Zobrazeno 1 - 10
of 45
pro vyhledávání: '"P D Loly"'
Publikováno v:
Linear Algebra and its Applications. 430:2659-2680
To study the eigenvalues of low order singular and non-singular magic squares we begin with some aspects of general square matrices. Additional properties follow for general semimagic squares (same row and column sums), with further properties for ge
Publikováno v:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 462:2271-2279
All 8th order Franklin bent diagonal squares with distinct elements 1, …, 64 have been constructed by an exact backtracking method. Our count of 1, 105, 920 dramatically increases the handful of known examples, and is some eight orders of magnitude
Autor:
P. D. Loly, Adam Rogers
Publikováno v:
European Journal of Physics. 26:809-813
Recent studies of the rotational properties of magic cubes are extended to a corresponding electrical problem. While expecting the dipole moments of magic cubes to vanish, it was a surprise to find their quadrupole moments also vanished. These proper
Autor:
M. J. Steeds, P. D. Loly
Publikováno v:
International Journal of Mathematical Education in Science and Technology. 36:375-388
An interesting class of purely pandiagonal, i.e. non-magic, whole number (integer) squares of orders (row/column dimension) of the powers of two which are related to Gray codes and square Karnaugh maps has been identified. Treated as matrices these s
Autor:
P. D. Loly, Adam Rogers
Publikováno v:
American Journal of Physics. 72:786-789
Magic cubes are shown to have maximally symmetric inertia tensors if they are interpreted as rigid body mass distributions. This symmetry is due to their semi-magic property where each row, column, and pillar has the same mass sum. The moment of iner
Publikováno v:
Journal of Physics: Condensed Matter. 4:5419-5432
The spectrum of two-magnon excitations is examined for a 2D triangular Heisenberg ferromagnet with various values of spin (S), Ising ( sigma ) and uniaxial (D) anisotropies and for total wavevectors K in three high-symmetry directions. In contrast to
Publikováno v:
Discussiones Mathematicae Probability and Statistics. 33:121
The 2010 study of the Shannon entropy of order nine Sudoku and Latin square matrices by Newton and DeSalvo [Proc. Roy. Soc. A 2010] is extended to natural magic and Latin squares up to order nine. We demonstrate that decimal and integer measures of t
Autor:
P. D. Loly
Publikováno v:
American Journal of Physics. 62:105-105
Publikováno v:
Journal of Physics C: Solid State Physics. 19:4729-4740
The two-magnon spectrum of the nearest-neighbour Heisenberg ferromagnet on a square lattice is studied. An exact Green function formalism is used to obtain the spectral functions at zero temperature. The lattice Green functions of this system are wri
Autor:
P D Loly, J A Ashraff
Publikováno v:
Journal of Physics C: Solid State Physics. 20:4823-4831
A numerical scheme is presented for the calculation of two-dimensional Brillouin zone lattice spectra. The method is based on the subdivision of the irreducible part of the first Brillouin zone into triangular subcells, within which the energy eigenv