We argue that the flat spacetime with inexact quantum mechanics in it is dual to the de Sitter spacetime with exact quantum mechanics in it, and the positive cosmological constant of this de Sitter spacetime is in the second order of the degree of the violation of the bulk quantum mechanics in the flat spacetime. The flat spacetime is holographic and has a dual time-contracted boundary conformal field theory with two redefined central charges at null infinity. The vanishing smallness of the observed positive cosmological constant suggests the extraordinary exactness of the bulk quantum mechanics in the flat spacetime.

The g-factor of the charged leptons has always been considered by many physicists, both experimentaly as well as theoretically. In fact the electron and muon g-factor play the main role in testing the QED as well as the standard model. Meanwhile, there is a discrepancy between the standard model prediction of the muon anomalies magnetic moment and its experimental determination as large as (25.5±8.0) ×10-10.Therefore the g-factor can be used as the best place to study the new physics beyond the standard model. In this article, we consider the g-factor of the lepton in the noncommutative space time as a new physics model. In the ordinary theory, Schwinger evaluated the first correction to the g-factor of free electron, which arises from the electron interaction with photon at one loop level in the QED. In noncommutative space time, we show that at one loop, there is an NC-contribution to the g-factor of leptons which leads to a new bound on the noncommutative parameter (NC parameter). The obtained bounds are comparable with the current bounds on the NC-parameters of the order TeV.

Topological order is a new type order that beyond Landau's symmetry breaking theory. It has some interesting properties, such as producing quasi-particles with fractional quantum numbers and fractional/Fermi statistics, robust gapless boundary modes and emergent gauge excitations. In this essay, we will show that the quantum gravity in AdS3 spacetime can also have topological orders. Actually the theory has all the three features that define the topological order. We conjecture that quantum gravity in four dimension can also have topological orders.

Recently, some techniques such as adding whiskers and attaching graphs to vertices of a given graph, have been proposed for constructing a new VERTEX decomposable graph. In this paper, we present a new method for constructing VERTEX decomposable graphs. Then we use this construction to generalize the result due to Cook and Nagel.

The conflict between the Newtonian and the Leibnizian picture of spacetime is well-known and widely discussed in the literature. However, two competing metaphysical pictures of spacetime have not been addressed so far: The Newtonian and the Lagrangian pictures. According to the Newtonian picture, spacetime can be considered as the time evolution of a spatial hypersurface. According to the Lagrangian picture, spacetime is a unified whole that can be examined in an all-at-once manner, and its (temporal) evolution is not meaningful, except locally or quasi-locally. Although the Newtonian picture has been the dominant metaphysical picture since Newton's time, our explicit familiarity with these two competing pictures is recent. It is rooted in Smolin's criticism of modern cosmology and Wharton's research on the foundations of quantum mechanics. Here, we describe the views of Smolin and Wharton, then we will argue that two famous formulations of general relativity, namely the Hamiltonian formulation and the Lagrangian formulation, require the Newtonian and the Lagrangian picture, respectively. Also, we will argue that: (1) the Lagrangian picture is more compatible with the philosophy of relativity theory than the Newtonian picture, while the Newtonian picture is only acceptable for practical and computational purposes. And, (2) the Lagrangian picture is universal and applicable to any spacetime, while the Newtonian picture can only be used for certain spacetimes. Therefore, the Lagrangian picture is a more plausible metaphysical picture than the Newtonian.

Let $G$ be a simple graph with VERTEX set $V=V(G)$ and edge set $E=E(G)$. For a real function $f$ defined on nonnegative real numbers, the VERTEX-degree function index $H_{f}(G)$ is defined as $$H_{f}(G)=\sum_{u\in V(G)}f(d_{u}).$$ In this paper we introduce the VERTEX-degree function index $H_{f}(D)$ of a digraph $D$. After giving some examples and basic properties of $H_{f}(D)$, we find the extremal values of $H_{f}$ among all tournaments with a fixed number of vertices, when $f$ is a continuous and convex (or concave) real function on $\left[ 0,+\infty \right)$.

The VERTEX version of PI index is a molecular structure descriptor which is similar to VERTEX version of Szeged index. In this paper, we compute the VERTEX-PI index of TUC4C8(S), TUC4C8(R) and HAC5C7[r, p].