We consider holomorphic BF theories, their solutions and symmetries. The equivalence ofČech and Dolbeault descriptions of holomorphic bundles is used to develop a method for calculating hidden (nonlocal) symmetries of holomorphic BF theories. A special cohomological symmetry group and its action on the solution space are described.

The following article investigates buckling of moderately thick circular Nano plates with an orthotropic property under uniform radial compressive in-plane mechanical load. Taking into account nonlocal elasticity theory (Eringen), principle of virtual work, first order shear deformation plate theory (FSDT) and nonlinear Von-Karman strains, the governing equations are obtained based on displacem...

We describe constructing solutions of the field equations of Chern-Simons and topological BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations) are considered. A method of calculating (nonlocal) dressing symmetries in Chern-Simons and topological BF theories is formulated.

We prove in two ways that, for a special class of nonlocal field theories consistent with linear and non-linear stability at the classical level, unitarity super-renormalizability or finiteness quantum $n$-point tree-level scattering amplitudes are same as those underlying local theory. In particular, gravity, without coupling to matter, Einstein's general relativity.

Based on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are considered based on Gurtin-Murdoch continuum theory. Using Von Karman geometric nonlinearity, governing equations are derived bas...

Puff field theory (PFT) is a low energy decoupling regime of string theory that still retains the nonlocal attributes of the parent theory—while preserving isotropy for its nonlocal degrees of freedom. It realizes an extended holographic dictionary at strong coupling and dynamical nonlocal states akin to defects or the surface operators of local gauge theories. In this work, we probe the nonloc...

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...