Editor’s Choice Articles

In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented, and some important classes of the kernels that satisfy this condition are introduced. Whereas the kernels of the general fractional derivatives of arbitrary order possess integrable singularities at the point zero, the kernels of the general fractional integrals can—depending on their order—be both singular and continuous at the origin. For the general fractional integrals and derivatives of arbitrary order with the kernels introduced in this paper, two fundamental theorems of fractional calculus are formulated and proved. Full article

Biometric classification plays a key role in fingerprint characterization, especially in the identification process. In fact, reducing the number of comparisons in biometric recognition systems is essential when dealing with large-scale databases. The classification of fingerprints aims to achieve this target by splitting fingerprints into different categories. The general approach of fingerprint classification requires pre-processing techniques that are usually computationally expensive. Deep Learning is emerging as the leading field that has been successfully applied to many areas, such as image processing. This work shows the performance of pre-trained Convolutional Neural Networks (CNNs), tested on two fingerprint databases—namely, PolyU and NIST—and comparisons to other results presented in the literature in order to establish the type of classification that allows us to obtain the best performance in terms of precision and model efficiency, among approaches under examination, namely: AlexNet, GoogLeNet, and ResNet. We present the first study that extensively compares the most used CNN architectures by classifying the fingerprints into four, five, and eight classes. From the experimental results, the best performance was obtained in the classification of the PolyU database by all the tested CNN architectures due to the higher quality of its samples. To confirm the reliability of our study and the results obtained, a statistical analysis based on the McNemar test was performed. Full article

The charmonium-like exotic states $Y\left(4230\right)$ and the less known $Y\left(4320\right)$, produced in $e^{+}{e}^{-}$ collisions, are sources of positive parity exotic hadrons in association with photons or pseudoscalar mesons. We analyze the radiative and pion decay channels in the compact tetraquark scheme, with a method that proves to work equally well in the most studied $D^{\ast }\to \gamma /\pi +D$ decays. The decay of the vector Y into a pion and a $Z_c$ state requires a flip of charge conjugation and isospin that is described appropriately in the formalism used. Rates are found to depend on the fifth power of pion momentum, which would make the final states $\pi Z_c\left(4020\right)$ strongly suppressed with respect to $\pi Z_c\left(3900\right)$. The agreement with BES III data would be improved considering the $\pi Z_c\left(4020\right)$ events to be fed by the tail of the $Y\left(4320\right)$ resonance under the $Y\left(4230\right)$. These results should renovate the interest in further clarifying the emerging experimental picture in this mass region. Full article

All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time $V_4$ a group of motion $G_3$ acts simply transitively on a non-null subspace of transitivity $V_3$. It is shown that in the case of a Riemannian space $V_n$, in which the group $G_r$ acts simply transitively, the algebra of symmetry operators of the n-dimensional Klein-Gordon-Fock equation in an external admissible electromagnetic field coincides with the algebra of operators of the group $G_r$. Full article

Observations of the synchrotron and inverse Compton emissions from ultrarelativistic electrons in astrophysical sources can reveal a great deal about the energy–momentum relations of those electrons. They can thus be used to place bounds on the possibility of Lorentz violation in the electron sector. Recent $\gamma$-ray telescope data allow the Lorentz-violating electron $c^{\nu \mu }$ parameters to be constrained extremely well, so that all bounds are at the level of $7\times {10}^{-16}$ or better. Full article

Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension (SME) has been widely used as a phenomenological framework in investigations of spacetime symmetry breaking. Until recently, it was thought that the SME was suitable only for theories with spontaneous spacetime symmetry breaking due to consistency conditions stemming from the Bianchi identities. However, it has recently been shown that, particularly with matter couplings included, the consistency conditions can also be satisfied in theories with explicit breaking. An overview of how this is achieved is presented, and two examples are examined. The first is massive gravity, which includes a nondynamical background tensor. The second is a model based on a low-energy limit of Hořava gravity, where spacetime has a physically preferred foliation. In both cases, bounds on matter–gravity interactions that explicitly break diffeomorphisms are obtained using the SME. Full article

The rapid and selective responses to changes in habitat structure and climate have made butterflies valuable environmental indicators. In this study, we asked whether the decline in butterfly populations near the copper-nickel smelter in Monchegorsk in northwestern Russia is accompanied by phenotypic stress responses to toxic pollutants, expressed as a decrease in body size and an increase in fluctuating asymmetry. We measured the concentrations of nickel and copper, forewing length, and fluctuating asymmetry in two elements of wing patterns in Boloria euphrosyne, Plebejus idas, and Agriades optilete collected 1–65 km from Monchegorsk. Body metal concentrations increased toward the smelter, confirming the local origin of the collected butterflies. The wings of butterflies from the most polluted sites were 5–8% shorter than those in unpolluted localities, suggesting adverse effects of pollution on butterfly fitness due to larval feeding on contaminated plants. However, fluctuating asymmetry averaged across two hindwing spots did not change systematically with pollution, thereby questioning the use of fluctuating asymmetry as an indicator of habitat quality in butterfly conservation projects. Full article

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions $({\partial }_1{u}_1,{\partial }_1{b}_1)$, $({\partial }_2{u}_2,{\partial }_2{b}_2)$ and $({\partial }_3{u}_3,{\partial }_3{b}_3)$ in anisotropic Lorentz space. Full article

High precision atomic data are indispensable for studies of fundamental symmetries, tests of fundamental physics postulates, developments of atomic clocks, ultracold atom experiments, astrophysics, plasma science, and many other fields of research. We have developed a new parallel atomic structure code package that enables computations that were not previously possible due to system complexity. This code package also allows much quicker computations to be run with higher accuracy for simple systems. We explored different methods of load-balancing matrix element calculations for many-electron systems, which are very difficult due to the intrinsic nature of the computational methods used to calculate them. Furthermore, dynamic memory allocation and MPI parallelization have been implemented to optimize and accelerate the computations. We have achieved near-perfect linear scalability and efficiency with the number of processors used for calculation, paving the way towards the future where most open-shell systems will finally be able to be treated with good accuracy. We present several examples illustrating new capabilities of the newly developed codes, specifically correlating up to all 60 electrons in the highly charged Ir${}^{17+}$ ion and predicting certain properties of Fe${}^{16+}$. Full article

The paper considers a solution to the problem of developing two-stage hybrid SVM-kNN classifiers with the aim to increase the data classification quality by refining the classification decisions near the class boundary defined by the SVM classifier. In the first stage, the SVM classifier with default parameters values is developed. Here, the training dataset is designed on the basis of the initial dataset. When developing the SVM classifier, a binary SVM algorithm or one-class SVM algorithm is used. Based on the results of the training of the SVM classifier, two variants of the training dataset are formed for the development of the kNN classifier: a variant that uses all objects from the original training dataset located inside the strip dividing the classes, and a variant that uses only those objects from the initial training dataset that are located inside the area containing all misclassified objects from the class dividing strip. In the second stage, the kNN classifier is developed using the new training dataset above-mentioned. The values of the parameters of the kNN classifier are determined during training to maximize the data classification quality. The data classification quality using the two-stage hybrid SVM-kNN classifier was assessed using various indicators on the test dataset. In the case of the improvement of the quality of classification near the class boundary defined by the SVM classifier using the kNN classifier, the two-stage hybrid SVM-kNN classifier is recommended for further use. The experimental results approve the feasibility of using two-stage hybrid SVM-kNN classifiers in the data classification problem. The experimental results obtained with the application of various datasets confirm the feasibility of using two-stage hybrid SVM-kNN classifiers in the data classification problem. Full article

The majority of people with Multiple Sclerosis (pwMS), report lower limb motor dysfunctions, which may relevantly affect postural control, gait and a wide range of activities of daily living. While it is quite common to observe a different impact of the disease on the two limbs (i.e., one of them is more affected), less clear are the effects of such asymmetry on gait performance. The present retrospective cross-sectional study aimed to characterize the magnitude of interlimb asymmetry in pwMS, particularly as regards the joint kinematics, using parameters derived from angle-angle diagrams. To this end, we analyzed gait patterns of 101 pwMS (55 women, 46 men, mean age 46.3, average Expanded Disability Status Scale (EDSS) score 3.5, range 1–6.5) and 81 unaffected individuals age- and sex-matched who underwent 3D computerized gait analysis carried out using an eight-camera motion capture system. Spatio-temporal parameters and kinematics in the sagittal plane at hip, knee and ankle joints were considered for the analysis. The angular trends of left and right sides were processed to build synchronized angle–angle diagrams (cyclograms) for each joint, and symmetry was assessed by computing several geometrical features such as area, orientation and Trend Symmetry. Based on cyclogram orientation and Trend Symmetry, the results show that pwMS exhibit significantly greater asymmetry in all three joints with respect to unaffected individuals. In particular, orientation values were as follows: 5.1 of pwMS vs. 1.6 of unaffected individuals at hip joint, 7.0 vs. 1.5 at knee and 6.4 vs. 3.0 at ankle (p < 0.001 in all cases), while for Trend Symmetry we obtained at hip 1.7 of pwMS vs. 0.3 of unaffected individuals, 4.2 vs. 0.5 at knee and 8.5 vs. 1.5 at ankle (p < 0.001 in all cases). Moreover, the same parameters were sensitive enough to discriminate individuals of different disability levels. With few exceptions, all the calculated symmetry parameters were found significantly correlated with the main spatio-temporal parameters of gait and the EDSS score. In particular, large correlations were detected between Trend Symmetry and gait speed (with rho values in the range of −0.58 to −0.63 depending on the considered joint, p < 0.001) and between Trend Symmetry and EDSS score (rho = 0.62 to 0.69, p < 0.001). Such results suggest not only that MS is associated with significantly marked interlimb asymmetry during gait but also that such asymmetry worsens as the disease progresses and that it has a relevant impact on gait performances. Full article

Three (Z)-5-(azulen-1-ylmethylene)-2-thioxo-thiazolidin-4-ones are electrochemically characterized by cyclic voltammetry, differential pulse voltammetry, and rotating disk electrode voltammetry. The electrochemical investigations revealed that the redox potential is influenced by the number and position of the alkyl groups, and the possible oxidation mechanism is proposed. These compounds, after their immobilization on glassy carbon electrodes during oxidative electropolymerization, were examined as complexing ligands for heavy metal ions from aqueous solutions through adsorptive stripping voltammetry. Full article

Data hiding is a technique that embeds a secret message into a cover medium and transfers the hidden information in the secret message to the recipient. In the past, several data hiding methods based on magic matrix have used various geometrical shapes to transmit secret data. The embedding capacity achieved in these methods was often limited due to simple geometrical layouts. This paper proposes a data hiding scheme based on a double-layer octagon-shaped shell matrix. Compared to previous octagon-shaped data hiding methods, the proposed method embeds a total of 7 bits in each pixel pair, reaching an embedding capacity of 3.5 bits per pixel (bpp). Experimental results show that the proposed scheme has a higher embedding capacity compared to other irreversible data hiding schemes. Using the proposed method, it is possible to maintain the Peak Signal to Noise Ratio (PSNR) within an acceptable range with the embedding time less than 2 s. Full article

Motivated by the work of Saridakis (Phys. Rev. D102, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. The literature demonstrates that dark energy (DE) may result from electroweak symmetry breaking that triggers a phase transition from early inflation to late-time acceleration. In the present study, we incorporated viscosity in the Barrow HDE. A reconstruction scheme is presented for the parameters associated with Barrow holographic dark energy under the purview of viscous cosmology. The equation of state (EoS) parameter is reconstructed in this scenario and quintessence behaviour is observed. Considering Barrow HDE as a specific case of Nojiri–Odintsov (NO) HDE, we have observed quintom behaviour of the EoS parameter and for some values of n the EoS has been observed to be very close to $-1$ for the current universe. The generalised second law of thermodynamics has come out to be valid in all the scenarios under consideration. Physical viability of considering Barrow HDE as a specific case of NO HDE is demonstrated in this study. Finally, it has been observed that the model under consideration is very close to $\Lambda$CDM and cannot go beyond it. Full article

Intra- and inter-molecular interactions were studied in 2,3-dichloro-5,8-dihydroxy-1,4-naphthoquinone and 1,4-dihydroxy-anthraquinone to shed more light on the molecular assembly phenomena. The electronic ground and excited states features of the compounds were investigated to find structure-property dependencies. The theoretical study was carried out on the basis of Density Functional Theory (DFT), its Time-Dependent (TD-DFT) extension, and using Car–Parrinello Molecular Dynamics (CPMD). In order to show how the environmental effects modulate the physico-chemical properties, the simulations were performed in vacuo, with the solvent reaction field (Polarizable Continuum Model (PCM) and water as a solvent) and crystalline phase. The intramolecular hydrogen bonds and the bridged proton dynamics were analyzed in detail. The aromatic rings and electronic structure changes were estimated using the Harmonic Oscillator Model of Aromaticity (HOMA) and Atoms in Molecules (AIM) theory. The Symmetry-Adapted Perturbation Theory (SAPT) was employed for interaction energy decomposition in the studied dimers and trimers. It was found that the presence of a polar solvent decreased the energy barrier for the bridged proton transfer. However, it did not significantly affect the aromaticity and electronic structure. The SAPT results showed that the mutual polarization of the monomers in the dimer was weak and that the dispersion was responsible for most of the intermolecular attraction. The intermolecular hydrogen bonds seem to be much weaker than the intramolecular bridges. The TD-DFT results confirmed that the electronic excitations do not play any significant role in the intramolecular proton transfer. The CPMD results indicated that the protons are very labile in the hydrogen bridges. Short proton transfer and proton-sharing events were observed, and a correlation between them in the twin bridges was noticed, especially for the first investigated compound. Full article

The non-alternant aromatic azulene, an isomer of alternant naphthalene, differs from the latter in peculiar properties. The large polarization of the π-electron system over the seven and five rings gives to azulene electrophile property a pronounced tendency to donate electrons to an acceptor, substituted at azulene 1 position. This paper presents cases in which azulene transfers electrons to a suitable acceptor as methylium ions, positive charged heteroaromatics and examples of neutral molecules that can accept electrons. The proposed product synthesis was outlined and the expected electron transfer was highlighted by analyzing the NMR, UV-Vis spectra and the pK_R⁺ values. Full article

Atomic cascades are ubiquitous in nature and they have been explored within very different scenarios, from precision measurements to the modeling of astrophysical spectra, and up to the radiation damage in biological matter. However, up to the present, a quantitative analysis of these cascades often failed because of their inherent complexity. Apart from utilizing the rotational symmetry of atoms and a proper distinction of different physical schemes, a hierarchy of useful approaches is therefore needed in order to keep cascade computations feasible. We here suggest a classification of atomic cascades and demonstrate how they can be modeled within the framework of the Jena Atomic Calculator. As an example, we shall compute within a configuration-average approach the stepwise decay cascade of atomic magnesium, following a $1s$ inner-shell ionization, and simulate the corresponding (final) ion distribution. Our classification of physical scenarios (schemes) and the hierarchy of computational approaches are both flexible to further refinements as well as to complex shell structures of the atoms and ions, for which the excitation and decay dynamics need to be modeled in good detail. Full article

Our main focus in this work is the classical variational inequality problem with Lipschitz continuous and pseudo-monotone mapping in real Hilbert spaces. An adaptive reflected subgradient-extragradient method is presented along with its weak convergence analysis. The novelty of the proposed method lies in the fact that only one projection onto the feasible set in each iteration is required, and there is no need to know/approximate the Lipschitz constant of the cost function a priori. To illustrate and emphasize the potential applicability of the new scheme, several numerical experiments and comparisons in tomography reconstruction, Nash–Cournot oligopolistic equilibrium, and more are presented. Full article

Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is to exploit a decomposition-based approach, such that the global impulse response of the system can be estimated using a combination of shorter adaptive filters. The algorithms are mainly tailored for multiple-input/single-output system identification problems, where the input data and the channels can be grouped in the form of rank-1 tensors. Nevertheless, the approach could be further extended for single-input/single-output system identification scenarios, where the impulse responses (of more general forms) can be modeled as higher-rank tensors. As compared to the conventional adaptive filters, which involve a single (usually long) filter for the estimation of the global impulse response, the tensor-based algorithms achieve faster convergence rate and tracking, while also providing better accuracy of the solution. Simulation results support the theoretical findings and indicate the advantages of the tensor-based algorithms over the conventional ones, in terms of the main performance criteria. Full article

In this paper, we study possible mathematical connections of the Clifford algebra with the $su\left(N\right)$-Lie algebra, or in more physical terms the links between space-time symmetry (Lorentz invariance) and internal $SU\left(N\right)$ gauge-symmetry for a massive spin one-half fermion described by the Dirac equation. The related matrix algebra is worked out in particular for the $SU\left(2\right)$ symmetry and outlined as well for the color gauge group $SU\left(3\right)$. Possible perspectives of this approach to unification of symmetries are briefly discussed. The calculations make extensive use of tensor multiplication of the matrices involved, whereby our focus is on revisiting the Coleman–Mandula theorem. This permits us to construct unified symmetries between Lorentz invariance and gauge symmetry in a direct product sense. Full article

This study has focused on the structure, bonding, and reactivity analysis of closo-borate anions [B_nH_n]²⁻ (n = 5–12). Several descriptors of B–H interactions have been calculated. It has been found that the values of electron density and total energy at bond critical point are the most useful descriptors for investigation of B–H interactions. Using results from the descriptor analysis, one may conclude that orbital interactions in [B_nH_n]²⁻ increase with increasing the boron cluster size. Several approaches to estimate atomic charges have been applied. Boron atoms in apical positions have more negative values of atomic charges as compared with atoms from equatorial positions. The mean values of boron and hydrogen atomic charges tend to be more positive with the increasing of boron cluster size. Global and local reactivity descriptors using conceptual density functional theory (DFT) theory have been calculated. Based on this theory, the closo-borate anions [B_nH_n]²⁻ (n = 5–9) can be considered strong and moderate electrophiles, while the closo-borate anions [B_nH_n]²⁻ (n = 10–12) can be considered marginal electrophiles. Fukui functions for electrophilic attack have been calculated. Fukui functions correlate well with atomic charges of the closo-borate anions. Boron atoms in apical positions have the most positive values of Fukui functions. Full article

Two new hydrated multicomponent crystals of zwitterionic 2-aminonicotinic acid with maleic and fumaric acids have been obtained and thoroughly characterized by a variety of experimental (X-ray analysis and terahertz Raman spectroscopy) and theoretical periodic density functional theory calculations, followed by Bader analysis of the crystalline electron density) techniques. It has been found that the Raman-active band in the region of 300 cm⁻¹ is due to the vibrations of the intramolecular O-H...O bond in the maleate anion. The energy/enthalpy of the intermolecular hydrogen bonds was estimated by several empirical approaches. An analysis of the interaction networks reflects the structure-directing role of the water molecule in the examined multicomponent crystals. A general scheme has been proposed to explain the proton transfer between the components during the formation of multicomponent crystals in water. Water molecules were found to play the key role in this process, forming a “water wire” between the COOH group of the dicarboxylic acid and the COO^– group of the zwitterion and the rendering crystal lattice of the considered multicomponent crystals. Full article

In a previous paper, we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light in vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conservation was discussed in a pervious paper, while preliminary results regarding energy conservation where discussed in some additional papers. Here we give a complete analysis of the exchange of energy between the mechanical part of the relativistic engine and the field part, the energy radiated from the relativistic engine is also discussed. We show that the relativistic engine effect on the energy is 4th-order in $\frac{1}{c}$ and no lower order relativistic engine effect on the energy exists. Full article

The Newton–Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is defined by invariance and reciprocity of the action in the form of Hamilton’s characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of the Green function satisfying the radial Schrödinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb–Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential. Full article

We present a review of the possibilities to conduct experiments of high efficiency in the nuclear and high energy physics with spin-polarized beams in a collider complex, configuration of which includes Siberian snakes or figure-8 collider ring. Special attention is given to the recently elicited advantageous possibility to conduct high precision experiments in a regime of the spin transparency (ST) when the design global spin tune is close to zero. In this regime, the polarization control is realized by use of spin navigators (SN), which are compact special insertions of magnets dedicated to a high flexibility spin manipulation including frequent spin flips. Full article

To address the problem that traditional stream ciphers are not sensitive to changes in the plaintext, a novel plaintext-related color image encryption scheme is proposed in this paper, which combines the 6-dimensional cellular neural network (CNN) and Chen’s chaotic system. This encryption scheme belongs to symmetric cryptography. In the proposed scheme, the initial key and switching function generated by the plaintext image are first utilized to control the CNN to complete the scrambling process. Then, Chen’s chaotic system is used to diffuse the scrambled image for realizing higher security. Finally, extensive performance evaluation is undertaken to validate the proposed scheme’s ability to offer the necessary security. Furthermore, the scheme is compared alongside state-of-the-art algorithms to establish its efficiency. Full article

Background: We analyze several constraints on the nuclear equation of state (EOS) currently available from neutron star (NS) observations and laboratory experiments and study the existence of possible correlations among properties of nuclear matter at saturation density with NS observables. Methods: We use a set of different models that include several phenomenological EOSs based on Skyrme and relativistic mean field models as well as microscopic calculations based on different many-body approaches, i.e., the (Dirac–)Brueckner–Hartree–Fock theories, Quantum Monte Carlo techniques, and the variational method. Results: We find that almost all the models considered are compatible with the laboratory constraints of the nuclear matter properties as well as with the largest NS mass observed up to now, $2.{14}_{-0.09}^{+0.10}{M}_{\odot }$ for the object PSR J0740+6620, and with the upper limit of the maximum mass of about 2.3–2.5$M_{\odot }$ deduced from the analysis of the GW170817 NS merger event. Conclusion: Our study shows that whereas no correlation exists between the tidal deformability and the value of the nuclear symmetry energy at saturation for any value of the NS mass, very weak correlations seem to exist with the derivative of the nuclear symmetry energy and with the nuclear incompressibility. Full article

Research on trajectory tracking is crucial for the development of autonomous vehicles. This paper presents a trajectory tracking scheme by utilizing model predictive control (MPC) and preview-follower theory (PFT), which includes a reference generation module and a MPC controller. The reference generation module could calculate reference lateral acceleration at the preview point by PFT to update state variables, and generate a reference yaw rate in each prediction point. Since the preview range is increased, PFT makes the calculation of yaw rate more accurate. Through physical constraints, the MPC controller can achieve the best tracking of the reference path. The MPC problem is formulated as a linear time-varying (LTV) MPC controller to achieve a predictive model from nonlinear vehicle dynamics to continuous online linearization. The MPC-PFT controller method performs well by increasing the effective length of the reference path. Compared with MPC and PFT controllers, the effectiveness and robustness of the proposed method are proved by simulations of two typical working conditions. Full article

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories. Full article

Heavy hadron spectroscopy was well understood within the naive quark model until the end of the past century. However, in 2003, the $X\left(3872\right)$ was discovered, with puzzling properties difficult to understand in the simple naive quark model picture. This state made clear that excited states of heavy mesons should be coupled to two-meson states in order to understand not only the masses but, in some cases, unexpected decay properties. In this work, we will give an overview of a way in which the naive quark model can be complemented with the coupling to two hadron thresholds. This program has been already applied to the heavy meson spectrum with the chiral quark model, and we show some examples where thresholds are of special relevance. Full article

The complexation of (3aR,7aR)-N-(3,5-bis(trifluoromethyl)phenyl)octahydro-2H-benzo[d]imidazol-2-imine (BTI), as a guest, to ethane-bridged bis(zinc octaethylporphyrin), bis(ZnOEP), as a host, has been studied by means of ultraviolet-visible (UV-Vis) and circular dichroism (CD) absorption spectroscopies, single crystal X-ray diffraction, and computational simulation. The formation of 1:2 host-guest complex was established by X-ray diffraction and UV-Vis titration studies. Two guest BTI molecules are located at the opposite sides of two porphyrin subunits of bis(ZnOEP) host, which is resting in the anti-conformation. The complexation of BTI molecules proceed via coordination of the imine nitrogens to the zinc ions of each porphyrin subunit of the host. Such supramolecular organization of the complex results in a screw arrangement of the two porphyrin subunits, inducing a strong CD signal in the Soret (B) band region. The corresponding DFT computational studies are in a good agreement with the experimental results and prove the presence of 1:2 host-guest complex as the major component in the solution (97.7%), but its optimized geometry differs from that observed in the solid-state. The UV-Vis and CD spectra simulated by using the solution-state geometry and the TD-DFT/ωB97X-D/cc-pVDZ + SMD (CH2Cl2) level of theory reproduced the experimentally obtained UV-Vis and CD spectra and confirmed the difference between the solid-state and solution structures. Moreover, it was shown that CD spectrum is very sensitive to the spatial arrangement of porphyrin subunits. Full article

The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance. Full article

The self-association of phosphonic acids with general formula RP(O)(OH)₂ in solution state remains largely unexplored. The general understanding is that such molecules form multiple intermolecular hydrogen bonds, but the stoichiometry of self-associates and the bonding motifs are unclear. In this work, we report the results of the study of self-association of tert-butylphosphonic acid using low temperature liquid-state ¹H and ³¹P NMR spectroscopy (100 K; CDF₃/CDF₂Cl) and density functional theory (DFT) calculations. For the first time, we demonstrate conclusively that polar aprotic medium tert-butylphosphonic acid forms highly symmetric cage-like tetramers held by eight OHO hydrogen bonds, which makes the complex quite stable. In these associates. each phosphonic acid molecule is bonded to three other molecules by forming two hydrogen bonds as proton donor and two hydrogen bonds as proton acceptor. Though the structure of such cage-like tetramers is close to tetrahedral, the formal symmetry of the self-associate is C₂. Full article

Chiral symmetry, and its dynamical breaking, has become a cornerstone in the description of the hadron’s phenomenology at low energy. The present manuscript gives a historical survey on how the quark model of hadrons has been implemented along the last decades trying to incorporate, among other important non-perturbative features of quantum chromodynamics (QCD), the dynamical chiral symmetry breaking mechanism. This effort has delivered different models such as the chiral bag model, the cloudy bag model, the chiral quark model or the chiral constituent quark model. Our main aim herein is to provide a brief introduction of the Special Issue “Advances in Chiral Quark Models” in Symmetry and contribute to the clarification of the differences among the above-mentioned models that include the adjective chiral in their nomenclature. Full article

Given an integral commutative residuated lattices $\mathbf{L}=(L,\vee ,\wedge )$, its full twist-product $(L^2,\bigsqcup ,\sqcap )$ can be endowed with two binary operations ⊙ and ⇒ introduced formerly by M. Busaniche and R. Cignoli as well as by C. Tsinakis and A. M. Wille such that it becomes a commutative residuated lattice. For every $a\in L$ we define a certain subset $P_a\left(\mathbf{L}\right)$ of $L^2$. We characterize when $P_a\left(\mathbf{L}\right)$ is a sublattice of the full twist-product $(L^2,\bigsqcup ,\sqcap )$. In this case $P_a\left(\mathbf{L}\right)$ together with some natural antitone involution ${}^{\prime }$ becomes a pseudo-Kleene lattice. If $\mathbf{L}$ is distributive then $(P_a\left(\mathbf{L}\right),\bigsqcup ,\sqcap ,{}^{\prime })$ becomes a Kleene lattice. We present sufficient conditions for $P_a\left(\mathbf{L}\right)$ being a subalgebra of $(L^2,\bigsqcup ,\sqcap ,\odot ,\Rightarrow )$ and thus for ⊙ and ⇒ being a pair of adjoint operations on $P_a\left(\mathbf{L}\right)$. Finally, we introduce another pair ⊙ and ⇒ of adjoint operations on the full twist-product of a bounded commutative residuated lattice such that the resulting algebra is a bounded commutative residuated lattice satisfying the double negation law, and we investigate when $P_a\left(\mathbf{L}\right)$ is closed under these new operations. Full article

In view of the slow convergence speed, difficulty of escaping from the local optimum, and difficulty maintaining the stability associated with the basic whale optimization algorithm (WOA), an improved WOA algorithm (REWOA) is proposed based on dual-operation strategy collaboration. Firstly, different evolutionary strategies are integrated into different dimensions of the algorithm structure to improve the convergence accuracy and the randomization operation of the random Gaussian distribution is used to increase the diversity of the population. Secondly, special reinforcements are made to the process involving whales searching for prey to enhance their exclusive exploration or exploitation capabilities, and a new skip step factor is proposed to enhance the optimizer’s ability to escape the local optimum. Finally, an adaptive weight factor is added to improve the stability of the algorithm and maintain a balance between exploration and exploitation. The effectiveness and feasibility of the proposed REWOA are verified with the benchmark functions and different experiments related to the identification of the Hammerstein model. Full article

We theoretically show that isolated agents that locally and symmetrically consume resources and sense positive resource gradients can generate constant motion via bootstrapped resource gradients in the absence of any externally imposed gradients, and we show a realization of this motion using robots. This self-generated agent motion can be coupled with neighboring agents to act as a spontaneously broken symmetry seed for emergent collective dynamics. We also show that in a sufficiently weak externally imposed gradient, it is possible for an agent to move against an external resource gradient due to the local resource depression on the landscape created by an agent. This counter-intuitive boot-strapped motion against an external gradient is demonstrated with a simple robot system on an light-emitting diode (LED) light-board. Full article

Accurate prediction of photovoltaic power is conducive to the application of clean energy and sustainable development. An improved whale algorithm is proposed to optimize the Support Vector Machine model. The characteristic of the model is that it needs less training data to symmetrically adapt to the prediction conditions of different weather, and has high prediction accuracy in different weather conditions. This study aims to (1) select light intensity, ambient temperature and relative humidity, which are strictly related to photovoltaic output power as the input data; (2) apply wavelet soft threshold denoising to preprocess input data to reduce the noise contained in input data to symmetrically enhance the adaptability of the prediction model in different weather conditions; (3) improve the whale algorithm by using tent chaotic mapping, nonlinear disturbance and differential evolution algorithm; (4) apply the improved whale algorithm to optimize the Support Vector Machine model in order to improve the prediction accuracy of the prediction model. The experiment proves that the short-term prediction model of photovoltaic power based on symmetry concept achieves ideal accuracy in different weather. The systematic method for output power prediction of renewable energy is conductive to reducing the workload of predicting the output power and to promoting the application of clean energy and sustainable development. Full article

Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D_6h and D_4h of the nuclear scaffolds are conserved. At the same time, the symmetries of the one-electron densities are broken, however, to specific subgroups of G for the excited superposition states. These subgroups depend on the polarization and on the electric fields of the laser pulses. They can be determined either by inspection of the symmetry elements of the one-electron density which represents charge migration after the laser pulse, or by a new and more efficient group-theoretical approach. The results agree perfectly with each other. They suggest laser control of symmetry breaking. The choice of the target subgroup is restricted, however, by a new theorem, i.e., it must contain the symmetry group of the time-dependent electronic Hamiltonian of the oriented molecule interacting with the laser pulse(s). This theorem can also be applied to confirm or to falsify complementary suggestions of electron symmetry breaking by laser pulses. Full article

On 14 August 2019, the LIGO/Virgo collaboration observed a compact object with mass $\sim {2.59}_{-0.09}^{+0.08}{M}_{\odot }$, as a component of a system where the main companion was a black hole with mass $\sim 23M_{\odot }$. A scientific debate initiated concerning the identification of the low mass component, as it falls into the neutron star–black hole mass gap. The understanding of the nature of GW190814 event will offer rich information concerning open issues, the speed of sound and the possible phase transition into other degrees of freedom. In the present work, we made an effort to probe the nuclear equation of state along with the GW190814 event. Firstly, we examine possible constraints on the nuclear equation of state inferred from the consideration that the low mass companion is a slow or rapidly rotating neutron star. In this case, the role of the upper bounds on the speed of sound is revealed, in connection with the dense nuclear matter properties. Secondly, we systematically study the tidal deformability of a possible high mass candidate existing as an individual star or as a component one in a binary neutron star system. As the tidal deformability and radius are quantities very sensitive on the neutron star equation of state, they are excellent counters on dense matter properties. We conjecture that similar isolated neutron stars or systems may exist in the universe and their possible future observation will shed light on the maximum neutron star mass problem. Full article

Soft diffraction phenomena in elastic nucleon scattering are considered from the viewpoint of the spin dependence of the interaction potential. Spin-dependent pomeron effects are analyzed for elastic $pp$ scattering, and spin-dependent differential cross sections and spin correlation parameters are calculated. The spin correlation parameter $A_N$ is examined on the basis of experimental data from $\sqrt{s}=4.9$ GeV up to $23.4$GeV in the framework of the extended High Energy Generalized Structure (HEGS) model. It is shown that the existing experimental data of proton-proton and proton-antiproton elastic scattering at high energy in the region of the diffraction minimum and at large momentum transfer give the support of the existence of the energy-independent part of the hadron spin flip amplitude. Full article

Objective: The main objective of the tests conducted was to analyze the position variability of the human body’s center of gravity during propelling the wheelchair, and to demonstrate the properties enabling the description of this variability by means of plane figures with a symmetry axis. A secondary objective was to show the impact of the used manual propulsion type and the wheelchair inclination angle in relation to the plane on the dimensions of the position variability areas of the center of gravity. Method and materials: Three patients participated in the research representing 50 centiles of anthropometric dimensions. Each patient carried out fifteen measurement tests on three wheelchairs for three inclination angles of the wheelchair frame in relation to the level. Each measurement test consisted of five propulsion cycles for which the positions of the center of gravity were determined with the sampling frequency of 100 Hz. The measured positions of the center of gravity were approximated with ellipses containing 95.4% of the measurements conducted, assuming their dimension scaling basis in the form of the double value of standard deviation defined based on the registered results. Results: Based on the measurements conducted, the average values of five ellipses parameters were determined for nine cases in which a variable was the type of wheelchair propulsion and its inclination angle in relation to the level. The area of the highest variability of the position of the center of gravity was measured for the wheelchair with a multispeed transmission. The average dimensions of the ellipse semi-axis amounted to 108.53 mm for the semi-axis a and 29.75 for the semi-axis b, the average position of the ellipse center amounted to x = 114.51 mm and y = −10.53 mm, and the average inclination angle of the ellipse α amounted to −6.92°. The area of the lowest variability of the position of the center of gravity was measured for the wheelchair with a hybrid transmission. In this case, the average dimensions of the ellipse semi-axis amounted to 64.07 mm for the semi-axis a and 33.85 for the semi-axis b; whereas, the average position of the ellipse center amounted to x = 245.13 mm and y = −28.24 mm, and the average inclination angle of the ellipse α amounted to −0.56°. Full article

Robust pole-placement based on convex $D_R$-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is non-convex, having a “cardioid” shape. In this paper, we further develop our recent results on the inner convex approximations of the cardioid, present systematical analysis of its design parameters and their influence on the corresponding closed loop performance (measured by standard integral of absolute error (IAE) and Total Variance criteria). The application of a robust controller designed with the proposed convex approximation of the discrete-time pole region is illustrated and evaluated on a real laboratory magnetic levitation plant. Full article

In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of the high harmonics of undulator radiation (UR). The effect on the spontaneous and stimulated UR was explored. The exact integral forms for the Bessel coefficients were obtained for undulators with general symmetric and asymmetric field harmonics. Spectral properties of the radiation from several configurations of the undulator fields with harmonics were compared with each other. The resulting spontaneous UR spectrum and harmonic intensities were obtained analytically in the form of integrals and compared with the respective results that were obtained numerically with SPECTRA program. The dimensionless scaling parameter of a free electron laser (FEL)—the Pierce parameter (ρ)—was computed and compared for the different considered undulators. We studied the differences in the behavior of the high-gain single pass FEL harmonics and the spontaneous UR harmonics in the same undulators. The undulators with variable deflection parameter (k) were considered. The effect of the k parameter (deflection parameter for a common planar undulator) on the spontaneous UR and on the high-gain FEL radiation was explored. In this context, an experiment with variable strength undulators at FLASH 2 FEL was analyzed; the shorter saturated length in high harmonic self-seeding (HHSS) regime vs. self-amplified spontaneous emission (SASE) is explained. Full article

We review the method of quantizers and dequantizers to construct an invertible map of the density operators onto functions including probability distributions and discuss in detail examples of qubit and qutrit states. The biphoton states existing in the process of parametric down-conversion are studied in the probability representation of quantum mechanics. Full article

The article deals with dendritic structures resulting from self-organization processes in aqueous solutions of albumin proteins. The methods for obtaining the structures and experimental results are presented. It is shown that dendrites are fractal structures that are symmetric under certain conditions of their formation and can have different characteristics depending on the isothermal dehydration of liquid samples. The fractal dimension of the structures in films of the albumin protein solution has been calculated. Dependences of the fractal dimension on the concentrations of salts and protein in the initial solutions and also on the dehydration temperature have been revealed. It has been shown that as the protein concentration in the solution grows, the salt concentration for the initiation of the dendritic structure formation increases. It has been found that the temperature dependences of the fractal dimension of the structures become smoother with increasing protein concentration in solutions. The relationship between geometric characteristics of dendrites and self-organization parameters during drying is discussed. Full article

This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received much attention in the literature, and may be of interest for theoretical and practical purposes. Basic statistical properties of the newly defined distribution are derived, including moments, skewness, kurtosis and order statistics. For the related model, the parametric estimation is examined through different methods. We assess the performance of the obtained estimates by two complementary simulation studies. Also, the quantile regression model based on the proposed distribution is introduced. Applications to three real datasets show that the proposed models are quite competitive in comparison to well-established models. Full article

We construct scalarized wormholes with a NUT charge in higher curvature theories. We consider both Einstein-scalar-Gauss-Bonnet and Einstein-scalar-Chern-Simons theories, following Brihaye, Herdeiro and Radu, who recently studied spontaneously scalarised Schwarzschild-NUT solutions. By varying the coupling parameter and the scalar charge we determine the domain of existence of the scalarized nutty wormholes, and their dependence on the NUT charge. In the Gauss-Bonnet case the known set of scalarized wormholes is reached in the limit of vanishing NUT charge. In the Chern-Simons case, however, the limit is peculiar, since with vanishing NUT charge the coupling constant diverges. We focus on scalarized nutty wormholes with a single throat and study their properties. All these scalarized nutty wormholes feature a critical polar angle, beyond which closed timelike curves are present. Full article

Since in many particular cases checking directly the conditions from the definitions of starlikeness or convexity of a function can be difficult, in this paper we use the theory of differential subordination and in particular the method of admissible functions in order to determine conditions of starlikeness and convexity for the confluent (Kummer) hypergeometric function of the first kind. Having in mind the results obtained by Miller and Mocanu in 1990 who used $a,c\in \mathbb{R}$, for the confluent (Kummer) hypergeometric function, in this investigation a and c complex numbers are used and two criteria for univalence of the investigated function are stated. An example is also included in order to show the relevance of the original results of the paper. Full article