The modulus method introduced by H. Grötzsch yields bounds for a mean distortion functional of quasiconformal maps between two annuli mapping the respective boundary components onto each other. P. P. Belinskĭı studied these inequalities in the plane and identified the family of all minimisers. Beyond the Euclidean framework, a Grötzsch–Belinskĭı-type inequality has been previously considered fo...

Phase diagram of the spin-1 quantum Heisenberg model with both exchange as well as single-ion anisotropy is constructed within the framework of pair approximation formulated as a variational procedure based on the Gibbs-Bogoliubov inequality. In this form adapted variational approach is used to obtain the results equivalent with the Oguchi’s pair approximation. It is shown that the single-ion a...

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...

The quadratic-phase Fourier transform (QPFT) has gained much popularity in recent years because of its applications image and signal processing. However, the QPFT is inadequate for localizing spectrum, which required some applications. In this paper, wave packet (QP-WPT) proposed to address problem, based on (WPT) QPFT. Firstly, we propose definition QP-WPT give relation with windowed (WFT). Se...

Entanglement calculations have received renewed interest with the advances observed in field of quantum computing. Alternative methods to calculate entanglement that can be applied broader classes problems become increasingly necessary. In this letter, we show measure using generalized Bell inequality and distance between states coincide when use Hilbert–Schmidt norm. Our conclusions apply spin...

We establish Hardy inequalities involving a weight function on complete, not necessarily reversible Finsler manifolds. prove that the superharmonicity of provides sufficient condition to obtain inequalities. Namely, if $$\rho $$ is nonnegative and $$-\varvec{\Delta } \rho \ge 0$$ in weak sense, where $$\varvec{\Delta }$$ Finsler–Laplace operator defined by \varvec{\Delta = \mathrm {div}(\varvec...