Journal Description
Foundations
Foundations
is an international, peer-reviewed, open access journal on all areas of the natural sciences and high-tech fields published quarterly online by MDPI.
- Open Access—Free to download, share, and reuse content. Authors receive recognition for their contribution when the paper is reused.
- Rapid Publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 25 days after submission; acceptance to publication is undertaken in 4.5 days (median values for papers published in this journal in the second half of 2021).
- Recognition of Reviewers: APC discount vouchers, optional signed peer review, and reviewer names published annually in the journal.
- Foundations is a companion journal of Molecules, Entropy, Biology and Mathematics.
Latest Articles
Some Asian Women Pioneers of Chemistry and Pharmacy
Foundations 2022, 2(2), 475-487; https://doi.org/10.3390/foundations2020031 - 13 May 2022
Abstract
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
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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.
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(This article belongs to the Section Chemical Sciences)
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Location, Separation and Approximation of Solutions for Quadratic Matrix Equations
Foundations 2022, 2(2), 457-474; https://doi.org/10.3390/foundations2020030 - 12 May 2022
Abstract
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
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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.
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(This article belongs to the Special Issue Iterative Methods with Applications in Mathematical Sciences)
Open AccessEditorial
Gertrude Belle Elion, Chemist and Pharmacologist, Discoverer of Highly Relevant Active Substances
Foundations 2022, 2(2), 443-456; https://doi.org/10.3390/foundations2020029 - 06 May 2022
Abstract
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
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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.
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(This article belongs to the Section Medical Sciences)
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Open AccessReview
Stochastic Interpretation of Quantum Mechanics Assuming That Vacuum Fields Are Real
Foundations 2022, 2(2), 409-442; https://doi.org/10.3390/foundations2020028 - 04 May 2022
Abstract
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
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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–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.
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(This article belongs to the Section Physical Sciences)
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Medical Records in Community Pharmacies: The Cases of UK and Australia
by
Foundations 2022, 2(2), 399-408; https://doi.org/10.3390/foundations2020027 - 23 Apr 2022
Abstract
Background: Lack of access to patients’ 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’ health
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Background: Lack of access to patients’ 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’ 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’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’ outcomes.
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Nonlocal ψ-Hilfer Generalized Proportional Boundary Value Problems for Fractional Differential Equations and Inclusions
Foundations 2022, 2(2), 377-398; https://doi.org/10.3390/foundations2020026 - 22 Apr 2022
Abstract
In this paper, we establish existence and uniqueness results for a new class of boundary value problems involving the -Hilfer generalized proportional fractional derivative operator, supplemented with mixed nonlocal boundary conditions including multipoint, fractional integral multiorder and derivative multiorder operators. The given
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In this paper, we establish existence and uniqueness results for a new class of boundary value problems involving the -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.
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(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inclusions)
Open AccessArticle
Onicescu’s Informational Energy and Correlation Coefficient in Exponential Families
Foundations 2022, 2(2), 362-376; https://doi.org/10.3390/foundations2020025 - 19 Apr 2022
Abstract
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The informational energy of Onicescu is a positive quantity that measures the amount of uncertainty of a random variable. However, contrary to Shannon’s entropy, the informational energy is strictly convex and increases when randomness decreases. We report a closed-form formula for Onicescu’s informational
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The informational energy of Onicescu is a positive quantity that measures the amount of uncertainty of a random variable. However, contrary to Shannon’s entropy, the informational energy is strictly convex and increases when randomness decreases. We report a closed-form formula for Onicescu’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.
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Extending King’s Method for Finding Solutions of Equations
Foundations 2022, 2(2), 348-361; https://doi.org/10.3390/foundations2020024 - 18 Apr 2022
Abstract
King’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
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King’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’s method may converge. That is why the new analysis uses only the operators and their first derivatives which appear in King’s method. The article contains the semi-local analysis for complex plane-valued functions not presented before. Numerical applications complement the theory.
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(This article belongs to the Special Issue Iterative Methods with Applications in Mathematical Sciences)
Open AccessArticle
Extending the Local Convergence of a Seventh Convergence Order Method without Derivatives
Foundations 2022, 2(2), 338-347; https://doi.org/10.3390/foundations2020023 - 12 Apr 2022
Abstract
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,
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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.
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(This article belongs to the Special Issue Iterative Methods with Applications in Mathematical Sciences)
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Non-Equilibrium Thermodynamic Foundations of the Origin of Life
Foundations 2022, 2(1), 308-337; https://doi.org/10.3390/foundations2010022 - 21 Mar 2022
Abstract
There is little doubt that life’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
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There is little doubt that life’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 “Thermodynamic Dissipation Theory for the Origin of Life” 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.
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(This article belongs to the Special Issue The Non-equilibrium Thermodynamic Foundations of Fundamental Problems from Nature)
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Generalized Fractional Integrals Involving Product of a Generalized Mittag–Leffler Function and Two H-Functions
Foundations 2022, 2(1), 298-307; https://doi.org/10.3390/foundations2010021 - 11 Mar 2022
Abstract
The objective of this research is to obtain some fractional integral formulas concerning products of the generalized Mittag–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
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The objective of this research is to obtain some fractional integral formulas concerning products of the generalized Mittag–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.
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(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inclusions)
Open AccessArticle
A Note on a Coupled System of Hilfer Fractional Differential Inclusions
Foundations 2022, 2(1), 290-297; https://doi.org/10.3390/foundations2010020 - 03 Mar 2022
Cited by 1
Abstract
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
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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.
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(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inclusions)
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Fundamental Spacetime Representations of Quantum Antenna Systems
by
Foundations 2022, 2(1), 251-289; https://doi.org/10.3390/foundations2010019 - 02 Mar 2022
Abstract
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
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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 “quantum radiation.” 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’s function of a source—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- particles, gravitons, antiparticles, higher spin particles, and so on.
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(This article belongs to the Special Issue Advances in Fundamental Physics)
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On the Local Convergence of a (p + 1)-Step Method of Order 2p + 1 for Solving Equations
Foundations 2022, 2(1), 242-250; https://doi.org/10.3390/foundations2010018 - 20 Feb 2022
Abstract
The local convergence of a generalized -step iterative method of order is established in order to estimate the locally unique solutions of nonlinear equations in the Banach spaces. In earlier studies, convergence analysis for
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The local convergence of a generalized -step iterative method of order 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 Fréchet 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.
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(This article belongs to the Special Issue Iterative Methods with Applications in Mathematical Sciences)
Open AccessFeature PaperArticle
On the Semi-Local Convergence of a Jarratt-Type Family Schemes for Solving Equations
Foundations 2022, 2(1), 234-241; https://doi.org/10.3390/foundations2010017 - 17 Feb 2022
Abstract
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
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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.
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(This article belongs to the Special Issue Iterative Methods with Applications in Mathematical Sciences)
Open AccessCommunication
Peculiar Features of Molecular Hydrogen Ions Formed by Proton Collisions with Hydrogen Atoms of the Second Flavor
by
Foundations 2022, 2(1), 228-233; https://doi.org/10.3390/foundations2010016 - 14 Feb 2022
Abstract
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
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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 5fσ and 4dσ. We calculate the position of the edge of the corresponding molecular band and find it to be at the frequency 14,700 cm−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 5fσ and 4dσ of the MHIs, would be enhanced compared to the absence of the SFHA.
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(This article belongs to the Special Issue Advances in Fundamental Physics)
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Binding and Recombination Energies of Quasi-One-Dimensional Excitonic Complexes in Ellipsoidal Quantum Dot
Foundations 2022, 2(1), 219-227; https://doi.org/10.3390/foundations2010015 - 12 Feb 2022
Abstract
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.
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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.
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(This article belongs to the Special Issue Infrared Spectroscopy: Principles and Instrumentation)
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Open AccessEditorial
Acknowledgment to Reviewers of Foundations in 2021
Foundations 2022, 2(1), 218; https://doi.org/10.3390/foundations2010014 - 11 Feb 2022
Abstract
Rigorous peer-reviews are the basis of high-quality academic publishing [...]
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On Fractional Lyapunov Functions of Nonlinear Dynamic Systems and Mittag-Leffler Stability Thereof
Foundations 2022, 2(1), 209-217; https://doi.org/10.3390/foundations2010013 - 07 Feb 2022
Abstract
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.
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(This article belongs to the Special Issue Recent Advances in Fractional Differential Equations and Inclusions)
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Conditions for Scalar and Electromagnetic Wave Pulses to Be “Strange” or Not
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and
Foundations 2022, 2(1), 199-208; https://doi.org/10.3390/foundations2010012 - 07 Feb 2022
Abstract
Vector-valued electromagnetic waves for which the integral of the electric field over time is zero at every location in space were characterized as “usual” by Bessonov several decades ago. Otherwise, they were called “strange”. Recently, Popov and Vinogradov studied conditions leading to usual
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Vector-valued electromagnetic waves for which the integral of the electric field over time is zero at every location in space were characterized as “usual” by Bessonov several decades ago. Otherwise, they were called “strange”. 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.
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(This article belongs to the Special Issue Advances in Fundamental Physics)
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The Non-equilibrium Thermodynamic Foundations of Fundamental Problems from Nature
Guest Editor: Karo MichaelianDeadline: 30 June 2022
Special Issue in
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Advances in Fundamental Physics
Guest Editor: Eugene OksDeadline: 31 July 2022
Special Issue in
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Solid Catalysts as Greener Promoters of Cleaner Chemical Processes
Guest Editor: Stefania De LucaDeadline: 31 August 2022
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Recent Advances in Fractional Differential Equations and Inclusions
Guest Editor: Sotiris K. NtouyasDeadline: 30 September 2022