Books
Links
Publications
arXiv also has a list of preprints.
- A. Fošner, Y. Hardy and B. Zinsou,
Block determinants, partial determinants and the exponential map,
Linear and Multilinear Algebra,
72, 2879—2914, 2024.
- Y. Hardy and B. Zinsou,
Canonical forms for boundary conditions of self-adjoint differential operators,
Journal of Applied Analysis & Computation,
14, 1854—1868, 2024.
- Y. Hardy, W.-H. Steeb and G. Kemp,
Matrices and Their (Un)Faithful Fermi-quadratic Forms,
International Journal of Theoretical Physics,
58, 1470—1481, 2019.
- Y. Hardy and A. Fošner,
Linear maps preserving Kronecker quotients,
Linear Algebra and its Applications,
556, 200—209, 2018.
- W.-H. Steeb and Y. Hardy,
Eigenvalue Problem, Spin Systems, Lie Groups, and Parameter Dependence,
Zeitschrift für Naturforschung A,
70, 605—609, 2015.
- W.-H. Steeb and Y. Hardy,
Exponential of a matrix, a nonlinear problem, and quantum gates,
Journal of Mathematical Physics,
56, 012201, 2015.
Preprint available on arXiv.org.
- Y. Hardy,
On Kronecker Quotients,
Electronic Journal of Linear Algebra,
27, 172—189, 2014.
Also available on arXiv.org.
- W.-H. Steeb and Y. Hardy,
Exceptional points, non-normal matrices, hierarchy of spin matrices and an eigenvalue problem,
International Journal of Modern Physics C,
25, 1450059, 2014.
Preprint available on arXiv.org.
- W.-H. Steeb and Y. Hardy,
Majorana Fermions on a Lattice and a Matrix Problem,
Zeitschrift für Naturforschung,
69a, 108—110, 2014.
Preprint available on arXiv.org.
- W.-H. Steeb and Y. Hardy,
An eigenvalue problem for a Fermi system and Lie algebras,
Quantum Information Processing,
13, 299—308, 2014.
Preprint available on arXiv.org.
- Y. Hardy, A. Fošner and W.-H. Steeb,
Cayley transform and the Kronecker product of Hermitian matrices,
Linear Algebra and its Applications,
439, 4023—4031, 2013.
Preprint available on arXiv.org.
- W.-H. Steeb and Y. Hardy,
Hamilton Operators, Discrete Symmetries, Brute Force and SymbolicC++,
International Journal of Modern Physics C,
24, 1250095, 2013.
Preprint available on arXiv.org.
- Y. Hardy and W.-H. Steeb,
A Sequence of Quantum Gates,
International Journal of Geometric Methods in Modern Physics,
9, 1220013, 2012.
Preprint available on arXiv.org.
- W.-H. Steeb and Y. Hardy,
Dynamical Systems, Vector Fields and Commutators,
Nonlinear Dynamics of Electronic Systems, Proceedings of NDES 2012,
1—4, 2012.
- W.-H. Steeb, Y. Hardy and I. Tanski,
Vector Fields, Variational Equations and Commutators,
International Journal of Bifurcation and Chaos,
22, 1250190, 2012.
- W.-H. Steeb, Y. Hardy and J. de Greef,
Spin Hamilton Operators, Symmetry Breaking, Energy Level Crossing,
and Entanglement,
Zeitschrift für Naturforschung,
67a, 608—612, 2012.
Preprint available on arXiv.org.
- W.-H. Steeb and Y. Hardy,
Entanglement, Kronecker Product, Pauli Spin Matrices
and a Nonlinear Eigenvalue Problem,
Open Systems & Information Dynamics,
19, 1250004, 2012.
- Y. Hardy and W.-H. Steeb,
Unitary Matrices and Commutators,
International Journal of Geometric Methods in Modern Physics,
8, 1583—1592, 2011.
- W.-H. Steeb, Y. Hardy and I. Tanski,
Vector Product and an Integrable Dynamical System,
Communications in Theoretical Physics,
56, 992—994, 2011.
- W.-H. Steeb and Y. Hardy,
N-tangle, Entangled Orthonormal Basis,
and a Hierarchy of Spin Hamilton Operators,
Zeitschrift für Naturforschung,
66a, 615—619, 2011.
- Y. Hardy and W.-H. Steeb,
Genetic Algorithms and Optimization Problems
in Quantum Computing,
International Journal of Modern Physics C,
21, 1359—1375, 2010.
- Y. Hardy and W.-H. Steeb,
Vec-Operator, Kronecker Product and Entanglement,
International Journal of Algebra and Computation,
20, 71—76, 2010.
- W.-H. Steeb and Y. Hardy,
A Chaotic Map and Data Communication,
Zeitschrift für Naturforschung,
65a, 613—614, 2010.
- W.-H. Steeb and Y. Hardy,
Unitary Operators, Entanglement,
and Gram-Schmidt Orthogonalization,
International Journal of Modern Physics C,
20, 891—899, 2009.
- W.-H. Steeb and Y. Hardy,
A hierarchy of Hamilton operators and entanglement,
Central European Journal of Physics,
7, 854—859, 2009.
- W.-H. Steeb and Y. Hardy,
Quantum optics networks, unitary operators
and computer algebra,
International Journal of Modern Physics C,
19, 1069—1078, 2008.
- Y. Hardy and D. Sabatta,
Encoding, symbolic dynamics, cryptography
and C++ implementations,
Physics Letters A,
366, 575—584, 2007.
- W.-H. Steeb and Y. Hardy,
One-Dimensional Cellular Automata, Conservation Laws and Partial
Differential Equations,
Zeitschrift für Naturforschung,
62a, 569—572, 2007.
- Y. Hardy and W.-H. Steeb,
Decomposing the SWAP Quantum Gate,
Journal of Physics A: Math. and Gen,
39, 1463—1467, 2006.
- W.-H. Steeb and Y. Hardy,
Quantum Gates and Hamilton Operators,
International Journal of Theoretical Physics,
45, 953—961, 2006.
- W.-H. Steeb and Y. Hardy,
Supersymmetric Hamilton Operator and Entanglement,
Zeitschrift für Naturforschung,
61a, 139—140, 2006.
- Y. Hardy, W.-H. Steeb and R. Stoop,
Genetic Algorithms, Floating Point Numbers and Applications,
International Journal of Modern Physics C,
16, 1811—1816, 2005.
- W.-H. Steeb, Y. Hardy and R. Stoop,
Bell-CHSH Inequality and Genetic Algorithms,
Zeitschrift für Naturforschung,
60a, 865—866, 2005.
- Y. Hardy and W.-H. Steeb,
Fermi-Bose Systems, Macroscopic Quantum Superposition States
and Entanglement,
International Journal of Theoretical Physics,
43, 2207—2213, 2004.
- Y. Hardy and W.-H. Steeb,
Entanglement, Hubbard Model and Symmetries,
International Journal of Theoretical Physics,
43, 341—347, 2004.
- Y. Hardy, W.-H. Steeb and R. Stoop,
Entanglement, Disentanglement and Wigner Functions,
Physica Scripta,
69, 166—169, 2004.
- Y. Hardy, W.-H. Steeb and R. Stoop,
Fully Entangled Quantum States in CN2
and Bell Measurement,
International Journal of Theoretical Physics,
42, 2865—2872, 2003.
- W.-H. Steeb and Y. Hardy,
Chaotic Maps, Invariants, Bose Operators, and Coherent States,
International Journal of Theoretical Physics,
42, 85—88, 2003.
- W.-H. Steeb, Y. Hardy and R. Stoop,
Lax Representation and Kronecker Product,
Physica Scripta,
67, 464—465, 2003.
- W.-H. Steeb, Y. Hardy and R. Stoop,
Discrete Wavelets and Perturbation Theory,
Journal of Physics A: Mathematical and General,
36, 6807—6811, 2003.
- Y. Hardy and W.-H. Steeb,
Gene Expression Programming and One-dimensional Chaotic Maps,
International Journal of Modern Physics C,
13, 13—24, 2002.
- W.-H. Steeb and Y. Hardy,
Entangled Quantum States and the Kronecker Product,
Zeitschrift für Naturforschung,
57a, 689—691, 2002.
- W.-H. Steeb, Y. Hardy and R. Stoop,
Discrete Wavelets and Filtering Chaotic Signals,
International Journal of Modern Physics C,
13, 771—776, 2002.
- Y. Hardy and W.-H. Steeb,
Fermi Systems, Hubbard Model and a SymbolicC++ Implementation,
International Journal of Modern Physics C,
12, 235—245, 2001.
- W.-H. Steeb, Y. Hardy Y. and R. Stoop,
Energy Eigenvalue Level Motion with Two Parameters,
Zeitschrift für Naturforschung,
56a, 565—567, 2001.
- W.-H. Steeb, Y. Hardy and R. Stoop,
Bessel Functions, Recursion and a Nonlinear Field Equation,
Zeitschrift für Naturforschung,
56a, 710—711, 2001.
- Y. Hardy, W.-H. Steeb and C.M. Villet,
Stabilization of Chaotic Systems with Phase Coupling,
Zeitschrift für Naturforschung,
55a, 847—850, 2000.
- W.-H. Steeb and Y. Hardy,
Quantum Computing and SymbolicC++ Simulations,
International Journal of Modern Physics C,
11, 323—334, 2000.
- W.-H. Steeb and Y. Hardy,
Entangled Quantum States and a C++ Implementation,
International Journal of Modern Physics C,
11, 69—77, 2000.
- Y. Hardy, W.-H. Steeb and R. Stoop,
Jacobi Elliptic Functions, Nonlinear Evolution Equations
and Recursion,
International Journal of Modern Physics C,
11, 27—31, 2000.
- W.-H. Steeb and Y. Hardy,
Energy Eigenvalue Level Motion and a SymbolicC++ Implementation,
International Journal of Modern Physics C,
11, 1347—1356, 2000.
- W.-H. Steeb and Y. Hardy,
Entangled Quantum States,
International Journal of Theoretical Physics,
39, 2765—2770, 2000.
- Y. Hardy and W.-H. Steeb,
The Rikitake Two-Disk Dynamo System
and Domains with Periodic Orbits,
International Journal of Theoretical Physics,
38, 2413—2417, 1999.