in this note, by considering the notions of the intuitionistic general l-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{l}$, there exists a minimal intuitionistic general l-fuzzy automaton recognizing $mathcal{l}$.we prove that the minimal intuitionistic general l-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...

The antiferromagnetic $J_1-J_2$ model is a spin-1/2 chain with isotropic exchange $J_1 > 0$ between first neighbors and $J_2 = \alpha J_1$ second neighbors. supports both gapless quantum phases nondegenerate ground states gapped $\Delta(\alpha) doubly degenerate states. Exact thermodynamics limited to $\alpha 0$, the linear Heisenberg antiferromagnet (HAF). diagonalization of small systems at f...

In this article, the open problem of finding exact value norm Hilbert matrix operator on weighted Bergman spaces \(A^p_\alpha\) is adressed. The was conjectured to be \(\frac{\pi}{\sin \frac{(2+\alpha)\pi}{p}}\) by Karapetrovic. We obtain a complete solution conjecture for \(\alpha > 0\) and \(2+\alpha+\sqrt{\alpha^2+\frac{7}{2}\alpha+3} \le p < 2(2+\alpha)\) partial \(2+2\alpha 2+\alpha+\sqrt{...