A bstract theory with a non-compact form-symmetry is described by two closed form fields of degrees k and d – . Effective examples are non-linear electrodynamics, photon field coupled to neutron field, low energy Goldstone boson. We show these models cannot be completed in the UV without breaking down compact one. This amounts existence electric or magnetic charges. an unbroken -form symmetry m...

today each city due to natural limitations, facilities and planning policies has different growth pattern which according to its spread, has different consequences and results. although there is a wide range of urban growth patterns, but the important thing is not diversity and number of models but is the absence of rules and methods of transition from one to another pattern (form). so this art...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.