We analyze different approaches to Quantum Gravity. It is stressed that nonperturbative methods to quantise Gravity and the usage of diffeomorphism-invariant variables are very important. We pay attention on the Wheeler--DeWitt equation in the framework of canonical Quantum Gravity. The Wheeler--DeWitt equation is presented in the first order formalism with the hope that this form can solve some problems such as singularities and the ordering. Also, there is a problem of defining the time.

We elaborate on some recent results on a solution of the Hilbert-space problem in minisuperspace Quantum cosmology and discuss the consequences of making the (geometry of the) Hilbert space of ordinary no relativistic Quantum systems time-dependent. The latter reveals a remarkable similarity between Quantum Mechanics and General Relativity.

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.

The modification of laws of physics at short intervals is an important result of the theory of Quantum Gravity. For instance, commutative relations of standard Quantum mechanics change on scales of length-called Planck length. It should be noted that these changes can be neglected at low energy levels but they are considerable only at high energy levels such as the initial universe. In this regard, the principle of uncertainty of standard Quantum mechanics is changed with modified relations of uncertainty including a visible minimum of Planck order. Early moments of the universe, which included the inflation period, was a period with noticeable effects of Quantum Gravity due to the high energy level, and as such, the effects can be studied during this period. To do this, characteristics of the inflation period can be examined according to initial parameters of the universe such as the initial fluctuations in the formation of the universe structure and the spectral index. On the other hand, vector cosmology models have been taken into consideration by researchers. These models include an action in which a vector field (in addition to the scalar field) is included to investigate effects of violation of the Lorentz invariance in observations. The present paper investigated effects of Quantum Gravity (with effects on non-commutative geometry and generalization of the uncertainty principle) on parameters of a vector cosmological model. The vector model was used as this scenario had acceptable adaptation to parameters of cosmology after inflation (e. g. the transition from the Phantom boundary, etc. ) (Nozari and Sadatian, 2009). Furthermore, the present study could test this vector model for determining parameters of the inflation period based on effects of Quantum Gravity. According to calculations in the present paper, we concluded that, first: the density of scalar perturbations decreased in the vector model based on effects of Quantum Gravity (the reduction of standard model was more considerable), and second: due to the ignorance of effects Quantum Gravity, the scalar spectral index parameter remained invariant as observations indicate, but due to large enough gravitational effects (depending on amount of β), the spectral index parameter is not maintained its invariance scale. According to obtained modification in the present study, the Quantum Gravity can be tested for the density of scalar perturbation (which can be measured by observing the spectrum of cosmic microwave background radiation). In order to compare our results with other studies, we can refer to (Zhu et al, 2014) where they examined the spectral index in accordance with high-order correction mechanism. It also indicated that a single asymmetric approximation does not lead to a considerable error value for the spectral index, and the invariance scale is maintained. Furthermore, the paper (Hamber and Sunny Yu, 2019) found the same results for invariance scale of the spectral index according to the Wilson normalization analysis method. Therefore there was no need to have common assumptions in the inflation period. Finally, it should be noted that despite a great number of studies on effects of Quantum Gravity, the reviewed model of this paper considers a state in which the effects can be investigated at all stages of the universe evolution from inflation till now.

Gravitons and axions play an important role with regards to dark matter. Here, by appeal to developments of Gupta and Feynman and using a novel mathematical theory based on Ultrahyperfunctions [1] , we are able to provide an exact, Quantum relativistic expression for the gravitons and axions self-energies. For a complete explanation of Ultrahyperfunctions and their uses in Quantum Field Theory see [2]. Ultrahyperfunctions (UHF) are in the most cases the generalization and extension to the complex plane of Schwartz ’tempered distributions. For example, in our book [2] and in the references [3, 4, 5, 6] you can find a large number of examples of Ultrahyperfunctions. This manuscript is an application to Einstein’s Gravity and Dark Matter (EG) of the mathematical theory developed by Bollini et al [3, 4, 5, 6] and continued for more than 25 years by one of the authors of this paper. We will quantize EG using the most general quantization approach, the Schwinger-Feynman variational principle [15], which is more appropriate and rigorous than the popular functional integral method (FIM). FIM is not applicable here because our Lagrangian contains derivative couplings. We use the Einstein Lagrangian as obtained by Gupta [16, 17, 18], but we added a new constraint to the theory. Thus the problem of lack of unitarity for the S matrix that appears in the procedures of Gupta and Feynman disappear Furthermore, we considerably simplify the handling of constraints, eliminating the need to appeal to ghosts for guarantying unitarity of the theory. Our theory is obviously non-renormalizable. However, this inconvenience is solved by resorting to the theory developed by Bollini et al. [3, 4, 5, 6] This theory is based on the thesis of Alexander Grothendieck [19] and on the theory of Ultrahyperfunctions Based on these papers, a complete theory has been constructed for 25 years that is able to quantize non-renormalizable Field Theories (FT).Because we are using a Gupta-Feynman based EG Lagrangian and to the new mathematical theory we have avoided the use of ghosts, as we have already mentioned, to obtain a unitary QFT of EG Moreover the self-energy of the graviton changes its mass and propagator upon interaction with the axion. The mass of the graviton can increase and the bare propagator changes to the dressed propagator. This phenomenon is measurable, but very difficult to detect since the bare mass of the graviton is zero and that of the axion is extremely small. Also, for the first time in the literature, we give explicit formulas for the self-energy of the graviton, interacting and non-interacting with axions. Also, for the first time in the literature, we present 17 graphs corresponding to those self-energies.

Currently, carbon Quantum dots have attracted considerable attention due to their unique properties and desirable advantages. High crystallinity, water solubility, good dispersibility, small size, low toxicity, inexpensive raw materials, high chemical stability, environmental compatibility, low cost, stability under light, desirable charge transfer with advanced electronic conductivity, as well as specific thermal and mechanical properties are some of these features. Carbon Quantum dots have various applications in different fields. Fabrication of precise chemical and biological sensors, bioimaging, solar cells, drug tracking, nanomedicine, light-emitting diodes (LEDs), and electrocatalysts are some of these applications. Biological sensors based on carbon Quantum dots are capable of detecting various metal ions, acids, proteins, biotin, polypeptides, DNA and miRNA, water pollutants, hematin, drugs, vitamins, and other chemicals. In the present study, the properties of carbon Quantum dots and some of their fabrication and applications methods have been addressed. In continuation of the paper, the effect of carbon Quantum dots on important factors in plants such as growth and development, photosynthesis, absorption and transportation of substances, resistance to biotic and abiotic stresses, as well as their application in agriculture has been investigated.

Progressive collapse studies generally assess the performance of the structure under Gravity and blast loads, while earthquakes may also lead to the progressive collapse of a damaged structure. In this study, the progressive collapse response of concentrically braced dual systems with steel moment-resisting frames was assessed under seismic loads through pushover analysis using triangular and uniform lateral load patterns. Two different bracing types (X and inverted V braces) were considered, and their performances were compared under different lateral load patterns using the nonlinear static alternate path method recommended in the Unified Facilities Criteria (UFC) guideline. Eventually, the seismic progressive collapse resistance of models was compared to their progressive collapse response under Gravity loads. These studies showed that models under the seismic progressive collapse loads satisfied UFC acceptance criteria and limited rehabilitation objective. The structures had better performance under seismic progressive collapse than models under Gravity loads because of more resistance, ductility, suitable load redistribution, and more structural elements that participated in load redistribution. Furthermore, despite studies on progressive collapse under Gravity loads, the dual system with X braces showed better progressive collapse performance (more resistance, residual reserve strength ratio and ductility) under seismic loads than the model with inverted V braces.

A great deal of attention has been paid to quantitative interpretation in recent years Two methods, namely the analytic signal an4 the Euler deconvolution (EULDPH) were discussed in this paper. After a short review on the mathematical bases of the methods. two field examples were used to examine the efficiency and limits of the methods when they are applied on a complex geology structure. These methods have already been applied to synthetic models and high - resolution data such as gradiometeric or microGravity data. Noisy Gravity data especially in areas of complex geology has rarely been used by these methods and the field examples are exceptions. The low- resolution Gravity data was used to provide with residual anomalies. Gravity gradients were generated ftom the residual anomaly values. Then applying the Gravity gradients to the analytic signal and EULDPH methods. we determine the coordinates of a perturbing body in the field of data. Two field examples, one in the west of Tehran (Mardabad) and another in the southwest of Iran are considered. In the first field we were to determine the location of a hydrocarbon density anomaly. In the second field, we were to determine a Choromit anomaly.

Gravity and its usage in Gravity interpretation is still a challenging field. It is not easy to compute these gradients especially in the case of noisy data. Analytical signal is one of the new methods that uses Gravity gradients to locate the perturbing body. This method had already been used for high-resolution magnetic and Gravity data and rarely used for low-quality Gravity data. The Gravity gradients and analytical signal have been applied in two different areas, Zahedan where we are looking for Choromite anomalies and Tehran (Mard Abad) where we are investigating for low density anomaly, Probably hydrocarbon.