Foundations, Volume 1, Issue 2 (December 2021) – 12 articles

Miniaturized Fourier transform infrared spectrometers serve emerging market needs in many applications such as gas analysis. The miniaturization comes at the cost of lower performance than bench-top instrumentation, especially for the spectral resolution. However, higher spectral resolution is needed for better identification of the composition of materials. This article presents a convolutional neural network (CNN) for 3X resolution enhancement of the measured infrared gas spectra using a Fourier transform infrared (FTIR) spectrometer beyond the transform limit. The proposed network extracts a set of high-dimensional features from the input spectra and constructs high-resolution outputs by nonlinear mapping. The network is trained using synthetic transmission spectra of complex gas mixtures and simulated sensor non-idealities such as baseline drifts and non-uniform signal-to-noise ratio. Ten gases that are relevant to the natural and bio gas industry are considered whose mixtures suffer from overlapped features in the mid-infrared spectral range of 2000–4000 ${\mathrm{cm}}^{-1}$. The network results are presented for both synthetic and experimentally measured spectra using both bench-top and miniaturized MEMS spectrometers, improving the resolution from 60 ${\mathrm{cm}}^{-1}$ to 20 ${\mathrm{cm}}^{-1}$ with a mean square error down to $2.4\times {10}^{-3}$ in the transmission spectra. The technique supports selective spectral analysis based on miniaturized MEMS spectrometers. Full article

The existence of a parametric fractional integral equation and its numerical solution is a big challenge in the field of applied mathematics. For this purpose, we generalize a special type of fixed-point theorems. The intention of this work is to prove fixed-point theorems for the class of $\beta -$G, $\psi -$G contractible operators of Darbo type and demonstrate the usability of obtaining results for solvability of fractional integral equations satisfying some local conditions in Banach space. In this process, some recent results have been generalized. As an application, we establish a set of conditions for the existence of a class of fractional integrals taking the parametric Riemann–Liouville formula. Moreover, we introduce numerical solutions of the class by using the set of fixed points. Full article

In a dominance drawing $\Gamma$ of a directed acyclic graph (DAG) G, a vertex v is reachable from a vertex u if, and only if all the coordinates of v are greater than or equal to the coordinates of u in $\Gamma$. Dominance drawings of DAGs are very important in many areas of research. They combine the aspect of drawing a DAG on the grid with the fact that the transitive closure of the DAG is apparently obvious by the dominance relation between grid points associated with the vertices. The smallest number d for which a given DAG G has a d-dimensional dominance drawing is called dominance drawing dimension, and it is NP-hard to compute. In this paper, we present efficient algorithms for computing dominance drawings of G with a number of dimensions respecting theoretical bounds. We first describe a simple algorithm that shows how to compute a dominance drawing of G from its compressed transitive closure. Next, we describe a more complicated algorithm, which is based on the concept of modular decomposition of G, and obtaining dominance drawings with a lower number of dimensions. Finally, we consider the concept of weak dominance, a relaxed version of the dominance, and we discuss interesting experimental results. Full article

Measurements of cross-sections of charge exchange between hydrogen atoms and low energy protons (down to the energy ~10 eV) revealed a noticeable discrepancy with previous theories. The experimental cross-sections were systematically slightly higher—beyond the error margins—than the theoretical predictions. In the present paper, we study whether this discrepancy can be eliminated or at least reduced by using the Second Flavor of Hydrogen Atoms (SFHA) in calculations. We show that for the SFHA, the corresponding cross-section is noticeably larger than for the usual hydrogen atoms. We demonstrate that the allowance for the SFHA does bring the theoretical cross-sections in a noticeably better agreement with the corresponding experiments within the experimental error margins. This seems to constitute yet another evidence from atomic experiments that the SFHA is present within the mixture of hydrogen atoms. In combination with the first corresponding piece of evidence from the analysis of atomic experiments (concerning the distribution of the linear momentum in the ground state of hydrogen atoms), as well as with the astrophysical evidence from two different kinds of observations (the anomalous absorption of the redshifted 21 cm radio line from the early universe and the smoother distribution of dark matter than that predicted by the standard cosmology), the results of the present paper reinforce the status of the SFHA as the candidate for dark matter, or at least for a part of it. Full article

A non-uniform (skewed) mixture of probability density functions occurs in various disciplines. One needs a measure of similarity to the respective constituents and its bounds. We introduce a skewed Jensen–Fisher divergence based on relative Fisher information, and provide some bounds in terms of the skewed Jensen–Shannon divergence and of the variational distance. The defined measure coincides with the definition from the skewed Jensen–Shannon divergence via the de Bruijn identity. Our results follow from applying the logarithmic Sobolev inequality and Poincaré inequality. Full article

Neutron stars are the densest known objects in the universe and an ideal laboratory for the strange physics of super-condensed matter. Theoretical studies in connection with recent observational data of isolated neutron stars, as well as binary neutron stars systems, offer an excellent opportunity to provide robust solutions on the dense nuclear problem. In the present work, we review recent studies concerning the applications of various theoretical nuclear models on a few recent observations of binary neutron stars or neutron-star–black-hole systems. In particular, using a simple and well-established model, we parametrize the stiffness of the equation of state with the help of the speed of sound. Moreover, in comparison to the recent observations of two events by LIGO/VIRGO collaboration, GW170817 and GW190425, we suggest possible robust constraints. We also concentrate our theoretical study on the resent observation of a compact object with mass ∼$2.{59}_{-0.09}^{+0.08}{M}_{\odot }$ (GW190814 event), as a component of a system where the main companion was a black hole with mass ∼$23M_{\odot }$. There is scientific debate concerning the identification of the low mass component, as it falls into the neutron-star–black-hole mass gap. This is an important issue since understanding the nature of GW190814 event will offer rich information concerning the upper limit of the speed of sound in dense matter and the possible phase transition into other degrees of freedom. We systematically study the tidal deformability of a possible high-mass candidate existing as an individual star or as a component in a binary neutron star system. Finally, we provide some applications of equations of state of hot, dense nuclear matter in hot neutron stars (nonrotating and rapidly rotating with the Kepler frequency neutron stars), protoneutron stars, and binary neutron star merger remnants. Full article

The interpretation of optical spectra requires thorough comprehension of quantum mechanics, especially understanding the concept of angular momentum operators. Suppose now that a transformation from laboratory-fixed to molecule-attached coordinates, by invoking the correspondence principle, induces reversed angular momentum operator identities. However, the foundations of quantum mechanics and the mathematical implementation of specific symmetries assert that reversal of motion or time reversal includes complex conjugation as part of anti-unitary operation. Quantum theory contraindicates sign changes of the fundamental angular momentum algebra. Reversed angular momentum sign changes are of a heuristic nature and are actually not needed in analysis of diatomic spectra. This review addresses sustenance of usual angular momentum theory, including presentation of straightforward proofs leading to falsification of the occurrence of reversed angular momentum identities. This review also summarizes aspects of a consistent implementation of quantum mechanics for spectroscopy with selected diatomic molecules of interest in astrophysics and in engineering applications. Full article

The effect of atomic and molecular microfield dynamics on spectral line shapes is under consideration. This problem is treated in the framework of the Frequency Fluctuation Model (FFM). For the first time, the FFM is tested for the broadening of a spectral line by neutral particles. The usage of the FFM allows one to derive simple analytical expressions and perform fast calculations of the intensity profile. The obtained results are compared with Chen and Takeo’s theory (CT), which is in good agreement with experimental data. It is demonstrated that, for moderate values of temperature and density, the FFM successfully describes the effect of the microfield dynamics on a spectral line shape. Full article

The “line-by-line” method is used for the evaluation of thermal emission of the standard atmosphere toward the Earth. Accounting for thermodynamic equilibrium of the radiation field with air molecules and considering the atmosphere as a weakly nonuniform layer, we reduce the emission at a given frequency for this layer containing molecules of various types to that of a uniform layer, which is characterized by a certain radiative temperature $T_{\omega }$, an optical thickness $u_{\omega }$ and an opaque factor $g\left(u_{\omega }\right)$. Radiative parameters of molecules are taken from the HITRAN database, and an altitude of cloud location is taken from the energetic balance of the Earth. Within the framework of this model, we calculate the parameters of the greenhouse effect, including the partial radiative fluxes due to different greenhouse components in the frequency range up to 2600 cm${}^{-1}$. In addition, the derivations are determined from the radiative flux from the atmosphere to the Earth over the concentration logarithm of greenhouse components. From this, it follows that the observed rate of growth of the amount of atmospheric carbon dioxide accounts for a contribution of approximately $30\%$ to the observed increase in the global atmosphere during recent decades. If we assume that the basic part of the greenhouse effect is determined by an increase in the concentration $c\left(H_{2}O\right)$ of water atmospheric molecules, it is approximately $dlnc(H_{2}O/dt)=0.003$ yr${}^{-1}$. This corresponds to an increase in the average moisture of the atmosphere of 0.2%/yr. Full article

Nowadays, knowledge about the uses of medicinal plants is growing exponentially, and in order to conserve and valorize this knowledge, the European Union has set up multiple regulations to control their usage by the population. In this framework, this work is based on EU regulations to elaborate a new phytomedicine for intestinal comfort. The phytomedicine subject of elaboration is under the category of Traditional Use Herbal Medicine Products (TUHMPs), containing plants of approved medicinal use of at least 30 years, including 15 years in the European Union (Myrtus communis L. leaves (MC), Pimpinella anisum L. seeds (PA) and Carum carvi L. (CC) fruit). The EU pharmacopeia and monographs recognize the individual effect of each plant selected, and this work aims to study their combined effect using a mixture design. Acetic acid-induced writhing test in mice is used to study the efficacy of the mixture as pain relief and for intestinal comfort. According to the test result, the individual, binary and ternary combination were very effective compared to negative and positive control approving by that the synergy between the plants. Following the mixture design analysis, the best formulation was a ternary combination with different ratios (MC: 45%, PA: 52% and CC with 3%). The predicted formulation was studied after that and approved by the test result. This work provided a practical way to establish new phytomedicines within the EU and could be a model for new outcoming phytomedicine in the market. Full article

E.G. Bessonov suggested the time integrated strength of an electric field ${{\displaystyle \int }}_{-\infty }^{\infty }\mathit{E}\left(\mathit{r},t\right)dt={\mathit{S}}_{\mathit{E}}\left(\mathit{r}\right)$ as a parameter to classify electromagnetic (EM) waves. Since then, this parameter has been studied and used in many works on microwave and laser physics, especially when it comes to unipolar, bipolar and few cycle EM pulses. In this paper, it is shown that ${\mathit{S}}_{\mathit{E}}\left(\mathit{r}\right)=0$ is an identity for a wide class of free space pulses of finite total energy. This property can be useful in various applications of few cycle radiation and as a benchmark in EM and QED computations. Full article