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Electrical arc fault detector development requires many tests to develop and validate detection algorithms. The use of artificial intelligence or mathematical transformation requires the use of consequential datasets of current signatures corresponding to as many different situations as possible. In addition, one of the main drawbacks is that these experiments take a great deal of time and are often laborious in the laboratory. To overcome these limitations, a virtual test bench based on the modeling of a modular 230 VAC electrical circuit has been developed. The simulated network is composed of different home appliances (resistor, vacuum cleaner, dimmer, etc.) and its configurations are those of single and combined loads. The fault modeled is an electric arc, modeled by active diode switching, which can be inserted at any point of the circuit. This arc model takes into account the random variations in the restrike and arc voltage. All the appliance models are validated by comparing the frequential (harmonic distortion) and temporal (agreement index) signatures of the measured currents in real situations to those obtained by modeling. The results obtained using the model and experiment network show that the current signatures are comparable in both cases. Further, two detection algorithms are tested on those current signatures obtained by the modeling and experimentation. The results are comparable and provide identical detection thresholds. [ABSTRACT FROM AUTHOR]

The study of the extensive data sets generated by spectrometers, which are of the type commonly referred to as big data, plays a crucial role in extracting valuable information on mineral composition in various fields, such as chemistry, geology, archaeology, pharmacy and anthropology. The analysis of these spectroscopic data falls into the category of big data, which requires the application of advanced statistical methods such as principal component analysis and cluster analysis. However, the large amount of data (big data) recorded by spectrometers makes it very difficult to obtain reliable results from raw data. The usual method is to carry out different mathematical transformations of the raw data. Here, we propose to use the affine transformation for highlight the underlying features for each sample. Finally, an application to spectroscopic data collected from minerals or rocks recorded by NASA's Jet Propulsion Laboratory is performed. An illustrative example has been included by analysing three mineral samples, which have different diageneses and parageneses and belong to different mineralogical groups. [ABSTRACT FROM AUTHOR]

Predictive information on plant diseases could help to reduce and optimize the usage of pesticides in agriculture. This research presents classification procedures with linear discriminant analysis to predict three possible severity levels of net blotch in spring barley in Finland. The weather data utilized for classification included mathematical transformations, namely features of outdoor temperature and air humidity with calculated dew point temperature values. Historical field observations of net blotch density were utilized as a target class for the identification of classifiers. The performance of classifiers was analyzed in sliding data windows of two weeks with selected, cumulative, summed feature values. According to classification results from 36 yearly data sets, the prediction of net blotch occurrence in spring barley in Finland can be considered as a linearly separable classification task. Furthermore, this can be achieved with linear discriminant analysis by combining the output probabilities of separate binary classifiers identified for each severity level of net blotch disease. In this case, perfect classification with a resolution of three different net blotch severity levels was achieved during the first 50 days from the beginning of the growing season. This strongly suggests that real-time classification based on a few weather variables measured on a daily basis can be applied to estimate the severity of net blotch in advance. This allows application of the principles of integrated pest management (IPM) and usage of pesticides only when there is a proven need. [ABSTRACT FROM AUTHOR]

Leaf nitrogen content (LNC) is an important indicator for scientific diagnosis of the nutrition status of crops. It plays an important role in the growth, yield and quality of wolfberry. This study aimed to develop new spectral indices (NSIs) and constructed machine learning regression (MLR) models for predicting wolfberry tree LNC. By utilizing four smoothing methods and five mathematic transformation methods, we obtained the original spectral dataset and five spectral transformation datasets for quantitative analysis and model establishment. Subsequently, published vegetation indices (PVIs) were acquired, sensitive wavelengths (SWs) were screened and NSIs were calculated based on SWs. Then MLR models were constructed by combining NSIs from six spectral datasets with three machine learning algorithms. Finally, a comparison was made among the MLR models. The study indicated that the application of mathematical transformation highlighted the differences in spectra, the square root, first-derivative and second-derivative transformation improved the prediction accuracy of MLR models constructed based on NSIs (MLR-NSIs models). However, these transformations had little impact on improving the prediction ability of MLR models constructed based on PVIs (MLR-PVIs models). Additionally, The optimal model for predicting the LNC of wolfberry tree was obtained by using the Random Forest (RF) algorithm combined with NSIs developed by first-derivative transformation spectra. The determination coefficient of validation (Rv2) and ratio of percentage deviation (RPD) was 0.71 and 1.90, respectively. In conclusion, this study has demonstrated that the combination of hyperspectral transformation and machine learning is useful for improving the accuracy of LNC estimation in wolfberry trees. [ABSTRACT FROM AUTHOR]

The development of ultrasensitive electronic sensors for in vitro diagnostics is essential for the reliable monitoring of asymptomatic individuals before illness proliferation or progression. These platforms are increasingly valued for their potential to enable timely diagnosis and swift prognosis of infectious or progressive diseases. Typically, the responses from these analytical tools are recorded as digital signals, with electronic data offering simpler processing compared to spectral and optical data. However, preprocessing electronic data from potentiometric biosensor arrays is still in its infancy compared to more established optical technologies. This study utilized the Single‐Molecule with a Large Transistor (SiMoT) array, which has achieved a Technology Readiness Level of 5, to explore the impact of data preprocessing on electronic biosensor outcomes. A dataset consisting of plasma and cyst fluid samples from 37 patients with pancreatic precursor cyst lesions was analyzed. The findings revealed that standard signal preprocessing can produce misleading conclusions due to artifacts introduced by mathematical transformations. The study offers strategies to mitigate these effects, ensuring that data interpretation remains accurate and reflective of the underlying biochemical information in the samples. [ABSTRACT FROM AUTHOR]

To explore the influencing factors of surface topography and roughness in ultrasonic elliptical vibration cutting, this study proposed a new prediction model based on the formation mechanism of ultrasonic elliptical vibration cutting surface topography. Applying mathematical transformation ideas and discretization processing, the model considers linear velocity, rear face extrusion, and material rebound and utilizes MATLAB to carry out a simulation analysis of the surface topography. It also verifies the validity and accuracy of the model through experiments. The effects of cutting mode, velocity ratio, feed amount, and tool radius on the surface morphology of ultrasonic elliptical vibration cutting were analyzed using the proposed model. Results show that under the condition of Km < -tanα, the rear face extrusion and material rebound will have a specific impact on the 2-D residual height. In particular, the error between the theoretical roughness of the model and the actual roughness is 20.85%, which can provide some theoretical basis for the selection of machining parameters. [ABSTRACT FROM AUTHOR]

This paper is about the immanence between architecture and mathematics. At the peak of the use of digital design tools, the aim of this paper is to explain the definition of “parametric architect”, which is thought to be known by everyone. In this study, where the definition of parametric architecture is sought in the relationship that architecture establishes with mathematics, firstly, a historical projection is cast to explain the derivation of the concept of “parametric architect” through different concepts, from the platonic dimensions of mathematics to architecture's search for perfection; the need for precision and accuracy; and the transformation of geometric and graphic intuition into representation. The virtuosity of “parametric architects” is then discussed through the representations of virtuoso architects such as Zaha Hadid and Antoni Gaudí. This is followed by a discussion of the mathematical transformation required of the “parametric architect” working to meet the materialist demands of architectural manipulations as a field of computational thinking. Instead of compressing it into power-producing positions such as the starchitect and God's architect, the discussion of virtuosity, which this paper seeks to underline, gives place to the recreation of the “parametric architect” through Patrik Schumacher and Mark Burry. As a result, the insights gained from this research define “parametric architecture”, which seems to be a way to overcome the architectural practice trapped in the limits of descriptive geometrical thinking, as a new and evolving virtual ground shift/joining through the creativity-oriented relationship established with mathematics. Thus, it offers implications for architectural practice and theory. [ABSTRACT FROM AUTHOR]

In discrete dynamical systems, the ultimate goal is to understand the asymptotic behavior of all points under iterated compositions of a certain transformation (self-map) of a certain space. In arithmetic dynamics, the asymptotic behavior of points with coordinates of arithmetic interest (algebraic numbers or p-adic numbers) is examined. In connection with arithmetic dynamics, some problems are reduced to the determination of rational points on curves. This article introduces the issues in arithmetic dynamics related to these problems. [ABSTRACT FROM AUTHOR]

This paper proposes a new intelligent optimization algorithm named Black Eagle Optimizer (BEO) based on the biological behaviour of the black eagle. The BEO algorithm combines the biological laws of the black eagle and mathematical transformations to guide the search behaviour of the particles. The highly adaptive BEO algorithm has strong optimisation capabilities due to its unique algorithmic structure and novel iterative approach. In the performance testing experiments of the BEO algorithm, this paper firstly conducts the parametric analysis experiments of the BEO algorithm, then analyses the complexity of the BEO algorithm, and finally conducts a comprehensive testing of the performance of the BEO algorithm on 30 CEC2017 test functions with the widest variety of functions and 12 newest CEC2022 test functions, and its performance is compared with the seven state-of-the-art optimization algorithms. The test results show that the convergence accuracy of the BEO algorithm reaches the theoretical value in 100% of unimodal functions, the convergence accuracy is higher than the comparison algorithm in 78.95% of complex functions, and the standard deviation ranks in the top three in 90.48% of functions, which demonstrates the outstanding local optimisation ability, global optimisation ability and stability of BEO algorithm. Meanwhile, the BEO algorithm also maintains a fast convergence speed. However, the complexity analysis shows that the BEO algorithm has the disadvantage of slightly higher complexity. In order to verify the optimisation ability of the BEO algorithm in real engineering problems, we used the BEO algorithm to deal with four complex engineering design problems. The experimental results show that the BEO algorithm has excellent convergence accuracy and stability when dealing with real engineering problems, but the real-time performance is slightly below average. Therefore, the BEO algorithm is optimal for handling non-real-time engineering optimisation problems. The source code of the BEO algorithm is available at https://github.com/haobinzhang123/A-metaheuristic-algorithm. [ABSTRACT FROM AUTHOR]

For decades, researchers have searched for an unsaturated soil effective stress that performs analogously to effective stress for saturated soils and provides some simplifications over net stress and suction approaches. A recent debate is whether problems identified with unsaturated soil effective stress can be resolved via elastoplastic analyses. Effective stress equations are reviewed and categorized as being based on volume change, shear strength, yield, or degree of saturation. These equations are evaluated for consistency with saturated soil effective stress expectations using the Barcelona basic model (BBM), simplified into an integrated elastoplastic framework using the modified state surface approach (MSSA). Under isotropic conditions, saturated soil constant volume and yield curves are coincident, and the effective stress principle applies. In contrast, unsaturated soil constant volume and yield curves diverge, which is at root to the indefinability of an effective stress for unsaturated soils. Although effective stress for saturated soils has been defined on the basis of volume change, unsaturated soil effective stress is often defined on shear strength or degree of saturation, with attempted extrapolation to more general volume change and yield responses. Effective stress equations, when used for constitutive modeling of unsaturated soils, cannot recover the form of saturated soil effective stress models, nor provide the often-asserted simplifications or analytical economies. It is demonstrated that volume change and/or yield can occur under any constant unsaturated soil effective stress. It is shown that it is impossible to define an effective stress for unsaturated soils that functions analogously to that of saturated soils. An effective stress approach for unsaturated soils is demonstrated to be, at most, a mathematical transformation, which may provide simplifications for some limited usages. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Henan Agricultural Sciences is the property of Editorial Board of Journal of Henan Agricultural Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In mathematics, students' abilities to make transformations between mathematical representations are fundamental. The recent implementation of digital technologies, such as Dynamic Geometry Environments (DGEs), have changed students' access to mathematical representations by providing a variety of different representations, available just by pressing a button. Students use of a DGE may change their mathematical communication to become more dynamic and active. However, it is not clear how the use of DGEs and the change in communication style relate to more epistemological aspects of students' mathematical work. This study, therefore, investigates the interplay between students' dynamic mathematical communication and their transformations of mathematical representations when using a DGE from a competency perspective. Based on analyses of instances of lower secondary school students' dynamic mathematical communication, findings indicate that students' mathematical communication reflect the new ways of engaging with mathematical representations when using a DGE. Hence, the communication becomes dynamic. Theoretically, the complexity of having "continuous" transformations of mathematical representations may reduce the readiness of the mathematical communication competency. The "continuous" transformation may in fact cause students to unintentionally ascribe dynamic properties to mathematical representation. [ABSTRACT FROM AUTHOR]

Controlled and multivariate synthesis of Fe2O3-CuO bimetallic oxide nanoparticles is achieved by coprecipitation method with different concentrations of iron and copper oxide, followed by their optimization at specific pH, temperature, and time of addition of reagent. Concentration studies revealed changes in spectral band position to a hyperchromic shift with relevant increase in the concentration of CuO (100%). Hybrids with higher CuO concentration lead to hybrids with smaller size and higher stability. Temperature-dependent synthesis of bimetallic hybrid oxide nanoparticles showed an increase in size at higher temperatures, while at lower temperatures, stable oxide particles are observed. For pH-dependent synthesis, controlled size is observed at higher pH. Increasing the time of addition of reactant for optimized synthesis of bimetallic oxide nanoparticles showed a gradual decrease in size, hence better control. The results of size and zeta potential are transformed by the application of probability distribution function and grow-decay model. [ABSTRACT FROM AUTHOR]

Copyright of Aydin Dental Journal is the property of Aydin Dental Journal and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Unmanned aerial vehicles (UAV) are rapidly evolving experimental platforms that play an important role in remote sensing. In this study, we investigated a machine learning method for monitoring soil nutrient content using UAV hyperspectral remote sensing. We employed machine learning techniques for feature extraction and soil hyperspectral information modelling. In contrast to traditional mathematical transformation methods, we adopted a combination of random forest and differential evolution algorithms to rank the weights of individual hyperspectral data, thereby obtaining a series of spectral feature subsets for soil organic matter, total nitrogen and available phosphorus and potassium. Furthermore, the analytic hierarchy process was used for weight analysis, and the characteristic bands of the four soil nutrients were successfully extracted. Next, a quantitative inversion model based on a back-propagation (BP) neural network was established to estimate soil nutrient content, with determination coefficients higher than 0.7 and 0.6 for the modelling and verification sets, respectively. The relative percent difference values were greater than 2, among which the highest was for available potassium, with determination coefficients of 0.95 and 0.84 for the modelling and verification sets, respectively. In addition, visualization distribution maps of soil nutrients were obtained by combining the BP model and original reflectance hyperspectral images, and the comparisons of content histograms showed a relatively consistent distribution between the sampling and inversion points. The results verified the effectiveness of the combined machine learning method for large-scale and high-precision monitoring and visualization of soil nutrient contents. [ABSTRACT FROM AUTHOR]

The effective identification of reclaimed vegetation species is important for the subsequent management of ecological restoration projects in mining areas. Hyperspectral remote sensing has been used for identifying vegetation species. However, few studies have focused on mine-reclaimed vegetation. Even if there are studies in this field, the methods used by the researches are mainly traditional discriminant analyses. The environmental conditions of reclaimed mining areas lead to significant intraclass spectral differences in reclaimed vegetation, and there is uncertainty in the identification of reclaimed vegetation species using traditional classification models. In this study, in situ hyperspectral data were used to analyze the spectral variation in the reclaimed vegetation canopy in mine restoration areas and evaluate their potential in the identification of reclaimed vegetation species. We measured the canopy spectral reflectance of five vegetation species in the study area using the ASD FieldSpec 4. The spectral characteristics of vegetation canopy were analyzed by mathematically transforming the original spectra, including Savitzky–Golay smoothing, first derivative, reciprocal logarithm, and continuum removal. In addition, we calculated indicators for identifying vegetation species using mathematically transformed hyperspectral data. The metrics were submitted to a feature selection procedure (recursive feature elimination) to optimize model performance and reduce its complexity. Different classification algorithms (regularized logistic regression, back propagation neural network, support vector machines with radial basis function kernel, and random forest) were constructed to explore optimal procedures for identifying reclaimed vegetation species based on the best feature metrics. The results showed that the separability between the spectra of reclaimed vegetation can be improved by applying different mathematical transformations to the spectra. The most important spectral metrics extracted by the recursive feature elimination (RFE) algorithm were related to the visible and near-infrared spectral regions, mainly in the vegetation pigments and water absorption bands. Among the four identification models, the random forest had the best recognition ability for reclaimed vegetation species, with an overall accuracy of 0.871. Our results provide a quantitative reference for the future exploration of reclaimed vegetation mapping using hyperspectral data. [ABSTRACT FROM AUTHOR]

This study presents the design, simulation, and prototype creation of a quadruped robot inspired by the Acinonyx jubatus (cheetah), specifically designed to replicate its distinctive walking, trotting, and galloping locomotion patterns. Following a detailed examination of the cheetah's skeletal muscle anatomy and biomechanics, a simplified model of the robot with 12 degrees of freedom was conducted. The mathematical transformation hierarchy model was established, and direct kinematics were simulated. A bio-inspired control approach was introduced, employing a Central Pattern Generator model based on Wilson–Cowan neural oscillators for each limb, interconnected by synaptic weights. This approach assisted in the simulation of oscillatory signals for relative phases corresponding to four distinct gaits in a system-level simulation platform. The design phase was conducted using CAD software (SolidWorks 2018), resulting in a 1:3-scale robot mirroring the cheetah's actual proportions. Movement simulations were performed in a virtual mechanics software environment, leading to the construction of a prototype measuring 35.5 cm in length, 21 cm in width, 27 cm in height (when standing), and weighing approximately 2.1 kg. The experimental validation of the prototype's limb angular positions and trajectories was achieved through the image processing of video-recorded movements, demonstrating a high correlation (0.9025 to 0.9560) in joint angular positions, except for the knee joint, where a correlation of 0.7071 was noted. This comprehensive approach from theoretical analysis to practical implementation showcases the potential of bio-inspired robotics in emulating complex biological locomotion. [ABSTRACT FROM AUTHOR]

We describe a pressure projection scheme for the simulation of incompressible flow in cubic domains with open boundaries based on fast Fourier transforms. The scheme is implemented in flow_solve, a numerical code designed for process studies of rotating, density‐stratified flow. The main algorithmic features of the open‐boundary code are the near‐spectral accuracy of the discrete differentiation and a dynamic two‐dimensional domain decomposition that scales efficiently to large numbers of processors. The simulated flows are not required to be periodic or to satisfy symmetry conditions at the open boundaries owing to the use of mixed series expansions combining cosine and singular Bernoulli polynomial basis functions. These expansions facilitate the imposition of inhomogeneous boundary conditions and allow the code to be used for offline, one‐way nesting within an arbitrarily embedded subdomain of a larger scale simulation. The projection scheme is designed to exploit a simple and powerful numerical engine: inversion of Poisson's equation with homogeneous Neumann boundary conditions using fast cosine transforms. Here, we describe the mathematical transformations used to accommodate the imposition of space‐ and time‐varying boundary conditions. The utility of the approach for process studies and for nesting within submesoscale‐resolving ocean models is demonstrated with simulations of wind‐driven near‐inertial waves in the upper ocean. Plain Language Summary: Internal gravity waves in the upper ocean are affected by the presence of features such as fronts, eddies, and geographically constrained winds and currents. Ocean models that are able to accurately capture geographic realism often lack the capacity to resolve the intricacies of the internal waves that may be generated. This paper presents a mathematical framework that combines the realism of ocean models with high‐fidelity simulation of small‐scale dynamics. The framework is demonstrated through a series of examples of increasing complexity, including wave trapping in a wind‐perturbed anticyclonic vortex and simulation of near‐inertial waves near a density front in the Gulf of Lion. The proposed methodology has the potential to take advantage of the increasing horizontal resolution and fine‐scale realism of ocean models, while also relaxing the approximations that limit their ability to resolve the detailed dynamics of the internal wave field. Key Points: A computational framework based on fast spectral transforms is developed for computing nonhydrostatic flow in domains with open boundariesMixed basis function expansions are formulated to differentiate discrete data lacking symmetry or periodicity with near‐spectral accuracyNested simulations of wave trapping in a vortex and near‐inertial waves near a density front in the Gulf of Lion demonstrate the approach [ABSTRACT FROM AUTHOR]

In contemporary digital security systems, the generation and management of cryptographic keys, such as passwords and pin codes, often rely on stochastic random processes and intricate mathematical transformations. While these keys ensure robust security, their storage and distribution necessitate sophisticated and costly mechanisms. This study explores an alternative approach that leverages biometric data for generating cryptographic keys, thereby eliminating the need for complex storage and distribution processes. The paper investigates biometric key generation technologies based on deep learning models, specifically utilizing convolutional neural networks to extract biometric features from human facial images. Subsequently, code-based cryptographic extractors are employed to process the primary extracted features. The performance of various deep learning models and the extractor is evaluated by considering Type 1 and Type 2 errors. The optimized algorithm parameters yield an error rate of less than 10 % , rendering the generated keys suitable for biometric authentication. Additionally, this study demonstrates that the application of code-based cryptographic extractors provides a post-quantum level of security, further enhancing the practicality and effectiveness of biometric key generation technologies in modern information security systems. This research contributes to the ongoing efforts towards secure, efficient, and user-friendly authentication and encryption methods, harnessing the power of biometric data and deep learning techniques. [ABSTRACT FROM AUTHOR]

We define two indices with which to measure the concentration and fragmentation of political power. Concentration (or fragmentation) indices comply with the cardinality property if they are based on mathematical distance, which makes homogeneous comparisons possible because the indices maintain proportions of values. These indices also operate under the unit interval, so the measurements can be interpreted as percentages, and the differences and ratios between measurements have an understandable meaning. Our indices indeed comply with the cardinality property, which allows us to reinterpret the well-known Gallagher disproportionality index as the transformation of mathematical distance. Our concentration index can be interpreted as the large political party's share of power, while our fragmentation index determines the smaller parties' share. We apply both indices to election results over the last four decades from the UK, Germany and Spain, revealing that vote fragmentation has significantly increased in Germany and Spain, but it does not have a steady trend in the UK. Further, whilst seat fragmentation has been observed in Germany and the UK since 2000, this phenomenon is more recent in Spain. [ABSTRACT FROM AUTHOR]

This work presents the concept of interval-valued neutrosophic INK-subalgebras, also known as IV N INKsubalg's, which are the level and strong level neutrosophic INK-subalgebras. Next, we establish and validate a few theorems that establish the connection between these concepts and neutrosophic INK-subalgebras. We define the images and inverse images of IV N INK-subalgebras and study the transformations of the homomorphic images and inverse images of interval valud neutrosophic (briefly, IV N) INK-subalgebra into IV N INK-subalgebras. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of event-triggered robust state and fault simultaneous estimation for nonlinear time-delay systems subject to actuator and sensor unknown disturbances. Based on a fault decomposition technique and some basic mathematical transformations, we obtain an augmented system where the state vector consists of the variable of the original system and the fault. Then a novel event-triggered state observer for the augmented system is proposed to robustly estimate the variable of the original system and the fault. We next established a sufficient condition for the existence of such an observer. We translated it into a linear matrix inequality (LMI), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, an illustrative example is applied to test the proposed method. [ABSTRACT FROM AUTHOR]

For Class I Bragg resonance excited by five types of finite periodic array of widely spaced bars (rectangular, parabolic, rectified cosinoidal, trapezoidal, and triangular bars), the average phase velocity between any two adjacent bars in each type of bar field has been specifically calculated by employing a mathematical transformation, and therefore, the excitation condition of Class I Bragg resonance excited by each bar field is clarified and the modified Bragg's law established by Xie and Liu becomes a quantitative form. On one hand, if the incident surface wavelength, L, is fixed in advance, then according to the excitation condition, we can directly obtain the critical bar spacing, d, at which Class I Bragg resonance occurs. On the other hand, if the bar spacing, d, is fixed, then according to the excitation condition, we can use an iteration scheme to find out the critical surface wavelength, L, at which Class I Bragg resonance will be excited. In comparison with existing experimental, numerical, and analytical results of Bragg resonance excited by the five types of bar fields, it is shown that the modified Bragg's law is much more accurate than the Bragg's law, and the phenomenon of phase downshift can be well explained. In the linear long-wave limit, owing to the simple dispersion relation, the modified Bragg's law becomes an explicit expression and coincides with Liu's approximate law very well, although the former is a straight line segment while the latter is a curved line segment. Finally, it is shown that the phase downshift of Bragg resonance becomes more significant as the cross-sectional area of bars increases. [ABSTRACT FROM AUTHOR]

Introduction/purpose: It has been known for a very long time that timedependent effects such as creep and shrinkage of concrete considerably influence the behavior of composite steel-concrete beams. It is therefore very important to take these effects into account when calculating the strength and safety of composite steel-concrete beams. To this end, many theoretical and numerical research studies have been established to control this phenomenon. Most of this research presents laborious processes and calculations requiring complex techniques. Methods: This model consists of combining the static equilibrium equations and the two compatibility relations, in curvature and in deformation, of the composite steel-concrete cross-section with the differential equation resulting from the creep rate theory (RCM). The idea of this work was to take this model and simplify it to avoid difficult mathematical transformations. Results: The results from this simplified approach are very satisfactory when compared to those given by the analytical model. Conclusion: To overcome an excessive number of calculations and various difficulties associated with analytical or numerical methods to estimate additional stresses brought by the shrinkage of concrete in composite steelconcrete beams, a simplified analytical methodology has been proposed here while ensuring desired safety. This work has tried to simplify an existing analytical model based on the theory of linear viscoelasticity established in 2012. [ABSTRACT FROM AUTHOR]

A new method for the design of event-triggered stabilizing state feedback controllers for nonlinear fractional-order interconnected systems is proposed in this paper. A new condition for the existence of state feedback controllers ensuring the closed-loop system is asymptotically stable is established based on fundamental mathematical transformations and linear matrix inequalities. Two numerical examples with simulation results are provided to demonstrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

An analytical solution is obtained for the problem of radial vibrations of disks of variable thickness. A disk is considered that is rigidly fixed along the inner circular contour (ρ=0.2) and free on the outer contour (ρ=1). The thickness of the disk varies according to the law H=H0(ρν+μ+Cρν-μ)², where H0, C, μ are arbitrary constants; ν is the Poisson’s ratio. The exact solution of the problem is known only for H=const and H=1/ρ³. However, these solutions are not sufficient to study the vibrations of disks of other configurations. The proposed law of thickness variation H(ρ) allows us to obtain exact solutions to the problem at any value of the constant coefficients H0, C, μ, ν. By varying the values of these coefficients within a single given function, it is possible to set the disk profile of the desired appearance. The methods used to obtain these solutions are based on appropriate mathematical transformations of the original equation. The problem of disk oscillations is solved for four variants of thickness change. The natural frequencies for the first three forms of vibration are calculated. Comparison of the natural frequencies found for the three cases of the disk profile gently sloping indicates an increase in their values with an increase in the bending of the disk thickness. Based on the obtained eigenfunctions, the stresses were calculated and the nature of their distribution along the radial coordinate of the disk was determined. The strength of the disks under resonant radial vibrations was evaluated using a special criterion. It is found that the most limiting, i.e., destructive principal stress σ1=σr at the first (main) form of vibration should be chosen from the ratio σr≈0.79 [σ-1], where [σ-1] is the endurance limit of the disk material under uniform loading. The results obtained can be used to predict the stress-strain state of disks of variable profile under their radial vibrations [ABSTRACT FROM AUTHOR]

We explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve drawn in the map of the tail-integrated cumulative population and wealth fractions. In particular, we rediscover Tsallis' q-entropy formula related to the Pareto distribution. As a novel result, we express the traditional entropy in terms of gintropy and reconstruct further non-additive formulas. A dynamical model calculation of the evolution of Gini index is also presented. [ABSTRACT FROM AUTHOR]

We propose a new method for music composition in the style of Johann Sebastian Bach, using geometrical transformations of the plane. The method consists of analyzing a classical opus, identifying the motif, and mapping the occurrences of this motif and its transformations throughout the original work. Then compose a new musical motif and use this map to create an entirely new piece while preserving the motivic structure and the style of the original composition. We provide an example in both musical notation and audio format. [ABSTRACT FROM AUTHOR]

We consider the Brans–Dicke theory in non-metricity gravity, which belongs to the family of symmetric teleparallel scalar–tensor theories. Our focus lies in exploring the implications of the conformal transformation, as we derive the conformal equivalent theory in the Einstein frame, distinct from the minimally coupled scalar field theory. The fundamental principle of the conformal transformation suggests the mathematical equivalence of the related theories. However, to thoroughly analyze the impact on physical variables, we investigate the spatially flat Friedmann–Lemaître–Robertson–Walker geometry, defining the connection in the non-coincidence gauge. We construct exact solutions for the cosmological model in one frame and compare the physical properties in the conformal related frame. Surprisingly, we find that the general physical properties of the exact solutions remain invariant under the conformal transformation. Finally, we construct, for the first time, an analytic solution for the symmetric teleparallel scalar–tensor cosmology. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to study about the representation symbolic 2-plithogenic matrices by linear transformations between symbolic 2-plithogenic vector spaces, where it proves that every symbolic 2-plithogenic matrix can be represented uniquely by a linear transformation between symbolic 2-plithogenic vector spaces. Also, this work proves that any linear function between symbolic 2-plithogenic vector spaces must be an AH-linear transformation. [ABSTRACT FROM AUTHOR]

The metal spinning process has been observed in recent major investigations carried out using finite element analysis. One interesting idea has proposed simulating a rotating disc for the simulation of the metal spinning process to reduce computational time. The development of this concept is presented in this paper, including the formal mathematical transformation from the inertial frame to the rotating reference frame, specific FEM configurations with mesh sizes based on a minimized aspect ratio, a mesh convergence study, and the application of a feed rate scale. Furthermore, in the context of the rotating reference frame, the flange geometry after wrinkle initiation is investigated, including the number of peaks and their amplitudes. Using this new approach, it was found that the number of peaks gradually increases from two to eight peaks while their amplitude decreases. In the case of severe wrinkles, the number of peaks stays at four while the amplitude increases dramatically. The intermediate path proves capable of increasing the number of peaks while maintaining a low amplitude. These results will make it possible to design new paths, facilitating the production of defect-free spun parts. [ABSTRACT FROM AUTHOR]

Ground roll is usually considered as a common linear noise in land seismic data. The existence of the ground roll often masks the effective reflection information of underground media, resulting in the deterioration of seismic data quality. Therefore, ground roll suppression is one of the main tasks in seismic data processing. A large number of previous studies have proved that the time‐frequency signal processing method based on mathematical transformation has shown excellent performance in ground roll attenuation and still has development potential. Meanwhile, a convolutional neural network, as one of the popular deep learning technologies, has also been widely used in the field of seismic signal processing. In this paper, we combine the convolutional neural network with the time‐frequency signal processing method based on mathematical transformation, that is, spatial domain synchrosqueezing wavelet transform, and propose a complete ground roll suppression workflow of shot gathers in spatial wavenumber domain, realizing high‐precision and automatic ground roll removal. Field data examples show that compared with bandpass filtering, FK filtering, time domain synchrosqueezing wavelet transform, spatial domain synchrosqueezing wavelet transform and the convolutional neural network, the spatial domain synchrosqueezing wavelet transform convolutional neural network has achieved satisfactory results in effectively attenuating ground roll and retaining valid information. [ABSTRACT FROM AUTHOR]

This paper focuses on the topic of adaptive neural tracking control for flexible‐joint manipulator systems with output restrictions and input saturation. With the aid of the error compensation mechanism, command filter‐based adaptive neural control is proposed for robotic systems driven by permanent magnet synchronous machine (PMSM). An auxiliary signal produced by the first‐order linear system designed by the property of unmodeled dynamics is used to erase the dynamical uncertainties. The input saturation of system is estimated by tanh$$ \tanh $$‐function with mathematical transformation. Using barrier Lyapunov function (BLF), each component constraint of output is tackled. During the virtual control design phase, radial basis function neural networks (RBFNNs) may reliably assess the unknown nonlinear continuous function. All the variables in the closed‐loop system are proved to be semiglobally uniform ultimate bounded (SGUUB) by integrating all compensation signals into the overall Lyapunov function and using the defined compact set in the stability analysis of dynamic surface control (DSC). An applied example on robotic system is used to verify the effectiveness of the constructed design idea. [ABSTRACT FROM AUTHOR]

Background and aims: Reduction–oxidation potential (Eh) determines element speciation and availability. Establishing rhizosphere surrounding with stable Eh by hydroponics plays an important role in several disciplines. But it's still a challenge to regulate nutrient solution Eh because practical Eh buffers aren't as mature as pH buffers. The compatibility for plants and nutrient components as well as potential environmental risks restrict their application. Methods: A series of redox buffers applicable for hydroponic cultivation were attempted to established in this study. Several oxidant-reductant couples were screened according to Eh and pH temporal stability and cultivation experiment for iron plaque formation on rice (Oryza sativa L.) root was conducted as an example. Results: Only Na2S2O4-H2O2, H2O2 and Na2S2O8 could maintain stable Eh and pH and didn't inhibit rice growth during 6-day cultivation. And their performances were also relative satisfactory after 30-day cultivation. Anyways, additional pH buffers, 2-morpholin-4-ylethanesulfonic acid, were recommended for counteracting the drift of Eh and pH caused by reductants reacting with oxygen in Na2S2O4-H2O2 and H2O2 case. According to the Eh regulation ranges and properties assay, the variation of Eh values could be regressed as the logarithmic functions of added oxidant or reductant concentration after mathematical transformation. The proper regulation ranges of Na2S2O4-H2O2, H2O2 and Na2S2O8 were 200–500 mV, 300–500 mV and 500–900 mV, respectively. Conclusion: These redox couples series could satisfy with stable nutrient solution Eh regulation desire of hydroponic experiments (from 200 to 900 mV under pH 5.5 condition) with satisfactory nutrient and plant compatibility. [ABSTRACT FROM AUTHOR]

This article is devoted to the criticism of the wave-particle dualism and the provisions of the special theory of relativity (SRT). The fallacy of accepting the extended principle of relativity and identifying particles and waves is shown. The substantiation is given that the own fields of physical objects, which are material substances and spatially connect physical objects with each other, are the medium of propagation of light waves. The causal and visual picture of the propagation of light waves is considered, and the features of the mechanism of their propagation in comparison with other types of waves are described. On the basis of an alternative method for obtaining the relativistic law of velocities addition, the inconsistency of the principle of invariance of the interval adopted in the framework of SRT is shown. The inconsistency of the SRT positions and conclusions regarding the so-called relativistic effects-time dilation, mass increase, length decrease, as well as the energy of relativistic particles is shown. The presence of the clock paradox is shown by a simple example. The conclusion is made about the incorrectness of using mathematical transformations of Lorentz and the four-dimensional continuum in the physical representation. [ABSTRACT FROM AUTHOR]

Qubits, as we know, have great benefits as compared to classical bits in computing, research and technology; if these qubits are replaced by qudits, the technological constraints can be further diluted, and more advantages can be gained. In this article, we motivate the reader as to what happens when we go from a quantum world of qubits to a world of qudits. Elementary mathematical analysis of the transformation between the computational basis of qudits and the generalized qudit Bell state basis are derived. In reverence to the overwhelming properties of qudits, we give a detailed discussion of the most generalized quantum teleportation protocol using qudits. From the pedagogical angle, we provide rigorous, indepth calculations for the special case of qutrits. Last but not least, an epigrammatic representation of quantum teleportation is provided to sharpen the reader's understanding. [ABSTRACT FROM AUTHOR]

The article titled "The Forgotten Mountain Plot—An Illustration of Bias across Lipase Methods" discusses the use of the mountain plot as an alternative to the difference plot in evaluating bias between lipase methods. The authors explain that the mountain plot is particularly useful when data is not normally distributed, as is often the case with proportional bias. They provide an example of evaluating a new lipase assay and demonstrate how the mountain plot can reveal the extent of bias and identify outliers. The authors emphasize the importance of using the mountain plot in conjunction with the difference plot to obtain a more reliable indication of bias across lipase methods. [Extracted from the article]

Line crossing detection is to check whether people or objects go across a given barrier line, which is quite common and important in our daily life, such as the electronic article surveillance (EAS) checkpoint in a retail store or the finish line in track and field. Although existing solutions to line crossing detection have achieved great advancement, they do not function well when multiple objects or people cross the line at the same time. In this paper, we propose a new radio frequency identification (RFID)-based solution called RF-Line to line crossing detection, especially for multiobject scenarios. The biggest challenge is that the RFID reader's coverage zone is invisible and irregular; we cannot roughly take the time when a tag is seen by the reader for the first time as the time when line crossing occurs. In RF-Line, we deploy two antennas opposite to each other and collect the RF phase profiles of two antennas at the same time. By a series of geometric transformations and mathematical derivations, we find that summing up the two phase profiles will get a new phase curve, in which the inflection point of the curve is the time of line crossing. In addition, we address the problem of turning back or long stay on the barrier line. We implement RF-Line with commodity RFID systems. Extensive experiments show that RF-Line can achieve accurate line crossing detection with a small error of 6.1 cm, with no need for any system calibration or complicated deployment. [ABSTRACT FROM AUTHOR]

This study aims to enhance the localization of the inner and outer circles of the iris while addressing issues of excessive invalid computations and inaccuracies. To achieve this objective, diverse methods are employed to improve the process to varying extents. Initially, the image undergoes pre-processing operations, including grayscale conversion, mathematical morphological transformation, noise reduction, and image enhancement. Subsequently, the accurate localization of the inner and outer edges is achieved by applying algorithms such as Canny edge detection and the Hough transform, allowing for the determination of their corresponding center and radius values within the iris image. Lastly, an improvement is made to the particle swarm optimization algorithm by combining various algorithms, namely LinWPSO, RandWPSO, contraction factor, LnCPSO, and AsyLnCPSO, employing mechanisms such as simulated annealing and the ant colony algorithm. Through dual validation on the CASIA-Iris-Syn dataset and a self-built CASIA dataset, this approach significantly enhances the precision of iris localization and reduces the required iteration count. [ABSTRACT FROM AUTHOR]

As the next generation of green power system, smart grids have gradually enhanced the operation efficiency of power system. Meanwhile, the application of communication and intelligent technologies make the power grid more vulnerable to the emerging cyber‐physical attacks, such as the false data injection attack (FDIA). Particularly, the deception property of the FDIA on the output measurement estimation can fool the current security mechanism without triggering an alarm. Motivated by this problem, this paper aims at developing a novel detection and recovery mechanism against FDIA in smart grid. Based on the established state space grid model derived from the three‐phase sinusoidal voltage equations, an improved principal component analysis (PCA)‐based detection method is proposed. By introducing the mathematical transformation principle method, the detection performance such as detection rate and false positive rate can be improved. To keep the stable running of power system, a genetic optimization algorithm‐based linear quadratic regulator (LQR) defense method is developed. In addition, to improve the response performance to external attacks, an artificial intelligence method named genetic optimization algorithm is introduced to optimize the robust performance of the proposed defense method. Finally, the simulation results on the IEEE 6‐bus and 118‐bus grid system demonstrate the superiority of the proposed genetic algorithm optimization‐based LQR defense method. [ABSTRACT FROM AUTHOR]

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In this paper we consider a class of generalized nonlinear hyperbolic partial differential equations of the Hunter-Saxton-Calogero type, which arise in the theory of control of liquid crystals and in the control of unsteady gas flows. We found such conditions that the original equation can be reduced to linear one by contact transformations. The general exact multivalued solutions of the Hunter-Saxton-Calogero equation are found. The obtained solutions are visualized. [ABSTRACT FROM AUTHOR]

The Differential Evolution (DE) algorithm is one of the most successful evolutionary computation techniques. However, its structure is not trivially translatable in terms of mathematical transformations that describe its population dynamics. In this work, analytical expressions are developed for the probability of enhancement of individuals after each application of a mutation operator followed by a crossover operation, assuming a population distributed radially around the optimum for the sphere objective function, considering the DE/rand/1/bin and the DE/rand/1/exp algorithm versions. These expressions are validated by numerical experiments. Considering quadratic functions given by f (x) = x T D T D x and populations distributed according to the linear transformation D - 1 of a radially distributed population, it is also shown that the expressions still hold in the cases when f (x) is separable (D is diagonal) and when D is any nonsingular matrix and the crossover rate is C r = 1. 0. The expressions are employed for the analysis of DE population dynamics. The analysis is extended to more complex situations, reaching rather precise predictions of the effect of problem dimension and of the choice of algorithm parameters. [ABSTRACT FROM AUTHOR]