Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

The chiral optical Tamm state (COTS) is a special localized state at the interface of a handedness-preserving mirror and a structurally chiral medium such as a cholesteric liquid crystal or a chiral sculptured thin film. The spectral behavior of COTS, observed as reflection resonances, is described by the temporal coupled-mode theory. Mode coupling is different for two circular light polarizations because COTS has a helix structure replicating that of the cholesteric. The mode coupling for co-handed circularly polarized light exponentially attenuates with the cholesteric layer thickness since the COTS frequency falls into the stop band. Cross-handed circularly polarized light freely goes through the cholesteric layer and can excite COTS when reflected from the handedness-preserving mirror. The coupling in this case is proportional to anisotropy of the cholesteric and theoretically it is only anisotropy of magnetic permittivity that can ultimately cancel this coupling. These two couplings being equal results in a polarization crossover (the Kopp--Genack effect) for which a linear polarization is optimal to excite COTS. The corresponding cholesteric thickness and scattering matrix for COTS are generally described by simple expressions.

Frontal Polymerization (FP) is recognized as a polymer synthesis method capable of generating a highly localized and self-propagating exothermic front, considered a more rapid and energy-efficient manufacturing scheme for polymer-based fiber-reinforced composite materials. This study conducts a numerical investigation based on the Finite Element Method into the initiation and propagation of frontal polymerization of acrylamide. Utilizing Differential Scanning Calorimetry (DSC) experiments, the study phenomenologically tests the curing kinetics reactions of acrylamide (AM) in deep eutectic solvent (DES)-based polymerizable systems, thereby establishing a curing kinetics model for the autocatalytic reaction of polyacrylamide. By coupling the heat conduction diffusion equation of the frontal polymerization reaction, the Finite Element Method is employed to solve the reaction-diffusion model, aiming to explore the evolution of temperature and degree of curing during the manufacturing process. The results demonstrate the reliability and accuracy of the nth-order autocatalytic model in the study of curing kinetics for DES-based synthesis, indicating that the front propagation speed of the AM-based FP reaction is influenced by the activation temperature, duration of activation temperature, and initial temperature of the solution. Experimental validation of the polyacrylamide manufacturing through frontal polymerization corroborates the accuracy and reliability of the model predictions, providing a reference for the numerical model study and temperature control in the synthesis of acrylamide composite hydrogels via FP.

The authors argue that despite significant numbers of foreign workers present in the Russian labor market Russia remains unattractive for highly skilled foreign workers. The economic crisis the country has faced since 2014 has resulted in a further outflow of foreign nationals from OECD countries. So Russia has to look for employees among newcomers from the former Soviet states, the majority of whom come from Central Asia. Russian politics with regard to immigration is characterized by the collision between “geopolitical” and domestic policy rationales. On one hand, seeking to maximize its influence in the post-Soviet space Russia provides preferential conditions of employment for citizens of partner countries in the framework of the Eurasian Economic Union. On the other hand, the Kremlin is afraid to liberalize its approach to immigration and the integration of immigrants through fear of losing popularity among the electorate. The second substantial feature of Russian immigration politics is an extreme level of securitization of migration issues. The government considers these issues primarily through a policing lens. One cannot claim that the Russian state does not take any steps to liberalize “migratory regulation”; however, the effect of these measures is being vastly reduced by new restrictions. In addition, liberally designed laws do not bring the expected results due to the corrupt practices that pervade the whole of migration regulation.

In this paper, a new type of self-excited thermomechanical oscillator containing an oscillating shape memory alloy (SMA) filament with two symmetrically arranged spheres is investigated. The self-excitation of the oscillations is due to a heater of constant temperature, which causes periodic contractions of the filament when it approaches it. The contracted filament moves away from the heater a distance sufficient to cool it. Under the action of the weight of the spheres, the cooled filament re-approaches the heater, causing the above processes to repeat periodically. On the basis of experimental studies, approximating functions of the heater's heat field distribution are derived. A dynamic model of the oscillator has been created, in which the minor and major hysteresis in the SMA alloy and the distribution of the heat field around the heater have been taken into account. By numerical solutions of the differential equations, the laws of motion of the spheres are obtained. The displacements of the spheres in two perpendicular directions were measured using an experimental system. The obtained experimental results validate the proposed dynamic model and its assumptions with a high degree of confidence. Conclusions are drawn about the stochastic nature of the oscillations due to the hysteresis properties of the SMA and the temperature variation of the natural frequency of the oscillating system.

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion of nano-beam. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of value and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency ratio and imperfection sensitivity of a curved SWCNT for various boundary conditions are investigated. The results show that the geometric imperfection plays a significant role in the nonlinear vibration characteristics of curved SWCNTs.

The effects of CO₂-water-rock interactions on the mechanical properties of shale are essential for estimating the possibility of sequestrating CO₂ in shale reservoirs. In this study, uniaxial compressive strength (UCS) tests together with an acoustic emission (AE) system and SEM & EDS analysis were performed to investigate the mechanical properties and microstructural changes of black shales with different saturation times (10 days, 20 days and 30 days) in water dissoluted with sub-/super-critical CO₂. According to the experimental results, the values of UCS, Young’s modulus and brittleness index decrease gradually with increasing saturation time in water with sub-/super-critical CO₂. Compared to intact samples, 30-days’ saturation causes reductions of 56.43% in UCS and 54.21% in Young’s modulus for sub-critical saturated samples, and 66.05% in UCS and 56.32% in Young’s modulus for super-critical saturated samples, respectively. The brittleness index also decreases drastically from 84.3% for intact samples to 50.9% for samples saturated in water with sub-critical CO₂, to 47.9% for samples saturated in water with super-critical carbon dioxide (SC-CO₂). SC-CO₂ causes a greater reduction of shale’s mechanical properties. The crack propagation results obtained from the AE system show that longer saturation time produces higher peak cumulative AE energy. SEM images show that many pores occur when shale samples are saturated in water with sub-/super-critical CO₂. The EDS results show that CO₂-water-rock interactions increase the percentages of C and Fe and decrease the percentages of Al and K on the surface of saturated samples when compared to intact samples.

The acoustic environment in learning spaces significantly influences learning effectiveness and occupant well-being. Recent studies have shown that a series of architectural factors within physical learning environments can impact students' educational experiences. This research delves into the relationship between architectural characteristics and the perceived acoustic environment among 467 primary students in 19 learning spaces across 9 schools in Chile. The survey comprises a student questionnaire, a checklist evaluating space characteristics, and acoustic measurements of indoor noise levels during occupied conditions. Examined topics include Indoor Environmental Quality (IEQ) comfort perception, noise annoyance, hearing ability, and acoustic preference. Architectural characteristics considered encompass flexible and acoustic space design parameters. The results indicated that noise discomfort was a common issue, especially in traditional learning spaces without acoustic treatment. The type of learning space (traditional or flexible settings) has a greater impact on acoustic perception particularly concerning noise discomfort and acoustic preference. However, poorly acoustic spaces lacking absorbing materials or exhibiting lower spatial density (m2 per student) contribute to increased indoor noise levels affecting noise annoyance caused by children's talking inside. The study emphasizes the importance of considering both architectural design and acoustic conditioning for optimizing the acoustic experience in educational spaces.

We study in this work a dilute granular gas immersed in a thermal bath made of smaller particles with nonnegligible masses as compared with the granular ones. The kinetic theory for this system is developed and described by an Enskog--Fokker--Planck equation for the one-particle velocity distribution function. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is based on a nonlinear drag force plus a white-noise stochastic force. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects like Mpemba and Kovacs-like ones.

In wireless sensor networks (WSNs), each sensor node can estimate the global parameter from the local data in distributed manner. This paper proposed a robust diffusion estimation algorithm based on minimum error entropy criterion with self-adjusting step-size, which are referred to as diffusion MEE-SAS (DMEE-SAS) algorithm. The DMEE-SAS algorithm has fast speed of convergence and is robust against non-Gaussian noise in the measurements. The detailed performance analysis of the DMEE-SAS algorithm is performed. By combining the DMEE-SAS with diffusion minimum error entropy (DMEE) algorithms, an Improving DMEE-SAS algorithm is proposed, in non-stationary environment where tracking is very important. The Improving DMEE-SAS algorithm can avoid insensitivity of the DMEE-SAS algorithm due to the small effective step-size near the optimal estimator, and obtain a fast convergence speed. Numerical simulations are given to verify the effectiveness and advantages of these proposed algorithms.

The numerical implementation of the controllers allows the use of very complex algorithms with ease. However, in practice, due to its proven advantages, the PID controller (and its variants) is widely used in industrial control systems as well as in many other applications that require continuous control. Most of the methods for tuning the parameters of PID controllers are based on time-invariant linear models of the processes, which in practice can lead to poor performance of the control system. The paper presents an application of reinforcement learning algorithms in tuning of PID controllers for the control of some classes of continuous nonlinear systems. Tuning the parameters of PID controllers is done with the help of Twin Delayed Deep Deterministic Policy Gradients (TD3) algorithm which presents a series of advantages compared to other similar methods from Machine Learning dedicated to continuous state and action spaces. TD3 algorithm is an off-policy Actor-Critic based method and was used as it does not require a system model. The presented technique is applied for control of a biotechnological system which has a strongly nonlinear dynamic. The proposed tuning method is compared to the classical tuning methods of PID controllers. The performance of the tuning method based on the TD3 algorithm is demonstrated through simulation illustrating the effectiveness of the proposed methodology.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

While numerous studies have explored the correlation between the built environment and ride-hailing demand, few have assessed their nonlinear interplay. Utilizing ride-hailing order data and multi-source built environment data from Nanjing, China, this paper uses the machine learning method, eXtreme Gradient Boosting (XGBoost), combined with SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP) to investigate the impact of built environment factors on ride-hailing travel demand, including their non-linear and threshold effects. The findings reveal that dining facilities have the most significant impact, with a contribution rate of 30.75%, on predicting ride-hailing travel demand. Additionally, financial, corporate, and medical facilities also exert considerable influence. The built environment factors need to reach a certain threshold or within a certain range to maximize the impact of ride-hailing travel demand. population density, land use mix and distance to the subway station collectively influence ride-hailing demand. The results are helpful for TNCs to allocate network ride-hailing resources reasonably and effectively.

This article delves into the enduring relevance of Liberal International Relations (IR) Theory amidst persistent criticisms regarding power dynamics and its applicability in emerging states. Despite its detractors, Liberal IR Theory offers a nuanced understanding of state behavior, blending social contexts with power dynamics. It recognizes the intricacies of economic interdependence and advocates for a balanced approach in advancing democracy and human rights. While nationalism poses challenges to international institutions, their adaptability endures. Leaders, albeit constrained, retain the capacity to foster peace through visionary leadership and global cooperation. By acknowledging its limitations and fostering open dialogue, Liberal IR Theory continues to evolve, poised to contribute to a just and peaceful global order.

The theory of water transport in trees, according to which the main driving force of water movement is the suction created by the evaporation of water by the meniscus (the curved surface of the capillary liquid column) on the evaporating elements, supported from below by root pressure, is flawed. The capillary effect in nature is around one meter. In the case of open-air gaps, the leaf cannot suck in the water against gravity because, in this case, the plant would not be sucking in water, but air through the open-air gap. If not, how do trees transport water? When evaporation occurs, there is no suction towards the canopy, but pressure is due to a reduction in the cross-section of the water pipe caused by heat loss through evaporation. At night, when evaporation stops, a thermal equilibration process is triggered, which restores the original cross-section of the pipe. This generates suction and draws water from the soil. As the hydrostatic pressure in the pipe is high for tall trees, the pipe is cut off. To prove my theory, I have given several examples. Water transport is not based on physical mechanical laws alone. There may be complex physiological, biochemical, and biophysical processes behind the operation of the pipe system.

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.

In contemporary construction, the prevalence of vibration serviceability issues in lightweight and slender structures has become increasingly common, owing to advancements in building materials and construction methods. While these structures often meet the criteria for ultimate limit states, they can still elicit complaints due to excessive vibrations induced by human activity. To address this challenge, the Integral Resonant Control (IRC) technique has emerged as a favored approach for actively damping vibrations in various systems. This study introduces a fresh perspective on implementing a multi-input multi-output (MIMO) IRC scheme for active vibration control (AVC) specifically tailored for pedestrian structures utilizing inertial mass actuators. Building upon a common framework and design methodology outlined in previous research, this work presents a novel application of MIMO IRC for AVC. The designed controller is rigorously tested and implemented on a laboratory floor structure to validate its efficacy.

Current VAT rules for cross-border e-commerce companies in the EU are not sustainable, because they are extremely complex and often opaque, due to the lack of tax harmonization. The aim of the research is to explore, using a qualitative method, what kind of harmonization would make the current legislation more uniform, simpler, more transparent, and easier to understand, without conflicting with the rules of any Member State. To this end, the aspects of the new platform regulation introduced on 1 July 2021 and its potential for expansion are assessed through information from possible sales models. The research suggests that the rules on platforms do not cover all possible sales models, which in our view imposes an unnecessary extra administrative burden on some businesses and makes their tax activities less transparent. In the light of the results of the research, we propose that the current EU platform regulation should be extended to cover B2B, B2C transactions and services. As a result of this suggested harmonization, a simpler, more transparent, uniform and sustainable tax system would contribute to the whitening of the economy, generating additional tax revenue for Member States.

In current transportation hubs, it is a common phenomenon that passengers travel with necessary wheeled-luggage or suitcases. Due to the fact that most luggage occupies certain space within dense passenger crowds with giant mass inertia, its abnormal motions, such as drifting, frequently trig unavoidable local disturbances and turbulence in surrounding pedestrian flows, further increasing security risk. While, current researches primarily concentrate on examining the impact of luggage on crowd evacuation efficiency through scenario-based experiments and analyzing the spatial characteristics of crowd distribution in surveillance videos. There still lacks of the dynamic disturbance mechanisms and crowd stability associated with the combined motion of passengers and luggage. Therefore, this study considers the luggage-laden passenger as a deformable particle, the resulting disturbance on surrounding non-luggage passengers is analyzed and quantified into a nonlinear pressure term. Subsequently, the disturbance propagation model of passenger-luggage is developed by adapting the classical Aw-Rascle traffic flow model with incorporation of the pressure term. Simulation experiments of disturbances caused by luggage drifting and retrograding validate that the proposed propagation model aligns with real-world situations in transportation hubs. Quantitively, when luggage-laden passenger drifted left, the disturbing force of left side crowd can reach a peak of 238N in the passenger density of 3.0 p/m2, and the maximum difference between the left and right sides disturbing force can reach 153N. Furthermore, it is recommended that the proposed model can be applied to crowd flow analysis and risk assessment.

After UV excitation, gas phase thymine returns to ground state in 5 to 7 ps, showing multiple time constants. There is no consensus on the assignment of these processes, with a dispute between models claiming that thymine is trapped either in the first (S1) or in the second (S2) excited states. In the present study, nonadiabatic dynamics simulation of thymine is performed on the basis of ADC(2) surfaces, to understand the role of dynamic electron correlation on the deactivation pathways. The results show that trapping in S2 is strongly reduced in comparison to previous simulations considering only non-dynamic electron correlation on CASSCF surfaces. The reason for the difference is traced back to the energetic cost for formation of a CO p bond in S2.

This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attack and packet loss. Firstly, the stochastic characteristics of DoS attack and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of systems. Then, by constructing a general common Lyapunov functional and combining with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through a numerical example.

This paper addresses the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries. This is a further work of the linear structural acoustic problem in a well-known acoustic book. In fact, the acoustic boundaries of an enclosed space sometimes are non-rigid and the structural vibration responses are nonlinear. These two points are the focuses of this paper. The multi-level residue harmonic balance method is applied to this nonlinear structural acoustic problem. The results obtained from the multi-level residue harmonic balance method and numerical method are generally in good agreement. The effects of excitation magnitude, tube length, and phase shift parameter etc. are examined.

With the rapid evolution of SARS-CoV-2, the emergence of new strains is an intriguing question. This paper presents an evolutionary theory to analyze the mutations of the virus and identify the conditions that lead to the generation of new strains. We represent the virus variants using a 4-letter sequence based on amino acid mutations on the spike protein and employ an n-distance algorithm to derive a variant phylogenetic tree. We show that the theoretically-derived tree aligns with experimental data on virus evolution. Additionally, we propose an A-X model, utilizing the set of existing mutation sites (A) and a set of randomly generated sites (X), to calculate the emergence of new strains. Our findings demonstrate that a sufficient number of random iterations can predict the generation of new macro-lineages when the number of sites in X is large enough. These results provide a crucial theoretical basis for understanding the evolution of SARS-CoV-2.

Driving factors of smart city construction are exploratively studied by grounded theory method based on text sources from journal papers in SCI and CSSCI databases. Initial scale of driving factors about smart city construction is obtained on the basis of above analyses. This paper modifies measuring items of the initial scale with a small sample pretest and reliability test, then forms final items by exploratory factor analysis. According to the above scale, questionnaires are designed to obtain empirical data, and confirmatory factor analysis is used to verify further validity and reliability of the scale. The results show that driving factors of smart city construction include three main dimensions: problem-oriented factors, business- or technology-driven factors and endogenous development requirements.

We review time expansion wave theory and refine our model showing it to accurately match observed cosmological luminosity data. The theory augments general relativity to create a container within which quantum effects can be explained by treating time as an artefact of a fourth spatial dimension that we observe as the expansion of the universe. This leads us to explain mass creation, the speed of light limit, gravity, black holes without singularities and other macroscopic effects. Our model leads to an expansion velocity of 6.87 0.36 × 106 ms-1, which results in a Hubble expansion rate constant of 71.3 3.7 km/s/Mpc. Because of the finite window of time in which we exist, an extra a degree of freedom is available leading to interesting interpretations at the subatomic level. At this size range, then a spin is allowed within the time dimension explaining why wave particle duality occurs and explains the electromagnetic force and other quantum mechanical properties. It provides a solution to the double slit conundrum and can explain how quantum entangled partners can behave in a quantum way and pass seemingly time-defying information. The potential quantitative origin of the fine structure constant which governs the size of the electromagnetic force is also strongly indicated by this theory.

The paper examines the impact of inward remittances flows on per capita GDP growth in Bangladesh during 1976-2012. We find that the growth effect of remittances is negative at first but becomes positive at a later stage, an evidence of a non-linear. Unproductive use of remittances was rampant in the beginning when they were received by migrant families but better social and economic investments led to more productive utilisation of remittances receipts at later periods. This was the possible mechanism behind the U-shaped relationship. Unlike what is suggested in the literature that the effect of remittances is more pronounced in a less financially developed economy, our evidence do not show that the effect of remittances on per capita GDP growth in Bangladesh is conditional on the level of financial development.

Local food has continued to become more popular in both the home and as featured ingredients in all segments of food service. Numerous studies have explored the motivating factors for consumer purchasing motivators. However, no known study has explored if there is a correlation between ego and intent to buy local foods. This study adopted a modified version of the Theory of Trying and surveyed a sample of 237 food service buying agents in South Carolina to examine their perceptions of buying local. Results suggest that ego is a predictor of trying to purchase local foods for restaurants. It was also found that the modified model is an acceptable model for predicting buyer intent. These findings support the majority of the studies looking at ego-centric behaviors with green purchases and could potentially help local food suppliers to better market their products to foodservice establishments. This study could also act as the foundation for future studies to explore the full extent of ego’s motivational effect on purchasing intentions in the food service industry.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

The paper presents the design and the implementation of different advanced control strategies that are applied to a nonlinear model of a thermal unit. A data–driven grey–box identification approach provided the physically meaningful nonlinear continuous–time model, which represents the benchmark exploited in this work. The control problem of this thermal unit is important since it constitutes the key element of passive air conditioning systems. The advanced control schemes analysed in this paper are used to regulate the outflow air temperature of the thermal unit by exploiting the inflow air speed, whilst the inflow air temperature is considered as an external disturbance. The reliability and robustness issues of the suggested control methodologies are verified with a Monte–Carlo analysis for simulating modelling uncertainty, disturbance and measurement errors. The achieved results serve to demonstrate the effectiveness and the viable application the suggested control solutions to air conditioning systems. The benchmark model represents one of the key issues of this study, which is exploited for benchmarking different model–based and data–driven advanced control methodologies through extensive simulations. Moreover, this work highlights the main features of the proposed control schemes, while providing practitioners and heating, ventilating and air conditioning engineers with tools to design robust control strategies for air conditioning systems.

In a bid to resolve lingering problems in cosmology, more focus is being tilted towards cosmological models in which physical constants of nature are not necessarily real constants, but varying with cosmic time. In this paper we have study cosmology in nonlinear electrodynamics with the Newton's gravitational constant $G$ not a constant but vary in form of power-law of the scale factor of the universe. The evolution of the scale factor $a (t)$ is studied in this model which depends on nonlinear electrodynamics fine tuning term of $\alpha$. Then we check the stability of the model using the speed of sound.

We discuss methods for calculation of critical indices and amplitudes from the perturbative expansions. Several important examples of the Stokes flow through 2D and 3D channels are brought up. Power series for the permeability derived for small values of amplitude are employed to calculation of various critical exponents in the regime of large amplitudes. Special nonlinear approximations valid for arbitrary values of the wave amplitude are derived from the expansions. The technique developed for critical phenomena is applied then for relaxation phenomena. The concept of time-translation invariance is discussed, its spontaneous violation and restoration considered. Emerging probabilistic patterns correspond to a local breakdown of time-translation invariance. Their evolution leads to the timetranslation symmetry complete (or partial) restoration. We estimate typical time extent, amplitude and direction for such restorative process. The new technique is based on explicit introduction of origin in time. After some transformations we come to the exponential and generalized, exponential-type solution with explicit finite time scale, which was only implicit in initial parametrization with polynomial approximation. The concept of crash as a relaxation phenomenon, consisting of time-translation invariance breaking and restoration, is put forward. COVID-19 related mini-crash in the time series for Shanghai Composite is discussed as an illustration.

Time evolution of the quantum correlation of the hybrid qubit-qutrit system in multilocal and global dephasing under the effect of a classical noises environment is presented. We considered the qutrit in z direction and the qubit x direction. In addition, our system presents two configurations: the different and the common environment and our discussion involves three types of noises: A Static Noise (SN), Random Telegraph Noise (RTN) and Ornstein- Uhlenbeck noise (OU). By using the density matrix approach to determine the evolution of the state of the system, the found that the static noise is fatal for the quantum entanglement, the quantum correlation and for RTN and OU noises the quantum entanglement, the quantum correlation decreases monotonically with a sufficiently long time. Therefore, we can say that, entanglement and the quantum correlation are more robust to the noise precisely those Random telegraph noise and Ornstein-Uhlenbeck noise.

This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by . Moreover, its multiplicative structure and the multiplicative structure of mortality makes the model separable. In this setting it is shown that the number of births in unit time is given by a system of nonlinear ordinary differential equations. The steady state solution together with the equilibrium solution is found explicitly.

We show that one of the two important uncertainty principles derived by Maccone and Pati \textit{[Phys. Rev. Lett., 2014]} can be derived for arbitrary maps defined on subsets of $\mathcal{L}^p$ spaces for $1< p<\infty$. Our main tool is the Clarkson inequalities. We also derive a nonlinear uncertainty principle for weak parallelogram spaces and Type-p Banach spaces.

According to our current understanding of quantum mechanics, a `measurement' violates unitarity. In other words as the act of measurement `resets' the probabilities described by the Schrödinger equation, in the very `moment' of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the `fluid of probability' we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.

Continuation methods are presented that are capable of treating frequency-domain flutter equations including multiple nonlinearities represented by describing functions. A small problem demonstrates how a series of continuation processes can find all limit-cycle oscillations within a specified region with a reasonable degree of confidence. Curves of the limit-cycle amplitude variation with velocity, indicating regions of stability and instability with colors give a compact view of the nonlinear behavior throughout the flight regime. A continuation technique for reducing limit-cycle amplitudes by adjusting various system parameters is presented. These processes are economical enough to be a routine part of aircraft design and certification.

The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

The principles of causality and unitarity are studied within rational nonlinear electrodynamics proposed earlier. We investigate dyonic and magnetized black holes and show that in the self-dual case, when the electric charge equals the magnetic charge, corrections to Coulomb's law and Reissner-Nordstrom solutions are absent. In the case of the magnetic black hole, the Hawking temperature, the heat capacity and the Helmholtz free energy are calculated. It is shown that there are second-order phase transitions and it was demonstrated that at some range of parameters the black holes are stable.

This paper investigates the influence of magnetic field for a two dimensional deformations on a two temperature problem at the free surface of a semi-infinite semiconducting medium under the effect of mechanical force during a photothermal theory and the effect of hydrostatic initial stress on the medium. The Harmonic Wave Method (Normal Mode Analysis) has been used to obtain the equations of elastic waves, heat conduction equation, quasi-static electric field, carrier density, two temperature coefficient, ratios, and constitutive relationships for the thermo-magnetic-electric medium. The effects of several parameters as thermoelastic and thermoelectric coupling parameters and two temperature parameter of this force on the displacement component, force stress, carrier density and temperature distribution has been depicted graphically.

Re-shaping of thermodynamics with the graph theory and Ramsey theory is suggested. Maps built of thermodynamic states are addressed. Thermodynamic states may be attainable and non-attainable by the thermodynamic process in the system of constant mass. We address the following question how large should be a graph describing connections between discrete thermodynamic states to guarantee the appearance of thermodynamic cycles? The Ramsey theory supplies the answer to this question. Direct graphs emerging from the chains of irreversible thermodynamic processes are considered. In any complete directed graph, representing the thermodynamic states of the system the Hamiltonian path is found. Transitive thermodynamic tournaments are addressed. The entire transitive thermodynamic tournament built of irreversible processes does not contain a cycle of length 3, or in other words, the transitive thermodynamic tournament is acyclic and contains no directed thermodynamic cycles.

We show that Universe inflation occurs when Einstein's gravity couples to nonlinear electromagnetic fields with cosmic stochastic magnetic fields background. Nonlinear electrodynamics with two parameters is used. The strength of magnetic fields to have the Universe inflation is obtained. It is shown that singularities of the energy density and pressure are absent for any scale factors. At large scale factors one arrives at equation of state for ultra-relativistic case. It is demonstrated that the curvature invariants do not have singularities. By computing the deceleration parameter we show that graceful exit takes place with reasonable e-folding number. The duration of Universe inflation as a function of model parameters is obtained. The classical stability and causality are analyzed by calculating the speed of the sound.

We derive an uncertainty principle for Lipschitz maps acting on subsets of Banach spaces. We show that this nonlinear uncertainty principle reduces to the Heisenberg-Robertson-Schrodinger uncertainty principle for linear operators acting on Hilbert spaces.

The article analyzes existing materials and structures with quadratic-nonlinear optical properties that can be used to generate a difference frequency in the terahertz and sub-terahertz frequency ranges. The principle of constructing a nonlinear optical-radio converter, based on an optical focon (a focusing cone), is proposed. Based on the assumption that this focon can be implemented from the metal-organic framework (MOF), we propose a technique for modeling its parameters. The mathematical model of the process of propagation and nonlinear interaction of waves inside the focon is based on a simplification of the nonlinear wave equation. Within the framework of the developed model, the following parameters are approximately determined: the 3D gradient of the linear refractive index and the function determining the geometric profile of the focon, which provide a few-mode-based generation of the difference frequency.

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.

This study aims to explain individual engagement in sustainable waste management behaviors (SWMBs) based on the application of protection motivation theory (PMT). SWMBs include waste avoidance, green purchasing behavior, reuse and recycle, and waste disposal behaviors. This study applies PMT to explore how individuals’ SWMBs are influenced by their perceived threats caused by environmental contamination from waste disposal and their perceived coping capability. The Bangkok metropolitan area was selected as a case study because it has faced serious waste management problems caused by massively increasing amounts of solid waste during the last ten years. Questionnaire surveys were conducted with 193 public and private officers residing in the city of Bangkok. The one-way analysis of variance (ANOVA) was performed to justify the effect of individual threat appraisal and coping appraisal on the engagement in SWMBs. The results demonstrated that respondents’ self-efficacy highly influenced all types of SWMBs. The perceived probability of being impacted from pollutants influenced all of the SWMBs except green purchasing behaviors. Response efficacy did not influence all SWMBs; however, the perceived severity of adverse consequences caused by pollutants highly influenced reuse and recycle behaviors. It could be suggested that PMT is well suited for investigating low-cost and simple SWMBs. It could also be suggested that different communication campaigns should be established to enhance citizens’ engagement in each type of SWMB.

The quest to comprehend the nature of consciousness has spurred the development of many theories that seek to explain its underlying mechanisms and account for its neural correlates. In this paper, I compare my own conscious electromagnetic information field (cemi field) theory with integrated information theory and global workspace theory for their ability to ‘carve nature at its joints’ in the sense of predicting the entities, structures, states and dynamics that are conventionally recognized as being conscious or nonconscious. I demonstrate the cemi field theory shares features with both integrated information theory and global workspace theory but consistently outperforms both by correctly predicting the entities, structures, states and dynamics that support consciousness. I argue that the simplest solution to the question of why cemi field theory consistently outperforms rival theories of consciousness is that the brain’s EM field is consciousness.

The paper presents a new type of hydraulic clutch operating with magnetorheological (MR) fluids and the results achieved from both theoretical analysis and experimental measurement. The hy-draulic clutch system of its own design with MR working fluid and a rotating magnetic field lo-cated is designed. The principle of this clutch is to use a rotating magnetic field created by an al-ternating current electromagnet to set the MR fluid in motion. In the tests of the hydraulic clutch with a rotating magnetic field, MR fluid produced on their own, consisting of solid iron particles of various diameters mixed with a silicone oil, are used as working fluids. The rheological properties of MR fluids are assessed on the basis of tests carried out with a Brookfield DV2T rheometer equipped with a magnetic device for generating the magnetic field of its own design. The char-acteristics of the hydraulic clutch with MR working fluid and the rotating magnetic field are tested on a specially built test stand. As a result of the research, it has been found that the torque transmitted by the clutch is the greater, the higher the rotational speed of the magnetic field and the lower the rotational speed of the beaker in which the working fluid is placed, and that the greatest torque occurs for the working fluid with the highest iron content. Based on the analysis of the structure and characteristics of the clutch in which the magnetic field is used, it has been shown that the design of the developed clutch is similar to that of an induction clutch, and its characteristics correspond to the characteristics of the eddy current clutch. Therefore, the proposed new clutch working with MR fluid and the rotating magnetic field can be applied to stationary power transmission system similarly to an eddy current clutch.

We present three reduced integrable hierarchies of nonlocal integrable NLS type equations from a vector integrable hierarchy associated with a matrix Lie algebra, not being A type. Three similarity transformations are taken to keep the invariance of the transformed zero curvature equations. The key step is to formulate a solution to a reduced stationary zero curvature equation so that the zero curvature formulation works for a reduced case.

In this study, we focus on an abstract form of summation equations, which can be regarded as a particular class of nonlinear difference equations. We investigate sufficient conditions for the existence of discrete almost automorphic solutions by appealing to the fixed point theory and establish a linkage between the existence of discrete almost automorphic solutions and the existence of bounded solutions for the nonlinear difference equations in the spotlight. Consequentially, we propose a discrete counterpart of the Bohr-Neugebauer theorem for the qualitative theory of difference equations.

The widespread integration and growing dependence among currency, stock and commodity markets make these markets often very vulnerable to shocks and at risk of collapse at the same time. As a result, these trends threaten the sustainability of the entire financial system. In this study, we explore the spillovers and nonlinear dependences between the seven major foreign ex-change rates, crude oil and gold prices, a global stock price index, and oil and stock implied volatility indices as proxy variables for global risk factors by em-ploying directional spillover network approach. We also use multi-scale de-composition method and nonlinear causality test between these variables to capture multi-level relationships at short and long horizons. Major findings are summarized as follows. First, from the multi-scale decomposition analysis, we identify that Granger causality test results and the direction and strength of return spillovers change with the level of decomposition. Second, the results of nonlinear causality tests show variation in both the significance and direction of Granger causality relationships between the decomposed currency and other series at different timescales, especially for the decomposed oil, gold, and OVX series. Third, the measured directional spillover indices identify the EUR as the largest contributor of connectedness to the other series. The central role of the EUR is a net transmitter of connectedness to gold, oil, the GBP, JPY, and CHF.

The article is devoted to issues related to the propagation and transformation of vortexes in the optical range of frequency. Within the framework of the traditional and modified model of slowly varying envelope approximation (SVEA), the process of converting vortex beams of the optical domain into vortex beams of the terahertz radio range based on nonlinear generation of a difference frequency in a medium with a second-order susceptibility is considered. The modified SVEA splits a slowly varying amplitude into two factors, which makes it possible to more accurately describe the three-wave mixing process. The theoretical substantiation of the rule of vortex beams topological charges conversion is given – the topological charge of the output radio-vortex beam is equal to the difference between the topological charges of the input optical vortex beams. A numerical simulation model of the processes under consideration has been implemented and analyzed.

The particulars of stimulus-response experiments done on dynamic biosystems clearly limit what one can learn and validate about their structural interconnectivity (topology), even when collected kinetic output data are perfect (noise-free). As always, available access ports and other data limitations rule. For linear systems, exponential modes, visible and hidden, play an important role in understanding data limitations, embodied in what we call dynamical signatures in the data. We show here how to circumscribe and analyze modal response data in compartmentalizing model structures – so that modal analysis can be used constructively in systems biology model building – for nonlinear (NL) as well as linear biosystems. We do this by developing and exploiting the modal basis for dynamical signatures in hypothetical (perfect) input-output data associated with a structural model – one that includes inputs and outputs explicitly – and for NL as well as linear biosystems. The methodology establishes model dimensionality (size, complexity) from particular data sets; helps select among multiple candidate models (model distinguishability); helps in designing new experiments to extract “hidden” structure; and helps to simplify (reduce) models to their essentials. For NL biosystems, results are not as comprehensive, similarly informative about their dominant dynamical properties, and unified with linear models on invariant 2-dimensional manifolds in phase space. Some automation of these highly technical aspects of biomodeling is also introduced.

An algorithm for the treatment of images affected by both blurring and salt&pepper noise is proposed with a cost only proportional to the number of pixels. The methodology uses a discretization scheme for the Laplace operator multiplied by a suitable nonlinear term depending on the gradient. Even if this approach resembles a diffusion type algorithm, only one step of the procedure is applied, leading to significant time savings. The procedure is successfully tested on some standard black&white natural images.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Reliable fatigue design rules affect the proactive identification of safety parameters in aerospace industry. Numerous fatigue crack initiation and propagation models, linear and nonlinear, have been developed for designing purposes or estimation of the remaining life of aging airplanes. Depending on the adopted assumptions, the accuracy varies for different loading histories, loading types, and materials. Semi empirical models are simple but yield significant inaccuracies. Models with better theoretical basis provide better accuracy, but implementation in real conditions is problematic. In the present work, a review of author’s recent fatigue crack initiation and propagation models based on physical mechanisms is presented and improvements are proposed. Verification of the models on test results is provided and discussed.

The author introduces a novel theoretical framework that suggests matter and energy are both converted from curved space. In Space Theory, gravitation is generated by the flow of space, instead of being transmitted by the graviton as in String Theory. This theory also suggests that Newton's gravitational constant, denoted as G, may not be truly constant but could vary over time. The equivalent equation of space is S=Ec²=mc⁴, and the gravitation of hollow sphere space is S_μν=4πGm=(4/3)π((r+a)³-r³). The Space Theory also predicts that the surface gravitational acceleration of the neutron star Crab Pulsar (PSR B0531+21) is approximately 8.21924883×10⁶ m/s².

In 2020 the world experienced the threat of the COVID-19 epidemic, as seniors and chronic disease patients typically try to reduce their exercise and social activities to avoid increasing the risk of infection, which could lead to increased loneliness and even many diseases. This research combining golf croquet games with AIoT companion robots constructs a home-based intelligent exercise system thus uses the Technology Acceptance Model (TAM), deduces users’ intention to use this system based on perceived usefulness and perceived ease of use, and adds the needs of love and belonging, esteem, cognitive, aesthetic, and self-actualization in Maslow’s needs theory to conduct system needs analysis. The analysis results show that participants have a high level of acceptance of this system, believing that it is easy to learn and operate, can increase interaction with others, also found that this system can improve self-confirmation, satisfying the third for knowledge, feeling happy, and self-actualization needs are easier to fulfill. In the future, we shall collect and record the seniors in the process of use, so as to find out their health problems as soon as possible, expand their daily life through this exercise, and achieve the goal of happy living and health care.

Re-interpretation of the Fermat principle governing propagation of light in media within the Ramsey Theory is suggested. Complete bi-colored graphs corresponding to the light propagation in media are considered. The vertices of the graphs correspond to the points of the real physical space, in which light sources or sensors are placed. Red links in the graphs correspond to the actual optical paths, emerging from the Fermat principle. A variety of optical events: refraction, reflection, etc. may be involved in the light propagation. Green links, in turn, denote the trial/virtual optical paths, which actually do not occur. The Ramsey Theorem states that within the graph containing six points, inevitably, actual or virtual optical cycle will be necessarily present. Implementation of the Ramsey Theorem to the light propagation in metamaterials is discussed. The Fermat Principle states that in metamaterials a light ray in going from point S to point P must traverse an optical path length L that is stationary with respect to variations of this path. Thus, bi-colored graphs built of links corresponding to maxima or minima of optical paths become possible. Graphs, comprising six vertices, inevitably will demonstrate optical cycles, built of the mono-colored links corresponding to the maxima or minima of the optical path. The notion of the “inverse graph” is introduced and discussed. The total number of triangles in the “direct” (source) and “inverse” Ramsey optical graphs is the same, Optical interpretation of the infinite Ramsey Theorem is suggested.

Recent advances in understanding the Planck scale have led to a new, straightforward method for quantizing the general theory of relativity. This results in a theory of gravity that predicts the same outcomes as general relativity with greater fundamental comprehension connected directly to the Planck scale.

This essay critically discusses the integration of queer theory into human geography while emphasizing its ties to the principles of traditional geography. The need for a separate sub-discipline called queer geography is questioned. At the same time, legitimate concerns about possible departures from the fundamental goals of geography and the risks of anachronistic interpretations in applying modern concepts to historical landscapes are acknowledged. In this discourse, we strongly advocate for values such as freedom of speech, freedom of expression, and international human rights. It is important to emphasize that it is not the intent of this essay to denigrate campaigns for feminism or equality or to disparage the scholarship that emerges from the application of queer theory. On the contrary, we recognize the emergence of gender theories out of a need to advance social justice approaches. We believe that traditional human geography, itself, is capable of comprehensively examining space, time, and the complexity of human experience and offering workable solutions within its established framework. We therefore believe that the inclusion of queer theory can be harmoniously integrated into the contours of human geography, eliminating the need for a separate sub-discipline while preserving the integrity and purpose of the discipline.

Modern exchange theories model a large market, but do not explain single exchange. The paper considers the phenomenon of single exchange and formulates the general exchange problem in the form of a system of two equations, subjective and objective. Subjective equilibrium is given by the Walras-Jevons marginal utility equation. Objective equilibrium equations by Walras and Jevons are averaged over all transactions in the market and can only give a rough general picture without explaining the specific price of an individual exchange. An exchange micro-condition must be found that, when averaged, will give the Walras market equilibrium macro-condition. The study of the internal structure of exchange leads to the need to consider power. The concept of generalized power is introduced. It is generalized power that serves as the primary comparable and measurable objective basis of exchange. The power theory of exchange provides the objective price-equation. It is demonstrated that money is a measure of generalized power in exchange and a certification of generalized power in subsequent exchanges. The proposed theory is able to uniformly explain any exchange, including a single one, which is impossible with the existing theories of exchange.

Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. QFI topic is a very active research area and it has many possible usage areas in quantum information domain. In this study, we review quantum Fisher information research with both from theoritical and application perspective.

Mathematics first is a logical system. But, the Mathematics Crisis showed that we cannot have a logical self-consistent mathematics system. Physics is a kind of applied science. It first need be valid to invent new production and understand new observation. In one theory of physics, the studied object is usually defined as an abstract concept. For example, the Sun is defined as a point particle in the Newtonian theory of gravity. In different theories of physics, the abstract concept for a same object is different. It determines that logical self-consistent is not needed for different theories of physics. Physics only can be developed from observation and experiment. But, in the past a century, physicists’ main attempt is to have a standard model, such as the Grand Unification or the Theory for Everything, from mathematics derivation. Therefore, the current attempt to develop new physics is questioned. In recent, the strong gravitational field was studied. It is found that the fundamental physical constants which are measured in the weak field shall be varied in a super strong field. For the two reasons, modern physics need be advanced greatly.

In this paper we introduce an ODE system to model the interaction between nature resources and human exploitation in a rich consumeristic society. In this model the rate of change of population depends on wealth per capita, and the rate of consumption has a quadratic growth with respect to population and wealth. As in our previous work \cite{BaCra_1}, we distinguish between renewable and non renewable resources, and we introduce a replenishment term for non renewable resources. We first get some information on the asymptotic behaviour of wealth and population, then we compute all the equilibria of the system and we study their stability when the parameter of exploitation of resources is small. Some numerical simulations confirm the theoretical results, and give suggestions for future research.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.

As a rapidly expanding family of two-dimensional (2D) materials, MXenes have recently gained considerable attention due to their appealing properties. Here, by developing a solution-based coating method that enables transfer-free and layer-by-layer film coating, we investigate the layer-dependent nonlinear optical absorption of Ti₃C₂T_x films ‒ an important member of the MXene family. By using the Z-scan technique, we characterize the nonlinear absorption of the prepared MXene films consisting of different numbers of monolayers. The results show that there is a strong and layer-dependent nonlinear absorption behavior, transitioning from revisable saturable absorption (RSA) to saturable absorption (SA) as the layer number increases from 5 to 30. Notably, the nonlinear absorption coefficient β varies significantly within this range, changing from ~7.13 × 10² cm/GW to ~-2.69 × 10² cm/GW. We also characterize the power-dependent nonlinear absorption of the MXene films at various incident laser intensities, and a decreasing trend in β is observed for increasing laser intensity. These results reveal the intriguing layer-dependent nonlinear optical properties of 2D MXene films, highlighting their versatility and potential for implementing high-performance nonlinear photonic devices.

Soft tactile sensors based on piezoresistive materials have various large-area sensing applications. However, their accuracy is often affected by hysteresis, a phenomenon that poses a significant challenge during operation. This paper introduces a novel approach that employs a backpropagation (BP) neural network to address the hysteresis nonlinearity in conductive fibre-based tactile sensors. To assess the effectiveness of the proposed method, four sensor units with different layer configurations (1, 3, 6, and 12) were designed. These sensor units underwent force sequences to collect corresponding output resistances. A backpropagation network was trained using these force sequences, thereby correcting the resistance values. The training process exhibited excellent convergence, effectively adjusting the network's parameters to minimize the error between predicted and actual resistance values. As a result, the trained BP network accurately predicted the output resistances. Several validation experiments were conducted to highlight the primary contribution of this research. The proposed method reduced the maximum hysteresis error from 24.2% of the sensor's full-scale output to 13.5%. This improvement establishes the approach as a promising solution for enhancing the accuracy of soft tactile sensors based on piezoresistive materials. By effectively mitigating hysteresis nonlinearity, the capabilities of soft tactile sensors in various applications can be enhanced. These sensors become more reliable and more efficient tools for force measurement and control, particularly in the fields of soft robotics and wearable technology. Consequently, their widespread applications extend to robotics, medical devices, consumer electronics, and gaming. Notably, the complete elimination of hysteresis in tactile sensors may not be feasible. Nevertheless, the proposed method effectively modifies the hysteresis nonlinearity, leading to improved sensor output accuracy.

This paper presents the common methods and corresponding drawbacks concerning nonlinear analysis of fluxgate excitation circuits and emphasizes the importance of nonlinear analysis for these circuits. With regard to the nonlinearity of the excitation circuit, this paper proposes the use of the core-measured hysteresis curve for mathematical analysis and the use of a nonlinear model that considers the coupling effect of the core and winding and influence of the historical magnetic field on the core for simulation analysis. The feasibility of mathematical calculations and simulation for the nonlinear study of fluxgate excitation circuit is verified via experiments. The results demonstrate that, in this regard, the simulation is better than a mathematical calculation. The simulation and experimental results of the excitation current and voltage waveforms under different excitation circuit parameters and structures are essentially consistent with each other, thereby verifying the effectiveness of the nonlinear excitation analysis method.

With correct dynamic system parameters (embodied in self-awareness statements), a controller can provide precise signals for tracking desired state trajectories. If dynamic system parameters are initially guessed incorrectly, a learning method may be used to find the correct parameters. In the deterministic artificial intelligence method, self-awareness statements are formed as mathematical expressions of the governing physics. When the nonlinear, coupled expressions are precisely parameterized as the product of known matrix components and unknown victrix (i.e., a regression form) tracking errors may be projected onto the known matrix to update the unknown victrix in an optimal form (in a two-norm sense). In this work, a modified learning method is proposed and proved to have global convergence of both state error and parameter estimation error. The modified learning method is compared with those in the prequels using simulation experiments of three-dimensional rigid body dynamic rotation motion. The modified approach is two magnitudes better than the methods in the prequels in terms of state error convergence.

Integrated photonic devices operating via optical nonlinearities offer a powerful solution for all-optical information processing, yielding processing speeds that are well beyond that of electronic processing as well as providing the added benefits of compact footprint, high stability, high scalability, and small power consumption. The increasing demand for high-performance nonlinear integrated photonic devices has facilitated the hybrid integration of novel materials to address the limitations of existing integrated photonic platforms, such as strong nonlinear optical absorption or an inadequate optical nonlinearity. Recently, graphene oxide (GO), with its large optical nonlinearity, high flexibility in altering its properties, and facile fabrication processes, has attracted significant attention, enabling many hybrid nonlinear integrated photonic devices with improved performance and novel capabilities. This paper reviews the applications of GO to nonlinear integrated photonics. First, an overview of GO’s optical properties and the fabrication technologies needed for its on-chip integration is provided. Next, the state-of-the-art GO nonlinear integrated photonic devices are reviewed, together with comparisons of the nonlinear optical performance of different integrated platforms incorporating GO. Finally, the challenges and perspectives of this field are discussed.

Cellular Nonlinear Networks (CNN) are a concept introduced in 1988 by Leon Chua and Lin Yang as a bio-inspired architecture, capable of massively parallel computation. Later on, CNN have been enhanced by incorporating designs that incorporate memristors to profit from their processing and memory capabilities. In addition, Stochastic Computing (SC) can be used to optimize the quantity of required processing elements; thus it provides a lightweight approximate computing framework, quite accurate and effective, though. In this work, we propose utilization of SC in designing and implementing a memristor-based CNN. As a proof of the proposed concept, an example of application is presented. This application combines Matlab and a FPGA in order to create the CNN. The implemented CNN has then been used to perform three different real-time applications on a 512x512 gray-scale and a 768x512 color image: storage of the image, edge detection, and image sharpening. It has to be pointed out that the same CNN has been used for the three different tasks, with the sole change of some programmable parameters. Results show an excellent capability with significant accompanying advantages, like the low number of needed elements further allowing for a low cost FPGA-based system implementation, something confirming the system’s ability for real time operation.

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

Backward electromagnetic waves are extraordinary waves with contra-directed phase velocity and energy flux. Unusual properties of the coherent nonlinear optical coupling of the phase-matched ordinary and backward electromagnetic waves with contra-directed energy fluxes are described which enable greatly-enhanced frequency and propagation direction conversion, parametrical amplification, as well as control of shape of the light pulses. Extraordinary transient processes that emerge in such metamaterials in pulsed regimes are described. The results of the numerical simulation of particular plasmonic metamaterials with hyperbolic dispersion are presented, which prove the possibility to match phases of such coupled guided ordinary and backward electromagnetic waves. Particular properties of the outlined processes in the proposed metamaterial are demonstrated through numerical simulations. Potential applications include ultra-miniature amplifiers, frequency changing reflectors, modulators, pulse shapers, and remotely actuated sensors.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

We have investigated the canine of olive flounder in terms of the nonlinear optical signals of two-photon excitation autofluorescence (2PEF) and second harmonic generation (SHG), whereby two kinds of nonlinear microscope images of the canine were obtained using ~140 femtosecond pulses. For increasing excitation power of laser pulses, a photobleaching effect was found to be significant in the red and green ranges of autofluorescence, where a double-exponential decay of the intensity occurs within hundreds of second due to collagen fluorophores in the canine. In the blue range of autofluorescence, the photobleaching is suppressed due to an energy conversion of the incident laser pulse to SHG signal. As a result, the signal in blue range remains constant for long term exposure to laser. We have also found that the SHG intensity depends on the orienta-tion of linearly polarized excitation, and the optical anisotropy of SHG can be attributed to the collagen alignment of canines.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

Gol'denveizer's problem of a torus has been analyzed by Audoly and Pomeau (2002) and Sun (2021). However, all of the investigations of Gol'denveizer's problem of an elastic torus have been linear. In this paper, the finite element method is used to more accurately address this problem. Furthermore, Sun (2021) cannot be solved by nonlinear analysis. We research the nonlinear mechanical properties of Gol'denveizer's problem of circular and elliptic tori, and relevant nephograms are given. We study the buckling of Gol'denveizer's problem of an elastic torus, and propose failure patterns and force-displacement curves of tori in the nonlinear range. Investigations reveal that circular tori have more rich buckling phenomena as the parameter a increases. Gol'denveizer's problem of the buckling of an elliptic torus is analyzed, and we find a new buckling phenomenon called a "skirt." As a/b increases, the collapse load of an elliptic torus of the Gol'denveizer problem is enhanced gradually.

Bayesian nonlinear mixed effects models for data in the form of continuous, repeated measurements from a population, also known as Bayesian hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individual specific characteristics and relevant uncertainty quantification. Due to the limitation of computational power, this framework was relatively dormant until the late 1980s, but in recent years, the statistical research community saw vigorous development of new methodological and computational techniques for these models, the emergence of software, and wide application of the models in numerous industrial and academic fields. This article presents an overview of the formulation, interpretation, and implementation of Bayesian nonlinear mixed effects models and surveys recent advances and applications.

This paper presents sufficient conditions for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems. Techniques from the stability analysis of switched systems have been combined with the multiple Lyapunov density approach - recently proposed by the authors for the almost global stability of nonlinear switched systems composed of stable subsystems. By using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times are obtained. In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, we have obtained a lower bound for an average dwell time.

Principle of memristor presented by Leon Chua and time reversal based non-linear elastic wave spectroscopy (TR-NEWS) which can be applied to acoustic tomography are reviewed. Correlation of acoustic or electromagnetic nonlinear waves and its time reversed wave can produce strong signal. Materials like transducer or biological skin can be assumed to be composed of a large number of small elastic unit: hysteretic elementary unit (HEU), and one can take a HEU as a memristor whose operation depends on time. Relation between TR-NEWS and solitonic wave in fluid, and relation between decomposition of time reversal operator (DORT) and chaotic oscillation are discussed.

Nonlinear rheological properties of chiral crystal cholesteryl oleyl carbonate (COC) in blue phase III are investigated under different shear deformations; large amplitude oscillatory shear, step shear deformation, and continuous shear flow. Rheology of the liquid crystal is significantly affected by structural rearrangement of defects under shear flow. One of the examples on the defect-mediated rheology is the blue phase rheology. Blue phase is characterized by three dimensional network structure of the disclination lines. It has been numerically studied that the rheological behavior of the blue phase is dominated by destruction and creation of the disclination networks. In this study, we find that the nonlinear viscoelasticity of BPIII is characterized by the fracture of the disclination networks. Depending on the degree of the fracture, the nonlinear viscoelasticity is divided into two regimes; the weak nonlinear regime where the disclination network locally fractures but still show elastic response, and the strong nonlinear regime where the shear deformation breaks up the networks, which results in a loss of the elasticity. Continuous shear deformation reveals that a series of the fracture process delays with shear rate. The shear rate dependence suggests that force balance between the elastic force acting on the disclination lines and the viscous force determines the fracture behavior.

This article attempts to formulate a mathematical model for a potential explanation regarding the unavoidable impact of a rigid body's peculiar shape on the seamless flow over it. The solid body completely immersed in a Newtonian fluid and respectively has a relative open circuit flow on it will typically experience various observable phenomena like flow separation, flow transition, down-wash, stalling at the higher angle of attack, stalling velocity and how cambered airfoil can typically generate lift at a zero incidence angle. This article respectively represents an understanding of the laminar flow over a rigid body's external surface with due respect to its distinctive shape and size. This working paper formulates a more realistic and simplified mathematical model for open circuit laminar flow over a body, based on the historical data of aerodynamics and theoretical mechanics. This is intended to properly estimate forces on the continuous surface of the body in a laminar flow, to properly explain, understand and predict mentioned phenomena. Most of all the mechanism of streamline formation and its deformation with due regards to flow, shape and size of the body in an open-circuit laminar are formulated mathematically to enhance better design theory which can reduce experimentation while designing a streamlined body.

The following series of Articles about a contextual system-theory, with focus on biological systems, shall give a guideline of how to explore complex systems. It is written not only for scientists, and therefore I will try to describe part of the way of understanding as an intuitive approach. This approach will also help scientists to get a deeper understanding of complexity. Some definitions and rules may seem at first simple and obvious. If practiced in a multidimensional complex system, one will see the difficulties. Even without mathematization or computer modeling the multidimensional sub space, which we try to describe phenomenologically for approaching the understanding of this Subsystem, will need a lot of training. Easily we get lost in the multidimensional world. Some of the chapters here and in the following publications of this series are written for specialists, but it will always come back to the essence of a phenomenological description. Concepts like Symbolic programming, Object oriented modeling, simulation and optimizing as well as experimental and mathematical approaches are the described tools to unpuzzle a complex scenario.

After reviewing foundational literature by Snyder, I will demonstrate how hope theory has been used in psychological interventions and psychiatry, how hope influences learning and medical outcomes, and how hope can be applied to difficult life circumstances. Using this literature review, hope theory will be interrogated. I will argue that hope theory has developed its way through the years to garner many strengths, however a few weaknesses do exist and will be described. I will conclude with recommendations for using hope theory in practice, including the medical field, psychological interventions and counseling, and student development.

Alzheimer's disease still holds many mysteries that are yet to be revealed. Exploring the reasons behind the increase in suicidal behavior in patients undergoing promising treatments for Alzheimer's disease is a scientific endeavor. Research practices must be built upon strong theoretical frameworks that can guide the investigation. Throughout decades of professional experience in caring for suicidal individuals and elderly people with cognitive disorders, we have noticed a connection that requires further exploration. It seems that existential distress may trigger various outcomes. At one end of the spectrum, we observe individuals who strongly resist adverse situations, making them more prone to developing suicidal behaviors. At the other end, we see individuals who exert great biological effort to adapt to the ongoing stresses of life, with Alzheimer's disease being a neurological consequence of this adaptation. To develop our understanding, we conducted an existentialist analysis to conceptualize the underpinnings of the human experience in a stress-filled world.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

The study presents an assertion and explanation that major and minor numerical progressions occur that depend on the representation contained in physical space. In general cases, larger numbers are multiples and smaller numbers are simple, because multiple numbers contain more numbers in many physical spaces than simple numbers. In specific cases, they depend on the statement of what the specific representation is, and different realities from general cases may occur. Also, the theory explains the change in the number of prime numbers.

Application of the Ramsey Theory to the set of the points placed in the plane is discussed. Consider a set of N points located in the same plane. The straight lines connecting these points are yikx=αikx+βik i,k=1...N. Listed below values of slopes αik are possible: αik&gt;0; αik=0; αik is not defined; αik&lt;0. Following coloring procedure is introduced: we connect the pairs of points for which αik&gt;0, αik=0 or αik is not defined, with the red links, and the pairs of points for which αik&lt;0 place with green links. The suggested coloring procedure enables building of the complete bi-colored graph for any set containing N points located in the same plane. We apply the Ramsey theorem to the complete graph emerging from the suggested coloring. For the set containing N=6 points at least one monochromatic triangle will necessarily appear in the graph. The values of the slopes αik depend on the chosen coordinate system. The rotation of coordinate axes changes the coloring of the graph; however, at least one monochromatic triangle will be present for N=6. The introduced coloring procedure diminishes the order of the symmetry group of the regular hexagon, irrespectively to the orientation of the coordinate axes. We hypothesized that this will be true for arbitrary regular n-polygon, independently on the orientation of coordinate axes. The inverse bi-color Ramsey graphs arise, when we replace red links appearing in the source graph with red ones, and vice versa. The total number of triangles in the “direct” and “inverse” Ramsey graphs is the same. We considered the particular case of the set of points for which αik&gt;0 or αik&lt;0 is true in the given coordinates. In this particular case, the rotation of the Cartesian coordinate axes to the angle θ=π2 yields the inverse complete graph. Generalization of this coloring for an arbitrary number and arbitrary location of the source points is introduced.

There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for constructing such a theory, which is also a unification of the standard model with gravitation, are : (i) the pre-quantum theory of trace dynamics – a matrix-valued Lagrangian dynamics, (ii) the spectral action principle of non-commutative geometry, (iii) the number system known as the octonions, for constructing a non-commutative manifold and for defining elementary particles via Clifford algebras, (iv) a Lagrangian with $E_8 \times E_8$ symmetry. The split bioctonions define a sixteen dimensional space (with left-right symmetry) whose geometry (evolving in Connes time) relates to the four known fundamental forces, while predicting two new forces, $SU(3)_{grav}$ and $U(1)_{grav}$. This latter interaction is possibly the theoretical origin of MOND. Coupling constants of the standard model result from left-right symmetry breaking, and their values are theoretically determined by the characteristic equation of the exceptional Jordan algebra of the octonions. The quantum-to-classical transition, precipitated by the entanglement of a critical number of fermions, is responsible for the emergence of classical spacetime, and also for the familiar formulation of quantum theory on a spacetime background.

We apply the Ramsey theory to the analysis of geometrical properties of closed contours. Consider a set of six points placed on a closed contour. The straight lines connecting these points are yikx=αikx+βik i,k=1...6, αik≠0. We color the edges connecting the points for which αik&gt;0 holds with red, and the edges for which αik&lt;0 with green with red. At least one monochromic triangle should necessarily appear within the curve (according to the Ramsey number R3,3=6). This result is immediately applicable for the analysis of dynamical billiards. The second theorem emerges from the combination of the Jordan curve and Ramsey theorem. The closed curve is considered. We connect the points located within the same region with green links and the points placed within the different regions with red links. In this case, transitivity/intransitivity of the relations between the points should be considered. Ramsey constructions arising from the differential geometry of closed contours are discussed.

The steep rise in reinforcement learning (RL) in various applications in energy as well as the penetration of home automation in recent years are the motivation for this article. It surveys the use of RL in various home energy management system (HEMS) applications. There is a focus on deep neural network (DNN) models in RL. The article provides an overview of reinforcement learning. This is followed with discussions on state-of-the-art methods for value, policy, and actor–critic methods in deep reinforcement learning (DRL). In order to make the published literature in reinforcement learning more accessible to the HEMS community, verbal descriptions are accompanied with explanatory figures as well as mathematical expressions using standard machine learning terminology. Next, a detailed survey of how reinforcement learning is used in different HEMS domains is described. The survey also considers what kind of reinforcement learning algorithms are used in each HEMS application. It suggests that research in this direction is still in its infancy. Lastly, the article proposes four performance metrics to evaluate RL methods.

Socio-demography of statuses reflects the demographic and social roles and achievements of an individual(s) in a population. In the theoretical frameworks, little was known about the theory, analytical measures, and evolutionary mechanism of the socio-demographics of statuses of an individual(s). In this paper, three (3) methodological issues regarding the concept of socio-demographics were proposed, these are: (a) identified the basic features that clarify our understanding about the conception of the socio-demographic statuses of an individual(s) as common, universal, and desirable positions, achievements, and advantages every individual strives and competes to attain, achieve, maintain, update, and upgrade which are determined by biological and social environments, driven and regulated by a continuum of competitions and natural selections; (b) presented a new paradigm of analytical measures of an individual’s socio-demographic statuses and the established hierarchical transitions; (c) proposed theoretical assumptions for the evolution of a socio-demographically unique population. Seven (7) factors (the driving forces) and eight (8) conditions responsible for the evolution of socio-demographically unique populations were identified and explained. The evolutionary transitions were organized into six (6) socio-demographic ranks.

The General equilibrium theory tries to show how and why all free markets tend toward equilibrium in the long run. However, what is meant by equilibrium in this paper is more from a thermodynamical point of view. In order to understand the actual situation, it is necessary to study open systems which are complex. In physics, such a behavior in a complex system can be explain by using Non Equilibrium Thermodynamics. A system is able to self-organize and sustain itself away from equilibrium. Economic systems may fluctuate around a particular point. To sustain it far from the equilibrium state, it needs to degrade more energy and materials. In this study, the energy consumption patterns of Sri Lanka and USA are discussed. The pattern concerning Sri Lanka is close to the model proposed here, whereas the energy consumption pattern of USA is more complicated due to external factors.

We describe here the coherent formulation of electromagnetism in the nonrelativistic quantummechanical many-body theory. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because of the manifold of misinterpretations emerging from the hystorical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions inspired from the classical electromagnetic theory of point-like charges. However, this later is known to be inconsistent due to the self-interaction. This way could not be continued further to include properly the magnetic forces between the charged particles and lead to a lot of confusion about the interpretation of the magnetic field in the Hamiltonian, as well as about the gauge invariance. We emphasize the importance of the distinction between the applied (external fields) and the field in the matter. All these problems are length properly solved within the non-relativistic QED, nevertheless the confusion dominates in all the problems related to the magnetic properties of the solid state.

Two major sample configurations are adopted in all the instruments for fabric hand measurement, flat sample as in KES and FAST types machines, and wrinkled sample as in PhabrOmeter. This paper compares the two sample types to examine which one if any offers a better coverage and reflection of the fabric sensory attributes. Fabrics have unique behaviors of drape, wrinkle and tactile sense which are entirely due to the simultaneous occurrence of both in-plane membrane deformation and out-of-plane bending deformation in multiple curvature. Such singular deformation mode cannot be detected by any machines using flat sample, whereas during a PhabrOmeter test, the fabric sample genuinely produces drape, wrinkle in addition to other related deformations. This paper then introduced the theoretical research pertaining to the measurement. Then a split sample experiment is conducted to demonstrate the importance of the internal connections in fabric during drape and wrinkle processes. As such fabric interconnection will be barely disclosed during tests using flat samples, another important advantage of PhabrOmeter is hence clearly shown.

We propose a new hierarchy of the vector derivative nonlinear Schr{\"o}dinger equations and consider the simplest multiphase solutions of this hierarchy. The study of the simplest solutions of these equations led to the following results. First, the three-leaf spectral curves $\Gamma=\{(\mu,\lambda)\}$ of the simplest multiphase solutions have a quite simple symmetry. They are invariant with respect to holomorphic involution $\tau$. The type of this involution depends on the genus of the spectral curve. Or the involution has the form $\tau:(\mu,\lambda)\to(\mu,-\lambda)$, or $\tau:(\mu,\lambda)\to(-\mu,-\lambda)$. The presence of symmetry leads to the fact that the dynamics of the solution is determined not by the entire spectral curve $\Gamma$, but by its factor $\Gamma/\tau$, which has a smaller genus. Secondly, it turned out that the dynamics of the two-component vector $\bp=(p_1,p_2)^t$ is determined, first of all, by the dynamics of its length $\abs{\bp}$. Independent equations determine the dependence of the direction of the vector $\bp$ from its length. In cases where the direction of the vector $\bp$ is fixed, the corresponding spectral curve splits into separate components. In conclusion, we note that, as in the case of the Manakov system, the equation of the spectral curve is invariant with respect to the orthogonal transformation of the vector solutions. I.e., the solution can be found from the spectral curve up to the orthogonal transformation. This fact indicates that the spectral curve does not depend on the individual components of the solution, but on their symmetric functions. Thus, the spectral data of multiphase solutions have two symmetries. These symmetries make it difficult to reconstruct signals from their spectral data. The work contains examples illustrating these statements.

In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

An exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics (NED) is obtained. The NED Lagrangian is given by ${\cal L}_{NED} = -{\cal F}/(1+\sqrt[4]{2\beta{\cal F}})$, where ${\cal F}$ is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radii are calculated. It is shown that when increasing the nonlinearity parameter $\beta$ the BH shadow radius is decreased.

Our earlier work has tentatively shown that the hierarchy of fermion masses and mixing angles follows from the universal behavior of nonlinear dynamics. In this brief sequel we survey a similar scenario in which the Cabibbo angle arises from the nonlinear dynamics of charged-current interactions.

The necessary and sufficient conditions of existence of the nonlinear operator equations' branches of solutions in the neighbourhood of branching points are derived. The approach is based on reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory based on index of Kronecker-Poincare, Morse-Conley index, power geometry and other methods are employed. Proposed methodology enables justification of the theorems on existence of bifurcation points and bifurcation sets in the nonstandard models. Formulated theorems are constructive. For a certain smoothness of the nonlinear operator, the asymptotic behaviour of the solutions is analysed in the neighbourhood of the branch points and uniformly converging iterative schemes with a choice of the uniformization parameter enables the comprehensive analysis of the problems details. General theorems are illustrated on the nonlinear integral equations.