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

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

This paper presents the preservation property of the average intensity order and the preservation property of the monotonic average intensity classes under distorted distributions. Several sufficient conditions are given to get the preservation properties. It is shown that the imposed conditions are achievable as we examine in some examples. The preservation of the average intensity order and the preservation of the decreasing average intensity class under the structure of a parallel system with independent and identically distributed components' lifetime are made. A lower bound for the average intensity function of a random lifetime with an increasing failure rate in average distribution is derived. The results are applied to some semiparametric models as a particular standard family of distorted distribution.

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

What is an observer? What is an observation? How do observations inform beliefs? What is the relationship between observers and physical objects in spacetime? These are central, and as yet unresolved, questions in the foundations of physics and consciousness science. We propose an answer taking consciousness as fundamental, resulting in a theory of conscious agents whose mutual interaction is governed by Markov chains. We describe observation via a new trace order on Markov chains. In this context, no observer is aloof: it must be an integral part of any system it observes. We find that the trace order forms a non-Boolean logic, mapping homomorphically to the “Lebesgue” logic” of probabilistic beliefs. We explore implications of conscious agent theory for the “hard problem” of consciousness, and propose a route to empirical tests using data from scattering experiments with subatomic particles.

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

This paper presents the analysis of four error models that can appear in the field of adaptive systems, where adaptive laws for parameter estimation are represented as fractional order differential equations whose order can switch between an order within the range (0,1) and 1. These switched adaptive laws have been proposed in the past few years to improve the balance between control energy and system performance, which is often a challenge when using traditional integer-order or fractional-order adaptive laws in adaptive identification and control. Boundedness of the solutions is proved for all cases, together with the convergence to zero of the estimation/tracking error. Additionally, sufficient conditions for parameter convergence are presented, showing that the excitation condition required for parameter convergence in the vector case is also sufficient for parameter estimation in the matrix case.

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

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

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

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

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

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

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

In this work, we explore Conjecture 1 proposed in the newly released pioneering paper “Volatility transformers: an optimal transport-inspired approach to arbitrage-free shaping of implied volatility surfaces” by Zetocha Valer, which posits that the “One-X” property is both a necessary and sufficient condition for convex order between non-negative continuous strictly increasing distributions with the same mean. We provide a counterexample demonstrating that the conjecture, as originally stated, does not hold. By examining stochastic orders, particularly the increasing convex order, and the “One-X” property, we propose an enhanced version of the conjecture which is shown to be valid. Furthermore, we discuss the implications of these findings in the context of equity implied volatility fitting and the construction of implied volatility surfaces, highlighting the challenges posed by real-market conditions. In the end, we propose several applications in implied volatility surface construction or simulation.

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

We investigated the dynamics of a simple master equation describing the evolution of a probability distribution between two states, \( p_1 \) and \( p_2 \) (with \( p_1 + p_2 = 1 \)). Our focus is on the behavior of the entropy \( S \), the distance \( D \) from the uniform distribution (\( p_1 = p_2 = 1/2 \)), and the free energy \( F \). We define two ratios, \( \eta_S = \frac{dS/dt}{dF/dt} \) and \( \eta_D = \frac{dD/dt}{dF/dt} \), and find that both diverge to plus-minus infinity as the system evolves towards the uniform distribution. This divergence marks a critical transition point where the master equation temporarily loses physical meaning. However, after this divergence, the system settles into a new, well-behaved regime where the solutions stabilize at finite values, representing a new equilibrium or steady state. This two-regime behavior underscores the intricate dynamics of simple probabilistic systems as they approach and surpass equilibrium, providing insights into the complex interplay of entropy, distance, and free energy in statistical mechanics.

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

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

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

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

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

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

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

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

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

This study aimed to assess the predictive performance of first and second-order regression models in optimizing bedaquiline (BQ) solid lipid nanoparticles (SLNs) formulations. Employed a central composite design and graphical optimization process using three steps. A design of experiments to evaluate the impact of BQ, Tween 80 (T80), polyethylene glycol (PEG), and lecithin on the formulations' response variables: Z-average (PSD), polydispersibility index (PdI), and Zeta potential (ZP). Secondly, quantified the relationship between experimental variables using the regression model coefficients. Lastly, predicted the responses and verified the models’ adequacies to ensure accurate representation and effective optimization. First-order polynomial showed poor model adequacy that required further refinement. The second-order models provided superior fitness, sensitivity to variability, complexity, and prediction consistency. The optimized formulation achieved a desirability value of 0.9998 indicating alignment with the desired criteria. Specifically, the levels of BQ (19.4mg), T80 (25.2mg), PEG (39.2mg), and Lecithin (200mg) corresponded to PdI (0.41), PSD (250.99 nm), and ZP (-25.95 mV). Maintaining BQ concentration between 10-20% and T80 between 15-18% is vital for maximizing ZP and minimizing PdI and PSD, ensuring stable SLN formulations. The study underscores significance of precise model selection and statistical analysis in pharmaceutical formulation optimization for enhanced drug delivery systems.

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.

Understanding the contribution of protected areas to pollinating insect conservation is crucial, especially in Haiti because of intense deforestation and environmental degradation. We compared pollinating insect assemblage composition and abundance in two protected areas: the suburban Wynne Farm Ecological Reserve (WFER) and the Urban National Park of Martissant (UNPM). Both sites encompass forest patches, agroforestry, and agricultural crops. Using colored pan-traps, we collected 3722 insects from six Orders, with 68.2% identified to family level due to taxonomic limitations. WFER exhibited significantly higher insect abundance than UNPM, though habitat differences varied between sites. Site, habitat, and their interaction significantly influenced insect composition. Among 118 identified families, only 30.51% were shared between sites. Our data suggest combined protection offers broader and more even insect diversity. We discovered patrimonial lepidopteran and hymenopteran species previously unrecorded in Haiti, emphasizing the importance of protected areas and the need for enhanced entomological expertise.

This paper presents an observer-based dynamic output feedback controller design procedure using Linear Matrix Inequality (LMI) optimization for second-order systems with uncertainty and persistent perturbation in the states. Using linear-quadratic criteria, cost functions are minimized in a two-stage procedure to compute optimal state feedback gains, and observer gains are coupled into a dynamic output feedback optimal controller. The LMI set used in the two stages is matrix inversion-free, a key issue for polytope formulation when uncertainty is present. The approach is tested in a mobile inverted pendulum robotic platform, and the effectiveness is verified in this underactuated and undesensed case.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

In the paper the new, fractional order, state space model of a heat transfer in a one- 1 dimensional metallic rod is addressed. The fractional orders of derivative along space and time 2 are not exactly known and they are described by intervals. The proposed model is the interval 3 expanding of the state space fractional model of the one dimensional heat transfer. It is expected to 4 better describe the reality because interval order of each real process is hard to estimate. Elementary 5 properties of the proposed model are analysed. Theoretical results are experimentally validated using 6 data from real experimental laboratory system.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

When a rotary machine is running, from which the acquired vibro-acoustic signals enable to reveal its operation status and health condition. The study proposed a DSP-based adaptive angular-velocity Vold-Kalman filtering order tracking (AV2KF_OT) algorithm with an online real-time nature for signal interpretation and machine condition monitoring. Theoretical derivation and numerical implementation of computation schemes are briefly introduced. An online real-time monitoring system based on the AV2KF_OT algorithm, which was implemented through both a digital signal processor and a user interface coded by using LabVIEW, was developed. Two experimental tasks were applied to justify the proposed technique, including (i) the detection of startup on the fluid-induced whirl performed through a journal-bearing rotor rig, and (ii) the separation of close orders from the measured signals of a multifunction transmission-element ball-bearing bench.

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

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

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

Estimation of core and surface temperature is one of the crucial functionalities of the lithium-ion Battery Management System (BMS) towards providing effective thermal management, fault detection and operational safety. While, it is impractical to measure core temperature using physical sensors, implementing a complex estimation strategy in on-board low-cost BMS is challenging due to high computational cost and the cost of implementation. Typically, a temperature estimation scheme consists of a heat generation model and a heat transfer model. Several researchers have already proposed ranges of thermal models having different levels of accuracy and complexity. Broadly, there are first-order and second-order heat capacitor-resistor-based thermal models of lithium-ion batteries (LIBs) for core and surface temperature estimation. This paper deals with a detailed comparative study between these two models using extensive laboratory test data and simulation study to access suitability in online prediction and onboard BMS. The aim is to guide whether it’s worth investing towards developing a second-order model instead of a first-order model with respect to prediction accuracy considering modelling complexity, experiments required and the computational cost. Both the thermal models along with the parameter estimation scheme are modelled and simulated using MATLAB/Simulink environment. Models are validated using laboratory test data of a cylindrical 18650 LIB cell. Further, a Kalman Filter with appropriate process and measurement noise levels are used to estimate the core temperature in terms of measured surface and ambient temperatures. Results from the first-order model and second-order models are analyzed for comparison purposes.

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

A new family of inequality indices based on the deviation between the expected maximum and the expected minimum of random samples, called the nth Gini index is presented. These indices generalize the Gini index. At the same time, this family of indices and the S-Gini index are generalised by proposing the uv−Gini index, which turns out to be a convex combination of the S-Gini index and the Lorenz family of inequality measures. This family of Gini indices provides a methodology for achieving perfect equality in a given distribution of incomes. This is achieved through a series of successive and equal increases in the incomes of each individual.

Metagenomic analysis of soil bacterial communities based on 16S rRNA reflects typical a community composition containing a low number of high abundance types and a very high number of low abundance types. Here, the formation of characteristic rank order functions of bacterial abundance is investigated by modelling the dynamics of soil bacterial communities assuming a succession of different bacterial populations that grow rapidly and decay more slowly. It was found that the characteristic shape of typical rank order functions is well reflected by the simulations. In addition, the model allowed to investigating strong disturbances of the soil, which could be expected in case of strongly changing local environmental conditions in the soil, e.g. by translocation and covering of soil material. Such events could lead to the formation of shoulders in the rank order functions. Abundance rank orders observed in case of some archaeological soil samples do indeed show such a shoulder and could be well interpreted by simulated rank order functions. As a result, it can be concluded that the investigations support the hypothesis, that abundance rank orders contain information about the temporal order of developing bacterial types in changing communities and thus store information about local environmental conditions in the past, including ancient human impacts on soil.

The atomic structures of Zn and Na borophosphate glasses were studied by X-ray and neutron diffraction. Peaks assigned to the B−O, P−O, and O−O distances confirm that only BO4 units co-exist with the PO4 tetrahedra. The Zn−O and Na−O coordination numbers are found to be a little larger than four. The narrowest peaks of the Zn−O first-neighbor distances exist for the glasses along a line connecting the Zn(PO3)2 and BPO4 compositions (50 mol% P2O5) which is explained by networks of ZnO4, BO4, and PO4 tetrahedra with twofold coordinated oxygens. Calculated amounts of the available oxygen support this interpretation. Broadened peaks occur for glasses with lower P2O5 contents, consistent with the presence of threefold coordinated oxygens. The two distinct P−O peak components of the Zn and Na borophosphate glasses differ in their relative abundances which is interpreted by Na+ cations that coordinate oxygens in some P−O−B bridges, something not seen for the Zn2+ ions.

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

Collatz conjecture (3x+1 problem) is a natural phenomenon in set theory that may be reconstructed using known combinatorics and order theory. Construction begins by selecting a specific order isomorphism with a bijectional order-embedding. Mapping by 3x+1 induces a unique property to only members of the mapped embedding. Under selective congruence from recursive division by two, that complex controls sequence behavior. This demonstration uses an order isomorphism consisting of two linear orders: the (1) odd positive integers and the always odd (2) Rule 50 Jacobsthal numbers, as the embedding. The argument proceeds by cardinality. When the order isomorphism is mapped under 3x+1, all Rule 50 Jacobsthal numbers are mapped to all the powers of four. This one-to-one correspondence guarantees that every odd integer is assigned to a Rule 50 Jacobsthal number, and subsequently, to a power of four. To align this construction with the conjecture, expand the set to all positive integers by showing that: (1) the powers of four embed the powers of two, in a natural way, and (2) the unique factorization of any positive even integer, not congruent to a power of two, is simply an odd integer, once the factorized power of two is divided out. In other words, if the initial choice for a positive integer is not congruent to a power of two, then recursion continues until a Rule 50 Jacobsthal number (guaranteed by cardinality) is attained. Since this value mapped by 3x+1 is always a power of four, repeated division by two will always send the sequence to one. Because this same process occurs for any choice of positive integer, Collatz conjecture is true.

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

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

In this study, we introduce the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers and conduct a comprehensive analysis to explore its theoretical aspects and examine the crossover effect within the HBV model. To investigate the crossover behavior of the operators, we divide the study interval into two subintervals. In the first interval, the classical derivative is employed to study the qualitative properties of the proposed system, while in the second interval, we utilize the ABC fractional differential operator. Consequently, the study is initiated using the piecewise Atangana-Baleanu derivative framework for the systems. The HBV model is then analyzed to determine the existence, Hyers-Ulam (HU) stability, and disease-free equilibrium point of the model. Moreover, we showcase the application of an Adams-type predictor-corrector (PC) technique for Atangana-Baleanu derivatives and an extended Adams-Bashforth-Moulton (ABM) method for Caputo derivatives through numerical results. Subsequently, we employ computational methods to numerically solve the models and visually present the obtained outcomes using different fractional-order values. This network is designed to provide more precise information for disease modeling, considering that communities often interact with one another, and the rate of disease spread is influenced by this factor.

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

The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand-new and distinguished with the existing literature, which fill the gaps of studies for admissibility. These approaches are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). In addition, a method involved least real decision variables in terms of strict LMIs is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of proposed results.

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

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

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

We analyze different approaches to quantum gravity. It is stressed that nonperturbative methods to quantise gravity and the usage of diffeomorphism-invariant variables are very important. We pay attention on the Wheeler--DeWitt equation in the framework of canonical quantum gravity. The Wheeler--DeWitt equation is presented in the first order formalism with the hope that this form can solve some problems such as singularities and the ordering. Also, there is a problem of defining the time.

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

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

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

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

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

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

This note shows that the well-known reverse order law $(AB)^{\dag} = B^{\dag}A^{\dag}$ for the Moore--Penrose inverse of matrix product is equivalent to many other equalities for that are composed of multiple products $(AB)^{\dag}$ and $B^{\dag}A^{\dag}$ by means of the definition of the Moore--Penrose inverse and orthogonal projector theory.

The semi-logarithmic plot of the cumulative number of cases of epidemics resembles the response of a first-order systems for a step load. This similarity was utilized to develop a first order model that can be used for extracting information about the dynamics of infectious disease epidemics. The developed model was validated using COVID-19 data of China. It was also heuristically fitted to other 13 countries. Obtained results indicated that the model can reliably forecasts the number of infected person, epidemic growth speed towards steady-state condition (process time constant, T), and time to reach steady-state condition (4T). The developed model will help public health authorities in developing more effective control strategies of epidemics.

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

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

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams-Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches

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

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

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

A reduced order model is developed to monitor aeroengines condition (defining their degradation from a baseline state) in real-time, by using data collected in specific sensors. This reduced model is constructed by applying higher order singular value decomposition plus interpolation to appropriate data, organized in tensor form. Such data are obtained using a detailed engine model that takes the engine physics into account. Thus, the method synergically combines the advantages of data-driven (fast online operation) and model-based (the engine physics is accounted for) condition monitoring methods. Using this reduced order model as surrogate of the engine model, two gradient-like condition monitoring tools are constructed. The first tool is extremely fast and able to precisely compute `on the fly’ the turbine inlet temperature, which is a paramount parameter for the engine performance, operation, and maintenance, and can only be roughly estimated by the engine instrumentation in civil aviation. The second tool is not so fast (but still reasonably inexpensive) and precisely computes both, the engine degradation and the turbine inlet temperature at which sensors data have been acquired. These tools are robust in connection with random noise added to the sensors data and can be straight forwardly applied to other mechanical systems.

This paper presents an approach to the Euler-Bernoulli beam theory (EBBT) using the finite difference method (FDM). The EBBT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally, the finite difference approximations are derived based on fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection curve; the FOPH is made for the fourth and third derivative of the deflection curve while the SOPH is made for its second and first derivative. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. In this paper, the FOPH was made for all of the derivatives of the deflection curve, and additional points were introduced at the beam’s ends and positions of discontinuity (concentrated loads or moments, supports, hinges, springs, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends and to satisfy the boundary and continuity conditions. Moreover, grid points with variable spacing were also considered, the grid being uniform within beam segments. First-order analysis, second-order analysis, and vibration analysis of structures were conducted with this model. Furthermore, tapered beams were analyzed (element stiffness matrix, second-order analysis). Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was increased through a grid refinement. Especially in the first-order analysis of uniform beams, the results were exact for uniformly distributed and concentrated loads regardless of the grid. Further research will be needed to investigate polynomial refinements (higher-order polynomials such as fifth-order, sixth-order…) of the deflection curve; the polynomial refinements aimed to increase the accuracy, whereby non-centered finite difference approximations at beam’s ends and positions of discontinuity would be used.

This work presents an illustrative application of the newly developed “Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-FASAM-NODE)” methodology to determine most efficiently the exact expressions of the first- and second-order sensitivities of NODE-decoder responses to the neural net’s underlying parameters (weights and initial conditions). The application of the 2nd-FASAM-NODE methodology will be illustrated using the Nordheim-Fuchs phenomenological model for reactor safety, which describes a short-time self-limiting power transient in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted. The representative model responses that will be analyzed in this work include the model’s the time-dependent total energy released, neutron flux, temperature and thermal conductivity. The 2nd-FASAM-NODE methodology yields the exact expressions of the first-order sensitivities of these decoder responses with respect to the underlying uncertain model parameters and initial conditions, requiring just a single large-scale computation per response. Furthermore, 2nd-FASAM-NODE methodology yields the exact expressions of the second-order sensitivities of a model response requiring as few large-scale computations as there are features/functions of model parameters, thereby demonstrating its unsurpassed efficiency for performing sensitivity analysis of NODE-nets.

A topological representation theory of chiral spin liquid is proposed to unify the integral and fractional quantum Hall fluid based on hyperbolic geometry, knot lattice and Thurston's train track theory. The integral and fractional Hall resistivity obeys an exact unified equation, $R_{xy} = (h/e^2)B_{e}$, $B_{e} = (n+\nu)^{-1}$, with respect to the bulk energy gap ${\Delta}E = {\hbar{e}B_{e}}/{Mc}$. The Wen-Zee matrix formulation of topological fluid for quantum Hall effect is constructed by topological surgery and train track. The chirality of spin liquid is spontaneously distinguished by Jones polynomial. The integral Chern number for Hall conductance is fractionalized by generalizing Thurston's train track to folding laminations in three dimensions, which spontaneously bring fractional quantum Hall fluid and anyons into three dimensions and provided an theoretical explanation on the competing fractional quantum Hall states. The many body system of interacting fermions or bosons are mapped into many interacting liquid droplets that interwind into knot lattice, which provide an effective topological representation for superfluid and superconductor, the strange metal state in superconductor is explained by topological dislocation and topological surgery. The Kauffman decomposition rule in knot theory is extended to describe the topological relations between different two dimensional manifolds, which further reveals the non-trivial relationship between the partition functions of pairing fermions and free electrons. The minimal energy state is the most stable topological state, even thought it maybe shares the same topological number with the excited states. The topological representation theory predicts a circular motion of electrons in hyperbolic space, that is implementable and testable by inhomogeneous magnetic field in three dimensions. The folding lamination representation of topological quantum fluid provides an promising implementation of string theory in high energy physics.