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...

Cosmological observations suggest the existence of two different kinds of energy densities dominating at small (< ∼ 500 Mpc) and large (> ∼ 1000 Mpc) scales. The dark matter component, which dominates at small scales, contributes Ωm ≈ 0.35 and has an equation of state p = 0, while the dark energy component, which dominates at large scales, contributes ΩV ≈ 0.65 and has an equation of state p ≃ ...

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 ...

Existence and stability of stationary internal layered solutions to a rescaled diblock copolymer equation are studied in higher dimensional space. Rescaling is necessary since the characteristic domain size of any stable pattern eventually vanishes in an appropriate singular limit. A general sufficient condition for the existence of singularly perturbed solutions and the associated stability cr...

It is possible to place n points in d-space so that, given any two-coloring of the points, there exists a halfspace within which one color dominates the other by as much as cn 1=2d, for some constant c > 0. This result was proven in a slightly weaker form by Beck and the bound was later tightened by Alexander. It was shown to be quasi-optimal by Matou sek, Welzl, and Wernisch. The lower bound p...

Decision-DNNF is a strict subset of decomposable negation normal form (DNNF) that plays a key role in analyzing the complexity of model counters (the searches performed by these counters have their traces in Decision-DNNF). This paper presents a number of results on Decision-DNNF. First, we introduce a new notion of CNF width and provide an algorithm that compiles CNFs into Decision-DNNFs in ti...

Terpyridine-based ligands form octahedral complexes with Co(2+) at low cation concentrations to form helical assemblies which provide a supramolecular gel framework. Increasing the Co(2+) concentration above 0.6 equiv. reveals a second, co-existing square pyramidal complex derived assembly, having a distinct helicity. While this geometry dominates at 1 equiv. of Co(2+), we find this unique form...

This paper is concerned with estimation of a predictive density with parametric constraints under Kullback-Leibler loss. When an invariance structure is embedded in the problem, general and unified conditions for the minimaxity of the best equivariant predictive density estimator are derived. These conditions are applied to check minimaxity in various restricted parameter spaces in location and...