To formulate gravity in spacetimes bounded by a null boundary, an arbitrary hypothetical surface, boundary degrees of freedom (d.o.f) should be added to account for the d.o.f and dynamics spacetime regions excised behind boundary. In D dimensional example, are labelled charges defined at D-2 spacelike slices While modes can have their own dynamics, interaction with bulk is governed flux-balance...

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

In this paper, we show that an n-dimensional connected noncompact Ricci soliton isometrically immersed in the ‡at complex space form (C n+1 2 ; J; h; i), with potential vector …eld of the Ricci soliton is the characteristic vector …eld of the real hypersurface is an Einstein manifold. We classify connected Hopf hypersurfaces in the ‡at complex space form (C n+1 2 ; J; h; i) and also obtain a ch...

a reproducing kernel hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. in this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. the analytical solution is represented in the form of series in the reproducing kernel space. some numerical ...

urban green spaces are one of the most important services in modern cities and form a set of urban sustainable development factors which receive considerable attention from urban planners. this paper explains how land use can be optimally allocated to urban public green spaces. in this study, some of the factors influencing urban green spaces in a period from 1373 to 1384 were studied. moreover...