Foundations doi: 10.3390/foundations2020031

Authors: Juan Núñez Valdés Fernando de Pablos Pons Antonio Ramos Carrillo

At present, several countries on the Asian continent are still very closed off to the idea of allowing not only the work of women, but also even the fact that they can study university degrees and, after finishing them, go on to practice their professions. In addition, if we go back to the beginning of the 20th century, this situation was even more serious. However, this was not an impediment for some women from these countries to achieve their goals of pursuing higher education and then serving society with their work. This article is dedicated to showing the biographies of three of them, the Indian chemist Asima Chatterjee and Philippine pharmacists Matilde S. Arquiza and Filomena Francisco. The most relevant features of their personal and professional lives are presented and previous biographies about them are completed. The main objective of this work is to show these figures to society and hold them up as references to other people, and the methodology followed has been the search for data about their lives and work that would allow us to complete the previous existing biographies about them. A brief biography on Janaki Ammal, the first Indian woman to obtain a doctorate, is also included.

]]>Foundations doi: 10.3390/foundations2020030

Authors: Miguel Á. Hernández-Verón Natalia Romero

In this work, we focus on analyzing the location and separation of the solutions of the simplest quadratic matrix equation. For this, we use the qualitative properties that we can deduce of the study of the convergence of iterative processes. This study allow us to determine domains of existence and uniqueness of solutions, and therefore to locate and separate the solutions. Another goal is to approximate a solution of the quadratic matrix equation. For this, we consider iterative processes of fixed point type. So, analyzing the convergence of these iterative processes of fixed point type, we locate, separate and approximate solutions of quadratic matrix equations.

]]>Foundations doi: 10.3390/foundations2020029

Authors: Juan Núñez Valdés Fernando de Pablos Pons Antonio Ramos Carrillo

Gertrude Belle Elion was a woman who had to overcome many difficulties to achieve her dream of studying to be able to cure illnesses, especially those of the heart. These difficulties were imposed both by the limited economic resources of herself and her family, which did not allow her to pay the academic fees of the university in which she wanted to enroll, as well as gender, since she also had to fight against inequalities of that type prevalent in the society of her time. However, and despite these obstacles, she managed to graduate in Chemistry, based on interest, effort and tenacity, and later began a research career full of successes, which led her to discover relevant active substances which allow her to be awarded the Nobel Prize in Physiology or Medicine in 1988. This article presents the most relevant features of her personal and professional life and completes previous biographies about her life. Its main objective is to reintroduce her to society and put her as a reference to other people. The methodology followed has been the search for those data about her life and work that would allow completing the previous existing biographies about her.

]]>Foundations doi: 10.3390/foundations2020028

Authors: Emilio Santos

We characterize the electromagnetic vacuum as a stochastic field. Some consequences, like the particle behaviour of light, are studied. The stochastic approach is connected with the standard Hilbert space formalism via the Weyl transform. Several experiments involving spontaneous parametric down conversion are studied comparing Hilbert space and Weyl&ndash;Wigner formalisms. This allows an intuitive picture of entanglement to be obtained as a correlation between field fluctuations in distant places, involving the vacuum fields. The analysis shows that the Bell definition of local realism is not general enough, whence the reported violation of Bell inequalities does not refute local realism.

]]>Foundations doi: 10.3390/foundations2020027

Authors: Carla Pires

Background: Lack of access to patients&rsquo; digital health records by community pharmacists can negatively impact pharmaceutical care. Access to these records by community pharmacists is only available in some countries. Thus, the study aim was to compare and discuss the shared patients&rsquo; health records between the National Health Systems and Community Pharmacies in UK and Australia. Methods: Two platforms were selected: Summary Care Records (SCR) (UK) and My Health Record (MyHR) (Australia). A qualitative and descriptive study was carried out. The type of shared health records was collected in public/official websites. Qualitative classifiers/descriptors were created to classify the shared health records. Results: The common classifiers/descriptors between both SCR and MyHR were medicines, medicines/immunization, and medical history. However, MyHR seems to comprise more details/information, such as patient&rsquo;s discharge summaries, specialist letters, or documents to communicate significant patient information from one healthcare provider to another. Conclusion: Community pharmacists can update or consult SCR and MyHR to provide direct patient care in UK and Australia, respectively. The profile of shared health records with community pharmacies was not equal between SCR (UK) and MyHR (Australia). More studies are recommended to evaluate the benefits and risks of using these platforms on patients&rsquo; outcomes.

]]>Foundations doi: 10.3390/foundations2020026

Authors: Sotiris Ntouyas Bashir Ahmad Jessada Tariboon

In this paper, we establish existence and uniqueness results for a new class of boundary value problems involving the ψ-Hilfer generalized proportional fractional derivative operator, supplemented with mixed nonlocal boundary conditions including multipoint, fractional integral multiorder and derivative multiorder operators. The given problem is first converted into an equivalent fixed point problem, which is then solved by means of the standard fixed point theorems. The Banach contraction mapping principle is used to establish the existence of a unique solution, while the Krasnosel’skiĭ and Schaefer fixed point theorems as well as the Leray–Schauder nonlinear alternative are applied for obtaining the existence results. We also discuss the multivalued analogue of the problem at hand. The existence results for convex- and nonconvex-valued multifunctions are respectively proved by means of the Leray–Schauder nonlinear alternative for multivalued maps and Covitz–Nadler’s fixed point theorem for contractive multivalued maps. Numerical examples illustrating the obtained results are also presented.

]]>Foundations doi: 10.3390/foundations2020025

Authors: Frank Nielsen

The informational energy of Onicescu is a positive quantity that measures the amount of uncertainty of a random variable. However, contrary to Shannon&rsquo;s entropy, the informational energy is strictly convex and increases when randomness decreases. We report a closed-form formula for Onicescu&rsquo;s informational energy and its associated correlation coefficient when the probability distributions belong to an exponential family. We show how to instantiate the generic formula for several common exponential families. Finally, we discuss the characterization of valid thermodynamic process trajectories on a statistical manifold by enforcing that the entropy and the informational energy shall vary in opposite directions.

]]>Foundations doi: 10.3390/foundations2020024

Authors: Samundra Regmi Ioannis K. Argyros Santhosh George Christopher I. Argyros

King&rsquo;s method applies to solve scalar equations. The local analysis is established under conditions including the fifth derivative. However, the only derivative in this method is the first. Earlier studies apply to equations containing at least five times differentiable functions. Consequently, these articles provide no information that can be used to solve equations involving functions that are less than five times differentiable, although King&rsquo;s method may converge. That is why the new analysis uses only the operators and their first derivatives which appear in King&rsquo;s method. The article contains the semi-local analysis for complex plane-valued functions not presented before. Numerical applications complement the theory.

]]>Foundations doi: 10.3390/foundations2020023

Authors: Ioannis K. Argyros Debasis Sharma Christopher I. Argyros Sanjaya Kumar Parhi

For the purpose of obtaining solutions to Banach-space-valued nonlinear models, we offer a new extended analysis of the local convergence result for a seventh-order iterative approach without derivatives. Existing studies have used assumptions up to the eighth derivative to demonstrate its convergence. However, in our convergence theory, we only use the first derivative. Thus, in contrast to previously derived results, we obtain conclusions on calculable error estimates, convergence radius, and uniqueness region for the solution. As a result, we are able to broaden the utility of this efficient method. In addition, the convergence regions of this scheme for solving polynomial equations with complex coefficients are illustrated using the attraction basin approach. This study is concluded with the validation of our convergence result on application problems.

]]>Foundations doi: 10.3390/foundations2010022

Authors: Karo Michaelian

There is little doubt that life&rsquo;s origin followed from the known physical and chemical laws of Nature. The most general scientific framework incorporating the laws of Nature and applicable to most known processes to good approximation, is that of thermodynamics and its extensions to treat out-of-equilibrium phenomena. The event of the origin of life should therefore also be amenable to such an analysis. In this review paper, I describe the non-equilibrium thermodynamic foundations of the origin of life for the non-expert from the perspective of the &ldquo;Thermodynamic Dissipation Theory for the Origin of Life&rdquo; which is founded on Classical Irreversible Thermodynamic theory developed by Lars Onsager, Ilya Prigogine, and coworkers. A Glossary of Thermodynamic Terms can be found at the end of the article to aid the reader.

]]>Foundations doi: 10.3390/foundations2010021

Authors: Prakash Singh Shilpi Jain Praveen Agarwal

The objective of this research is to obtain some fractional integral formulas concerning products of the generalized Mittag&ndash;Leffler function and two H-functions. The resulting integral formulas are described in terms of the H-function of several variables. Moreover, we give some illustrative examples for the efficiency of the general approach of our results.

]]>Foundations doi: 10.3390/foundations2010020

Authors: Aurelian Cernea

A coupled system of Hilfer fractional differential inclusions with nonlocal integral boundary conditions is considered. An existence result is established when the set-valued maps have non-convex values. We treat the case when the set-valued maps are Lipschitz in the state variables and we avoid the applications of fixed point theorems as usual. An illustration of the results is given by a suitable example.

]]>Foundations doi: 10.3390/foundations2010019

Authors: Said Mikki

We utilize relativistic quantum mechanics to develop general quantum field-theoretic foundations suitable for understanding, analyzing, and designing generic quantum antennas for potential use in secure quantum communication systems and other applications. Quantum antennas are approached here as abstract source systems capable of producing what we dub &ldquo;quantum radiation.&rdquo; We work from within a generic relativistic framework, whereby the quantum antenna system is modeled in terms of a fundamental quantum spacetime field. After developing a framework explaining how quantum radiation can be understood using the methods of perturbative relativistic quantum field theory (QFT), we investigate in depth the problem of quantum radiation by a controlled abstract source functions. We illustrate the theory in the case of the neutral Klein-Gordon linear quantum antenna, outlining general methods for the construction of the Green&rsquo;s function of a source&mdash;receiver quantum antenna system, the latter being useful for the computation of various candidate angular quantum radiation directivity and gain patterns analogous to the corresponding concepts in classical antenna theory. We anticipate that the proposed formalism may be extended to deal with a large spectrum of other possible controlled emission types for quantum communications applications, including, for example, the production of scalar, fermionic, and bosonic particles, where each could be massless or massive. Therefore, our goal is to extend the idea of antenna beyond electromagnetic waves, where now our proposed QFT-based concept of a quantum antenna system could be used to explore scenarios of controlled radiation of any type of relativistic particles, i.e., effectively transcending the well-known case of photonic systems through the deployment of novel non-standard quantum information transmission carriers such as massive photons, spin-1/2 particles, gravitons, antiparticles, higher spin particles, and so on.

]]>Foundations doi: 10.3390/foundations2010018

Authors: Janak Raj Sharma Ioannis K. Argyros Harmandeep Singh Michael I. Argyros

The local convergence of a generalized (p+1)-step iterative method of order 2p+1 is established in order to estimate the locally unique solutions of nonlinear equations in the Banach spaces. In earlier studies, convergence analysis for the given iterative method was carried out while assuming the existence of certain higher-order derivatives. In contrast to this approach, the convergence analysis is carried out in the present study by considering the hypothesis only on the first-order Fr&eacute;chet derivatives. This study further provides an estimate of convergence radius and bounds of the error for the considered method. Such estimates were not provided in earlier studies. In view of this, the applicability of the given method clearly seems to be extended over the wider class of functions or problems. Moreover, the numerical applications are presented to verify the theoretical deductions.

]]>Foundations doi: 10.3390/foundations2010017

Authors: Christopher I. Argyros Ioannis K. Argyros Stepan Shakhno Halyna Yarmola

We study semi-local convergence of two-step Jarratt-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis we use the approach of restricted convergence regions in combination to majorizing scalar sequences and our technique of recurrent functions. Finally, the numerical example is given.

]]>Foundations doi: 10.3390/foundations2010016

Authors: Eugene Oks

We analyze Molecular Hydrogen Ions (MHIs) formed by collisions of low-energy protons with the Second Flavor of Hydrogen Atoms SFHA, whose existence was previously proven by two kinds of atomic experiments and also evidenced by two kinds of astrophysical observations. We find that the resulting MHIs would lack a significant number of terms compared to the MHIs formed by collisions of low-energy protons with the usual hydrogen atoms. We show that, in this situation, the radiative transition between the terms of such MHIs of the lowest quantum numbers would be between the terms 5f&sigma; and 4d&sigma;. We calculate the position of the edge of the corresponding molecular band and find it to be at the frequency 14,700 cm&minus;1 or equivalently at the wavelength of 680 nm, which belongs to the visible range. It should be easier to observe this band compared to the spectral bands that are completely beyond the visible range. We emphasize that these results open up another avenue for finding an additional experimental proof of the existence of the SFHA. Namely, if the SFHA is present in gas (in addition to the usual hydrogen atoms), on which a beam of low-energy protons is incident, then the relative intensity of the band, corresponding to the radiative transitions between the terms 5f&sigma; and 4d&sigma; of the MHIs, would be enhanced compared to the absence of the SFHA.

]]>Foundations doi: 10.3390/foundations2010015

Authors: David B. Hayrapetyan

In the framework of the effective mass approximation, negative and positive trions, exciton, and biexciton states are investigated in strongly prolate ellipsoidal quantum dots by the variational method. Since the ellipsoidal quantum dot has a prolate character, all excitonic complexes are considered quasi-one-dimensional. As in such a system, the analytical solution does not exist for the many-particle problem, it is solved by the variational method. The trial variation functions based on the one-particle wave functions are used to construct the wavefunctions for the excitonic complexes. The energy spectrum, binding, and recombination energies dependent on the geometrical parameters of the ellipsoidal quantum dots are calculated for the excitons, negative and positive trions, and biexcitons. The radiative lifetime of exciton complexes in ellipsoid is estimated.

]]>Foundations doi: 10.3390/foundations2010014

Authors: Foundations Editorial Office Foundations Editorial Office

Rigorous peer-reviews are the basis of high-quality academic publishing [...]

]]>Foundations doi: 10.3390/foundations2010013

Authors: Attiq ul Rehman Ram Singh Praveen Agarwal

In this paper, fractional Lyapunov functions for epidemic models are introduced and the concept of Mittag-Leffler stability is applied. The global stability of the epidemic model at an equilibrium state is established.

]]>Foundations doi: 10.3390/foundations2010012

Authors: Peeter Saari Ioannis M. Besieris

Vector-valued electromagnetic waves for which the integral of the electric field over time is zero at every location in space were characterized as &ldquo;usual&rdquo; by Bessonov several decades ago. Otherwise, they were called &ldquo;strange&rdquo;. Recently, Popov and Vinogradov studied conditions leading to usual waves using a spectral representation. Their main result is that pulses of finite energy in free space are usual and, consequently, bipolar. However, they do not exclude the possibility of the existence of finite-energy strange pulses, although quite exotic, in a vacuum. Our emphasis in this article is to examine what the relevant necessary and sufficient conditions are for usual and strange waves, particularly for scalar pulses. Illustrative examples are provided, including spherical symmetric collapsing pulses, propagation-invariant, and the so-called almost undistorted spatiotemporally localized waves. Finally, source-generated strange electromagnetic fields are reported.

]]>Foundations doi: 10.3390/foundations2010011

Authors: Valeriy Evgenjevich Ogluzdin

In the review, based on the analysis of the results published in the works of domestic and foreign researchers, a variant of an unconventional interpretation of the photoluminescence of dispersive media in the energy range of 0.5&ndash;3 eV is proposed. The interpretation meets the requirements of the energy conservation law for photons and axions participating in the photoluminescence process. The participation of axions in the process is consistent with Primakov&rsquo;s hypothesis. The role of nonradiative relaxation at the stage of axion decay is noted. The axion lifetimes are estimated for a number of dispersive media.

]]>Foundations doi: 10.3390/foundations2010010

Authors: Ahmed M. A. El-Sayed Hind H. G. Hashem Shorouk M. Al-Issa

Quadratic integral equations of fractional order have been studied from different views. Here we shall study the existence of continuous solutions of a &#981;&minus; fractional-orders quadratic functional integral equation, establish some properties of these solutions and prove the existence of maximal and minimal solutions of that quadratic integral equation. Moreover, we introduce some particular cases to illustrate our results.

]]>Foundations doi: 10.3390/foundations2010009

Authors: Nandhihalli Srinivas Gopal Jagan Mohan Jonnalagadda

In this paper, we look at the two-point boundary value problem for a finite nabla fractional difference equation with dual non-local boundary conditions. First, we derive the associated Green&rsquo;s function and some of its properties. Using the Guo&ndash;Krasnoselkii fixed point theorem on a suitable cone and under appropriate conditions on the non-linear part of the difference equation, we establish sufficient requirements for at least one and at least two positive solutions of the boundary value problem. Next, we discuss the existence and uniqueness of solutions to the considered problem. For this purpose, we use Brouwer and Banach fixed point theorem, respectively. Finally, we provide a few examples to illustrate the applicability of established results.

]]>Foundations doi: 10.3390/foundations2010008

Authors: Christopher I. Argyros Ioannis K. Argyros Stepan Shakhno Halyna Yarmola

We study the semi-local convergence of a three-step Newton-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis, we use the approach of restricted convergence regions in combination with majorizing scalar sequences and our technique of recurrent functions. Finally, a numerical example is given.

]]>Foundations doi: 10.3390/foundations2010007

Authors: Sasmita Kumari Pradhan Sunil Kumar Tripathy Zashmir Naik Dipanjali Behera Mrutunjaya Bhuyan

In this work, we present a Big Rip scenario within the framework of the generalized Brans-Dicke (GBD) theory. In the GBD theory, we consider an evolving BD parameter along with a self-interacting potential. An anisotropic background is considered to have a more general view of the cosmic expansion. The GBD theory with a cosmological constant is presented as an effective cosmic fluid within general relativity which favours a phantom field dominated phase. The model parameters are constrained so that the model provides reasonable estimates of the Hubble parameter and other recent observational aspects at the present epoch. The dynamical aspects of the BD parameter and the BD scalar field have been analysed. It is found that the present model witnesses a finite time doomsday at a time of tBR&#8771;16.14Gyr, and for this scenario, the model requires a large negative value of the Brans-Dicke parameter.

]]>Foundations doi: 10.3390/foundations2010006

Authors: Samundra Regmi Christopher I. Argyros Ioannis K. Argyros Santhosh George

The celebrated Traub&rsquo;s method involving Banach space-defined operators is extended. The main feature in this study involves the determination of a subset of the original domain that also contains the Traub iterates. In the smaller domain, the Lipschitz constants are smaller too. Hence, a finer analysis is developed without the usage of additional conditions. This methodology applies to other methods. The examples justify the theoretical results.

]]>Foundations doi: 10.3390/foundations2010005

Authors: Nikolay Kryukov Eugene Oks

Previously published analytical results for the effects of a high-frequency laser field on hydrogen Rydberg atoms demonstrated that the unperturbed elliptical orbit of the Rydberg electron, generally is engaged simultaneously in the precession of the orbital plane about the direction of the laser field and in the precession within the orbital plane. These results were obtained while disregarding relativistic effects. In the present paper, we analyze the relativistic effect for hydrogenic Rydberg atoms or ions in a high-frequency linearly- or circularly-polarized laser field, the effect being an additional precession of the electron orbit in its own plane. For the linearly-polarized laser field, the general case, where the electron orbit is not perpendicular to the direction of the laser field, we showed that the precession of the electron orbit within its plane can vanish at some critical polar angle &theta;c of the orbital plane. We calculated analytically the dependence of the critical angle on the angular momentum of the electron and on the parameters of the laser field. Finally, for the particular situation, where the electron orbit is perpendicular to the direction of the laser field, we demonstrated that the relativistic precession and the precession due to the laser field occur in the opposite directions. As a result, the combined effect of these two kinds of the precession is smaller than the absolute value of each of them. We showed that by varying the ratio of the laser field strength F to the square of the laser field frequency &omega;, one can control the precession frequency of the electron orbit and even make the precession vanish, so that the elliptical orbit of the electron would become stationary. This is a counterintuitive result.

]]>Foundations doi: 10.3390/foundations2010004

Authors: Tolulope Majekodunmi Joshua Nishu Jain Raj Kumar Khairul Anwar Nooraihan Abdullah Mrutunjaya Bhuyan

A new &alpha;-emitting 214U has been recently observed experimentally. This opens the window to theoretically investigate the ground-state properties of the lightest known even&ndash;even neutron deficient 214,216,218U isotopes and to examine &alpha;-particle clustering around the shell closure. The decay half-lives are calculated within the preformed cluster-decay model (PCM). To obtain the &alpha;-daughter interaction potential, the RMF densities are folded with the newly developed R3Y and the well-known M3Y NN potentials for comparison. The alpha preformation probability (P&alpha;) is calculated from the analytic formula of Deng and Zhang. The WKB approximation is employed for the calculation of the transmission probability. The individual binding energies (BE) for the participating nuclei are estimated from the relativistic mean-field (RMF) formalism and those from the finite range droplet model (FRDM) as well as WS3 mass tables. In addition to Z=84, the so-called abnormal enhancement region, i.e., 84&le;Z&le;90 and N&lt;126, is normalised by an appropriately fitted neck-parameter &Delta;R. On the other hand, the discrepancy sets in due to the shell effect at (and around) the proton magic number Z=82 and 84, and thus a higher scaling factor ranging from 10&minus;8&ndash;10&minus;5 is required. Additionally, in contrast with the experimental binding energy data, large deviations of about 5&ndash;10 MeV are evident in the RMF formalism despite the use of different parameter sets. An accurate prediction of &alpha;-decay half-lives requires a Q-value that is in proximity with the experimental data. In addition, other microscopic frameworks besides RMF could be more reliable for the mass region under study. &alpha;-particle clustering is largely influenced by the shell effect.

]]>Foundations doi: 10.3390/foundations2010003

Authors: Said Mikki

An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonlocality starting from general considerations, going through spatial dispersion, and ending up with a broad formulation that unveils the link between general topology and nonlocality in generic material media. It is shown that nonlocality naturally leads to a Banach (vector) bundle structure serving as an enlarged space (superspace) inside which physical processes, such as the electromagnetic ones, take place. The added structures, essentially fibered spaces, model the topological microdomains of physics-based nonlocality and provide a fine-grained geometrical picture of field&ndash;matter interactions in nonlocal metamaterials. We utilize standard techniques in the theory of smooth manifolds to construct the Banach bundle structure by paying careful attention to the relevant physics. The electromagnetic response tensor is then reformulated as a superspace bundle homomorphism and the various tools needed to proceed from the local topology of microdomains to global domains are developed. For concreteness and simplicity, our presentations of both the fundamental theory and the examples given to illustrate the mathematics all emphasize the case of electromagnetic field theory, but the superspace formalism developed here is quite general and can be easily extended to other types of nonlocal continuum field theories. An application to fundamental theory is given, which consists of utilizing the proposed superspace theory of nonlocal metamaterials in order to explain why nonlocal electromagnetic materials often require additional boundary conditions or extra input from microscopic theory relative to local electromagnetism, where in the latter case such extra input is not needed. Real-life case studies quantitatively illustrating the microdomain structure in nonlocal semiconductors are provided. Moreover, in a series of connected appendices, we outline a new broad view of the emerging field of nonlocal electromagnetism in material domains, which, together with the main superspace formalism introduced in the main text, may be considered a new unified general introduction to the physics and methods of nonlocal metamaterials.

]]>Foundations doi: 10.3390/foundations2010002

Authors: Neelma Eiman Kamal Shah

This current work is devoted to develop qualitative theory of existence of solution to some families of fractional order differential equations (FODEs). For this purposes we utilize fixed point theory due to Banach and Schauder. Further using differential transform method (DTM), we also compute analytical or semi-analytical results to the proposed problems. Also by some proper examples we demonstrate the results.

]]>Foundations doi: 10.3390/foundations2010001

Authors: Eugene Oks

Many totally different kinds of astrophysical observations demonstrated that, in our universe, there exists a preferred direction. Specifically, from observations in a wide range of frequencies, the alignment of various preferred directions in different data sets was found. Moreover, the observed Cosmic Microwave Background (CMB) quadrupole, CMB octopole, radio and optical polarizations from distant sources also indicate the same preferred direction. While this hints at a gravitational pull from the &ldquo;outside&rdquo;, the observational data from the Plank satellite showed that the bulk flow velocity was relatively small: much smaller than was initially thought. In the present paper we propose a configuration where two three-dimensional universes (one of which is ours) are embedded in a four-dimensional space and rotate about their barycenter in such a way that the centrifugal force nearly (but not exactly) compensates their mutual gravitational pull. This would explain not only the existence of a preferred direction for each of the three-dimensional universes (the direction to the other universe), but also the fact that the bulk flow velocity, observed in our universe, is relatively small. We point out that this configuration could also explain the perplexing features of the Unidentified Aerial Phenomena (UAP), previously called Unidentified Flying Objects (UFOs), recorded by various detection systems&mdash;the features presented in the latest official report by the US Office of the Director of National Intelligence. Thus, the proposed configuration of the two rotating, parallel three-dimensional universes seems to explain both the variety of astrophysical observations and (perhaps) the observed features of the UAP.

]]>Foundations doi: 10.3390/foundations1020022

Authors: Samar Elaraby Sherif M. Abuelenin Adel Moussa Yasser M. Sabry

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&ndash;4000 cm&minus;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 cm&minus;1 to 20 cm&minus;1 with a mean square error down to 2.4&times;10&minus;3 in the transmission spectra. The technique supports selective spectral analysis based on miniaturized MEMS spectrometers.

]]>Foundations doi: 10.3390/foundations1020021

Authors: Vishal Nikam Dhananjay Gopal Rabha W. Ibrahim

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;&minus;G, &psi;&minus;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&ndash;Liouville formula. Moreover, we introduce numerical solutions of the class by using the set of fixed points.

]]>Foundations doi: 10.3390/foundations1020020

Authors: Giacomo Ortali Ioannis G. Tollis

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.

]]>Foundations doi: 10.3390/foundations1020019

Authors: Eugene Oks

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.

]]>Foundations doi: 10.3390/foundations1020018

Authors: Takuya Yamano

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.

]]>Foundations doi: 10.3390/foundations1020017

Authors: Polychronis S. Koliogiannis Alkiviadis Kanakis-Pegios Charalampos C. Moustakidis

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+0.08M⊙ (GW190814 event), as a component of a system where the main companion was a black hole with mass ∼23M⊙. 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.

]]>Foundations doi: 10.3390/foundations1020016

Authors: Christian G. Parigger

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.

]]>Foundations doi: 10.3390/foundations1020015

Authors: Andrei Letunov Valery Lisitsa Valery Astapenko

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.

]]>Foundations doi: 10.3390/foundations1020014

Authors: Boris Michailovich Smirnov Dmitri Alexandrovich Zhilyaev

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 Tω, an optical thickness uω and an opaque factor g(uω). 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(H2O) of water atmospheric molecules, it is approximately dlnc(H2O/dt)=0.003 yr−1. This corresponds to an increase in the average moisture of the atmosphere of 0.2%/yr.

]]>Foundations doi: 10.3390/foundations1020013

Authors: Imane Es-safi Hamza Mechchate Amal Amaghnouje Fatima Zahra Jawhari Dalila Bousta

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.

]]>Foundations doi: 10.3390/foundations1020012

Authors: Nikolay L. Popov Alexander V. Vinogradov

E.G. Bessonov suggested the time integrated strength of an electric field ∫−∞∞E(r,t)dt=SE(r) 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 SE(r)=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.

]]>Foundations doi: 10.3390/foundations1020011

Authors: Marcelo Amaral Fang Fang Dugan Hammock Klee Irwin

In light of the self-simulation hypothesis, a simple form of implementation of the principle of efficient language is discussed in a self-referential geometric quasicrystalline state sum model in three dimensions. Emergence is discussed in the context of geometric state sum models.

]]>Foundations doi: 10.3390/foundations1010010

Authors: José Guilherme Chaui-Berlinck José Eduardo Pereira Wilken Bicudo

The cardiovascular system is an apparatus of mass convection, and changes in organismic size impart changes in variables of this system, namely scaling effects. Blood flow depends on pressure and conductance, and the maintenance of flow results in entropy production, that is, loss of available work. In terms of scaling, it is well known that blood pressure is kept constant while blood volume varies linearly with body mass. Yet, such expected rules have never been proven. The present study shows that these scaling rules derive from the simultaneous optimization of blood flow and entropy production in circulation and how these impact the transition from ecto- to endotermy. Thus, for the first time in almost a century of data collection, these observed relationships are explained from a theoretical standpoint. The demonstration presented herein is a building block to form a solid basis for the other scaling rules of the cardiovascular system as well as of other organic systems. The approach is of wide interest in any area where generalized flow is analyzed in terms of system optimization, giving a broad perspective on change in either engineered or naturally evolving systems.

]]>Foundations doi: 10.3390/foundations1010009

Authors: Alexander Robitzsch

This article investigates the comparison of two groups based on the two-parameter logistic item response model. It is assumed that there is random differential item functioning in item difficulties and item discriminations. The group difference is estimated using separate calibration with subsequent linking, as well as concurrent calibration. The following linking methods are compared: mean-mean linking, log-mean-mean linking, invariance alignment, Haberman linking, asymmetric and symmetric Haebara linking, different recalibration linking methods, anchored item parameters, and concurrent calibration. It is analytically shown that log-mean-mean linking and mean-mean linking provide consistent estimates if random DIF effects have zero means. The performance of the linking methods was evaluated through a simulation study. It turned out that (log-)mean-mean and Haberman linking performed best, followed by symmetric Haebara linking and a newly proposed recalibration linking method. Interestingly, linking methods frequently found in applications (i.e., asymmetric Haebara linking, recalibration linking used in a variant in current large-scale assessment studies, anchored item parameters, concurrent calibration) perform worse in the presence of random differential item functioning. In line with the previous literature, differences between linking methods turned out be negligible in the absence of random differential item functioning. The different linking methods were also applied in an empirical example that performed a linking of PISA 2006 to PISA 2009 for Austrian students. This application showed that estimated trends in the means and standard deviations depended on the chosen linking method and the employed item response model.

]]>Foundations doi: 10.3390/foundations1010008

Authors: Marianito R. Rodrigo Mandy Li

Two new transforms with piecewise linear kernels are introduced. These transforms are analogues of the classical Laplace transform and Z-transform. Properties of these transforms are investigated and applications to ordinary differential equations and integral equations are provided. This article is ideal for study as a foundational project in an undergraduate course in differential and/or integral equations.

]]>Foundations doi: 10.3390/foundations1010007

Authors: Sotiris K. Ntouyas

This paper is a survey of the recent results of the author for various classes of boundary value problems for Hilfer fractional differential equations and inclusions of fractional order in (1,2] supplemented with different kinds of nonlocal boundary conditions.

]]>Foundations doi: 10.3390/foundations1010006

Authors: Carlo Cafaro Sean A. Ali

We discuss the fundamental theoretical framework together with numerous results obtained by the authors and colleagues over an extended period of investigation on the Information Geometric Approach to Chaos (IGAC).

]]>Foundations doi: 10.3390/foundations1010005

Authors: Zhongqi He David Zhang Huai N. Cheng

Due to their hygroscopic characteristics, equilibrium moisture contents of agricultural products and byproducts are important factors of their quality. Defatted cottonseed meal (CSM), washed cottonseed meal (WCSM) and cottonseed protein isolate (CSPI) can be used as energy and protein sources of animal feedstuff or industrial raw materials. Information on their moisture adsorption behaviors is needed for their storage conditions and quality control. Thus, this work measured the equilibrium moisture sorption isotherms of CSM, WCSM and CSPI, at 15, 25, 35 and 45 °C. When the moisture contents of the samples were compared at a constant temperature, the general trend of decreasing moisture content was in the order of CSPI &lt; WCSM &lt; CSM for water activity &lt;0.6, but the trend reversed to the order of CSM &lt; WCSM &lt; CSPI for water activity &gt;0.6. Relevant sorption isotherm equations were tested for accurate fit to the moisture adsorption data. Modelling results indicated that the G.A.B. (Guggenheim-Anderson-de Boer) model was a consistently good fit for the data among all sample types and all temperatures. This work provides some insight on designing or selecting appropriate procedures for the handling, aeration, storage and processing of these cottonseed meal products. In particular, it suggests that moisture content should be kept at around 8% for safe storage of these products at room temperature (around 25 °C) but below 5% when they are exposed to higher temperature conditions (e.g., &gt;45 °C).

]]>Foundations doi: 10.3390/foundations1010004

Authors: Samundra Regmi Christopher Argyros Ioannis Argyros Santhosh George

The goal is to extend the applicability of Newton-Traub-like methods in cases not covered in earlier articles requiring the usage of derivatives up to order seven that do not appear in the methods. The price we pay by using conditions on the first derivative that actually appear in the method is that we show only linear convergence. To find the convergence order is not our intention, however, since this is already known in the case where the spaces coincide with the multidimensional Euclidean space. Note that the order is rediscovered by using ACOC or COC, which require only the first derivative. Moreover, in earlier studies using Taylor series, no computable error distances were available based on generalized Lipschitz conditions. Therefore, we do not know, for example, in advance, how many iterates are needed to achieve a predetermined error tolerance. Furthermore, no uniqueness of the solution results is available in the aforementioned studies, but we also provide such results. Our technique can be used to extend the applicability of other methods in an analogous way, since it is so general. Finally note that local results of this type are important, since they demonstrate the difficulty in choosing initial points. Our approach also extends the applicability of this family of methods from the multi-dimensional Euclidean to the more general Banach space case. Numerical examples complement the theoretical results.

]]>Foundations doi: 10.3390/foundations1010003

Authors: Andreas E. Schlatter Shu-Kun Lin

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]]>Foundations doi: 10.3390/foundations1010002

Authors: Claudio Luparello

It is known that in breast cancer biology, autophagy mainly plays a cytoprotective and anti-apoptotic role in vitro, being conceivably responsible for cell resistance to drug exposure and a higher metastatic attitude in vivo. Thus, the development of novel autophagy-targeting agents represents a valuable strategy to improve the efficacy of anticancer interventions. It is widely acknowledged that the enormous biodiversity of marine organisms represents a highly promising reserve for the isolation of bioactive primary and secondary metabolites targeting one or several specific molecular pathways and displaying active pharmacological properties against a variety of diseases. The aim of this review is to pick up selected studies that report the extraction and identification of marine animal-derived extracts or isolated compounds which exert a modulatory effect on the autophagic process in breast cancer cells and list them with respect to the taxonomical hierarchy of the producing species. Where available, the molecular and biochemical aspects associated with the molecules or extracts under discussion will be also summarized.

]]>Foundations doi: 10.3390/foundations1010001

Authors: Martin Bohner

Fundamental or basic research is the cornerstone of building knowledge in science [...]

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