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...

BACKGROUND Unbearable suffering is an important issue in end-of-life decisions. However, there has been no systematic, prospective, patient-oriented research which has focused on unbearable suffering, nor is there a suitable measurement instrument. This article describes the methodological development of a quantitative instrument to measure the nature and intensity of unbearable suffering, prac...

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{...