This paper is a contribution to harmonic analysis of compact solvmanifolds. We consider the four-dimensional oscillator group ${\rm Osc}_1$, which semi-direct product three-dimensional Heisenberg and real line. classify lattices Osc}_1$ up inner automorphisms Osc}_1$. For every lattice $L$ in we compute decomposition right regular representation on $L^2(L\backslash{\rm Osc}_1)$ into irreducible...

in this work, time domain analysis is used to solve adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked lc and ring oscillators considering their time-varying nature. then, the analysis is verified...

Considering a multi-dimensional q-oscillator invariant under the (non quantum) group U(n), we construct a q-deformed Levi-Civita epsilon tensor from the inner product states. The invariance of this q-epsilon tensor is shown to yield the quantum group SLq(n) and establishes the relationship of the U(n) invariant q-oscillator to quantum groups and quantum group related oscillators. Furthermore th...

single-valence electron atoms are an important class of atoms. their oscillator strengths are their important properties. knowing the oscillator strengths one can easity calculate the transition probabilities of the spectral lines and hence the lifetimes of energy levels of most atoms. the oscillator strengths of the spectral lines of most atoms are not knoen with sufficient accuracy due to the...