In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty 1 principle. They both express Fourier dualities within the space of tempered distributions and 2 these dualities are furthermore the inverses of one another. While Poisson’s summation 3 formula expresses a duality between discretization and periodization, Heisenberg’s 4 uncertainty principle expresses a duality be...

We extend a space-time duality suggested by Kogan for 2 + 1-dimensional static classical solutions of Einstein Maxwell Chern-Simons theories to stationary rotating space-times. We also extend the original duality to other possible dualities of the same kind that constitute a close duality web. In 3 + 1-dimensions these dualities are only possible for systems which exhibit non-projected cylindri...

We first reobtain in a simpler way the Haldane fractional statistics at thermal equilibrium using an interpolation argument. We then show that the mean occupation number for fractional statistics is invariant to a group of duality transformations, a nonabelian subgroup of fractional linear group.

By choosing modular ground state as the reference state, this paper finds that three most frequently-used distances and a quantum quasi-distance, i.e. trace distance, Fubini-Study Bures distance R\'{e}nyi relative entropy, all have gravity dualities. Their dualities two equivalent descriptions: one is given by integration of area cosmic brane, other Euclidian on-shell action dual theory brane. ...

We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved. These extend the familiar Isbell and de Vries d...

Discrete dualities are developed for n-potent MTL–algebras and for 2-potent BL–algebras. That is, classes of frames, or relational systems, are defined that serve as dual counterparts to these classes of algebras. The frames defined here are extensions of the frames that were developed for MTL– algebras in [25], [26]; the additional frame conditions required are given here and also the proofs t...