Position vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3
In this paper, we study spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3 . We show that spacelike biharmonic curves are general helices. We characterize position vector of spacelike biharmonic general helices in terms of their curvature and torsion.
Time-Canal Surfaces Around Biharmonic Particles and Its Lorentz Transformations in Heisenberg Space-Time
In this work, we introduce a new space-time using Heisenberg group and call this space as “Heisenberg space-time” . We give a geometrical description of time-canal surfaces around timelike biharmonic particle in $\mathcal {H}_{1}^{4}$. Moreover, we obtain Lorentz transformations this particles. Additionally, we illustrate our results. Finally, we characterize charged bihamonic particles in electromagnetic fields on Heisenberg space-time.
Phase diagram and magnetic properties of the diluted fcc system NipMg1-pO.
Starting from Ni and Mg nitrates, about 20 samples of ${\mathrm{Ni}}_{\mathit{p}}$${\mathrm{Mg}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$O samples (with 0.06\ensuremath{\le}p\ensuremath{\le}0.86) were prepared and x-ray-diffraction studies showed the samples to have the NaCl structure with the lattice constant fitting the expression a(p)=4.2115-0.0340p \AA{}. Temperature-dependent magnetic-susceptibility (\ensuremath{\chi}) studies of the samples were carried out between 1.8 and 600 K using a superconducting-quantum-interference-device magnetometer and N\'eel temperatures ${\mathit{T}}_{\mathit{N}}$'s were determined from the peak in \ensuremath{\partial}(\ensuremath{\chi}T)/\ensuremath{\partial}T. The variation of t=${\mathit{T}}_{\mathit{N}}$(p)/${\mathit{T}}_{\mathit{N}}$(1) vs p is compared with that of ${\mathrm{Co}}_{\mathit{p}}$${\mathrm{Mg}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$O. For both systems, the variations for pg0.31 are found to fit the predicted values for a simple-cubic Heisenberg antiferromagnet and a theoretical basis for this anomalous result is advanced. The experimental percolation threshold ${\mathit{p}}_{\mathit{c}}$=0.15\ifmmode\pm\else\textpm\fi{}0.01 and for ${\mathit{p}}_{\mathit{c}}$p0.31, \ensuremath{\chi} below ${\mathit{T}}_{\mathit{N}}$ shows irreversible behavior for the zero-field-cooled and field-cooled cases, suggestive of spin-glass-like behavior also observed in other diluted fcc antiferromagnets, such as ${\mathrm{Co}}_{\mathit{p}}$${\mathrm{Mg}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$O and ${\mathrm{Eu}}_{\mathit{p}}$${\mathrm{Sr}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$Te. It is suggested that the differences in the t-vs-p variations for p0.31 in ${\mathrm{Ni}}_{\mathit{p}}$${\mathrm{Mg}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$O, ${\mathrm{Co}}_{\mathit{p}}$${\mathrm{Mg}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$O, and ${\mathrm{Eu}}_{\mathit{p}}$${\mathrm{Sr}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$Te may be related to the differences in the ratio of the next-nearest-neighbor to nearest-neighbor exchange constants in these systems.