In this work, with the help of the quantum hydrodynamic formalism, the gravitational equation associated with the classical Dirac field is derived. The hydrodynamic representation of the Dirac equation described by the evolution of four mass densities, subject to the theory-defined quantum potential, has been generalized to the curved space-time in the covariant form. Thence, the metric of space-time has been defined by imposing the minimum action principle. The derived gravity shows the spontaneous emergence of the “cosmological” gravity tensor (CGT), a generalization of the classical cosmological constant (CC), as a part of the energy-impulse tensor density (EITD). Even if the classical cosmological constant is set to zero, the CGT is non-zero, allowing a stable quantum vacuum (out of the collapsed branched polymer phase). The theory shows that in the classical macroscopic limit, the general relativity equation is recovered. In the perturbative approach, the CGT leads to a second-order correction to Newtonian gravity that takes contribution from the space where the mass is localized (and the space-time is curvilinear), while it tends to zero as the space-time approaches the flat vacuum, leading, as a means, to an overall cosmological constant that may possibly be compatible with the astronomical observations. The Dirac field gravity shows analogies with the modified Brans–Dicke gravity, where each spinor term brings an effective gravity constant G divided by its field squared. The work shows that in order to obtain the classical minimum action principle and the general relativity limit of the macroscopic classical scale, quantum decoherence is necessary. Full article

We construct polynomial dynamical systems $x^{\prime }=P\left(x\right)$ with symmetries present in the local phase portrait. This point of view on symmetry yields the approaches to ODEs construction being amenable to classical methods of the Spectral Analysis. Full article

In this paper, influential parameters on the hydraulic fracturing processes in porous media were investigated. Besides, the simultaneous stimulation of solids, fluids and fractures geomechanical equations were numerically analyzed as a developed 3D model. To do this, the Abacus software was used as a multi-objective program to solve the physical-mechanical symmetry law governing equations, according to the finite element method. Two different layers, A (3104–2984 m) and B (4216–4326 m), are considered in the model. According to the result of this study, the maximum fracture opening length in the connection of the wall surface is 10 and 9 mm for layer B and layer A, respectively. Moreover, the internal fracture fluid pressure for layer B and layer A is 65 and 53 Mpa. It is indicated that fracture fluid pressure reduced with the increase in fracture propagation length. Consequently, the results of this study would be of benefit for petroleum industries to consider several crucial geomechanical characteristics in hydraulic fractures simultaneously as a developed numerical model for different formation layers to compare a comprehensive analysis between each layer. Full article

Four-component relativistic atomic and molecular calculations are typically performed within the no-pair approximation where negative-energy solutions are discarded. These states are, however, needed in QED calculations, wherein, furthermore, charge conjugation symmetry, which connects electronic and positronic solutions, becomes an issue. In this work, we shall discuss the realization of charge conjugation symmetry of the Dirac equation in a central field within the finite basis approximation. Three schemes for basis set construction are considered: restricted, inverse, and dual kinetic balance. We find that charge conjugation symmetry can be realized within the restricted and inverse kinetic balance prescriptions, but only with a special form of basis functions that does not obey the right boundary conditions of the radial wavefunctions. The dual kinetic balance prescription is, on the other hand, compatible with charge conjugation symmetry without restricting the form of the radial basis functions. However, since charge conjugation relates solutions of opposite value of the quantum number $\kappa$ , this requires the use of basis sets chosen according to total angular momentum j rather than orbital angular momentum ℓ. As a special case, we consider the free-particle Dirac equation, where opposite energy solutions are related by charge conjugation symmetry. We show that there is additional symmetry in that solutions of the same value of $\kappa$ come in pairs of opposite energy. Full article

The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group G are governed by the well-known Wigner–Eckart relations. In the case of infinite-dimensional systems, with G spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases. Full article

In this note, we study the Ulam stability of a general functional equation in four variables. Since its particular case is a known equation characterizing the so-called bi-quadratic mappings (i.e., mappings which are quadratic in each of their both arguments), we get in consequence its stability, too. We deal with the stability of the considered functional equations not only in classical Banach spaces, but also in 2-Banach and complete non-Archimedean normed spaces. To obtain our outcomes, the direct method is applied. Full article

I consider two gamma-ray burst (GRB) correlations: Amati and Combo. After calibrating them in a cosmology-independent way by employing Beziér polynomials to approximate the Observational Hubble Dataset (OHD), I perform Markov Chain Monte Carlo (MCMC) simulations within the $\mathsf{\Lambda }$ CDM and the wCDM models. The results from the Amati GRB dataset do not agree with the standard $\mathsf{\Lambda }$ CDM model at a confidence level $\ge 3$ – $\sigma$ . For the Combo correlation, all MCMC simulations give best-fit parameters which are consistent within 1– $\sigma$ with the $\mathsf{\Lambda }$ CDM model. Pending the clarification of whether the diversity of these results is statistical, due to the difference in the dataset sizes, or astrophysical, implying the search for the most suited correlation for cosmological analyses, future investigations require larger datasets to increase the predictive power of both correlations and enable more refined analyses on the possible non-zero curvature of the Universe and the dark energy equation of state and evolution. Full article

For the first time, the paper considers in a unified work the possibility of the appearance of additional pulses in various structures based on modal filtration technology, which is used to improve protection against ultrashort pulses (USP). We analyzed meander lines (ML) with broad-side coupling, structures with modal reservation (MR), reflection symmetric MLs, and modal filters (MF) with a passive conductor in the reference plane cutout and obtained the following results. It was found that the main reason for the additional pulses to appear in these structures is the introduction of asymmetry (of the cross-section, boundary conditions, and excitation). It is theoretically and experimentally established that additional pulses are a new resource for increasing the efficiency of protective devices with modal decomposition, but the highest effectiveness could be achieved through careful optimization. Full article

In this paper, we study the problem of monocular 3D human pose estimation based on deep learning. Due to single view limitations, the monocular human pose estimation cannot avoid the inherent occlusion problem. The common methods use the multi-view based 3D pose estimation method to solve this problem. However, single-view images cannot be used directly in multi-view methods, which greatly limits practical applications. To address the above-mentioned issues, we propose a novel end-to-end 3D pose estimation network for monocular 3D human pose estimation. First, we propose a multi-view pose generator to predict multi-view 2D poses from the 2D poses in a single view. Secondly, we propose a simple but effective data augmentation method for generating multi-view 2D pose annotations, on account of the existing datasets (e.g., Human3.6M, etc.) not containing a large number of 2D pose annotations in different views. Thirdly, we employ graph convolutional network to infer a 3D pose from multi-view 2D poses. From experiments conducted on public datasets, the results have verified the effectiveness of our method. Furthermore, the ablation studies show that our method improved the performance of existing 3D pose estimation networks. Full article

The infectious disease COVID-19 has swept across the world in 2020, and it continues to cause massive losses of life and severe economic problems in all countries. Providing emergency supplies such as protective medical equipment and materials required to secure people’s livelihood is thus currently prioritized by governments. Establishing a reliable emergency logistics system is critical in this regard. This paper used the Delphi method to design a formal decision structure to assess emergency logistics system reliability (ELSR) by obtaining a consensus from a panel of experts. Assessing ELSR is a typical multiple-attribute decision making (MADM) problem, and the related MADM methods are usually on the basis of symmetry principles. A hybrid MADM model, called the Decision Making Trial and Evaluation Laboratory (DEMATEL)-based Analytical Network Process (D-ANP), was developed to identify the critical factors influencing ELSR. An analysis of empirical evidence showed that the emergency logistics command and coordination system and the emergency material supply system play important roles in ELSR, while the emergency logistics transportation and distribution system and the emergency information system are not so important. This conclusion is different from previous research about traditional disaster emergency logistics. Moreover, the cause–effect relationships among the key factors indicated that the system of command and coordination for emergency logistics and the supply system for emergency materials should be improved. Accordingly, effective suggestions for emergency logistics services for epidemic prevention are provided in this paper. The main contributions of this paper are (1) establishing a comprehensive and systematic evaluating index of ELSR for epidemic prevention; (2) employing a kind of structured, namely D-ANP, to identify the critical factors with non-commensurable and conflicting (competing) characteristics; and (3) comparing the differences of reliable criteria between the emergency logistics of epidemic prevention and the traditional disaster emergency logistics. Full article

We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, K-matrix approach, Inverse Amplitude Method, Padé approximants and the $N/D$ method. More details are given for the latter though. We also consider how to implement them in order to correct by final-state interactions. In connection with this some other methods are also introduced like the expansion of the inverse of the form factor, the Omnés solution, generalization to coupled channels and the Khuri-Treiman formalism, among others. Full article

Large Scale Wireless Sensor Networks (LS-WSNs) are Wireless Sensor Networks (WSNs) composed of an impressive number of sensors, with inherent detection and processing capabilities, to be deployed over large areas of interest. The deployment of a very large number of diverse or similar sensors is certainly a common practice that aims to overcome frequent sensor failures and avoid any human intervention to replace them or recharge their batteries, to ensure the reliability of the network. However, in practice, the complexity of LS-WSNs pose significant challenges to ensuring quality communications in terms of symmetry of radio links and maximizing network life. In recent years, most of the proposed LS-WSN deployment techniques aim either to maximize network connectivity, increase coverage of the area of interest or, of course, extend network life. Few studies have considered the choice of a good LS-WSN deployment strategy as a solution for both connectivity and energy consumption efficiency. In this paper, we designed a LS-WSN as a tool for collecting big data generated by smart cities. The intrinsic characteristics of big data require the use of heterogeneous sensors. Furthermore, in order to build a heterogeneous LS-WSN, our scientific contributions include a model of quantifying the kinds of sensors in the network and the multi-level architecture for LS-WSN deployment, which relies on clustering for the big data collection. The results simulations show that our proposed LS-WSN architecture is better than some well known WSN protocols in the literature including Low Energy Adaptive Clustering Hierarchy (LEACH), E-LEACH, SEP, DEEC, EECDA, DSCHE and BEENISH. Full article

This manuscript is concerned with the oscillatory properties of 4th-order differential equations with variable coefficients. The main aim of this paper is the combination of the following three techniques used: the comparison method, Riccati technique and integral averaging technique. Two examples are given for applying the criteria. Full article

Along with the fourth industrial revolution, the use of unmanned aerial vehicles (UAV) has grown very rapidly over the past decade. With this rapid growth, studies using UAVs are underway in various areas. UAVs are more economical and effective when utilizing several nodes rather than operating a single aircraft. In general, UAVs collect and transmit information to the control center (CC), and act on control commands from the CC. Communication between UAVs and the control center is usually achieved using modules such as radio frequency (RF), Bluetooth, Wireless Fidelity (Wi-Fi) and cellular. However, when multiple UAVs communicate directly with the CC, the limitations of communication technologies and problems with increasing nodes occur. To address these points, several studies have constructed an ad-hoc network of UAVs to address the limitations of Wi-Fi and Bluetooth communication range, or the high cost of cellular systems. However, previous studies have constructed fixed topology ad-hoc networks. These studies did not take into account the problem of changing network topology due to the rapid mobility and frequent formation changes of UAVs. Due to this, limits occurred such that UAVs moved only in the pre-built topology. In this paper, we propose a dynamic topology construction protocol for UAV swarms to address this problem. The main contents of this paper are as follows. We first look at the research and limitations of existing UAV communications, and propose a protocol to solve this problem. This paper proposes a protocol for UAV construction of ad-hoc networks when trying to perform missions using multiple UAVs, and also describes how the changed network topology is reconstructed when network topology changes due to changes in flight formation. Finally, we establish a situation and apply the proposed protocol, analyze the results and describe further required research. Full article

The aim of this work is to study a scalar-tensor theory where owing to Palatini’s variational method the space-time is endowed with a geometrical structure of Weyl integrable type. The geometrical nature of the scalar field is related to the non-metricity so that the theory is known as geometrical scalar-tensor. On the framework of Weyl transformations, a non-minimally coupled scalar-tensor theory on the Jordan frame corresponds to a minimally coupled Einstein–Hilbert action on the Einstein frame. The scalar potential is selected by the Noether symmetry approach in order to obtain conserved quantities for the FRW cosmological model. Exact solutions are obtained and analyzed in the context of the cosmological scenarios consistent with an expanding universe. A particular case is matched in each frame and the role of scalar field as a dark energy component is discussed. Full article