	2
Beyond the 10-fold Way: 13 Associative $$ {\mathbb Z}_2\times {\mathbb Z}_2$$-Graded Superdivision Algebras	2
Graded Symmetry Groups: Plane and Simple	2
The Fixed Points and Cross-Ratios of Hyperbolic Möbius Transformations in Bicomplex Space	2
Leibniz Bialgebras, Classical Yang–Baxter Equations and Dynamical Systems	2
The Symplectic Fueter–Sce Theorem	2
The Existence of Cauchy Kernels of Kravchenko-Generalized Dirac Operators	2
Binary Encoded Recursive Generation of Quantum Space-Times	2
Special Affine Fourier Transform for Space-Time Algebra Signals in Detail	2
Quaternionic Linear Canonical Wave Packet Transform	2
Beurling’s Theorem in the Clifford Algebras	2
Geometric Algebra Speaks Quantum Esperanto	2
Time Series, Hidden Variables and Spatio-Temporal Ordinality Networks	2
On the Supports of Functions Associated to the Radially Deformed Fourier Transform	2
Dual Hyperquaternion Poincaré Groups	2
Quaternion Quantum Neural Network for Classification	2
Certain Bases of Polynomials Associated with Entire Functions in Clifford Analysis	2
Hyperquaternion Conformal Groups	1
Concept of s-Numbers in Quaternionic Analysis and Schatten Classes	1
Constructions and $$T^{*}$$-Extensions of 3-BiHom-Lie Superalgebras	1
Riemann Boundary Value Problems for Monogenic Functions on the Hyperplane	1
Real Spinors and Real Dirac Equation	1
Pseudo-inverses Without Matrices	1
On Multi-conditioned Conic Fitting in Geometric Algebra for Conics	1
Two-sided Clifford-valued Linear Canonical Transform: Properties and Mustard Convolution	1
Clifford Algebra-Valued Segal–Bargmann Transform and Taylor Isomorphism	1
Bicomplex Neural Networks with Hypergeometric Activation Functions	1
A Version of Schwarz Lemma Associated to the k-Cauchy–Fueter Operator	1
On the Differential Equation of First and Second Order in the Zeon Algebra	1
The Supergeometric Algebra	1
Geometric Invariant Decomposition of $$\text {SU}(\textbf{3})$$	1
On Some Lie Groups in Degenerate Clifford Geometric Algebras	1
Two-Sided Fourier Transform in Clifford Analysis and Its Application	1
A New Way to Construct the Riemann Curvature Tensor Using Geometric Algebra and Division Algebraic Structure	1
Ellipticity of Some Higher Order Conformally Invariant Differential Operators	1
On Quaternionic Measures	1
Left-Right Symmetric Fermions and Sterile Neutrinos from Complex Split Biquaternions and Bioctonions	1
Dynamical Systems of Operators Induced by Scaled Hypercomplex Rings	1
The Rules of 4-Dimensional Perspective: How to Implement Lorentz Transformations in Relativistic Visualization	1
Biquaternionic Treatment of Inhomogeneous Time-Harmonic Maxwell’s Equations Over Unbounded Domains	1
On the Mean Ergodic Theorem in Bicomplex Banach Modules	1
Brauer–Clifford Group of ($$\varvec{S,{{\mathcal {G}}},H}$$)-Azumaya Algebras	1
Generalized $$(k_i)$$-Monogenic Functions	1
On the Structure of Ternary Clifford Algebras and Their Irreducible Representations	1
On Interactions of Quaternionic and Complex Structures of Linear Spaces	1
Leveraging Prior Known Vector Green Functions in Solving Perturbed Dirac Equation in Clifford Algebra	1
The Study Variety of Conformal Kinematics	1
Construction of a Few Quantum Mechanical Hamiltonians via Lévy-Leblond Type Linearization: Clifford Momentum, Spinor States and Supersymmetry	1
Conjugate Harmonic Functions of Fueter Type	1
Computational Aspects of Geometric Algebra Products of Two Homogeneous Multivectors	1
Clifford Valued Shearlet Transform	1
The Orthogonal Branching Problem for Symplectic Monogenics	1
Solving and Algorithm to System of Quaternion Sylvester-Type Matrix Equations with $$*$$-Hermicity	1
Functional Calculus for Dual Quaternions	1
Extensions and Crossed Modules of $$\varvec{n}$$-Lie–Rinehart Algebras	1
Riemann–Hilbert Problems for Axially Symmetric Monogenic Functions in $${\mathbb {R}}^{n+1}$$	1
Representations of Quaternion W-MPCEP, W-CEPMP and W-MPCEPMP Inverses	1
A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form	1
M, The Power Definition in Geometric Algebra that Unveils the Shortcomings of the Nonsinusoidal Apparent Power S	1
The Atiyah-Singer Index Theorem for a Family of Fractional Dirac Operators on Spin Geometry	1
Drinfeld Double for Infinitesimal BiHom-bialgebras	1