In economics, especially econometrics, fixed-effects are widely recognized as powerful tools for heterogeneity analysis of longitudinal data sets. However, the existing research pays more attention to such as the variable selection, parameter estimation and dimension reduction on linear relationships with too many assumptions while nonlinear relationships are ubiquitous. In this paper, an extension fixed-effects model is proposed on the curve_fit nonlinear least squares. First, with the help of expert knowledge, the series regressions between independent variables including time and dependent variable is estimated on each series data, and the parameters are estimated by curve_fit. Similarly, the coeffection between independent variables including time and dependent variable is also initially estimated on the whole panel data. Second, the distance between regressions is defined, and then the coeffect function between the series regressions is obtained on the initial co-effect with curve_fit. Third, the time-effects and individual fixed-effects for each series data in the panel data are estimated on the differences of series regressions and co-effect function. Additionally, the effectiveness of the proposed method is varified on the synthetic data.

Intelligent transportation systems (ITS) have recently evolved rapidly, which requires development of highly trustworthy and effective communication technologies for uses, including vehicle-to-vehicle (V2V) and vehicle-to-everything (V2X) communication; where Orthogonal Frequency Division Multiplexing (OFDM) is regarded as a strong candidate and highly popular option technique among these methods. However, the movement of vehicles introduces Doppler frequencies which produce inter-carrier interference (ICI), that is frequently occurs in V2X channels. This interference has the potential to compromise the integrity of subcarrier orthogonality within OFDM, leading to lower-quality communication and an increased likelihood of data transmission errors. When employing channels with doubly dispersive fading, OFDM necessitates the usage of a complex equalization based on the minimum mean-square error (MMSE) equalizer, which requires channel matrix inversion. Several low-complexity equalizers for OFDM have been developed and are based on band factorization, time domain LSQR (Least-Square QR) iterative computing, and banded minimum mean squared error (BMMSE). This paper proposes Conjugate Gradient Least Squares (CGLS), which is a novel iterative computation algorithm integrated with nonlinear equalizers. The suggested nonlinear equalization technique determines the trade-off between computations and performance. According to simulation data, the suggested nonlinear equalizer performs better than the current BMMSE and linear CGLS algorithms across doubly dispersive fading channels.

The purpose of this paper is threefold: (i) to introduce and study the Euler-Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on Riemannian manifolds; (ii) to analyze some decomposable multivariate dynamics represented by Euler-Lagrange PDEs of least squares Lagrangians generated by flatness PDEs and Riemannian metrics; (iii) to give examples of explicit flat extremals and non-flat approximations.

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.

In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares. In time-sensitive applications or in embedded systems with limited resources, the runtime of the approximate function is as crucial as its accuracy. The proposed algorithm search to find the Optimal Piecewise Polynomial (OPP) with minimum computational cost while ensuring the error below a specified threshold. This was accomplished by using smooth piecewise polynomials with optimal order and number of intervals. The computational cost only depends on polynomial complexity, i.e., the order and the number of intervals at runtime function call. For optimal approximation, computational costs for all the possible combinations of piecewise polynomials were calculated and tabulated as ascending order for the specific target CPU off-line. Each combination was optimized through constrained least squares and random selection method for given sample points. Afterward, whether the approximation error is below the predetermined value is examined. When the error is permissible, the combination is selected as the optimal approximation or the next combination was examined. To verify the performance, several representative functions were examined and analyzed.

Empirical equations representing, interpolating and smoothing groups of measurement results by regression methods are in widespread use in metrology and other fields of science and engineering. Standard equations for the propagation of measurement uncertainties to values computed from such equations are available but suffer from a lack of general acceptance and are only infrequently applied in practice. One reason for the slow uptake is the lack of clear methods to account for systematic error. In this paper, uncertainty propagation equations in terms of covariance matrices are generalized to allow for systematic errors in least-squares regression, and effects of the resulting uncertainties are investigated analytically. A stochastic ensemble model of systematic error is proposed for the computation of the non-diagonal elements of the weight matrix of the Generalized Least-Squares method (GLS) from the measurement uncertainty. A GLS projector formalism is described which separates the effects of measurement scatter on values calculated by the equation from those on the related “residuals”, i.e., the residual errors in the fitted data. The same projectors act similarly on the associated uncertainties and covariance matrices and permit the effects of systematic errors on the simulation covariance to be quantified. It is demonstrated that, in order to include systematic errors in the uncertainty estimates of GLS, covariance matrices may be substituted by novel, specifically defined dispersion matrices that are not specified yet by the GUM[1]. Systematic measurement errors may be estimated from various sources; a particularly easy way suggested here involves analyzing the structure in the regression residuals. It is demonstrated that GLS projectors exhibit inherent features of “error blindness” also with respect to systematic errors. [1] GUM: Guide to the Expression of Uncertainty in Measurement, http://www.bipm.org/en/publications/guides

The application of non-uniform spiral gratings to control structure, topological parameters and propagation of orbital angular momentum (OAM) beams was studied experimentally with coherent near-infrared light. Adapted digital spiral grating structures were programmed into the phase map of a high-resolution liquid-crystal-on-silicon spatial light modulator (LCoS-SLM). It is shown that characteristic spatio-spectral anomalies related to Gouy phase shift can be used as pointers to quantify rotational beam properties. Depending on sign and gradient of spatially variable periods of chirped spiral gratings (CSG), variations of rotation angle and angular velocity as a function of propagation distance were measured. Propagation-dependent self-torque is introduced in analogy to known local self-torque phenomena of OAM beams as obtained by the superposition of temporally chirped or phase modulated wavepackets.

We report on the use of quartz-enhanced photoacoustic spectroscopy (QEPAS) for multi-gas detection. Photo-acoustic (PA) spectra of mixtures of water (H2O), ammonia (NH3) and methane (CH4) were measured in the mid-infrared (MIR) wavelength range using a MIR (mid-infrared) optical parametric oscillator (OPO) light source. Highly overlapping absorption spectra is a common challenge for gas spectroscopy. To mitigate this, we use a partial least-squares regression (PLS) method to estimate the mixing ratio and concentrations of the individual gasses. The concentration range explored in the analysis varies from a few parts-per-million (ppm) to thousands of ppm. Spectra obtained from HITRAN and experimental single-molecule reference spectra of each of the molecular species were acquired and used as training data sets. These spectra were used to generate simulated spectra of the gas mixtures (linear combinations of the reference spectra). Here in this proof-of-concept experiment we demonstrate that after an absolute calibration of the QEPAS cell, the PLS analyses could be used to determine concentrations of single molecular species with a relative accuracy within a few % for mixtures of H2O, NH3 and CH4 and with an absolute sensitivity of approximately 300(±50) ppm/V, 50(±5) ppm/V and 5(±2) ppm/V for water, ammonia and methane, respectively. Thus, demonstrating that QEPAS assisted by PLS is a powerful approach to estimate concentrations of individual gas components with considerable spectral overlap, which is a typical scenario for real-life adoptions and applications.

This paper aims to propose improvements for plastic waste management in Salvador – the Brazilian third most populated metropolis – via Partial Least Squares Structural Equation Modeling (PLS-SEM). All indicators, constructs, and hypotheses regarding collection, sorting, recycling, and disposal in the proposed PLS model were derived from the literature review, and the dependence of the performance construct on efficiency, effectiveness, municipality's socioeconomic aspects and municipality infrastructure is evaluated. Academic and practitioner publics were surveyed, and after analysis in both SmartPLS and RStudio software, suggestions for improvement regarding plastics recycling rate, market maturity, and infrastructural aspects for optimized reverse logistics were made. Since almost double the minimum number of respondents answered the survey questionnaire and the PLS-SEM statistics showed that the modeling presents consistency, the discussion is relevant. The model can and will evolve, but examples of suggested improvement are the installation of Deposit-Return Systems (DRS) in parks, streets, and avenues for increasing selective collection and the direct purchasing of waste from residents by municipal administration, compensating them with vouchers for food. The model can be a basis for other cities worldwide sharing analogous characteristics. By considering it, organizations can contribute to both reduced Greenhouse Gas (GHG) emissions and reduced terrestrial pollution.

Spatial interpolation of meteorological data can have immense implications on risk management and climate change planning. Kriging with external drift (KED) is a spatial interpolation variant that uses auxiliary information in the estimation of target variable at unobserved locations. However, the traditional KED methods with linear trend functions may not be able to capture the complex and non-linear interdependence between target and auxiliary variables, which can lead to an inaccurate estimation. In this work, a novel KED method using least squares support vector regression (LSSVR) is proposed. This machine learning algorithm is employed to construct trend functions regardless of the type of variable interrelations being considered. To evaluate the efficiency of the proposed method (KED with LSSVR) relative to the traditional method (KED with a linear trend function), a systematic simulation study for estimating the monthly means temperature and pressure in Thailand in 2017 was conducted. The KED with LSSVR is shown to have superior performance over the KED with the linear trend function.

Introducing the Moving Least-Squares Aided Finite Element Method (MLS-FEM), we present a robust computational technique that effectively evaluates the development of mixing in polymeric mixing devices. Our approach uses the Moving Least-Squares (MLS) interpolant to enhance the classic finite element shape functions. As a result, it becomes possible to treat fixed or moving components, such as rotors of a mixer, as discontinuities within the flow domain. This allows analysis of the flow field with a background mesh independent of the rotors' shape, orientation, and position. We compared the MLS-FEM results with the classical boundary-fitted mesh FEM, which comprises the mesh regeneration steps by the movement of the rotors. We then showed that the new method provides accurate results for the flow field parameters (i.e., the velocity components and the pressure values) and the mixing evolution without requiring mesh regeneration and without compromising accuracy.

Acrylamide is probably carcinogenic to humans (International Agency for Research on Cancer, group 2A) with major occurrence in heated, mainly carbohydrate-rich foods. For roasted coffee, a European Union benchmark level of 400 µg/kg acrylamide is of importance. Regularly, the acrylamide contents are controlled using liquid chromatography combined with tandem mass spectrometry (LC-MS/MS). This reference method is reliable and precise but laborious because of the necessary sample clean-up procedure and instrument requirements. This research investigates the possibility of predicting the acrylamide content from proton nuclear magnetic resonance (NMR) spectra that are already recorded for other purposes of coffee control. In the NMR spectrum acrylamide is not directly quantifiable, so that the aim was to establish a correlation between the reference value and the corresponding NMR spectrum by means of a partial least squares (PLS) regression. Therefore, 40 commercially available coffee samples with already available LC-MS/MS data and NMR spectra were used as calibration data. To test the accuracy and robustness of the model and its limitations, 50 coffee samples with extreme roasting degrees and blends were additionally prepared as test set. The PLS model shows an applicability for the varieties C. arabica and C. canephora, which were medium to very dark roasted using drum or infrared roasters. The root mean square error of prediction (RMSEP) is 79 µg/kg acrylamide (n=32). The PLS model is judged as suitable to predict the acrylamide values of commercially available coffee samples. On the other hand, very light roasts containing more than 1000 µg/kg acrylamide are currently not suitable for PLS prediction.

Reverse-order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse-order laws for a matrix product AB is (AB)^(i,...,j) = B^(i,...,j)A^(i,...,j), where (·)^i,...,j denotes an {i,...,j}-generalized inverse of matrix. Because {i,...,j}-generalized inverse of a general matrix is not necessarily unique, the relationships between both sides of the reverse-order law can be divided into four situations for consideration. In this article, we first introduce a linear mixed model y = ABβ + Aγ + ε, present two least-squares methodologies to estimate the fixed parameter vector  in the model, and describe the connections between the two least-squares estimators and the reverse-order laws for generalized inverses of the matrix product AB. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of B^(i,...,j)A^(i,...,j), as well as necessary and sufficient conditions for B^(i,...,j)A^(i,...,j) to be invariant with respect to the choice of A^(i,...,j) and B^(i,...,j). We then present a unied approach to the 512 set inclusion problems {(AB)^(i,...,j) ⊇ {B^(i,...,j)A^(i,...,j)}for the eight commonly-used types of generalized inverses of A, B, and AB using the block matrix representation method (BMRM), matrix equation method (MEM), and matrix rank method (MRM), where {(·)^(i,...,j)} denotes the collection of all {i,...,j}-generalized inverse of a matrix.

Empirical models for intensive or extensive margins of trade that relate measures of exports to firm characteristics are usually estimated by variants of (generalized) linear models. Usually, the firm characteristics that explain these export margins enter the empirical model in linear form, sometimes augmented by quadratic terms or higher order polynomials, or interaction terms, to take care or test for non-linear relationships. If these non-linear relationships do matter and if they are ignored in the specification of the empirical model this leads to biased results. Researchers, however, can never be sure that all possible non-linear relationships are taken care of in their chosen specifications. This note uses for the first time the Kernel-Regularized Least Squares (KRLS) estimator to deal with this issue in empirical models for margins of exports. KRLS is a machine learning method that learns the functional form from the data. Empirical examples show that it is easy to apply and works well. Therefore, it is considered as a useful addition to the box of tools of empirical trade economists.

Stroke often results in impaired gait, which can limit community ambulation and the quality of life. Recent works have shown the feasibility of transcranial Direct Current Stimulation (tDCS) as an adjuvant treatment to facilitate gait rehabilitation. Since the cerebellum plays an essential role in balance and movement coordination, which is crucial for independent overground ambulation, so, we investigated the effects of cerebellar tDCS (ctDCS) on the post-stroke overground gait performance in chronic stroke survivors. Fourteen chronic post-stroke male subjects were recruited based on convenience sampling at the collaborating hospitals where ten subjects finally participated in the ctDCS study. We evaluated the effects of two ctDCS montages with 2mA direct current, a) optimized configuration for dentate stimulation with 3.14cm² disc anode at PO10h (10/5 EEG system) and 3.14cm² disc cathode at PO9h (10/5 EEG system), and b) optimized configuration for leg lobules VII-IX stimulation with 3.14cm² disc anode at Exx8 (electrodes defined by ROAST) and 3.14cm² disc cathode at Exx7. We found ctDCS to be acceptable by all the exposed subjects. The ctDCS intervention had an effect on the 'Normalised Step length Affected side' (p=0.1) and 'Gait Stability Ratio' (p=0.0569), which was found using Wilcoxon signed-rank test at 10% significance level. Also, ctDCS montage specific effect was found using a two-sided Wilcoxon rank-sum test at a 5% significance level for 'Step Time Affected Leg' (p=0.0257) and '%Stance Time Unaffected Leg' (p=0.0376). Moreover, the changes in the quantitative gait parameters across both the montages were found to be correlated to the mean electric field strength in the lobules based on partial least squares regression analysis (R² statistic = 0.6574) where the mean electric field strength at the cerebellar lobules, Vermis VIIIb, Ipsilesional IX, Vermis IX, Ipsilesional X, had the most loading. In conclusion, our feasibility study indicated the potential of a single session of ctDCS to contribute to the immediate improvement in the balance and gait performance in terms of gait-related indices and clinical gait measures.

Although, staging models gained momentum to stage define affective disorders, no attempts were made to construct mathematical staging models using clinical and biomarker data in patients with major depression and bipolar disorder.The aims of this study were to use clinical and biomarker data to construct statistically-derived staging models, which are associated with early lifetime traumata (ELTs), affective phenomenology and biomarkers.In the current study, 172 subjects participated, 105 with affective disorders (both bipolar and unipolar) and 67 controls. Staging scores were computed by extracting latent vectors (LVs) from clinical data including ELTs, recurring flare ups and suicidal behaviors, outcome data such as disabilities and health-related quality of life (HR-QoL), and paraoxonase (PON)1 actvities and nitro-oxidative stress biomarkers.Recurrence of episodes and suicidal behaviors could reliably be combined into a LV with adequate composite reliability (the “recurrence LV”), which was associated with female sex, the combined effects of multiple ELTs, disabilities, HR-QoL and impairments in cognitive tests. All those factors could be combined into a reliable “ELT-staging LV” which was significantly associated with nitro-oxidative stress biomarkers. A reliable LV could be extracted from serum PON1 activities, recurrent flare ups, disabilities and HR-QoL.Our ELT-staging index scores the severity of a relevant affective dimension, shared by both major depression and bipolar disorder, namely the trajectory from ELTs, a relapsing course and suicidal behaviors to progressive disabilities. Patients were classified into three stages, namely an early stage; a relapse-regression stage; and a suicidal-regression stage. Lowered lipid-associated antioxidant defenses may be a drug target to prevent the transition from the early to the later regression stages.

The concept of green energy is now at the forefront of development discourse, with the United Nations Sustainable Development Goals (SDGs) 7, 11, and 12 all aimed at promoting green energy consumption to combat the three planetary crises: climate change, biodiversity loss, and pollution. Similarly, issues regarding Africa’s natural resource curse have caused a stir in the growth and development literature for some time now and there is no sign that it will die out. This study, the first of its kind, simultaneously assesses the impact of green energy consumption and Africa’s natural resources rents on economic growth by applying the Feasible Generalized Least Square (FGLS) estimator and the dynamic panel models of the Pooled Mean Group (PMG) and Mean Group (MG) estimators on data from 1990 to 2020 for 24 selected African countries. The results show that green energy consumption has a short-run growth-limiting effect and a long-run growth-enhancing effect in Africa. The study also found evidence of the natural resource curse phenomenon in Africa. The study, therefore, calls for the advancement and usage of green energy for both domestic and industrial production in Africa. The study further calls for a revamp in the global tax policy to curb illicit financial activities and strengthening institutional quality for transparency and accountability in the entire value chain of natural resource management in Africa.

The article deals with auxetic structures made on the basis of suitably connected rigid rotating squares (from Grima and Evans), with axes of rotation on the squares’ surface. The geometric model and the resulting relationships that allow for the determination of Poisson’s ratio are considered in detail. It is demonstrated that changing the rotation axis position does not affect the negative Poisson’s ratio, equal to -1. The models built confirm the initial considerations and can offer new application possibilities.

As matrix representations of magic labelings of related hypergraphs, magic squares and their various variants have been applied to many domains. Among various subclasses, trimagic squares have been investigated for over a hundred years. The existence problem for trimagic squares with singly even orders and orders 16n has been solved completely. However, very little is known for the existence of trimagic squares with other even orders except for the only three examples and three families. We construct normal trimagic squares by using product constructions, row-square magic rectangles, and trimagic pairs of orthogonal diagonal Latin squares. We give a new product construction: For positive integers p, q, and r having the same parity other than 1, 2, 3, 6, if normal p × q and r × q row-square magic rectangles exist, then a normal trimagic square with order pqr exists. As its application, we construct normal trimagic squares of orders 8q^3 and 8pqr for all odd integers q not less than 7 and p,r ∈ {7, 11, 13, 17, 19, 23, 29, 31, 37}. Our construction can easily be extended to construct multimagic squares.

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.

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

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.

Accurate forecasting of icing thickness has a great significance for ensuring the security and stability of power grid. In order to improve the forecasting accuracy, this paper proposes an icing forecasting system based on fireworks algorithm and weighted least square support vector machine (W-LSSVM). The method of fireworks algorithm is employed to select the proper input features with the purpose of eliminating the redundant influence. In addition, the aim of W-LSSVM model is to train and test the historical data-set with the selected features. The capability of this proposed icing forecasting model and framework is tested through the simulation experiments using real-world icing data from monitoring center of key laboratory of anti-ice disaster, Hunan, South China. The results show that the proposed W-LSSVM-FA method has a higher prediction accuracy and it may be a promising alternative for icing thickness forecasting.

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.

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 study presents a comprehensive investigation on an innovative mechanical system inspired by recent advancements in metamaterials, more specifically the work is focused on Origami-type structures for their intriguing mechanical properties. Originating from the specific fields such as aerospace for their lightweight and foldable characteristics, Origami mechanical devices exhibit unique non-linear stiffness, in particular, when suitably designed, they show Quasi-Zero Stiffness (QZS) characteristics within a specific working range. The QZS property, aligned with the High Static Low Dynamic (HSLD) stiffness concept, suggests promising applications such as a low-frequency mechanical passive vibration isolator. The study explores the vibration isolation characteristics of Origami-type suspensions, with a particular emphasis on their potential application as low-frequency passive vibration isolators. The Kresling Origami Module (KOM) has been selected for its compactness and compatibility with 3D printers. A detailed analysis using 3D CAD, Finite Element Analysis, and experimental testing have been carried out. The investigation includes the analysis of the influence of geometric parameters on the non-linear Force-Displacement curve. Multibody simulations validate the low-frequency isolation properties within the QZS region, and disparities in dynamic properties beyond the QZS range. The study underscores the transformative potential of Origami-type metamaterials in enhancing low-frequency vibration isolation technology. It also highlights challenges related to material properties and loading mass variations, providing valuable insights for future developments in this promising field.

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.

This paper investigates the energy dissipation level of a nonlinear vehicle suspension system. The suspension system is modelled as a mass-spring-damper system, which is designed using the output frequency response function (OFRF) method. This method enables the derivation of an explicit relationship, between the system output spectrum (or Performance metric) and the system nonlinear parameters of interest. The OFRF polynomial, of the energy dissipation level, was derived in terms of the nonlinear parameters of interest. The results obtained show that the OFRF model, of the energy dissipation level, could be used to estimate the amount of heat dissipated, for a set of design parameters. This has potentials of providing some insights, in the design of vibration-based energy harvesters, as some of the wasted heat energy could be converted to electrical energy.

In nature and engineering applications, flexible fiber beds covering biological surfaces can play a role in reducing resistance. These fibers deform under the action of fluids, and this deformation affects the fluid flow state, forming a complex fluid-solid interaction phenomenon. To quantitatively analyze such issues, the physical model is simplified to the deformation problem of an soft hair bed caused by Stokes flow, and the deformation problem of a single fiber caused by Stokes flow is further studied. The deformation problem of an elastic single fiber in a channel caused by Stokes flow can be described by a nonlinear integral equation. We have obtained a new series solution, which has been compared with the previous perturbation method to verify the accuracy and effectiveness of the series solution. Meanwhile, we have further provided an extended form of flexible fiber deformation through experimental fitting. This fluid-solid interaction problem involves multiple fields and is very important in many natural and engineering systems. The research in this paper can not only help us better understand complex phenomena in nature but also delve into the interaction mechanism between fluids and solids, providing a theoretical basis for future scientific research and engineering applications.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

In two previous articles, the extended $(k, t)$--Fibonacci numbers were presented and some of their properties were studied, both in general and particularizing them for the Leonardo numbers. In a second article we study the sum of the extended $(k, t)$--Fibonacci numbers as well as the sums of these odd and even numbers.\\ In this article we study the sum of the squares of these numbers with their properties as well as the generating function, the recurrence relation and the Binet formula.\\ Finally we particularize these results for the generalized $t$--Leonardo numbers.

In this paper, closed forms of the summation formulas for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

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 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.

The nonlinear dynamics exhibited by aircraft flying at high angle of attack (AOA) pose great challenges to the design of flight control. The control design based on nonlinear dynamic inversion (NDI) is to reversely find the required control input based on the current nonlinear dynamics of the aircraft and the control objectives to be achieved. Since it is derived from the nonlinear dynamics of the aircraft, a single NDI controller can cover the entire flight envelope without the need for controller switching or gain scheduling. This paper employs the layered structure of the flight control loop to implement the NDI controller through the combination of aerodynamic control and thrust vectoring control (TVC). The resulting NDI controller is applied to an experimental F-16 installed with TVC to verify its high AOA maneuverability in the post-stall region. The verification simulation shows that the experimental F-16 under the NDI control can effectively track the high AOA command and successfully demonstrate the Herbst maneuver by performing the heading reversal with 70° AOA.

This paperfocusesontheoscillatorypropertiesofthesemi-canonicalnonlineardelaydifferential equation ofthird-order (δ2(t)(δ1(t)ζ′(t))′)′ + η(t)ζα(τ(t))= 0, t ≥ t0, under theconditions ∞t01δ2(t)dt = ∞ andZ ∞t01δ1(t)dt < ∞. Using the new canonical transform method, we transformed the studied equation into a canonical type equation and then we find the conditions for the oscillation of the studied equation from the canonical equations. The obtained results are new and complement to the existing results mentioned in the literature. Examples are provided to illustrate the importance and novelty of the main results.

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.

Background/Objectives: Dental implants have become a cornerstone of restorative dentistry, providing a long-lasting method for tooth replacement. The level of osseointegration has a big impact on the biomechanical stability at the bone-implant contact (BIC), which determines how long these implants will work. However, the exact consequences of changing osseointegration levels on different implant designs, especially in bones with variable densities, are not well known. Three short dental implants were tested in this study: BioMet 3iT3, Straumann® Standard Plus Short Regular Neck (SPS-RN), and Straumann® Standard Plus Short-Wide Neck (SPS-WN). 3D finite element analysis (FEA) was used to look at how well they worked biomechanically. This paper tests the implants at four stages of osseointegration: 25%, 50%, 75%, and 100% in both high-density (Bone Type III) and low-density (Bone Type IV) cancellous bone. It also created and examined realistic CAD models under static occlusal loading conditions to assess stress distribution and major strains at the bone-implant contact.; Results: The study discovered that as osteointegration increases, von Mises stress and principal strains go down significantly for all implant types. The SPS-WN implant had the lowest strain values, especially for bone with low density. These reductions demonstrate increased mechanical stability as the bone-implant inter-face becomes more capable of dispersing mechanical stresses, minimizing the potential for localized deformation and bone resorption.; Conclusions: The results highlight the importance of achieving optimum osseointegration to reduce mechanical stress and increase the lifespan of dental implants. The SPS-WN type implant performed better in biomechanical tests than the others, especially when bone conditions were not ideal. This makes it a great choice for clinical applications that need long-term implant success.

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.

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.

The following article analyzes Italian companies with more than 10 employees that use online sales tools. The data used were acquired from the ISTAT-BES database. The article first presents a static analysis of the data aimed at framing the phenomenon in the context of Italian regional disparities. Subsequently, a clustering with k-Means algorithm is proposed by comparing the Silhouette coefficient and the Elbow method. The investigation of the innovative and technological determinants of the observed variable is carried out through the application of a panel econometric model. Finally, different machine learning algorithms for prediction are compared. The results are critically discussed with economic policy suggestions.

Marine species are declining at an unprecedented rate, catalyzing many nations to adopt conservation and management targets within their jurisdictions. However, marine species and the biophysical processes that sustain them are naive to international borders. An understanding of the prevalence of cross-border species distributions is important for informing high-level conservation strategies, such as bilateral or regional agreements. Here, we examined 28,252 distribution maps to determine the number and locations of transboundary marine plants and animals. Over 90% of species have ranges spanning at least two jurisdictions, with 58% covering more than ten jurisdictions. All jurisdictions have at least one transboundary species, with the highest concentrations of transboundary species in the USA, Australia, Indonesia, and the Areas Beyond National Jurisdiction. Distributions of mapped biodiversity indicate that overcoming the challenges of multinational governance is critical for a much wider suite of species than migratory megavertebrates and commercially exploited fish stocks—the groups that have received the vast majority of multinational management attention. To effectively protect marine biodiversity, international governance mechanisms (particularly those related to the Convention on Biological Diversity, the Convention on Migratory Species, and Regional Seas Organizations) must be expanded to promote multinational conservation planning, and complimented by a holistic governance framework for biodiversity beyond national jurisdiction.

Nonlinear single unit activity (SUA) characteristics are the useful measures to reveal the information processing and transfer features associated with Parkinson’s disease (PD) in the basal ganglia. Most of the state-of-the-art approaches to compute such parameters in continuous and discrete forms are strongly dependent on SUA recording length, noise level and input parameters. Due to the specificity of SUA data collection (mainly short recordings with relatively low signal-to-noise ratio) new techniques to evaluate neuronal nonlinear properties are needed. We have developed an encoding technique based on a mean interspike interval (ISI) value to calculate spike train discrete nonlinear features. The approach to compute mutual information (MI) of isolated neurons with its unstructured activity was also proposed. The proposed technique of SUA nonlinear features evaluation slightly depends on spike train length, has low correlations with other SUA characteristics (firing rate, coefficient of ISI variance and asymmetry index). The derived entropy measure in the subthalamic nucleus has significant positive correlation with PD severity. The proposed approach provides nonlinear features that are slightly dependent on investigated sample size and independent on input parameters. Also, the developed mean ISI based measures reflect the more complex nature of oscillatory activity in the basal ganglia, than it was thought previously. Moreover, MI, unlike entropy, takes into account the position of the spike train elements, which allows us to investigate the amount of information retained after the occurrence of temporary failures. The developed approach may be useful in describing nonlinear features of basal ganglia activity contributing to PD pathophysiology probably associated with impaired information transfer in movement disorders.

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.

Due to an urgent need for reducing the fast progressing climate changes, a rapid, standardized and replicable solution for the infrastructure restructuring of heat demand coverage of buildings at district and city level must be developed. As more and more communities in Europe, especially in Germany, are obligated to have plans for coverage of heat demand, city planners, energy agencies seek a tool, which will help them to design the first drafts of heating network routes, which can supply whole districts and cities with renewable energy. ArcGIS Pro Tools like Least-Cost-Path-Analysis (LCPA) and Closest Facility (CF) allow to find the shortest and “cheapest” way between the heat source and heat consumers in the analyzed areas. Starting from the community level, through the district, county, voivodeship and whole country levels, the replication of the methods for generating district heating (DH) network infrastructure can be achieved. The proposed LCPA and CF based methods help to design the most suitable and efficient DH networks in the analyzed areas. As only few open-source data input, like street networks and building footprints are needed, the methods can be implemented in all communities of the country of Poland. In this paper one example of one community of Wroclaw county, called Siechnice and surroundings is presented.

The objective of this study was to develop the least-cost starter’s diet and evaluated its effect on the growth performance of Sasso breeds and Indigenous ecotype of chicks under the local condition of the South Gondar Zone. The effects of substitution of different levels of commercial starters ration with homemade diet on the growth performance of Sasso and Indigenous chicks were studied in Hiruy Abaregay village of Farta district. The research area is 586km distant from the capital city of Addis Ababa, Ethiopia. A total of 510 Sasso T-44 and 90 Indigenous local ecotypes day-old chicks were randomly divided into five groups, each with 102 and 18 chicks, respectively. These were assigned into five treatments in which 100 (T1), 75 (T2), 50 (T3), 25 (T4), and 0% (T5) of commercial starter’s diet in factorial completely randomized design (CRD) with 3 replications for 60 days feeding period. The results obtained indicated that increased levels of substitution of a commercial diet with a homemade diet significantly depressed (p<0.001) mean daily feed consumption and retention of dry matter, nitrogen, and metabolizable energy. Growth rate as measured by mean daily weight gain, mean final body weight, and total feed consumption and feed cost were significantly miserable (p<0.001) in an increased homemade diet. On the contrary, there was an increase in feed conversion ratio and fiber content in high-level dilution of starter’s commercial diet with a homemade diet. However, the groups of chicks on 0, 25, and 50% commercial starters diets replaced by homemade diet were significantly higher (p<0.001) in mean daily feed intake, daily weight gain, feed conversion ratio, and final body weight attained. The results of this study indicated that up to 50% of expensive commercial starter’s diet could economically be replaced with the least cost homemade diet without adversely affecting the growth performance of chicks.

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.

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.

Small Shallow Lakes (SSL) support exceptionally high and original biodiversity, providing numerous ecosystem services. Their small size makes them especially sensitive to anthropic activities, that causes a shift to dysfunctional turbid states and induces loss of services and biodiversity. In this study we investigated the relationships between environmental factors and macrophyte communities. Macrophytes play a crucial role in maintaining functional clear states. Better understanding factors determining the composition and richness of aquatic plant communities in least-impacted conditions may be useful to protect them. We inventoried macrophyte communities and collected chemical, climatic and morphological data from 89 least-impacted SSL widely distributed in France. SSL were sampled across four climatic ecoregions, various geologies and elevations. Hierarchical cluster analysis showed a clear separation of four macrophyte assemblages strongly associated with mineralisation. Determinant factors identified by db-RDA analysis are, in order of importance, geology, distance from source (DIS, a proxy for connectivity with river hydrosystems), surface area, climate and hydroperiod (water permanency). Surprisingly, at country-wide scale, climate and hydroperiod filter macrophyte composition weakly. Geology and DIS are the major determinants of community composition, whereas surface area determines floristic richness. DIS is identified as determinant in freshwater lentic ecosystems for the first time.

Identification of recurrent driver mutations in genes encoding tyrosine kinases has resulted in the development of molecularly targeted strategies designed to improve the outcomes for patients diagnosed with acute myeloid leukemia (AML). The receptor tyrosine kinase FLT3, is the most commonly mutated gene in AML, with internal tandem duplications within the juxtamembrane domain (FLT3-ITD) or missense mutations in the tyrosine kinase domain (FLT3-TKD), present in 30%-35% of AML patients at diagnosis. An established driver mutation and marker of poor prognosis, the FLT3 tyrosine kinase has emerged as an attractive therapeutic target, and thus has encouraged the development of FLT3 tyrosine kinase inhibitors (TKIs). However, the therapeutic benefit of FLT3 inhibition, particularly as monotherapy, frequently results in the development of treatment resistance and disease relapse. Commonly, FLT3 inhibitor resistance is induced by the emergence of secondary lesions in the FLT3 gene, particularly in the second tyrosine kinase domain at residue Asp835 (D835) to form a ‘dual mutation’ (ITD-D835). Individual FLT3-ITD and FLT3-TKD mutations influence independent signaling cascades however, currently little is known which divergent signaling pathways are controlled by each of these FLT3 specific mutations, particularly in the context of patients harboring dual ITD-D835 mutations. This review provides a comprehensive analysis of the known discrete and cooperative signaling pathways regulated by each of the FLT3 specific mutations, as well as the therapeutic approaches that hold the most promise for development of more durable and personalized therapeutic approaches targeting mutant FLT3, to improve the treatment of AML.

Forest resources are renewable,rational exploitation and utilization of forest resources are not only conducive to sustainable development of population, but also can obtain higher economic benefits. Based on actual timber harvesting problems,a combined harvesting model of timber and non-timber with nonlinear harvesting term was established.Firstly, using the qualitative theory of ordinary differential equations, the dynamic behavior of the model is studied, and the existence and stability of the equilibrium point of the model are proved .Secondly, the optimal control solution is obtained by using the optimal control theory.Finally, the optimal harvesting strategy of timber and non-timber products is given based on the numerical simulation results, which provides a certain theoretical basis for the sustainable development of forestry ecological economy.

The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e. stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T–S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T–S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

At the beginning of any electric arc welding process, a regime called transient regime will always occur, characterized by the continuous variation of the energy flow, also resulting in the variation of the cooling rate of the welded joint. Consequently, the weld bead hardness varies from a maximum value to an approximately constant value, and this phenomenon can be represented by an asymptotic exponential function. For several welded specimens, it would be possible to fit a non-linear regression for each specimen, however, it would be a difficult task to combine different regressions in a single analysis. The objective of this study is to evaluate the applicability of mixed-effects models and artificial neural networks to predict the longitudinal hardness of the weld bead in the initial transient regime. To this end, linearized and nonlinear mixed-effects models and artificial neural networks with different architectures were fitted. Finally, valid models were obtained with all approaches, with artificial neural network model slightly better fitted. However, the explainability capacity of the linearized mixed-effects model was superior, showing that the relative thickness, one of the predictor variables, was responsible for 48% of the variation in longitudinal hardness of weld bead.

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 COVID-19 pandemic has significantly impacted human health and daily life. Meteorological factors play a crucial role in virus transmission. Understanding these factors is critical for pandemic control, yet debates continue due to variations in research methods and data. This study uses a global dataset and focuses on administrative units smaller than 10,000 km². The relationship between daily COVID-19 incidence rates and meteorological factors—including temperature, relative humidity (RH), ultraviolet radiation (UVR), and diurnal temperature range (DTR)—was analyzed across 173 units in 62 countries. The results revealed significant nonlinear responses and lag effects between incidence rates and the meteorological factors. Key inflection points were observed at 0°C and 24°C for temperature, 63% for RH, 102 KJ/m² for UVR, and 15°C for DTR. Below 0°C, infection risk increased with rising temperatures; from 0°C to 24°C, risk decreased; and above 24°C, risk escalated rapidly. RH below 63% correlated inversely with infection risk, while above 63%, the correlation was positive. Infection risk decreased with UVR below 102 KJ/m² but increased beyond this threshold. These nonlinear responses are primarily driven by the differential effects of these factors on virus survival, transmission, and human immunity. Conditions around 24°C, 63% RH, 102 KJ/m² UVR, and DTR below 15°C appear optimal for human immunity, correlating with lower infection risk. High temperature and low UVR prompted immediate infection responses, while low temperatures, high UVR, and larger DTR showed delayed effects. These findings provide new, more reliable evidence for understanding the mechanisms driving COVID-19 pandemic dynamics and for preventing the future normalization of the epidemic.

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.

Historical city textures are living history embodying public open spaces of former civilizations, their landscapes and traditional life cultures, carrying them to the present and giving them life. The squares, which form the public open spaces, have been important meeting centers in the social lives of people. City furniture are the important elements in these public open spaces, reflecting the identity of the city and improving quality of life. City furniture improve the reflection of cultural value in historical city textures and their usability. The walled city center, where the historical city texture of Nicosia lies, has a very rich historical texture with the cultural heritage of various civilizations in the history of Cyprus. Public open spaces within the texture, which have acquired the quality of squares with their functions throughout the social history of Nicosia, are still important social spaces for the people of the city. This study analyzed Asmaaltı and Selimiye Squares, two important spaces of the walled city, through examining the city furniture in terms of their material, shape, and functionality, and their conformity with the historical texture. Their deficiencies and nonconformities with the historical texture were identified accordingly. In consideration with such examples, city furniture in historical city textures were assessed for their conformity with the texture characteristics, architectural styles, social, cultural, and economical characteristics, and relevant recommendations are presented respectively.

Tarihi kent dokuları, eski uygarlıkların kamusal açık alanlarını, peyzajlarını ve geleneksel yaşam kültürlerini bünyesinde barındıran, günümüze taşıyan ve yaşatan yaşayan bir tarihtir. Kamusal açık alanları oluşturan meydanlar, insanların sosyal yaşamlarında önemli buluşma merkezleri olmuştur. Kent mobilyaları bu kamusal açık alanlarda kentin kimliğini yansıtan ve yaşam kalitesini artıran önemli unsurlardır. Kent mobilyaları, kültürel değerlerin tarihi kent dokularına yansımasını ve kullanılabilirliğini artırır. Lefkoşa'nın tarihi kent dokusunun yattığı Suriçi kent merkezi, Kıbrıs tarihindeki çeşitli uygarlıkların kültürel mirası ile oldukça zengin bir tarihi dokuya sahiptir. Doku içinde kamusal açık alanlar, Lefkoşa'nın sosyal tarihi boyunca işlevleriyle meydan niteliği kazanan meydanlar, kent insanı için halen önemli sosyal mekanlardır. Bu çalışmada, Suriçi kentin iki önemli mekanı olan Asmaaltı ve Selimiye Meydanları, kent mobilyaları malzeme, biçim, işlevsellik ve tarihi dokuya uygunluk açısından incelenerek incelenmiştir. Buna göre eksiklikleri ve tarihi dokuya uymayanları tespit edilmiştir. Bu örnekler ışığında tarihi kent dokularındaki kent mobilyalarının doku özellikleri, mimari üsluplar, sosyal, kültürel ve ekonomik özelliklerle uygunluğu değerlendirilmiş ve öneriler sunulmuştur. kentliler için hala önemli sosyal mekanlardır. Bu çalışmada, Suriçi kentin iki önemli mekanı olan Asmaaltı ve Selimiye Meydanları, kent mobilyaları malzeme, biçim, işlevsellik ve tarihi dokuya uygunluk açısından incelenerek incelenmiştir. Buna göre eksiklikleri ve tarihi dokuya uymayanları tespit edilmiştir. Bu örnekler ışığında tarihi kent dokularındaki kent mobilyalarının doku özellikleri, mimari üsluplar, sosyal, kültürel ve ekonomik özelliklerle uygunluğu değerlendirilmiş ve öneriler sunulmuştur. kentliler için hala önemli sosyal mekanlardır. Bu çalışmada, Suriçi kentin iki önemli mekanı olan Asmaaltı ve Selimiye Meydanları, kent mobilyaları malzeme, biçim, işlevsellik ve tarihi dokuya uygunluk açısından incelenerek incelenmiştir. Buna göre eksiklikleri ve tarihi dokuya uymayanları tespit edilmiştir. Bu örnekler ışığında tarihi kent dokularındaki kent mobilyalarının doku özellikleri, mimari üsluplar, sosyal, kültürel ve ekonomik özelliklerle uygunluğu değerlendirilmiş ve öneriler sunulmuştur. ve tarihi dokuya uygunluğu. Buna göre eksiklikleri ve tarihi dokuya uymayanları tespit edilmiştir. Bu örnekler ışığında tarihi kent dokularındaki kent mobilyalarının doku özellikleri, mimari üsluplar, sosyal, kültürel ve ekonomik özelliklerle uygunluğu değerlendirilmiş ve öneriler sunulmuştur. ve tarihi dokuya uygunluğu. Buna göre eksiklikleri ve tarihi dokuya uymayanları tespit edilmiştir. Bu örnekler ışığında tarihi kent dokularındaki kent mobilyalarının doku özellikleri, mimari üsluplar, sosyal, kültürel ve ekonomik özelliklerle uygunluğu değerlendirilmiş ve öneriler sunulmuştur.

Lung cancer remains the most common cancer worldwide with a limited prognosis despite personalized treatment regimens. Low-dose computed tomography (CT) scanning as a means to early diagnosis has been disappointing due to the high false positive rate. Other non-invasive means of testing need to be developed that offer both timely diagnosis and predict prognosis. Methods: In the course of stool testing in a large-scale testing of 2,922 patients at increased risk of CRC we were able to ascertain 112 patients documented to have prospectively been diagnosed with lung cancer. Stool and colonic effluents were tested for p87 with anti-adenoma antibody (Adnab-9) reactivity by ELISA and western blot. Survival data were obtained where available. Results: Of 112 cancers, approximately 27.6% were squamous (SSC), 17.9% were adenocarcinoma, 8% small, 6.25% large cell and 3.57% were designated non-small cell cancer (NSCLC), 0.89% indeterminate, 0.89% lepidic spread (1), 3.57% had metastasis and in 31.25% data was unavailable. 49.1% of the lung cancer patients had fecal Adnab-9 testing. Overall, 60% had positive testing compared to 38%, which was significant (OR2.19[1/06-4.53];p=0.045). Cancers with higher lethality were less likely to test positive (approximately, 8.5% each for both small and large cell lung cancers), and higher, 56% with SCC and 25% for adenocarcinoma. 0% NSCLC). In the larger groups overall survival was worse in those testing positive: 474 testing positive versus 844 days in SCC and 54 testing positive versus 749 days in adenocarcinoma patients. Most importantly, the time from a positive test to the clinical diagnosis ranged from 2.72 years for small cell, 3.13 for adenocarcinoma, 5.07 for NSCLC, 6.07 for SSC, and 6.24 for large cell cancer. In excluded cases where cancer in the lung was believed to be metastatic,83.3% of cancers were positive. Conclusions: At a projected real-world sensitivity of 0.60 and specificity of 0.60 and the ability to predate diagnosis by up to 4.7 years overall, this test could help direct lung cancer screening. In addition, the Adnab-9 testing selectively detects worse tumor types (87.5%) and those with worse prognosis amongst the more common, favorable phenotypes thus making early diagnosis possible in those patients who stand to benefit most from this strategy. Metastatic lung cancer also detected by the test should be identified by the follow-up imaging studies and therefore would not be considered to be a major pitfall.

Partial least square (PLS) regression is a well-known chemometric method used for predictive modelling, especially in the presence of many variables. Although PLS was not initially developed as a technique for classification tasks, scientists have reportedly used this approach successfully for discrimination purposes. Whereas some non-supervised learning approaches including but not limited to PCA, and k-means clustering do well in identifying/understanding grouping and clustering patterns in multidimensional data, they are limited when the end target is discrimination, making PLS a preferable alternative. A total of fertilized 672 chicken egg hyperspectral imaging data, consisting of 336 white eggs and 336 brown eggs were used in this study. Hyperspectral images in the NIR region of 900-1700 nm wavelength range were captured prior to incubation on day 0 and on days 1-4 after incubation. Eggs were candled on incubation day 5 and broken out on day 10 to confirm fertility. While a total number of 312 and 314 eggs were found to be fertile in the brown and white egg batches respectively, total numbers of non-fertile eggs in the same set of batches were 23 and 21 respectively. Spectral information was extracted from a segmented region of interest (ROI) of each hyperspectral image and spectral transmission characteristics were obtained by averaging the spectral information. A moving-thresholding technique was implemented for discrimination based on PLS regression results on the calibration set. With true positive rates (TPR) of up to 100% obtained at selected threshold values of between 0.50-0.85 and on different days of incubation, the results indicated that the proposed PLS technique can accurately discriminate between fertile and non-fertile eggs. The adaptive PLS approach was thereby presented as suitable for handling hyperspectral imaging-based chicken egg fertility data

The increase in life expectancy, according to the World Health Organization, is a fact, and with it rises the incidence of age-related neurodegenerative diseases. The most recurrent symptoms are those associated with tremors resulting from Parkinson's Disease (PD) or Essential Tremors (ET). The main alternatives for the treatment of these patients are medication and surgical intervention, which sometimes have restrictions and side effects. Through computer simulations in Matlab software, this work investigates the performance of adaptive algorithms based on least mean squares (LMS) to suppress tremors in upper limbs, especially in the hands. The signals resulting from pathological hand tremors, related to PD, present components at frequencies that vary between 3~Hz and 6~Hz, with the more significant energy present in the fundamental and second harmonics, while physiological hand tremors, referred to as ET, vary between 4~Hz and 12~Hz. We simulated and used these signals as reference signals in adaptive algorithms, Filtered-x Least Mean Square (Fx-LMS), Filtered-x Normalized Least Mean Square (Fx-NLMS), and a hybrid Fx-LMS\&NLMS purpose. Our results showed that the vibration control provided by the Fx-LMS\&LMS algorithm is the most suitable for physiological tremors. For pathological tremors, we have used a proposed algorithm with a filtered sinusoidal input signal, Fsinx-LMS, which presented the best results in this specific case.

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 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.

Traditional population-based metaheuristic algorithms are effective in solving complex real-world problems but require careful strategy selection and parameter tuning. Parameter-less population-based optimization algorithms have gained importance due to their simplicity and efficiency. However, research on their applicability for solving large systems of nonlinear equations is still incipient. In this paper, a systematic review and detailed description of metaphor-less optimization algorithms is made, including the Jaya algorithm, the main Jaya variants for continuous optimization problems, with a focus on the Enhanced Jaya (EJAYA) algorithm, the three Rao algorithms, the best-worst-play (BWP) algorithm, and the very recent max-min-greedy-interaction (MaGI) algorithm. This paper also discusses a few previous parallelizations of the Jaya optimization algorithm, as well as recent GPU-based massively parallel implementations of the Jaya, Enhanced Jaya (EJAYA), Rao, and BWP algorithms developed by the authors. In addition, a novel GPU-accelerated version of the MaGI algorithm is proposed. The GPU-accelerated versions of the metaphor-less algorithms developed by the authors were implemented using the Julia programming language and tested primarily on GeForce RTX 3090 and NVIDIA A100 GPUs, as well as on Tesla V100S and Tesla T4 GPUs, using a set of difficult, large-scale nonlinear equation system problems. The computational experiments carried out produced quite significant speedups, which highlights the efficiency of the GPU-based versions of the metaphor-less algorithms developed for solving large-scale systems of nonlinear equations.

In this paper, the classical least square (CLS) method with molecular absorption spectrophotometric measurement was used to determine simultaneously of paracetamol (PAR), ibuprofen (IBU), and caffeine (CAF) in tablets. The absorbance spectra of the standard solutions and samples were measured over a wavelength from 220 to 300 nm with a 0.5 nm step. The concentration of PAR, IBU and CAF in the sample solutions were calculated by using a program called CLS-Excel written in Microsoft Excel 2016 and Visual Basic for Applications (VBA). The method and CLS-Excel program were tested on mixed standard laboratory samples with different PAR, IBU, and CAF concentration ratios, and they showed small errors and satisfying repeatability. An analytical procedure for tablets containing PAR, IBU, and CAF was developed. The reliability of the procedure was proved via the recovery and repeatability of the analysis results with an actual tablet sample and comparing the mean contents of active substances in the tablets obtained from the analytical procedure with the from the HPLC method. The procedure is simple with a reduced cost compared with the HPLC standard method.

Living processes are integral to open systems for multiple reasons. From a thermodynamic perspective, they reduce local entropy at the cost of increasing environmental entropy. Furthermore, these processes are inherently nonlinear owing to their feedback interactions with the environment. Nonlinear systems exhibit diverse behaviours: some stabilize at a constant value, whereas others display bifurcations and chaotic dynamics. This study introduces a model that describes living processes as the dynamics of nonlinear single-value diverging maps, whereas chaotic evolution is associated with the increasing entropy environment. This model enables us to describe the lifetime of different species simply by varying the model parameters. This model also simplifies explaining the transition from life to death.

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 article introduces a novel two-step fifth-order Jacobian-free iterative method aimed at efficiently solving systems of nonlinear equations. The method leverages the benefits of Jacobian-free approaches, utilizing divided differences to circumvent the computationally intensive calculation of Jacobian matrices. This adaptation significantly reduces computational overhead and simplifies the implementation process while maintaining high convergence rates. We demonstrate that this method achieves fifth-order convergence under specific parameter settings, with a broad applicability across various types of nonlinear systems. The effectiveness of the proposed method is validated through a series of numerical experiments which confirm its superior performance in terms of accuracy and computational efficiency compared to existing methods.

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 Totiviridae family of viruses has a unique genome consisting of double-stranded RNA with two open reading frames that encode the capsid protein (Cap) and the RNA-dependent RNA polymerase (RdRpol). Most virions in this family are isometric in shape, approximately 40 nm in diameter, and lack envelope. There are five genera within this family, including Totivirus, Victorivirus, Giardiavirus, Leishmaniavirus, and Trichomonasvirus. While Totivirus and Victorivirus primarily infect fungi, Giardiavirus, Leishmaniavirus, and Trichomonasvirus infect diverse hosts, including protists, insects, and vertebrates. Recently, new totivirus-like species have been discovered in fish and plant hosts, and through metagenomic analysis, a novel totivirus-like virus (named Tianjin totivirus) has been isolated from bat guano. Interestingly, Tianjin totivirus causes cytopathic effects in insect cells but cannot grow in mammalian cells, suggesting that it infects insects consumed by insectivorous bats. In this study, we used next-generation sequencing and identified totivirus-like viruses in liver tissue from Molossus molossus bats in the Amazon region of Brazil. Comparative phylogenetic analysis based on the RNA-dependent RNA polymerase region revealed that the viruses identified in Molossus bats belong to two distinct phylogenetic clades, possibly comprising different genera within the Totiviridae family. Notably, the mean similarity between Tianjin totivirus and the totiviruses identified in Molossus bats is less than 18%. These findings suggest that the diversity of totiviruses in bats is more extensive than previously recognized and highlight the potential for bats to serve as reservoirs for novel toti-like viruses.

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.

Based on the nonlinear failure criterion and modified tangential technique, the upper bound solutions of supporting pressure on the deep tunnel face were obtained under pore water pressure conditions. The influence of parameters on the supporting pressure and collapse range was investigated according to the unlimited block failure mechanism. It is found that the upper bound solutions of supporting pressure increase with the growth of the nonlinear coefficient and pore water pressure coefficient. The collapse range of the tunnel face scales out with the increase of the nonlinear coefficient and shrinks when increasing the pore water pressure coefficient. Moreover, with the increase of the nonlinear coefficient, the impact strength on supporting pressure and collapse range declines gradually. According to the calculating results, it is manifest that both the pore water pressure and nonlinear criterion factors have negative impacts on the stability of the tunnel face. Thus, more attention should be paid to these parameters to ensure face stability in deep tunnel construction.

Input noise causes inescapable bias to the weight vectors of the adaptive filters during the adaptation processes. Moreover, the impulse noise at the output of the unknown systems can prevent bias compensation from converging. This paper presents a robust bias compensation method for a sparse normalized quasi-Newton least-mean (BC-SNQNLM) adaptive filtering algorithm to address this issue. We have mathematically derived the biased-compensation terms in an impulse noisy environment. Inspired by the convex combination of adaptive filters' step sizes, we propose a novel variable-mixing-norm method to accelerate the convergence for our BC-SNQNLM algorithm, which is referred to as BC-SNQNLM-VMN. Simulation results confirm that the proposed method significantly outperforms other comparative works regarding normalized mean-squared deviation (NMSD) in the steady state.

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.

This research aims to investigate psychological anxiety factors, particularly Music Performance Anxiety (MPA), that influence the sustainability of music learning systems. This study employs an innovative integration of qualitative and quantitative methodologies, marking the first use of a nonlinear system paired with a comprehensive data framework for analyzing questionnaire responses. This approach allows for a detailed examination of the effects of these factors on academic outcomes. Previous research has primarily focused on the fragmented music learning system from the perspective of teachers' instructional strategies, emphasizing phased teaching methods and learning objectives which focus often neglected a significant subset of music learners. Addressing this oversight, the current study specifically centers on the emotional aspects of anxiety within music learning systems, with a particular emphasis on students, who play a crucial role in music education. This perspective enables a deep exploration of how MPA and other related emotional factors affect music learning systems. A notable innovation of this research is the development of a stochastic nonlinear system designed to model the psychological factors impacting student music learning, complemented by a quantitative model that assesses actual learning outcomes. By analyzing this nonlinear system, the research identifies weight values for various negative emotions, particularly those related to MPA, that significantly influence the music learning process. The integration of MPA and other anxiety related emotional factors with practical learning outcomes provides a comprehensive understanding of their combined impact on the music learning system. These insights are invaluable for educators and policymakers aiming to enhance both the effectiveness and emotional well-being within music education. This comprehensive approach offers a novel perspective in understanding and improving the dynamics of music education through a more empathetic and scientifically grounded lens.

Accurate and stable cost forecasting of substation projects is of great significance to ensure the economic construction and sustainable operation of power engineering projects. In this paper, a forecasting model based on the improved least squares support vector machine (ILSSVM) optimized by wolf pack algorithm(WPA) is proposed to improve the accuracy and stability of the cost forecasting of substation projects. Firstly, the optimal features are selected through the data inconsistency rate (DIR), which helps reduce redundant input vectors. Secondly, the wolf pack algorithm is used to optimize the parameters of the improved least square support vector machine. Lastly, the cost forecasting method of WPA-DIR-ILSSVM is established. In this paper, 88 substation projects in different regions from 2015 to 2017 are chosen to conduct the training tests to verify the validity of the model. The results indicate that the new hybrid WPA-DIR-ILSSVM model presents better accuracy, robustness and generality in cost forecasting of substation projects.

This text deals with exploring random solutions for generalized nonlinear variational inequality problems. Using the Fan-KKM theorem and Aumann's measurable selection theorem, we are able to prove the existence and uniqueness of random solution sets under the conditions of monotonicity and convexity. Additionally, we use Minty's lemma to demonstrate the compactness and convexity of the random solution sets.

Although it’s been some forty years since we started to teach combined modified Fault Tree / Event Tree acyclic digraphs, as much simpler Bow Tie diagrams, their popularity seems undimmed; as their pictorial and focussed discussion prompts, fulfil a valuable function in the safe design and operation of hazardous plants and installations. An excellent review of the current state of the art and an authoritative treatise on the terminology and issues involved has been produced as an internationally recognised standard for using the approach. But just as this model has augmented and helped formalise previous pictorial tools, (such as “Dominoes” and holey “Cheese” slices), this paper suggests and sets out to show how we can build on even this current cornerstone of practice and augment its versatility; with the ability to obtain, what engineers rely on, some more quantitative insights from these pictures. “Layers Of Protection Analysis” (LOPA), has already demonstrated a way of pulling together more quantitative predictions from the pictures. This paper would go further and by concentrating on the function not the physicality of a barrier, outlines a methodology that can extend, not just the quantification ability of the LOPA extension, but present a much more holistic view of how the Barriers, as functions, need to work together, interact and interdepend; often in nonlinear, unexpected ways, to give system designers and operators a much clearer view of actual performance predictions.

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.