In a difference or differential equation one is usually interested in finding solutions having certain properties, either intrinsic properties (e.g. bounded, periodic, almost periodic) or extrinsic properties (e.g. stable, asymptotically stable, globally asymptotically stable). In certain instances it may happen that the dependence of these equations on the state variable is such that one may (...

The purpose of this paper is to provide the new demicloseness principle– τ (weakly) demicloseness principle. We prove that if X is a Banach space with locally uniformly τ -Opial condition, where τ is a Hausdorff topology on X, C is a nonempty τ compact subset of X, and T : C → C is a asymptotically nonexpansive type mapping. If {xα} is a net in C which converges to x in the sense of τ topology ...

Hawking radiation remains a crucial theoretical prediction of semi-classical gravity and is considered one the critical tests for model quantum gravity. However, Hawking’s original derivation used field theory on fixed background. Efforts have been made to include space–time fluctuations arising from quantization dynamical degrees freedom itself study effects particles. Using analysis, we scala...

We show that delaying fully-expansive proof reconstruction for non-interactive decision procedures can result in a more efficient workflow. In contrast with earlier work, our approach to postponed proof does not require making deep changes to the theorem prover.

Certain non-asymptotically flat but supersymmetric classical solution of the type IIA supergravity can be interpreted as the infinitely-boosted version of the D-particle solution along the M-theory circle. By a chain of T -dual transformations, this analysis also applies to yield non-asymptotically flat solutions from the asymptotically flat and (non)-extremal solutions with intersecting D-stri...

As cities cope with rapid population growth—adding 2.5 billion dwellers by 2050—and grapple with expansive sprawl, politicians, planners, and architects have become increasingly interested in the vertical city paradigm. This paper reviews and examines shortfalls of tall buildings found in the literature to inform future developments. The paper gathers a vast amount of fragmented criticism and c...