Plato is accused by some of being a totalitarian, “top-down” thinker, claim that linked not just to his politics but philosophical proclivities more generally. This essay will argue Plato’s method and metaphysics collectively provide few avenues for questioning this outcome. I think Socratic-style provides resistance hegemonic carapaced metaphysics, moreover would there greater coherence betwee...

Representations of SO(5) q are constructed explicitly on the Chevalley basis for all q, generic and root of unity. Matrix elements of the generators are obtained for all representations depending on three variable indices, the maximal number being 4. A prescription for contraction is given such that a complete Hopf algebra is immediately obtained for the non-semisimple contracted case. For q a ...

We propose a Leibniz algebra, to be called DD$^+$, which is generalization of the Drinfel'd double. find that there one-to-one correspondence between DD$^+$ and Jacobi--Lie bialgebra, extending known Lie bialgebra then construct generalized frame fields $E_A{}^M\in\text{O}(D,D)\times\mathbb{R}^+$ satisfying algebra $\mathcal{L}_{E_A}E_B = - X_{AB}{}^C\,E_C\,$, where $X_{AB}{}^C$ are structure c...

when studying jurisprudential sources of shafeism, one may see many times statements like ‘ghala fi al-qadim’ and ‘ghala fi al-jadid’ which make researchers wonder whether imam shafi,i has really established two schools of thought! this claim does not seem to be correct and even shafi,i scholars have noticed it and allocated their phd theses to examine and prove their views regarding this matte...

We consider best-reply dynamics for voting games in which all players are strategic and no coalitions are formed. We study the class of scoring rules, show convergence of a suitably restricted version for the plurality and veto rules, and failure of convergence for other rules including k-approval and Borda. In particular, for 3 candidates convergence fails for all rules other than plurality an...