Chivalry is a concept that is both familiar and distant to many Japanese. There is no other social class in the world that resembles knights as much as the samurai in Japan. However, why is it that there is such a gap between knights and warriors, even though they are both warriors with the same social status and honor? This paper reviews the legal debates on the deposed sovereigns’ rights have emerged since 20th century. Among them, the right to appoint knights by heads of deposed royal families is one of the focal points. The author begins with a comprehensive review of legal debates on the subject. Six principles on the appointment are extracted from the review. Then, a comparison between chivalry and Bushido, the Japanese Samurai code, was carried out.

We monitored the water quality and hydrological conditions of a horizontal subsurface constructed wetland (HSSF-CW) in Beijing, China, for 2 years. We simulated the area rate constant and the temperature coefficient with the first-order kinetic model. We examined the relationships between the nitrogen (N) removal rate, N load, seasonal variations in the N removal rate, and environmental factors, such as the area rate constant, temperature, and dissolved oxygen (DO). The effluent ammonia (NH₄⁺-N) and nitrate (NO₃⁻-N) concentrations were significantly lower than the influent concentrations (p<0.01, n=38). The NO₃⁻-N load was significantly correlated with the removal rate (R²=0.9566, p<0.01), but the NH^₄+-N load was not correlated with the removal rate (R²=0.0187, p>0.01). The area rate constants of NO₃⁻-N and NH₄⁺-N at 20 °C were 27.01±26.49 and 16.63±10.58 m∙yr⁻¹, respectively. The temperature coefficients for NO₃⁻-N and NH₄⁺-N were estimated at 1.0042 and 0.9604, respectively. The area rate constants for NO₃⁻-N and NH₄⁺-N were not correlated with temperature (p>0.01). The NO₃⁻-N area rate constant was correlated with the corresponding load (R²=0.9625, p<0.01). The NH₄⁺-N area rate was correlated with DO (R²=0.6922, p<0.01), suggesting that the factors that influenced the N removal rate in this wetland met Liebig's law of the minimum.

This research focuses on the Hopf bifurcation occurring at a singular point with high-order degeneracy in a class of three-dimensional systems. Based on center manifold theorem, by expanding the technique for determining singular point values of degenerate singularities in two-dimensional systems, the formal series method to determine the singular point values at the high-order degenerate critical point is discussed. Furthermore, a class of specific three-dimensional differential systems with high-order degenerate singularities is explored. By computing the singular point values and determining center conditions, we proved that a minimum of 5 small-amplitude limit cycles in the vicinity of the origin. This research provides new perspectives on the center problem and limit cycle bifurcation in high-dimensional systems with high-order degenerate singular points.

For many engineering applications it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches length scale parameter have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modelling as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior.

Uncertain fractional differential equation (UFDE) is an excellent tool for describing complicated dynamic systems. This paper analyzes the valuation problems of currency option based on UFDE under optimistic value criterion. Firstly, an uncertain fractional currency model is formulated to describe the dynamics of foreign exchange rate. Then, the pricing formulae of European, American and Asian currency option are obtained under optimistic value criterion, respectively. Finally, numerical simulations are provided to illustrate the validity of our theoretical results.

Aiming at the development of the application of massive and heterogeneous LEO constellations, the influence of typical perturbation forces on the orbit prediction of LEO satellites at different altitudes is analyzed. Firstly, the main perturbation force model of LEO satellites is introduced. Then experiments for analyzing the influence of orbit prediction on LEO satellites at different altitudes are designed. Finally, the influence of typical perturbation forces on the orbit prediction under different prediction durations by numerical analysis is assessed systematically, and the orbit prediction of LEO satellites with different non-spherical gravitational field orders, ocean tide orders and atmospheric density models were compared and calculated. The research results show that different orders of non-spherical gravitational fields should be considered when the altitude of satellites is different, the reasonable gravitational field orders for LEO satellites at 500km, 1000km, 1500km and 2000km under 1-hour forecast time are 140x140, 80x80, 60x60 and 40x40 orders, the reasonable orders of ocean tide perturbation for 1500km and 2000km satellites are 20x20 orders. Under the 24-hour forecast time, atmospheric resistance has a great influence on the precision of LEO satellites at orbit altitude below 1,000km. The forecast deviation of the LEO satellites orbit at 500km reaches 8751.576m. The difference of orbit precision between different atmospheric density models is in the meter level. The orbit deviation by the Standard Atmosphere 1976 and NRLMSISE 2000 atmospheric models respectively reaches 25.494m. Relevant conclusions provide support for the optimization and selection of dynamical models in high precision orbit determination and fast orbit prediction of LEO satellites.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset.

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

By this contribution we would like to briefly highlight the problems in conceiving the “Hydrogen Bond” (HB) as a real short-range, directional, electrostatic, attractive interaction and to reframe its nature through the non-approximated view of condensed matter offered by a Quantum Electro-Dynamic (QED) perspective. We focus our attention on water, as the paramount case to show the effectiveness of this 40-years’ old theoretical background, which depicts water as a two-fluid system (where one of the two phases is coherent). The HB emerge to be the result of the electromagnetic field gradient in the coherent phase of water, whose vacuum level is lower than the non-coherent (gas-like) fraction. Thus, the HB can be properly looked at, i.e. no more as a “dipolar force” among molecules, but as the phenomenological effect of their collective thermodynamic tendency to occupy a lower ground-state, compatibly with temperature and pressure. This perspective allows to account for many “anomalous” behaviours of water and to understand why the calculated energy associated to HB should change when considering two molecules (water-dimer), or the liquid state, or the several kinds of ice. The emergence of a condensed, liquid, phase at room temperature is indeed the consequence of the boson condensation as described in the framework of spontaneous symmetry breakings (SSB). The switch from a still semi-classical Quantum Mechanical (QM) in the 1st quantization to a Quantum Field Theory (QFT) view embedded in the 2nd quantization is advocated for a more realistic and authentic description of water, condensed matter and living systems.

In this paper we consider a failed cold standby systems and obtain some stochastic bounds on the idle time of such systems. It is assumed that, at a time t the failure of a cold standby system is observed, but the actual time of the failure is a time before t. The idle time of the inactive cold standby system is measured as the time between the exact time of failure, which is a random variable, and time t. We use the idle times of the components of the system to obtain lower and upper bounds on the lifetime of the standby system to which they are assembled. We bring some examples to show that the results and the conditions imposed to get them are achievable.

The aim of the paper is to provide an overview of the monastic houses operated on the northernmost periphery of Roman Catholic Europe during the Middle Ages. The intention is to debunk the long-held theory of Iceland and Norse Greenland’s supposed isolation from the rest of the world, as it is clear that medieval monasticism reached both of these societies, just as it reached their counterparts elsewhere in the North Atlantic. During the Middle Ages, fourteen monastic houses were opened in Iceland and two in Norse Greenland, all following the Benedictine or Augustinian Order.

This paper presents a numerical algorithm for solving high-order BVPs. We introduce the construction method of multiscale orthonormal basis in W^m[0; 1] by multiscale orthonormal basis in W¹[0; 1]. We define approximate solution, and obtain the approximate solution of high-order BVPs by using the approximate theory. Moreover, the convergence and stability of the algorithm are improved. At last, several numerical experiments show the feasibility of the proposed method.

The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters. A higher-order scheme is used to discretize geometry of the structure as well as the relevant physical quantities. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss-Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve computational efficiency, a Chebyshev approximation approach is applied to a fast calculation of the Green function that needs evaluation thousands of times. In addition, OpenMP parallel technique is used to the formation of influence coefficient matrix, which significantly reduces CPU time. Finally, computations are performed on wave exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates good performance of the present method.

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold standby system with age t and the lifetime of a cold standby system consisting of used components with age t using the likelihood ratio order and the usual stochastic order. We use illustrative examples to explore the results presented.

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained.

: This paper presents a comparison between direct integer orders or classical model reference adaptive control (IO-DMRAC) versus its fractional orders counterpart (FO-DMRAC) applied to the F-16 aircraft longitudinal model pitch rate control. A substantial improvement is achieved when using fractional order adaptive control, since, in addition to performance indices, such as Integral Square-Error criterion (ISE) and Integral Square-Input criterion (ISU) being lower, the oscillations of the system output (pitch rate) in the transient period, are eliminated. Moreover, it is the first attempt in literature of adaptive control that a FO-DMRAC is applied to the pitch rate control of an aircraft. A F-16 short-period model, whose relative degree is equal to 1 (n^*=1) is analyzed by mean of simulations with good results. A FO-DMRAC is designed, for a specific operating flight conditions and compared with its IO-DMRAC counterpart. Furthermore, the boundedness of all signals, including the internal ones ω(t) are assured.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

In this work, we demonstrate that cutting diamond crystals with a laser (532 nm wavelength, 0.5 mJ energy, 200 ns pulse duration at 15 kHz) produces a ≲20nm thick surface layer with magnetic order at room temperature. We have measured the magnetic moment with a SQUID magnetometer of six natural and six CVD diamond crystals of different size, nitrogen content and surface orientations. A robust ferromagnetic response at 300 K is observed only for crystals that were cut with the laser along the (100) surface orientation. The magnetic signals are much weaker for the (110) and negligible for the (111) orientations. We attribute the magnetic order to the disordered graphite layer produced by the laser at the diamond surface. The ferromagnetic signal vanished after chemical etching or after moderate temperature annealing. The obtained results indicate that laser treatment of diamond may pave the way to create ferromagnetic spots at its surface.

W. L. Edge proved that the internal points of a conic in PG(2,5), together with the collinear triples on the non-secant lines, form the Desargues configuration. M. Saniga showed an intimate connection between Desargues configurations and the generalized quadrangles of order two, GQ(2,2), whose representation has been dubbed “the doily” by Stan Payne in 1973. In this paper we prove that the external points of a conic in PG(2,5), together with the collinear and non-collinear triples on the non-tangent lines, form the generalized quadrangle of order two.

In this paper, inspired by recent articles of G. Anatriello and G. Vincenzi (see \cite{Ana}), and G. Cerda-Morales (see \cite{Cer1,Cer2}), we will introduce the third-order $\overline{h}$-Jacobsthal and third-order $\overline{h}$-Jacobsthal--Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in \cite{Cer2}.

In the present study, nonlinear vibration of a nanobeam resting on fractional order viscoelastic Winkler-Pasternak foundaion is studied using nonlocal elasticity theory. D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. Detailled parametric study is conducted, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

I deal with perception and action (e.g. movements) using results from Synergetics, a comprehensive mathematical theory of the selforganized formation ("emergence“) of spatial, temporal, or functional structures in complex systems. I illustrate basic concepts such as order parameters (ops), enslavement, complexity reduction, circular causality first by examples of well known collective, spontaneous modes of human behavior such as rhythmic clapping of hands etc., and then by face recognition. The role played by ops depends on context. In the case of face (or pattern) recognition an op represents the concept of an individual face (action of mind) and it enslaves the action (firing rates) of neurons (body). This insight allows me to interpret syndroms as order parameters playing their mind/body double role. I present criteria for the identification of ops and discuss their general properties including error correction and "remedy“ of deficiencies. Contact is made with a recent paper by Sabine Koch on embodied aesthetics. My approach includes the saturation of attention at various time scales (ambiguous figures/fashion). Adopting a psychological perspective, I discuss some ingredients of beauty such as proportionality and symmetry, but also the importance of irregularities.

The Aβ cascade and alternations of biomarkers in neuro-inflammation, synaptic dysfunction and neuronal injury followed by Aβ have progressed. But the question is how to use the biomarkers. Here, we examine the evidence and pathogenic implications of protein interactions and the time order of alternation. After the deposition of Aβ, the change of tau, NfL and NG is the main alternation and connection to others. The neuro-inflammation, synaptic dysfunction and neuronal injury function is exhibited prior the structural and metabolic changes in the brain following Aβ deposition. The time order of such biomarkers compared to the tau protein is not clear. Despite the close relationship between biomarkers and plaque Aβ deposition, several factors favor one or the other. There is an interaction between the proteins that CSF SNAP-25, VILIP-1 and YKL-40 can predict the brain amyloid burden. The Aβ cascade hypothesis could be the pathway, but not all subjects are converted to AD, even with very high elevated Aβ. The interaction of biomarkers and the time order of change require further research to identify the right subjects and right molecular target for precision medicine therapies.

The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is “broken” by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses; but it is doubtful that such evanescent states can survive below the critical temperature of 159.5 GeV, where the known particles were actually created.

The beautiful structures of single and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein structures are considered to be aperiodic, and may have evolved this way for functional purposes, especially in instances that require a combination of softness and rigidity within the same molecule. By analyzing the solved protein structures, we show that orientational symmetry is broken in the aperiodic arrangement of the secondary structural elements (SSEs), which we deduce by calculating the nematic order parameter, $P_2$. We find that the folded structures are nematic droplets with a broad distribution of $P_2$. We argue that non-zero values of $P_2$, leads to an arrangement of the SSEs that can resist mechanical forces, which is a requirement for allosteric proteins. Such proteins, which resist mechanical forces in some regions while being flexible in others, transmit signals from one region of the protein to another (action at a distance) in response to binding of ligands (oxygen, ATP or other small molecules).

The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure.

Due to the nonlinear stiffness and fractional-order damping characteristics of some real suspension systems, coupled with the presence of viscoelastic materials, fractional-order nonlinear suspension system modeling has become a focus of research in recent years. In this study, an electric oil and gas actuator based on fractional-order PID position feedback control is proposed, through which the damping coefficient of the suspension system is adjusted to realize the active control of the suspension. A fractional order PID algorithm is used to control the motor's rotational angle to realize the damping adjustment of the suspension system. In this process, the road roughness is collected by the sensors as the criterion of damping adjustment, and the particle swarm algorithm is utilized to find the optimal objective function under different road surface slopes, to obtain the optimal cornering value. According to the mathematical and physical model of the suspension system, the simulation model and the corresponding test platform of this type of suspension system are built. The simulation and experimental results show that the simulation results of the fractional-order nonlinear suspension model are closer to the actual experimental values than those of the traditional linear suspension model, and the accuracy of each performance index is improved by more than 18.5%. The designed active suspension system optimizes the body acceleration, suspension dynamic deflection, and tire dynamic load to 89.8%, 56.7%, and 73.4% of the passive suspension, respectively. Notably, the designed fractional order PID control circuit for the motor shows better control results compared to the conventional PID control circuit. This study provides an effective theoretical and empirical basis for the control and optimization of fractional-order nonlinear suspension systems.

A novel phase-field method based numerical approach to modeling the compaction process of sedi- ments is presented. Water-logged rock or soil sediments are deposited on the water basins over time and the increasing volume of the sediment compacts under its own weight and external pressure. Coupled evolution of mass conservation, Darcy flow, and the viscoelastic constitutive response, in conjunction with the evolution of porosity and permeability, make this problem highly non-linear and involve moving boundaries. We adopt a phase-field approach to represent the moving sediment interface, and the underlying multiphasic model permits for studying compaction in dynamically evolving sediments. This approach does not necessitate a change of domain sizes as is the case of existing traditional models of sedimentation but rather treats sedimentation growth as a problem of interface motion. We first model a classical compaction problem in 1D to compare with existing results in the literature, and then extend the framework to 2D to model the compaction process taking place under the influence of gravity. The model is then extensively applied to understand the effect of the sediment initial state and the sediment material properties on the compaction process and its spatiotemporal evolution. Lastly, a strong validation of our phase-field treatment results against predictions from traditional methods of solving open boundary sediment compaction problems, and a good agreement between the conventional understanding and the numerical predictions of porosity dependence on the fluid pore pressure for various cases of geological interest, are used to demonstrate the applicability and scalability of this novel numerical framework to model more advanced sediment compaction problems and geometries.

We discuss the role of the opposing principles of order and disorder in physical and biological systems in determining stability, growth and evolution and bring forth the potential role of a cosmic ordering agency. We analyze its role in decreasing entropy by coarse-graining and hence in determining the initial low entropy state of the big bang universe. Since all physical and biological systems have either cycles of order and disorder alternating, or may have chaotic evolution with non-linear laws, the same is expected of the dynamics of the whole universe as well. The entropy of the initial state of the universe could be low because of the reduction of degrees of freedom (DoF) as one moves from physical encoding to neural encoding and then on to psychic encoding of information in a nested manner by coarse-graining. It is by such encoding that this cosmic agency enables the universe to pass through the big crunch phase and then rolls it out as the big bang universe from the initial state of low entropy.

COVID-19 outbreak started in the Chinese city of Wuhan and spread around the globe in months due to its high contagious level. Hence, this disease posed a great challenge to researchers and mathematicians. Numerous mathematical models have been suggested to visualize the spreading speed and trends of this pandemic. In this paper, a comparison of a widely established and accepted method, the Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP) model with a newly-proposed fractional-order SEIQRDP is studied. Densely populated Countries of Asia (Pakistan, India, and Bangladesh) have been chosen as data sets and both algorithms have been applied to their data. The same comparison technique has also been used on the data of two polar countries, New Zealand and Russia, that validated our findings. Error comparison of both algorithms has been recorded in a tabulated form which shows multi-fold erroneous trends over WHO data of selected countries.

The manufacturing geometrical variability in axial compressors is a stochastic source of uncertainty, implying that the real geometry differs from the nominal design. This causes the real geometry to lose the ideal axial symmetry. Considering the aerofoils of a stator vane, the geometrical variability affects the flow traversing it. This impacts the downstream rotor, especially when considering the aeroelastic excitation forces. Optical surface scans coupled with a parametrization method allow for acquiring the information relative to the real aerofoils geometries. The measured data are included in a multi-passage and multi-stage CFD setup to represent the mistuned flow. In particular, low excitation harmonics on the rotor vane are introduced due to the geometrical deviations of the upstream stator. The introduced low engine orders as well as their amplitude depend on the stator geometries and their order. A method is proposed to represent the phenomena in a reduced CFD domain, limiting the size and number of solutions required to probabilistically describe the rotor excitation forces. The resulting rotor excitation forces are reconstructed as a superposition of disturbances due to individual stator aerofoils geometries. This indicates that the problem is linear in in the combination of disturbances from single passages.

This work is intended to lead a study of necessary and sufficient optimality conditions for scalar optimization problems on Hadamard manifolds. In the context of this geometry, we obtain and present new function types characterized by the property of having all their second-order stationary points to be global minimums. In order to do so, we extend the concept convexity in Euclidean space to a more general notion of invexity on Hadamard manifolds. This is done employing notions of second-order directional derivative, second-order pseudoinvexity functions and the second-order Karush-Kuhn-Tucker-pseudoinvexity problem. Thus, we prove that every second-order stationary point is a global minimum if and only if the problem is either second-order pseudoinvex or second-order KKT-pseudoinvex depending on whether the problem regards unconstrained or constrained scalar optimization respectively. This result has not been presented in the literature before. Finally, examples of these new characterizations are provided in the context of \textit{"Higgs Boson like"} potentials among others.

This article introduces a new fractional approach to the concept of information dimension of complex networks, based on a (q,q′)-entropy proposed in the literature. The q parameter measures how far is the number of subsystems (for a given size ε) from the mean number of overall sizes. The q′ (interaction index) measures when the interactions between subsystems are greater (q′&gt;1), lesser (q′&lt;1) or equal to the interactions into these subsystems. The computations of the proposed information dimension are carried out on several real-world and synthetic complex networks. The results from the proposed information dimension are compared with those from the information dimension based on the Shannon entropy.

We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.

The photodegradation of azithromycin present was carried out in water using H2O2 under UV irradiation. The reaction variables considered in this study were the amount of H2O2 solution and the initial concentration of azithromycin to evaluate the performance of the photodegradation process. The azithromycin degradation was not observed in the dark during stirring for 20 minutes. The study showed efficient photodegradation of azithromycin using H2O2 as an oxidant in the presence of UV irradiation. The azithromycin degradation was affected significantly by the pH of the irradiated solution. The degradation was low at an acidic pH and showed an increasing trend as the pH changed to basic. The azithromycin degradation was increased with a higher amount (higher concentration) of H2O2. The degradation of azithromycin decreased with a higher concentration of azithromycin in the reacting solution. The highest degradation of AZT was achieved in 1 hour using a 1.0 ppm AZT solution containing 3 ml of H2O2. The experimental data obtained was well-fitted to zero-order reaction kinetics. The results of this study were found to be superior when compared with those reported in the literature, with photocatalysis using nanomaterials and photolysis using irradiation and H2O2. The UV/H2O2 system was found to be quite efficient for the photodegradation of azithromycin, and this system can be applied to degrade other organic pollutants present in industrial wastewater. To this point, such a study has not been reported specifically for AZT photodegradation.

In this article, an iterative method of two step is proposed for finding all roots simultaneously of polynomial equations. The order of convergence of the proposed algorithm is 2m, by using any iterative scheme of order m. Numerical tests are performed to confirm the theoretical results and to compare the proposed scheme with existing methods for finding all roots simultaneously.

All-optical signal processing based on nonlinear optical devices is promising for ultrafast information processing in optical communication systems. Recent advances in two-dimensional (2D) layered materials with unique structures and distinctive properties have opened up new avenues for nonlinear optics and the fabrication of related devices with high performance. This paper reviews the recent advances in research on third-order optical nonlinearities of 2D materials, focusing on all-optical processing applications in the optical telecommunications band near 1550 nm. First, we provide an overview of the material properties of different 2D materials. Next, we review different methods for characterizing the third-order optical nonlinearities of 2D materials, including the Z-scan technique, third-harmonic generation (THG) measurement, and hybrid device characterization, together with a summary of the measured n₂ values in the telecommunications band. Finally, the current challenges and future perspectives are discussed.

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium, given uncertainty inherent in the systems. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic systems and information geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time, and is called the information length. By using this concept, we investigate the information geometry of non-equilibrium processes involved in disorder-order transitions between the critical and subcritical states in a bistable system. Specifically, we compute time-dependent PDFs, information length, the rate of change in information length, entropy change and Fisher information in disorder-to-order and order-to-disorder transitions, and discuss similarities and disparities between the two transitions. In particular, we show that the total information length in order-to-disorder transition is much larger than that in disorder-to-order transition, and elucidate the link to the drastically different evolution of entropy in both transitions. We also provide the comparison of the results with those in the case of the transition between the subcritical and supercritical states and discuss implications for fitness.

Data-Flow and Higher-Order Mutation are white-box testing techniques. To our knowledge, no work has been proposed to compare data flow and higher-order mutation. This paper compares all def-uses data-flow and second-order mutation criteria. This compassion investigates the subsumption relation between these two criteria and evaluates the effectiveness of test data developed for each. To compare the two criteria, a set of test data satisfying each criterion is generated, which is used to explore whether one criterion subsumes the other criterion and assess the effectiveness of the test set that was developed for one methodology in terms of the other. The results showed that the mean mutation coverage ratio of the all du-pairs adequate test cover is 80.9%, and the mean data flow coverage ratio of the 2nd-order mutant adequate test cover is 98.7%. Consequently, 2nd-order mutation “ProbSubsumes” the all du-pairs data flow. The failure detection efficiency of the mutation (98%) is significantly better than the failure detection efficiency of data flow (86%). Consequently, 2nd-order mutation testing is “ProbBetter” than all du-pairs data flow testing. In contrast, the size of the test suite of 2nd-order mutation is more significant than the size of the test suite of all du-pairs.

We make use of generalized iterations of the Sacks forcing to define cardinal-preserving generic extensions of the constructible universe L in which the axioms of ZF hold and in addition either 1) the parameter-free countable axiom of choice AC* fails, or 2) AC* holds but the full countable axiom of choice AC fails in the domain of reals. In another generic extension of L, we define a set X⊆P(ω), which is a model of the parameter-free part PA2* of the 2nd order Peano arithmetic PA2, in which CA(Σ21) (Comprehension for Σ21 formulas with parameters) holds, yet an instance of Comprehension CA for a more complex formula fails. Treating the iterated Sacks forcing as a class forcing over $L_{\omega_1}$, we infer the following consistency results as corollaries. If the 2nd order Peano arithmetic PA2 is formally consistent then so are the theories: 1) PA2 + negation of AC*, 2) PA2 + AC* + negation of AC, 3) PA2* + CA(Σ21) + negation of CA.

A critical discussion on the computation of the dispersion diagram in periodic one-dimensional guiding structures is carried out. In particular, an analysis is presented of the pros and cons of combined methods that make use of full-wave simulations done with commercial software packages with further analytical post-processing based on simplifications brought by an equivalent circuit model of the structure. Some of the most common methods reported in the literature are reviewed and their advantanges and limitations highlighted. Our discussion is complemented with several selected numerical examples in order to discuss the most relevant aspects that a potential user of these methods should be aware of. Special attention is paid to the relevant role played by the high-order coupling between the two halves of a symmetric unit cell of the periodic structure.

Aim: To investigate the application of anterior and posterior corneal higher order aberrations (HOAs) in detecting keratoconus (KC) and suspect keratoconus (SKC). Method: This is a retrospective, case-control study which evaluated non-ectatic (normal) eyes, SKC eyes, and KC eyes. The Sirius Scheimpfug (CSO, Italy) analyzer was used to measure HOAs of the anterior and posterior corneal surfaces. Sensitivity, specificity and area under receiver operating characteristic curve (AUC) were calculated. Results: Two-hundred and twenty eyes were included in the analysis (normal n = 108, SKC n= 42, KC n= 70). Receiver operating characteristic (ROC) curve analysis revealed a high predictive ability for anterior corneal HOAs parameters: Root mean square (RMS) total corneal HOAs, RMS trefoil and RMS coma to detect keratoconus (AUC > 0.9 for all). RMS Coma (3, ±1) derived from the anterior corneal surface was the parameter with the highest ability to discriminate between suspect keratoconus and normal eyes (AUC = 0.922; cutoff > 0.2). All posterior corneal HOAs parameters were insufficient in discriminating between SKC and normal eyes (AUC < 0.8 for all). In contrast, their ability to detect KC was excellent with AUC of > 0.9 for all except RMS spherical aberrations (AUC = 0.846). Conclusion: Anterior and posterior corneal higher order aberrations can differentiate between keratoconus and normal eyes, with a high level of certainty. In suspect keratoconus disease however, only anterior corneal HOAs, and in particular coma-like aberrations, are of value. Corneal aberrometry may be of value in screening for keratoconus in populations with a high prevalence of the disease.

Endoscopic medical images can suffer from uneven illumination, low contrast, and lack of texture information due to the use of point directional light sources and the presence of narrow tissue structures, posing diagnostic difficulties for physicians. In this paper, a deep learning-based su-pervised illumination enhancement network is designed for low-light endoscopic images, aiming to improve both global illumination and local details. Initially, a global illumination enhancement module is formulated utilizing a higher-order curve function to improve global illumination. Sec-ondly, a local feature extraction module incorporating dual attention is designed to capture local detailed features. Considering the significance of color fidelity in biomedical scenarios, the designed loss function prioritizes introducing color loss to alleviate image color distortion. Compared with seven state-of-the-art enhancement algorithms on Endo4IE endoscopic datasets, experimental re-sults show that the proposed method can better enhance low-light endoscopic images and avoid image color distortion. It provides an efficient method to enhance images captured by endoscopes which can effectively assist clinical diagnosis and treatment.

Based on the fractional order of nonlinear system for love model with a periodic function as an external force, analyzed the characteristics of the chaotic dynamic in this study. The relationship between the chaotic dynamic of the fractional-love model with the external force and the fractional-order system was analyzed when the parameters are fixed. Further, we also studied the relationship between the chaotic systemic dynamic and the parameters when the fractional-order system is fixed. The results show that when the parameters are fixed, the fractional-order system exhibited segmented chaotic states for the different fractional orders of the system. When fixed the fractional-order system, the system exhibited the periodic and chaotic states as parameter changes.

This study presents a prediction model based on Logistic Growth Curve to evaluate the effectiveness of Movement Control Order (MCO) on COVID-19 pandemic spread. The evaluation assesses and predicts the growth models. The estimated model is a forecast-based model that depended on partial data from the COVID-19 cases in Malaysia. The model is then studied together with the effectiveness of the three phases of MCO implemented in Malaysia. Evidence from this study suggests that results of the LGC prediction model match with the progress and effectiveness of the MCO to flatten the curve, thus helped to control the spike in number of active COVID-19 cases and spread of COVID-19 infection growth.

Aiming to reveal the kinetic characteristics of ceramic ball grinding of fine magnetite comprehensively, two types of ceramic balls ground with the same filling rate and total weight as steel balls were researched. The results show that the breakage rate of ceramic ball grinding is only half of that of steel ball grinding with the same media filling rate. With the same total media weight and the feed size less than 0.212 mm, the breakage rate of the ceramic ball grinding approaches the steel ball grinding and is 21.43% higher than that of the steel ball grinding. The main crushing form of magnetite changed from impact to abrasion in ceramic ball grinding compared with steel ball grinding, which significantly affected the value of the zero-order output constant a. Consequently, there is a noticeable difference in the variation of the parameter β related to the fines generation rate of the ceramic ball grinding compared with the steel ball grinding.

This note addresses a fundamental problem in matrix theory on establishing and characterizing range equalities for matrix expressions that involve generalized inverses. We first establish a group of necessary and sufficient conditions for the matrix range equality ${\rm range}(D_1 - C_1A_1^{\dag}B_1) = {\rm range}(D_2 - C_2A_2^{\dag}B_2)$ to hold, where $(\cdot)^{\dag}$ denotes the Moore--Penrose inverse of matrix. We then give several groups of range equalities with extrusion properties for multiple matrix products associated with two matrices and their conjugate transposes and Moore--Penrose inverses.

The study of order patterns of three equally spaced values $x_t,x_{t+d},x_{t+2d}$ in a time series is a powerful tool. The lag $d$ is changed in a wide range so that differences of frequencies of order patterns become autocorrelation functions. Similar to a spectrogram in speech analysis, four ordinal autocorrelation functions are used to visualize big data series, as for instance heart and brain activity over many hours. The method applies to real data without preprocessing, outliers and missing data do not matter. On the theoretical side, we study properties of order correlation functions and show that the four autocorrelation functions are orthogonal in a certain sense. An analysis of variance of a modified permutation entropy can be performed with four variance components associated with the functions.

Abstract The last mile has to deliver the goods at the right time and at the right cost for business logistics services to enhance the customer service experience. The objective of this paper is to examine the challenges of retail omni-channel distribution influencing the effective last mile fulfilment operations processes in the apparel group (organisation phase). It further establishes the extent of how the last mile for demand-driven store replenishment influences the level of retailers’ order fulfilment (in full and on time) (environment phase). This paper, persistently assesses the contribution of integrated information systems on brick and mortar and virtual omni-channel distribution networks to improve timeousness, order accuracy and fill rate (technology phase). The mixed method has triangulated the methods from both quantitative methodology using frequencies and binomial testing and subjective thematic analysis of qualitative data from interviewees. The sample of 175 questionnaires were received with a response rate is 85 per cent (148 responses). The main findings of the paper revealed that the current order fulfilment process aligned with the last mile is effective on the basis of the fill rate, lead time and order condition of orders delivered via store economy and store express.

NMR Spectroscopy is used, in the temperature range 180-350K, to study local order and transport in liquid water (pure and confined) and its solutions with glicerol and methanol at different molar fractions. Being the liquid water thermodynamic dominated by polymorphism (two coexisting liquid phases: high- and low-density HDL and LDL) - with the LDL due to the hydrophilic HB interactions, originating in the supercooled regime the tetrahedral networking and the liquid-liquid transition – we focused our interest to hydrophobic effects (HE) on these. Nowadays, if compared to the hydrophilicity, little is known about hydrophobicity so that the main purpose of this study is to gain new information on it. We measured the relaxation times (T1 and T2) and the self-diffusion (DS). From the times we took advantage of the NMR property to follow the behaviors of each molecular component (the hydrophilic and hydrophobic groups) separately; they are studied directly and DS in terms of the Adam-Gibbs model: obtaining the configurational entropy (Sconf ) and the specific heat contributions (CP,conf ). Due to the HE all the studied quantities, behave differently. For water-glycerol the HB interaction is dominant for all the conditions, whereas for water-methanol are observable two different T-regions above and below 265 K, dominated respectively by the hydrophilicity and hydrophobicity. A situation linked to the water polymorphism. Below this temperature, where the LDL phase and the HB networking develops and grows, the times and CP,conf change behaviors leading to maxima and minima. Above it, where the HB becomes weak and less stable and the HDL dominates, the hydrophobicity determines the solution properties.

Super-resolution technology is important not only in bio-related fields but also in nanotechnology, particularly in the semiconductor industry, where fine patterning is required and super-resolution is essential. However, observing microstructures beyond the diffraction limit proposed by Abbe and Rayleigh is considered impossible because of diffraction in traditional optical microscopy ob-servation techniques. However, in recent years, it has been possible to observe microstructures beyond the Rayleigh criterion by analysing the phase distribution of light. This study investigated the physical reasons why phase analysis makes this new analysis technique possible using simula-tions. The results confirmed that the phase component of the zero-order diffracted light reflected from the microstructure and able to pass through the lens system contained the phase information related to the shape of the measured object. Analysis of this information demonstrates the possi-bility of realising super-resolution based on speckle interferometry.

Shown is the derivation of Lorentz-Einstein k-factor in SRT as an amplitude-term of oscillation-differential equations of second order.This case is shown for classical Lorentz-factor as solution of an equation for undamped oscillation as well as the developed theorem as a second solution for advanced SRT of fourth order with an equation for damped oscillation-states.This advanced term allows a calculation for any velocities by real rest mass.Also accelerated coordinate -frames are discussed.

In network analysis, links depict the connections between each pair of network nodes. However, such pairwise connections fail to consider the interactions among more agents, which may be indirectly connected. Such non-pairwise or higher-order connections can be signified by involving simplicial complexes. The higher-order connections become even more noteworthy when it comes to neuronal network synchronization, an emerging phenomenon responsible for the many biological processes in real-world phenomena. However, involving higher-order interactions may considerably increase the computational costs. To confound this issue, map-based models are more suitable since they are faster, simpler, more flexible, and computationally more optimal. Therefore, this paper addresses the impact of pairwise and non-pairwise neuronal interactions on the synchronization state of 10 coupled memristive Hindmarsh-Rose neuron maps. To this aim, electrical, inner linking, and chemical synaptic functions are considered as 2- and 3-body interactions in three homogenous and two non-homogenous cases. The results show that through chemical pairwise and non-pairwise synapses, the neurons achieve synchrony with the weakest coupling strengths.

The article is dedicated to the role of polychrome solutions of the architectonic order in the concept of the Baroque façade. The ancient principles of designing architectural structures, inherited from the Renaissance were subjected to reinterpretations in order to impart different expressive values. The arrangements of façades, initially balanced or even horizontal, were replaced by ambiguous bivalent compositions. Vertical layouts began to dominate in the Baroque. Appropriately selected polychrome of the elements of the order could emphasize the compositional expression. The relationship between the layout of the polychrome in a given architectural order and the expression of a work of art has been established for quite a long time. However, the generally available data on color schemes of architectural structures in baroque buildings are still not fully organized. The paper analyses examples of Baroque façades preserved in their original state and revalorized in recent years after thorough conservator’s research in the field of architecture and color. The examples are mainly designed in the so-called great order, i.e. pertaining largely to church façades. In the Baroque, the vertical direction of the composition was strongly emphasized by multiplying or applying perspective arrangements of supports, and finally by embattled entablatures. The decisive field of change became the shaping of the coloristic decoration of the entablature – decisions regarding the material and color separation of elements of the frieze above the supports. The uniform color of all vertical elements of the façade structure guaranteed an unambiguous verticality of the composition.

A premise of statistical learning research is that learners attend to and learn the frequencies of repeating or co-occurring elements in the input. When the input is a series of words, participants readily learn the frequencies of phoneme sequences, that is, to learn phonotactic frequencies. Inherent to the concepts of both frequency and phonotactics is order, or the temporal structure of the input. Order is similarly inherent to statistical learning, yet the effect of order on statistical learning is not well understood. In the present study, adult participants learned the relative frequencies of eight item-medial consonant sequences, for example, the /mk/ in /nʌmkət/. Across five ordering conditions, both familiarization and test stimuli were independently ordered and randomized, thus allowing for a relatively broad search for order effects in an established statistical learning paradigm. Participants learned the target frequencies equivalently across the five ordering conditions, indicating no modulating effect of order. Nevertheless, participants also approached the task by applying idiosyncratic, structured orders to their responses. The result is an unexpected but robust effect of order. Both the results and the design of the study also allow for increased integration of statistical learning with memory and other aspects of cognition.

The effects of mixing orders of tannic acid (TA), starch and α-amylase on the enzyme inhibition of TA were studied, including mixing TA with α-amylase before starch addition (order 1), mixing TA with pre-gelatinized starch before α-amylase addition (order 2) and co-gelatinizing TA with starch before α-amylase addition (order 3). It was found that the enzyme inhibition was always highest for order 1 because TA could bind with the enzyme active site thoroughly before digestion occurred. Both order 2 and 3 reduced α-amylase inhibition through decreasing binding of TA with the enzyme, which resulted from the non-covalent physical adsorption of TA with gelatinized starch. Interestingly, at low TA concentration, α-amylase inhibition for order 2 was higher than order 3, while at high TA concentration, the inhibition was shown with opposite trend, which arose from the difference in the adsorption property between the pre-gelatinized and co-gelatinized starch at the corresponding TA concentrations. Besides, both the crystalline structures and apparent morphology of starch were not significantly altered by TA addition for order 2 and 3. Conclusively, although a polyphenol may have an acceptable inhibitory activity in vitro, the actual effect may not reach the expected one when taking processing procedures into account.

Studying concurrent systems is to sort the read/write and control events in the concurrent system according to the order, or in partial order, or in strict order. Because of the concurrency of events and the timeliness of writing events, there will be overlap between events, which requires interval order analysis. A single start and end sequence to represent the entire hierarchical order structure as well as all equivalent spaced order observations.a single sequence of beginnings and endings to represent the entire stratified order structures as well as all equivalent interval order observations. Mazurkiewicz traces and Comtracks are hierarchical traces, but they cannot describe interval traces. In a few sentences of this summary, we can tell the problems (petri interval traces with data), the previous work (Mazurkiewicz traces, Comtracks), the reasons that cannot be solved, and our own solutions (DPN: Petri nets with data, interval traces). This paper focuses on a BE (Beginnings and Endings) sequence representing an equivalent class of runs, or targets. Our goal is to have a BE sequence to represent the entire hierarchical order structure, that is, all equivalent observable interval orders.

Initial periods of adsorption kinetics play an important role in estimating the initial adsorption rate and rate constant of adsorption process. Several adsorption processes rapidly occur, and the experimental data of adsorption kinetics under the initial periods can contain potential errors. The pseudo-second-order (PSO) kinetic model has been popularly applied in the field of adsorption. The use of the nonlinear optimization method to obtain the parameters of the PSO model can minimize error functions during modelling compared to the linear method. However, the nonlinear method has limitations in that it cannot directly recognize potential errors in the experimental points of time-dependent adsorption, especially under the initial periods. In this study, for the first time, the different linear types (Types 1–6) of the PSO model are applied to discover the error points under the initial periods. The result indicated that the fitting method using its linear equations (Types 2–5) is really helpful for identifying the error (doubtful) experimental points from the initial periods of adsorption kinetics. The imprecise points lead to low adjusted R2 (adj-R2), high reduced χ2 (red-χ2), and high Bayesian information criterion (BIC) values. After removing those points, the experimental data were adequately fitted with the PSO model. statistical analyses demonstrated that the nonlinear method must be used for modelling the PSO model because its red-χ2 and BIC were lower than the linear method. Type 1 has been extensively applied in the literature because of its very high adj-R2 (0.9999) and its excellent fitting to experimental points. However, its application should be limited because the potential errors from experimental points were not identified by this type. For comparison, the other kinetic models (i.e., pseudo-first-order, pseudo-nth-order, Avrami, and Elovich) are applied. The modelling result using the nonlinear forms of those models indicated that the fault experimental points from the initial periods were not detected.

We delve into the axion-dilaton model within the supergravity framework, with a specific focus on the intricacies of domain wall construction and stability. Employing holographic vitrification, we unravel the dynamics of domain wall formation in gauge theories featuring periodic vacuum structures. Our model, incorporating a QCD-like axion term and a stabilizing dilaton, undergoes scrutiny for conductivity variations under weak disorder. The investigation reveals the model's resilience, manifesting near-perfect conductivity under mild disorder conditions. However, the rigorous mathematical motivation for the holographic setup demands further elucidation. The scattered nature of our results prompts the necessity for a more systematic interpretation of QCD phenomena and conductivity transitions. This study contributes to the mathematical understanding of the axion-dilaton model's behavior, highlighting the imperative for a refined holographic framework and a more coherent interpretation of observed phenomena.

We characterize the form of the order divisor graph of cyclic groups based on the group order. Furthermore, we describe some topological indices of the order divisor graph of cyclic groups, including the Wiener index, Harary index, first Zagreb index, and second Zagreb index.

Most works related to the identification of mathematical nonlinear systems make one suppose that such approaches can always be directly applied to any nonlinear system. This misconception produces a great deal of discouragement when the obtained results are not the expected ones. Thus, the current work hypothesizes that the most information one has about the mathematical structure of the model, the most precise the identification result should be. Therefore, a variant of the Sparse Identification of Nonlinear Dynamics (SINDY) approach is presented to obtain the full mathematical nonlinear model of a high-order system with coupled dynamics, namely, a commercial quadcopter. Furthermore, due to its high sensitivity to inputs, a control system is devised using the identified model to stabilize the quadcopter. This illustrates the effectiveness of the proposed identification method.

Asymmetry in the upper and lower tails is an important feature in modeling bivariate distributions. This article focuses on the log ratio between the tail probabilities at upper and lower corners as a measure of tail asymmetry. Asymptotic behavior of this measure at extremely large and small thresholds is explored with particular emphasis on the skew-normal copula. Our numerical studies reveal that, when the correlation or skewness parameters are around at the boundary values, some asymptotic tail approximations of the skew-normal copulas proposed in the literature are not suitable to compute the measure of tail asymmetry with practically extremal thresholds.

The classical propositional calculus (zero-order logic, classical propositional logic), is the most fundamental two-valued logical system. In this paper we present a proof of inconsistency of the classical propositional calculus. Then, we get right away the conclusion that the metatheory of the classical propositional calculus is inconsistent.

In this paper, a robust nonlinear dynamic controller is designed for a wind turbine with a permanent magnet synchronous generator. The wind turbine is subject to variations in all the parameters appearing in its mathematical model. Furthermore, the wind velocity is considered unavailable for direct measurement. This situation is of particular interest in practical applications, where only the nominal parameter values are known, and accurate wind velocity measurement is challenging due to perturbations caused by the turbine itself, even with appropriate sensors. The problem addressed in this work involves tracking the reference angular velocity corresponding to the wind velocity. To achieve accurate tracking, appropriate compensation of the perturbation terms resulting from parameter uncertainties and wind estimation errors is required. To address this problem, an estimator of the wind velocity is utilized, along with high–order sliding mode parameter estimators, to ensure high–performance operation of the turbine.

A new approach is presented to defining the amount of information, in which information is understood as the data about a finite set as a whole, whereas the average length of an integrative code of elements serves as a measure of information. We obtain a formula for the syntropy of reflection, that is, the information that two intersecting finite sets reflect about each other. The specificities of reflection of discrete systems through the combination of their parts are considered, and it is shown that the additive syntropy and entropy of reflection are measures of structural order and chaos. Three information laws have been established: the law of conservation of the sum of chaos and order; information law of reflection; the law of conservation and transformation of information. An assessment of the structural organization and the level of development of discrete systems is presented. It is shown that various measures of information are structural characteristics of integrative codes of elements of discrete systems. The conclusion is made that, from the informational-genetic positions, the synergetic theory of information is primary in relation to the Hartley-Shannon information theory. In the appendix we consider the asymmetry of the mutual reflection of finite sets and the proportionality of arbitrary quantities.

The continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection) has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and management breakout poses a new kind of global hazard. The good news is that there is currently enough knowledge about the epidemic process to allow for the creation of mathematical forecasting models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although many US states and other nations around the world followed lockdown and reopening processes, we perform some analysis on using some techniques of the epidemic course. A new perspective of fractional calculus known as piecewise derivatives of fractional order is used to study the proposed model. Sufficient conditions are established to show the existence theory. In addition, a numerical scheme based on Newton’s polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Some real data results are also shown with comparison of the numerical results.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto optimal solutions have led to a wide range of new applications related to optimal and feedback control which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview over recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

In the study of materials and macromolecules by first-principle methods, the bond order is a useful tool to represent molecules, bulk materials and interfaces in terms of simple chemical concepts. Despite the availability of several methods to compute the bond order, most applications have been limited to small systems because a high spatial resolution of the wave function and an all-electron representation of the electron density are typically required. Both limitations are critical for large-scale atomistic calculations, even within approximate density-functional theory (DFT) approaches. In this work we describe our methodology to quickly compute delocalization indices for all atomic pairs, while keeping the same representation of the wave function used in most compute-intensive DFT calculations on high-performance computing equipments. We describe our implementation into a post-processing tool, designed to work with Quantum ESPRESSO, a popular open-source DFT package. In this way we recover a description in terms of covalent bonds from a representation of wave function containing no explicit information about atomic types and positions.

On-chip integration of two-dimensional (2D) materials with unique structures and distinctive properties endow integrated devices with new functionalities and improved performance. With a high flexibility in modifying its properties and a strong compatibility with various integrated platforms, graphene oxide (GO) becomes an attractive 2D material for implementing functional hybrid integrated devices. Here, we demonstrate novel functionalities that go beyond the capabilities of conventional photonic integrated circuits, by harnessing the photo-thermal effects in 2D GO films integrated onto them. These include all-optical control and switching, optical power limiting, and non-reciprocal light transmission. The 2D layered GO films are on-chip integrated with precise control of their thicknesses and sizes. Benefitting from the broadband response of 2D GO films, all the three functionalities feature a very wide operational bandwidth. By fitting the experimental results with theory, we also extract the changes in material properties induced by the photo-thermal effects, which reveal interesting insights about 2D GO films. These results highlight the versatility of 2D GO films in implementing functional integrated photonic devices for a range of applications.

Reading is a complex cognitive task involving processes from different systems. The present work aims to identify some points of divergence reported in the reading literature and discuss them in a new experimental paradigm framework. Inspired by the paradigms of perceptual identification and rapid parallel presentation (RPVP), we emphasize that the originality of our experimental paradigm lies in the recruitment of multi-stable Arabic percepts within the region where low-level processing occurs (i.e., the visual span area). With good flexibility, the current paradigm has reached higher-order processing levels. In agreement with previous works highlighting the parafoveal-on-foveal effect, results suggest parallel word processing. Furthermore, they suggest a rapid extraction of syntactic and semantic information from words in sentences while attributing an advantage to semantic processing in the emergence of the sentence superiority effect.

As various services have been generating large scale graphs to represent multiple relationships between objects, studies have been conducted to obtain subgraphs with particular patterns. In this paper, we propose a distributed query processing method to efficiently search a subgraph for a large graph on Spark. To reduce unnecessary processing costs, the search order is determined by filtering scores using the probability distribution. The partitioned queries are searched in parallel in the distributed graph of each slave node according to the search order, and the local search results obtained from each slave node are combined and returned. The query is partitioned in triplets based on the determined search order. The performance of the proposed method is compared with the performance of existing methods to demonstrate its superiority.

This paper proposes a forecast-centric adaptive learning model that engages with the past studies on the order book and high-frequency data, with applications to hypothesis testing. In line with the past literature, we produce brackets of summaries of statistics from the high-frequency bid and ask data in the CSI 300 Index Futures market and aim to forecast the one-step-ahead prices. Traditional time series issues, e.g. ARIMA order selection, stationarity, together with potential financial applications are covered in the exploratory data analysis, which pave paths to the adaptive learning model. By designing and running the learning model, we found it to perform well compared to the top fixed models, and some could improve the forecasting accuracy by being more stable and resilient to non-stationarity. Applications to hypothesis testing are shown with a rolling window, and further potential applications to finance and statistics are outlined.

A classical origin for the Bohmian quantum potential, as that potential term arises in the quantum mechanical treatment of black holes and Einstein-Rosen (ER) bridges, can be based on 4th-order extensions of Einstein's equations. In Bohm's ontological interpretation, black hole radiation, and the analogous tunneling process of quantum transmission through an ER bridge, are classically allowed if the dynamics are modified to include such a quantum potential. The 4th-order extension of general relativity required to generate the quantum potential is given by adding quadratic curvature terms with coefficients that maintain a fixed ratio, as their magnitudes approach zero. Quantum transmission through the classically non-traversable bridge is replaced by classical transmission through a traversable wormhole. If entangled particles are connected by a Planck-width ER bridge, as conjectured by Maldacena and Susskind, then the classical wormhole transmission effect gives the ontological nonlocal connection between the particles posited in Bohm's interpretation of their entanglement. It is hypothesized that higher-derivative extensions of classical gravity can account for the nonlocal part of the quantum potential generally.

Embracing innovative digital technologies within educational systems is essential for overcoming challenges in modern learning environments, especially in the post-COVID-19 era. Teaching sustainability management in higher education institutions with innovative digital tools plays a fundamental role in the transition toward sustainable societies. Suitable game design elements play a significant role in facilitating sustainable learning. This study explored the effectiveness of incorporating business simulation games with project-based learning (PBL) in a flipped classroom setting. This approach was adopted within the context of a university cross-border e-commerce course to prepare students for acquiring 21st -century skills as higher-order thinking skills in a rapidly changing educational landscape. A quasi-experimental method was employed, involving a total of 60 university students from China's Zhejiang Province. Participants completed an online questionnaire designed to assess their learning engagement across three dimensions (cognitive, emotional, and behavioral) as well as their higher-order thinking skills (problem-solving, critical thinking, and creativity). The results show that the business simulation games combined with flipped classroom learning had a significantly positive impact on students’ learning outcomes, enhancing their problem-solving, critical thinking, and creative capabilities. Importantly, this approach also improved student engagement and promoted sustainable practices by applying real-life scenarios in an interactive environment. We conclude that business simulation games integrated with project-based learning (PBL) in flipped classroom settings represent a valuable educational approach. This approach not only enhances learning engagement but also fosters the development of higher-order thinking skills, encouraging students to adopt sustainable learning practices.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

Chipman contends, in stark contrast to the conventional view, that utility is not a real number but a vector and is inherently lexicographic in nature. According to these views, it will be proved that, for every preordered topological space (X,≾,t), the assumption t to be finer than the order topology t≾ on (X,t), i.e. t⊇t≾, and the assumption the quotient topology t∣∼≾ that is defined on the preordered set (X∣∼,≾∣∼) of indifference classes of ≾ to be Hausdorff imply that a cardinal number κ and a (complete) preorder ≲ on {0,1}κ that is coarser than the lexicographical ordering ≤lex on {0,1}κ, i.e. ≤lex⊂≲, can be chosen in such a way that there exists a continuous order-embedding ϑ:(X,≾,t)⟶({0,1}κ,≲,t≤lex). This theorem will be compared with a theorem that, in particular, describes necessary and sufficient conditions for ≾ to have a continuous multi-utility representation.

This paper presents a theory on graph topological structure and graph coloring, proving that for any N-order graph structure (with a topological structure similar to ), the maximum number of colors required for coloring is less than or equal to . The Four Color Theorem is just one special case of this theory, with the maximum structure size for a four-color graph being a 4-order structure graph, hence requiring only a maximum of 4 colors for coloring.

Transcription factors (TFs) are proteins that recognize specific DNA fragments in order to decode the genome and ensure its optimal functioning. TFs work at the local and global scales by specifying cell type, cell growth and death, cell migration, organization and timely tasks. We investigate the structure of DNA-binding motifs with the theory of finitely generated groups. The DNA ‘word’ in the binding domain -the motif- may be seen as the generator of a finitely generated group Fdna on four letters, the bases A, T, G and C. It is shown that, most of the time, the DNA-binding motifs have subgroup structure close to free groups of rank three or less, a property that we call ‘syntactical freedom’. Such a property is associated to the aperiodicity of the motif when it is seen as a substitution sequence. Examples are provided for the major families of TFs such as leucine zipper factors, zinc finger factors, homeo-domain factors, etc. We also discuss the exceptions to the existence of such a DNA syntactical rule and their functional role. This includes the TATA box in the promoter region of some genes, the single nucleotide markers (SNP) and the motifs of some genes of ubiquitous role in transcription and regulation.

This study presents finite-time synchronization of chaotic fractional order systems with disturbance uncertainty and unknown time delay. First, a PID sliding surface is presented. Then, for the finite-time synchronization of the master and slave systems, a robust sliding-adaptive control method is provided. Update rules have been retrieved to estimate the system parameters by using the Lyapunov function while establishing the stability of the suggested mechanism and assuring the convergence of errors to zero. The proposed approach was used to solve the fractional order system of Gensou-Tsei with time-varying parameters, and the simulation results show that the presented approach performs well.

We investigate numerically the interactions of in-phase Airy beams modulated by a fundamental Gaussian beam and fourth-order diffraction in Kerr nonlinear media. Directly numerical simulations show that normal (anomalous) fourth-order diffractions and in-phase (out-of-phase) Gaussian beam affect the interactions of solitons generated from Airy beams in unique manners. Different from previous results that interactions between in-phase (out-of-phase) conventional beams are always attractive (repulsive), many anomalous interactions of Airy beams are obtained. Stable bound states of breathing Airy soliton pairs can be formed with the help of fourth-order diffraction and fundamental Gaussian beam.

Anyon is collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. So far, anyons with serial fractional charges only exist in fractional quantum Hall effect. It is still a challenge to find new serial of fractional charges in other physical system and develop an unified mathematical physics theory based on the same root. Here a topological path fusion theory of propagating electrons in magnetic flux lattice is proposed to explore the physical origin of fractional charges based on a generalization of Feynman's path integral theory and Thurston's train track theory. This mathematical physics theory generated the existed serial of fractional charges in fractional quantum Hall effect and predicted new serial of fractional charges. A serial of irrational charges are predicted in one dimensional lattice of magnetic fluxes. Fractionally charged anyons are also generated in two dimensional and three dimensional lattice of train tracks of electric currents, revealing an exact correspondence between knot lattice model and train track model. A new explanation for the modular symmetry of complex Hall conductance and composite fermion in fractional quantum Hall effect is also derived from this topological path fusion theory. Experimental observation of anyon in three dimensions can be realized by constructing three dimensional interlocking magnetic fluxes or mapping magnetic fluxes into forbidden zones in multi-connected space filled by solid state material. A photonic crystal with porous nano-structures is a promising system for detecting fractional charges and paves a new way for topological quantum computation.

As a manifestation of technological innovation achievements, patents reflect the frontier of technological development in the field. This paper constructs a multi-entity patent collaboration network and analyzes its evolution patterns to provide a reference for innovation organizations to grasp the general direction of innovation development and select partners. Based on the data of collaboration patents of two and three organizations in China's new energy vehicles (NEV) industry from 2008 to 2021, this paper constructs higher-order interaction collaboration innovation networks in different periods to analyze the spatial evolution of networks and patent cooperation activities. The results show that the generalized degree distribution of nodes and edges conforms to the power-law distribution. The two-dimensional simplex networks gradually form triangle groups centered on the core nodes, and the importance of key edges is beginning to emerge. Key organizations and partners, including State Grid Corporation of China, Tsinghua University, and China Electric Power Research Institute, will largely determine the direction for the future development of cooperation innovation. The study also reveals that Beijing, Jiangsu, Zhejiang, Guangzhou, and Shanghai are in central positions in the cooperative innovation network, based on their cooperation breadth and depth measures. Additionally, key links formed by Beijing as hubs are not only the center of information exchange but also function as bridges that connect to other regions.

Brazil, Russia, China, India, and the Republic of South Africa (BRICS) represent developing economies facing different energy and economic development challenges. The current study aims to forecast energy consumption in BRICS at aggregate and disaggregate levels using the annual time series data set from 1992 to 2019 and to compare results obtained from a set of models. The time-series data are from the British Petroleum (BP-2019) Statistical Review of World Energy. The forecasting methodology bases on a novel Fractional-order Grey Model (FGM) with different order parameters. This study contributes to the literature by comparing the forecasting accuracy and the forecasting ability of the FGM(1,1) with traditional ones, like standard GM(1,1) and ARIMA(1,1,1) models. Also, it illustrates the view of BRICS's nexus of energy consumption at aggregate and disaggregates levels using the latest available data set, which will provide a reliable and broader perspective. The Diebold-Mariano test results confirmed the equal predictive ability of FGM(1,1) for a specific range of order parameters and the ARIMA(1,1,1) model and the usefulness of both approaches for energy consumption efficient forecasting.

Given a square matrix $A$, we are able to construct numerous equalities that involve reasonable mixed operations of $A$ and its conjugate transpose $A^{\ast}$, Moore--Penrose inverse $A^{\dag}$, and group inverse $A^{\#}$. Such kind of equalities can be generally represented in the equation form $f(A, \, A^{\ast}, A^{\dag}, A^{\#}) =0$. In this article, the author constructs a series of simple or complicated matrix equalities, as well as matrix rank equalities involving the mixed operations of the four matrices. As applications, we give a sequence of necessary and sufficient conditions for a square matrix to be range-Hermitian.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

It is a classic topic in algebras to construct and verify equalities that are composed of various algebraic operations of elements and their inverses or generalized inverses. In this note, the author constructs a matrix equality $(AB)^{\dag} = B^{\ast}(A^{\ast}ABB^{\ast})^{\#}A^{\ast}$ (called a mixed reverse-order law), where $A$ and $B$ are two matrices of appropriate sizes, $(\cdot)^{\ast}$, $(\cdot)^{\dag}$, and $(\cdot)^{\#}$ denote the conjugate transpose, the Moore--Penrose inverse, and the group inverse of a matrix, respectively, and shows that the mixed reverse-order law always holds. A list of variation forms of this matrix equality are also given, and necessary and sufficient conditions are obtained for them to hold. Especially, we show a remarkable fact that the two reverse-order laws $(AB)^{\dag} = B^{\dag}A^{\dag}$ and $(A^{\ast}ABB^{\ast})^{\#} = (BB^{\ast})^{\#}(A^{\ast}A)^{\#}$ are equivalent.

This study presents an exact solution to the free vibration analysis of a uniform Timoshenko beam, with a harmonic vibration being assumed. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. In this paper, a moment-shear force-circular frequency-curvature relationship was presented. The complete study was based on this relationship and closed-form expressions of efforts and deformations were derived. The free vibration response of single-span systems and spring-mass systems was analyzed; closed-form formulations of matrices expressing the boundary conditions were presented and the natural frequencies were determined by solving the eigenvalue problem. Systems with intermediate mass, spring, or spring-mass system were also analyzed. Furthermore, first-order dynamic stiffness matrices in local coordinates were derived. Finally, a second-order analysis of beams resting on an elastic Winkler foundation was conducted. The results obtained in this paper were in good agreement with those of other studies.

Time series data having low signal-to-noise ratio, non-stationarity and non-linearity are commonly seen in high-frequency stock trading, where the objective is to increase the likelihood of profit by taking advantage of tiny discrepancies in prices and trading on them quickly and in huge quantities. For this purpose, it is essential to apply a trading method that is capable of fast and accurate prediction from such time series data. In this paper, we develop an online time series forecasting method for high-frequency trading (HFT) by integrating three neural network deep learning models, i.e., Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU) and Transformer; and we abbreviate the new method to online LGT or O-LGT. The key innovation underlying our method is its efficient storage management, which enables super-fast computing. Specifically, when computing the forecast for the immediate future time, we use only the output calculated from the previous trading data (rather than the previous trading data themselves) together with the current trading data. Thus, the computing involves updating only the current data into the process. We evaluate the performance of O-LGT by analyzing the high-frequency Limit Order Book (LOB) data from the China market. It shows that our model in most cases achieves similar speed with much higher accuracy than the conventional fast supervised learning models for HFT. However, with a slight sacrifice in accuracy, O-LGT is approximately 40 times faster than the existing high-accuracy neural network models for the LOB data in China market.

Despite the successes earned in cataloguing and finding the role of the most of molecular components in living matter, the “biochemical and molecular” perspective, popular in biology, medicine and genetics, is unable to give account for crucial topics as the faculty of living systems to “feel”, to “perceive” what a given stimulus implies (means, indeed) for their survival. Condensed matter physics too, if bounded to a local, short-range, and perturbative approach, fails dramatically. This is also due to the role commonly assigned to water – actually the main constituent of living matter – deemed for long time to be merely chemical (as “solvent” or a reactant/product). Nonetheless, today many evidences show how living matter can be right conceived as a super-structured coherent water-based matrix, suggesting that the characterization of bio(electro)chemical and physical processes undertaken at molecular level in living matter, would let us unable to answer a question like this: what allows an amoeba, moreover without any neurons, to “know” to get closer to a nutrient or escape away from a toxin? I propose that to pursue such a fundamental inquiry it’s necessary an essentially relational approach, that is: to consider the living being at its grounding as the outcome of a physical history of relationships where symmetry-breakings, dissipation and coherence yield the emergence of the living state of matter, conceivable only as a time-dependent open process, and not as a portraited “body”. The effective tools to build up such an approach may be retrieved in far-from-equilibrium thermodynamics (TD), symmetry-breakings and gauge-fields theory, science of complexity, within the framework of a Quantum Field Theory. Indeed, within a field-view of matter, and of water especially, as it has been developed by a Quantum Electrodynamic (QED) description of condensed matter, it’s possible to give account for a physical basis too such an epistemologically elusive, though crucial, feature of living systems (i.e.: perception and meaning). The emerging landscape allows some important meditations about adaptation, evolution, ecodynamics, and about different conceptions of complexity and “information” in living realm. Furthermore, some neuroscientific themes like consciousness, qualia and their links to artificial intelligence could be supplied with due insights.

In this paper, we give the Galois adjunction form of the regular relation, and by using residuated mapping, we find the connection between it and order-generating set. Furthermore, we obtain the equivalent conclusion of "regular". In addition, by using the specialization order of topological space and the lower approximate operator in the rough set, we find a continuous homeomorphic mapping from a regular space to a Alexandrov topological space

Resonant light scattering by mesoscale dielectric spheres has received enormous attention and found many interesting applications. The recently emerged field of Mesotronics provides novel opportunities for wavelength-scaled optics and new fundamental aspects are still being uncovered. It has recently been demonstrated that high-order Mie resonances can be excited in homogeneous low-dissipation mesoscale dielectric spheres, leading to the generation of intense magnetic fields. This Letter describes a simple and effective way to drastically enhance the superresonance effect. Proof-of-principle results for the first time show that yet one more novel phenomenon of increasing the intensity of the magnetic field without changing the resonant Mie size parameter of the sphere by introducing an air cavity. In such a dielectric cenosphere (from two Greek words “kenos” - hollow and “sphaira” - sphere), by correct choosing of the air cavity size, it is possible to increase the intensity of the electromagnetic fields at the poles of the sphere by an order of magnitude due to increasing of amplitude of resonant partial wave coefficient.

The efficiency of a new composite material of the layered double hydroxide (LDH) of ZnMgAl and rice husk biochar (RHB) for the removal of Cu(II) and Pb(II) ions from synthetic wastewater was investigated in this study. The images of scanning electron microscope showed extremely fine crystalline LDH particles decorated on the rough surface of the RHB while the succesful formation of the composite adsorbent (LDH/RHB) was confirmed by the corresponding energy dispersive X-ray and the Fourier-transform infrared spectroscopy. An equilibrium contact time of 30 and 15 min for Cu2+ and Pb2+, respectively, was proposed for the optimum performance of the batch adsorption process. The dose of the LDH/RHB adsorbent was optimized at 0.4 g yielding maximum adsorption capacities of 117 and 124 mg g-1 for Cu2+ and Pb2+, respectively, with corresponding maximum removal efficiencies of nearly 94% and 99%. The initial meta concentrations was optimized at 50 or 60 mg L-1 corresponding to maximum removal efficiencies or adsorption capacities. For the changing initial metal’s concentration, the removal efficiencies remained unchanged for up to 50 mg L-1 and decreased by about 50% by increasing the initial concentrations from 50 to 100 mg L-1. The adsorption capacities observed a linear increasing trend by increasing the initial concentrations from 5 to 60 mg L-1 and remained unchanged afterward up to 100 mg L-1. A solution pH of 6.0 yielded optimum results with an increasing trend in adsorption capacities and percentage removal by changing the solution pH from 2.0 to 7.0. Based on the best-fit of the pseudo second-order kinetic model to the experimental data, the chemisorption was suggested to be the controlling mechanism of adsorption. The fitting of the Langmuir model suggested a monolayer sorption of Cu2+ and Pb2+ in addition to a heterogeneous adsorption as supported by the fitting of the Temkin isotherm. The application of the Dubinin–Radushkevich isotherm proposed a physical adsorption (mean free energy of adsorption less than 8 kJ mol−1) of both heavy metal ions on the surface of the LDH/RHB adsorbent.

The operation status of manufacturing equipment is directly related to the reliability of the operation of manufacturing equipment and the continuity of operation of the production system. Based on the analysis of the operation status of manufacturing equipment and its characteristics, it is proposed that the concept of assessing the operation status of manufacturing equipment can be realized by applying real-time acquisition of accurate inspection data of important parts of weak motion units and comparing them with their motion status evaluation criteria. Through the study of the application characteristics of fractional-order calculus theory, a differential data fusion model based on the fractional-order differential operator is established. The advantages of Internet of Things (IoT）technology and fractional order differential fusion algorithm are integrated to obtain real-time high-precision data of the operating parameters of manufacturing equipment, and the research objective of operating condition assessment of manufacturing equipment is realized. The feasibility and effectiveness of the method are verified by the application of the method in machining center operation status assessment.

The higher-order interactions in complex systems are gaining attention. Extending the classic bounded confidence model where an agent’s opinion update is the average opinion of its peers, this paper proposes a higher-order version of the bounded confidence model. Each agent organizes a group opinion discussion among its peers. Then, the discussion’s result influences all participants’ opinions. Since an agent is also the peer of its peers, the agent actually participates in multiple group discussions. We assume the agent’s opinion update is the average over multiple group discussions. The opinion dynamics rules can be arbitrary in each discussion. In this work, we experiment with two discussion rules: centralized and decentralized. We show that the centralized rule is equivalent to the classic bounded confidence model. The decentralized rule, however, can promote opinion consensus. In need of modeling specific real-life scenarios, the higher-order bounded confidence is convenient to combine with other higher-order dynamics, from the contagion process to evolutionary dynamics.

A comprehensive presentation of a variety of biologically sounding properties of genomes is present; chloroplast genomes are used as a biological matter. Triplet frequency composition is the general issue standing behind the properties. Besides, the new alignment-free error-tolerant method of sequences comparison highly efficient for in/del mismatches is present, for transposons search. Triplet frequency dictionaries determined for a genome, or for a part of that latter were studied through various clustering techniques. The interplay between triplet composition and function reveals on tRNA genes unambiguously shows the prevalence of the function encoded in tRNA gene over the phylogeny: the genes gather into the clusters comprising the genes encoding the same amino acid; more exactly, few gene families exhibit fine cluster pattern corresponding the synonymous codons of amino acid. Previously reported symmetry in chloroplast genomes is shown for a set of gymnosperm: that is mirror symmetry, rotational symmetry, and the second Chargaff's parity rule asymmetry. A family of transposons was found in gymnosperm chloroplast genomes. This family is revealed through the novel comparison method based on convolution calculation, for a set of DNA sequences.

To quantify the time-varying reproduction number (Rt) for Malaysia using the COVID-19 incidence data., we used data the from the Johns Hopkins University Center for Systems Science and Engineering (JHU CCSE) Coronavirus repository. Day 1 was taken from the first assumed local transmission of COVID-19. Data was split into four intervals: a) Interval 1: from Day 1 to Day 10 MCO 1, b) Interval 2: from Day 1 to Day 10 MCO 2, c) Interval 3: from Day 1 to Day 10 MCO 3 and d) Interval 4: from Day 1 to Day 10 MCO 4. We estimated the Rt using the EpiEstim package. The means for Rt at Day 1, Day 5 and Day 10 for all MCOs ranged between 0.665 to 1.147. The average Rt gradually decreased in MCO 1 and MCO 2. However, Rt increased in MCO 3 before stabilized around 0.8 in MCO 4. MCO 1 and MCO 2 which were stricter coincide with the gradual reduction of Rt. However, the more relaxed MCO 3 and MCO 4 correspond to a slight increase in the Rt before it stabilized.