In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

In this paper, notions of L-topological derived internal relation space, interior operator enclosed space and closure are introduced. It is proved that all these spaces categorically isomorphic to space.

At a fixed point in spacetime (say, x0), gravitational phase space consists of the space of symmetric matrices {F ab} [corresponding to the canonical momentum π(x0)] and of symmetric matrices {Gab} [corresponding to the canonical metric gab(x0)], where 1 ≤ a, b ≤ n, and, crucially, the matrix {Gab} is necessarily positive definite, i.e. ∑ uGabu b > 0 whenever ∑ (ua)2 > 0. In an alternative quan...

Quantization of the Field This involves two main steps • make basic observables into operators, obeying canonical commutation relations (CCRs) • look for Hilbert space representations for these operators. Strategy: “put the field in a box” = pretend that the space is a torus = impose periodic boundary conditions of size L. The motivation for this is to get a discrete spectrum then to play with ...

We present the observed relation between ∆TSZ, the cosmic microwave background (CMB) temperature decrement due to the Sunyaev-Zeldovich (SZ) effect, and L, the X-ray luminosity of galaxy clusters. We discuss this relation in terms of the cluster properties, and show that the slope of the observed ∆TSZ−L relation is in agreement with both the L − Te relation based on numerical simulations and X-...

At a fixed point in spacetime (say, x0), gravitational phase space consists of the space of symmetric matrices {F ab} [corresponding to the canonical momentum π(x0)] and of symmetric matrices {Gab} [corresponding to the canonical metric gab(x0)], where 1 ≤ a, b ≤ n, and, crucially, the matrix {Gab} is necessarily positive definite, i.e. ∑ uGabu b > 0 whenever ∑ (ua)2 > 0. In an alternative quan...

The Cepheid period-luminosity (P-L) relation is regarded as a linear relation (in log[P]) for a wide period range from ∼ 2 to ∼ 100 days. However, several recent controversial works have suggested that the P-L relation derived from the Large Magellanic Cloud (LMC) Cepheids exhibits a non-linear feature with a break period around 10 days. Here we review the evidence for linear/non-linear P-L rel...