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In this work, a comparative study of four functional forms used to represent potential energy curves (PECs) is presented. The starting point is the Hulburt‐Hirschfelder, followed by the Extended Rydberg potential function, ending with two of the most recent potentials presented in the literature for diatomic systems: the Araújo‐Ballester potential and the Improved Extended Lennard‐Jones potential. The chosen potentials have in common the fact that all their parameters are algebraically calculated, without any fitting procedure, and all of them have direct dependence on Dunham's parameters. The mathematical behavior of these functions for the short‐ and long‐range regions is discussed. As study case, the diatomic system CO$$ \mathrm{CO} $$ in its ground electronic state was selected. To quantify the accuracy of the potential energy functions, the least‐squares Z‐test method, proposed by Murrell and Sorbie, is used. Furthermore, the main spectroscopic constants and vibrational energy levels are calculated and compared for all potentials. A comparative study on functions to represent the potential energy interactions of the CO diatomic system is presented. The Hulburt‐Hirschfelder, Extended Rydberg, Araújo‐Ballester and Improved Extended Lennard‐Jones potentials were chosen because they have in common the fact that all their parameters are calculated without any fitting procedure. To quantify the accuracy of potential energy functions, the least squares Z test method is used, and the main spectroscopic constants and vibrational energy levels are calculated. [ABSTRACT FROM AUTHOR]

In this paper, we have made a comparative study of α-α scattering using different phenomenological models like Morse, double Gaussian, double Hulthén, Malfliet-Tjon, and double exponential for the nuclear interaction, and atomic Hulthén as the screened Coulomb potential. The phase equations for S, D, and G channels have been numerically solved using the 5th -order Runge-Kutta method to compute scattering phase shifts (SPS) for the elastic scattering region consisting of energies up to 25.5 MeV. The model parameters in each of the chosen potentials were varied in an iterative fashion to minimize the mean absolute percentage error (MAPE) between simulated and expected SPS. A comparative analysis revealed that all the phenomenological models result in exactly similar optimized potentials with closely matching MAPE values for S, D, and G states. One can conclude that any mathematical function that can capture the basic features of two-body interaction will always guide the construction of optimized potentials correctly. [ABSTRACT FROM AUTHOR]

In E-commerce, one of the most essential reasons of company failures is conveying the right content of their product to the customers at the wrong time. This could include the company inability to adapt to their environment dynamically. With the existence of special circumstances like COVID-19 pandemic, companies require launching new techs, if they are to grow and stay competitive, and since the technology and related factors have a major effect on marketing success, "Systems Dynamic" sounds like a suitable tool in this regard. This article discusses augmented reality (AR) roles in contextual marketing (CM) using a system dynamics approach. After the identification of the key variables in both augmented technology and CM fields, casual relationships are defined. Then, the mathematical functions between these variables are extracted and the behavior of each factor is analyzed. Finally, based on this behavioral model, various scenarios are simulated to demonstrate how augmented reality technology can enhance the CM. [ABSTRACT FROM AUTHOR]

Digital models have become key sites of biological practice and science policy. This paper examines efforts to craft a digital salmon model for metabolic research. It traces the data configurations of feed, food, and health in Norway's bioeconomy aspirations—from cell culture studies in the lab to an integrated digital repository and public health nutrition trials in schools. A response to policy calls for more sustainable aquaculture, digital models become lynchpins for intensified data sourcing. I describe how datafication and digital model integration enact a particular mode of management, focused on profitability and human preferences, when optimizing fish feed to sustainability goals. Integrating molecular biology and mathematical functions, digital modeling promotes the idea of a prediction machine for preemptive optimization of feed and food across settings. Yet, unforeseen disruptions to aquaculture, for instance, by algae and lice, expose the complexity of marine food webs and the limitations of digital models. Even while in the making, the digital fish model becomes performative and shapes knowledge practices much beyond the lab. As knowledge infrastructures, models participate in the remaking of metabolic relations, recalibrating decision-making, while feeding back into and co-shaping the very entities and environments they were crafted to investigate. [ABSTRACT FROM AUTHOR]

This study investigates the analogies used by a sample of secondary mathematics teachers when they described the concept of function. The study is concerned with understanding what analogies were used by the participant teachers and conceptions of functions positioned in those analogies. Using examples from a set of responses to five open-ended questionnaire items, the article presents the main analogies found in the descriptions of the participant teachers and examines ways in which these are structurally mapped to function by applying Gentner's structure-mapping theory of analogy. Among those discussed are the child–mother linkage and machine/factory analogies. Of interest is the predominance of illustrations that show a correspondence approach to functions (mappings and input-output machines), while a covariation approach is entirely absent. The article makes the case for using the concept of analogy as a tool in research on teachers' Mathematical Knowledge for Teaching (MKT). [ABSTRACT FROM AUTHOR]

As a mature and reliable method, this study is based on the flow function method for mathematical modeling and establishes a class of mathematical models that are approximately realistic, flexible, and easy to calculate. According to the characteristics of fractional order calculus, the initial boundary conditions are modified and optimized to reduce the model error of this class of equations. According to the minimum energy principle and linearized integral calculation method, the multi-field multi-parameter non-linear coupling problem in the calculation process is solved, and the rapid calculation of the initial boundary model is realized. The accuracy of the model is tested by numerical simulation and simulation validation of different processes. A reliable theoretical and technical support is provided for the calculation of this type of equations. [ABSTRACT FROM AUTHOR]

We investigate whether varying wavefield contributions are the likely cause to variation in microtremor horizontal-to-vertical spectral ratio (MHVSR) amplification shape between six sites in the relatively homogeneous geologic setting of Windsor, Ontario. We quantify the MHVSR shape in terms of peak broadness and its fitness using mathematical functions to identify potential wave type contributions. We develop a technique that uses particle motion plots of cross-correlated microtremor recordings to establish the dominant wave types contributing to the microtremor wavefield within three important frequency bandwidths (below, spanning, and above the fundamental peak frequency). We investigate the variability in the inverted shear-wave velocity (VS) depth profile by performing 21 MHVSR inversions with varying Rayleigh, Love, and body wave contributions. The impact to seismic site characterization is that the depth and VS of the resonator (half-space) layer are overestimated consistently by an average of 28% compared to the often-default-assumed Rayleigh ellipticity forward amplification model. Our study demonstrates the importance of correctly identifying wave type contributions of the microtremor wavefield for the proper estimation of VS depth profiles, especially to obtain correct thickness of the sediment layer and resonator VS and thereby the average VS of the upper 30 m (VS30). [ABSTRACT FROM AUTHOR]

Cloud computing has become increasingly popular due to its scalability, cost-effectiveness, and ability to handle large volumes of data. However, entrusting (sensitive) data to a third party raises concerns about data security and privacy. Homomorphic encryption is one solution that allows users to store and process data in a public cloud without the cloud provider having access to it. Currently, homomorphic encryption libraries only support addition and multiplication; other mathematical functions must be implemented by the user. To this end, we discuss and implement the division, exponential, square root, logarithm, minimum, and maximum function, using the CKKS cryptosystem of the OpenFHE library. To demonstrate that complex applications can be realized with this extended function set, we have used it to homomorphically realize the Box–Cox transform, which is used in many real-world applications, e.g., time-series forecasts. Our results show how the number of iterations required to achieve a given accuracy varies depending on the function. In addition, the execution time for each function is independent of the input and is in the range of ten seconds on a reference machine. With this work, we provide users with insights on how to extend the original restricted function set of the CKKS cryptosystem of the OpenFHE library with basic mathematical functions. [ABSTRACT FROM AUTHOR]

This paper develops a method to integrate user knowledge into the optimization process by simultaneously modelling feasible design space and optimizing an objective function. In engineering, feasible design space is a constraint similar to those in optimization problems. However, not all constraints can be explicitly written as mathematical functions. This includes manufacturing concerns, ergonomic issues, complex geometric considerations, or exploring material options for a particular application. There needs to be a way to integrate designer knowledge into the design process and, preferably, use that to guide an optimization problem. In this research, these constraints are modeled using classification surrogate models and incorporated with Bayesian optimization. By suggesting design options to a user and allowing them to box off areas of feasible and infeasible designs, the method models both the feasible design space and an objective function probability of new design targets that are more optimal and have a high probability of being feasible. This proposed method is first proven with test optimization problems to show viability then is extended to include user feedback. This paper shows that by allowing users to box off areas of feasible and infeasible designs, it can effectively guide the optimization process to a feasible solution. [ABSTRACT FROM AUTHOR]

An increasing number of studies on non-contact vital sign detection using radar are now beginning to turn to data-driven neural network approaches rather than traditional signal-processing methods. However, there are few radar datasets available for deep learning due to the difficulty of acquiring and labeling the data, which require specialized equipment and physician collaboration. This paper presents a new model of heartbeat-induced chest wall motion (CWM) with the goal of generating a large amount of simulation data to support deep learning methods. An in-depth analysis of published CWM data collected by the VICON Infrared (IR) motion capture system and continuous wave (CW) radar system during respiratory hold was used to summarize the motion characteristics of each stage within a cardiac cycle. In combination with the physiological properties of the heartbeat, appropriate mathematical functions were selected to describe these movement properties. The model produced simulation data that closely matched the measured data as evaluated by dynamic time warping (DTW) and the root-mean-squared error (RMSE). By adjusting the model parameters, the heartbeat signals of different individuals were simulated. This will accelerate the application of data-driven deep learning methods in radar-based non-contact vital sign detection research and further advance the field. [ABSTRACT FROM AUTHOR]

Different from the Mittag–Leffler stability or asymptotic stability, the exponential stability issue, which provides faster and explicit convergence rate, is studied in this paper for fractional‐order uncertain systems with asynchronous switching and impulses, where the impulsive functions rely on not only switching modes but also impulsive time. Instead of using the inequality Eα(t)≤1αexp(t1α)(0<α<1)$$ {E}_{\alpha }(t)\le \frac{1}{\alpha}\exp \left({t}^{\frac{1}{\alpha }}\right)\kern0.3em \left(0<\alpha <1\right) $$, by utilizing the theory of fractional‐order differential equations, the methods of Lyapunov function and mathematical induction, some novel and less‐conservative stability criteria are developed, respectively, for the case of switched stable subsystems or switched unstable subsystems. The obtained results build a tradeoff between impulsive function, impulsive interval, average dwell time and fractional order. In addition, our results with α=1$$ \alpha =1 $$ are also novel in contrast with the ones of integer‐order switched impulsive systems. Finally, five numerical examples are given to show the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function is locally Lipschitz and path differentiable, i.e., admits a chain rule. Our study departs from other works in the sense that we focus on the behavior of the oscillations, and to do this we use closed measures, a concept that complements the technique of asymptotic pseudotrajectories developed in this setting by Benaïm--Hofbauer--Sorin. We recover known convergence results, establish new ones, and show a local principle of oscillation compensation for the velocities. Roughly speaking, the time average of gradients around one limit point vanishes. Various cases are discussed, providing new insight into the oscillation and the stabilization phenomena. [ABSTRACT FROM AUTHOR]

Continental margins develop long submarine slopes, linking the shallow shelves along the continental landmasses to the deep abyssal plain. They are the results of a complex interaction between destructive and constructive processes, although by and large they are sites of deposition. There is a great amount of variation between the length, height, smoothness, gradient and variation thereof between the slope profiles; however, there is also recurring similarity in their shape. The similitude has suggested systematic relationships between the shape and the processes forming them, and led to studies on geomorphological categorisation based on curvatures. The potential for prediction of along-strike variations and connection between morphology and sedimentary process is herein approached through broadening the mathematical functions used, detailed measurement, observation and curve-fitting of over 150 passive continental margins. Previously, three functions have been used to categorise submarine slopes. The present study finds that four mathematical functions closely match the slopes: Linear, Gaussian, exponential and quadratic (positive and negative/inverse), and reveals that the fourth slope, the quadratic, is by far the most common. While exponential and quadratic slopes are similar there is a crucial difference in the way in which the angle of the slope changes. This study suggests that quadratic slopes represent systematically decreasing sediment deposition with distance, previously attributed to exponential slopes. Exponential slopes meanwhile, represent slope readjustment profiles with upper sediment bypass and lower slope aggradation. Linear slopes, which form the longest low-angle slopes, form in response to high sediment input. Abrupt shelf-edges form in shallower water and develop longer slope aprons, suggesting formation from erosional processes. This implies that the quintessential sigmoidal (s-shaped, Gaussian function) slope, with a smooth rollover, represents the fundamental depositional slope profile. [ABSTRACT FROM AUTHOR]

We investigate the mathematical properties of the function , ϵ ∈ [−1, 1], which is a special Kapteyn series of the first kind. Unlike various other special Kapteyn series, the function T (ϵ) does not seem to possess a closed-form expression. We derive an integral representation for T (ϵ) from which various properties of T (ϵ) can be established. In particular, monotonicity and convexity properties of T (ϵ) and ϵ−1 T (ϵ) can be shown. Also, the behaviour of T (ϵ) as ϵ ↑ 1 can be determined from the integral representation. Furthermore, while the Kapteyn series representation of T (ϵ) is very slowly convergent when ϵ is close to ±1, a regularized form of the integral representation of T (ϵ) allows to compute T (ϵ) accurately using Simpson's rule with relatively few sample points of the involved integrand. [ABSTRACT FROM AUTHOR]

The Pev and Rv functions were introduced as a way of summarizing the mechanical phenomenon of root-soil interactions and the effect of root growth on soil volume. The Mohr-Coulomb criterion was applied to the Rv function to demonstrate the relationship between root morphology, soil mechanical properties, and soil stability. The theory of elasticity and plasticity was applied in the analysis of the Bio-Geo Interface, which showed that the force F generated by the roots increased with time due to the growth of the roots and the increase in their volume. The forces acting on the Bio-Geo Interface were represented mathematically through the use of vector arithmetic, which helped to calculate the direction of the forces acting on the system. The Pev function was used to study the evolution of the plant and how it affected the Rv function. The results showed that the interplay between plant growth and soil mechanics is crucial in understanding the behavior of the Bio-Geo Interface, and can provide valuable insights into the interactions between plants and soil in natural and engineered systems. In the study of soil-insect interaction, a mathematical function, Iev, was proposed to represent the insect's evolution in the soil environment. The function takes into account factors such as food sources and void ratio, which are important indicators of the biological and geotechnical aspects of the soil respectively. Despite the potential impact of insects on the soil environment, it has been concluded that their force resulting from their movement and behavior is negligible according to theories of elasticity and plasticity. This means that the impact of insects on the soil is minimal and does not significantly affect the soil's mechanical properties. However, the biological aspects of the soil, such as food sources, remain important factors in the study of insect evolution in the soil environment. [ABSTRACT FROM AUTHOR]

Current state-of-the-art techniques in 2D chart analysis primarily emphasize the recognition of textual information as a means of comprehending and summarizing chart contents. However, the effective analysis and understanding of information embedded in chart images depends on accurate reverse-engineering of the behavior of depicted variables. In this paper, we propose a methodology, named Abax, as an initial study for recognizing and approximating the mathematical functions that describe the behavior of variables illustrated in chart images, particularly those containing curves. Abax is focused on approximating the values of function parameters using spatial pixel information derived from the identified keypoints of each curve. Qualitative results of the described method are presented as a proof of concept, demonstrating accurate extraction of information from fives types of functions: linear, polynomial, asymptotic, sinusoidal and arbitrary. [ABSTRACT FROM AUTHOR]

This review aims to exploit a study on different benchmark test functions used to evaluate the performance of Meta-Heuristic (MH) optimization techniques. The performance of the MH optimization techniques is evaluated with the different sets of mathematical benchmark test functions and various real-world engineering design problems. These benchmark test functions can help to identify the strengths and weaknesses of newly proposed MH optimization techniques. This review paper presents 215 mathematical test functions, including mathematical equations, characteristics, search space and global minima of the objective function and 57 real-world engineering design problems, including mathematical equations, constraints, and boundary conditions of the objective functions carried out from the literature. The MATLAB code references for mathematical benchmark test functions and real-world design problems, including the Congress of Evolutionary Computation (CEC) and Genetic and Evolutionary Computation Conference (GECCO) test suite, are presented in this paper. Also, the winners of CEC are highlighted with their reference papers. This paper also comprehensively reviews the literature related to benchmark test functions and real-world engineering design challenges using a bibliometric approach. This bibliometric analysis aims to analyze the number of publications, prolific authors, academic institutions, and country contributions to assess the field's growth and development. This paper will inspire researchers to innovate effective approaches for handling inequality and equality constraints. [ABSTRACT FROM AUTHOR]

This paper investigates diverse classes of multidimensional Weyl and Doss ρ -almost periodic functions in a general measure setting. This study establishes the fundamental structural properties of these generalized ρ -almost periodic functions, extending previous classes such as m-almost periodic and (equi-)Weyl-p-almost periodic functions. Notably, a new class of (equi-)Weyl-p-almost periodic functions is introduced, where the exponent p > 0 is general. This paper delves into the abstract Volterra integro-differential inclusions, showcasing the practical implications of the derived results. This work builds upon the extensions made in the realm of Levitan N-almost periodic functions, contributing to the broader understanding of mathematical functions in diverse measure spaces. [ABSTRACT FROM AUTHOR]

This article introduces ways of performing numerical methods inside LATEX documents using a scripting programming language Lua. It mainly focuses on methods that use the load function in Lua to evaluate functions within the mathematics environment of Lua. These methods align with our work of creating computational packages for LATEX using Lua. The article includes a few simple Luacodes which illustrates different ways of using Lua for performing numerical methods in LATEX. The one purpose of using Lua for LATEX documents is to reduce the dependence of LATEX users on external software for computations. The other purpose is to develop methods and tools that can be deployed for pedagogical purposes. [ABSTRACT FROM AUTHOR]

The conversion of natural gas into liquefied natural gas (LNG) requires substantial energy consumption. This study proposes a deterministic mathematical model to find the optimal operation conditions for an LNG plant to minimize the energy consumption for turbomachinery and the total thermal conductance of the heat exchangers. General Algebraic Modeling System (GAMS) linked to a Dynamic Link Library was used to calculate the thermodynamic properties of the working fluids. A derivative-based optimization algorithm is used. Results indicate that the novel optimization approach allows the satisfactory management of the model nonlinearities associated, for example, with the bilinear terms involved in the energy balances and the mathematical functions used to calculate the thermodynamic properties. A preprocessing phase for initializing process variables is developed to facilitate model convergence. In comparison to an optimal design reported in the literature, which was obtained by integrating a well-established evolutionary optimization approach with the Aspen HYSYS simulator, the results indicated that the net electrical power could be reduced by up to 10% when the derivative-based optimization algorithm is used. The proposed deterministic approach, consisting of a mathematical model, an initialization phase, and an optimization algorithm, can help process engineers overcome the challenges associated with LNG process optimization. • A modeling framework for optimizing LNG processes is provided. • Dynamic link libraries with an optimization software program are coupled. • A rigorous thermodynamic model was implemented for optimization. • The proposed equation-based method handles the nonlinearities of the model. • The proposed initialization phase assures the convergence of the optimization model. [ABSTRACT FROM AUTHOR]

This article, published in Mathematical Notes, discusses lacunary recurrence relations with gaps of length 8 for the Bernoulli and Euler polynomials. The authors use standard notations for these polynomials and numbers and provide formulas and expansions for them. They also mention the history of lacunary recurrence relations for these numbers and polynomials and highlight their own contributions in finding such relations. The authors describe the method of proof for their main result, Theorem 1, and provide corollaries that extend the relations to the Bernoulli and Euler numbers. The article concludes by acknowledging funding support and declaring no conflicts of interest. [Extracted from the article]

A quasi total double Roman dominating function (QTDRD-function) on a graph G = (V(G),E(G)) is a function f: V(G) → {0, 1, 2, 3} having the property that (i) if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3; (ii) if f(v) = 1, then vertex v has at least one neighbor w with f(w) ≥ 2, and (iii) if x is an isolated vertex in the subgraph induced by the set of vertices assigned non-zero values, then f(x) = 2. The weight of a QTDRD-function f is the sum of its function values over the whole vertices, and the quasi total double Roman domination number γqtdR(G) equals the minimum weight of a QTDRD-function on G. In this paper, we show that for any tree T of order n ≥ 4, γqtdR(T) ≤ n+ s(T)/2, where s(T) is the number of support vertices of T, that improves a known bound. [ABSTRACT FROM AUTHOR]

For a graph G with chromatic number k, a dominating set S of G is called a chromatic-transversal dominating set (ctd-set) if S intersects every color class of any k-coloring of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by γct(G). A Roman dominating function (RDF) in a graph G is a function f: V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value w(f) =Σu∈V f(u). The minimum weight of a Roman dominating function of a graph G is called the Roman domination number of G and is denoted by γR(G). The concept of chromatic transversal domination is extended to Roman domination as follows: For a graph G with chromatic number k, a Roman dominating function f is called a chromatic-transversal Roman dominating function (CTRDF) if the set of all vertices v with f(v) > 0 intersects every color class of any k-coloring of G. The minimum weight of a chromatic-transversal Roman dominating function of a graph G is called the chromatic-transversal Roman domination number of G and is denoted by γctR(G). In this paper a study of this parameter is initiated. [ABSTRACT FROM AUTHOR]

In this paper, an improved whale optimization algorithm (WOA) based on the utilization of an interval type-2 fuzzy logic system (IT2FLS) is presented. The main idea is to present a proposal for adjusting the values of the r → 1 and r → 2 parameters in the WOA using an IT2FLS to achieve excellent results in the execution of the WOA. The original WOA has already proven itself as an algorithm with excellent results; therefore, a wide variety of improvements have been made to it. Herein, the main purpose is to provide a hybridization of the WOA algorithm employing fuzzy logic to find the appropriate values of the r → 1 and r → 2 parameters that can optimize the mathematical functions used in this study, thereby providing an improvement to the original WOA algorithm. The performance of the fuzzy WOA using IT2FLS (FWOA-IT2FLS) shows good results in the case study of the benchmark function optimization. An important comparative with other metaheuristics is also presented. A statistical test and the comparative with other bio-inspired algorithms, namely, the original WOA with type-1 FLS (FWOA-T1FLS) are analyzed. The performance index used is the average of the minimum errors in each proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive genetic algorithm (AGA) is presented for the optimization goals. The presented AGA is discussed and implemented on a power amplifier (PA), which is designed for 24 GHz and 5G applications and fabricated in a 65-nm CMOS process. The PA is optimized by the AGA for the high power-added efficiency (PAE), i.e., optimum. In the AGA, we aimed to avoid the local optima and slow convergence rate that exist in the conventional genetic algorithm (CGA). In the AGA, we proposed a parameter tuning method to fine-tune the set of PA circuit component values for faster optimization of the PA to have a high PAE. The proposed AGA provides a significant speed in optimization process as compared to the CGA, and the execution time of the AGA is faster than that of the CGA. The proposed AGA is also verified, and its performance is compared with that of the CGA through multiple multidimensional mathematical benchmark functions. The PA performance parameters are measured, and the results showed that the optimized PA achieves a high gain of 29.9 dB. The Psat of PA is measured as 14.21 dBm, and IIP3 is 13.8 dBm. The simulated result shows the optimized PA with the AGA has PAE of 49.7%, while that with the CGA has PAE of 47.5% at 24 GHz. The final measured PAE of AGA's optimized PA is 47.1%. The chip area of PA is 0.29 mm2. [ABSTRACT FROM AUTHOR]

This paper explores cost-effective alternatives for resource-constrained environments in the context of language models by investigating methods such as quantization and CPUbased model implementations. The study addresses the computational efficiency of language models during inference and the development of infrastructure for text document processing. The paper discusses related technologies, the CLARIN-PL infrastructure architecture, and implementations of small and large language models. The emphasis is on model formats, data precision, and runtime environments (GPU and CPU). It identifies optimal solutions through extensive experimentation. In addition, the paper advocates for a more comprehensive performance evaluation approach. Instead of reporting only average token throughput, it suggests considering the curve’s shape, which can vary from constant to monotonically increasing or decreasing functions. Evaluating token throughput at various curve points, especially for different output token counts, provides a more informative perspective. [ABSTRACT FROM AUTHOR]

This work employs a support vector machine (SVM) algorithm and laser-induced breakdown spectroscopy (LIBS) to identify diabetes mellitus in human urine. A total of 35 pathological urine samples from people with diabetes mellitus were obtained, whereas 35 non-diabetic control urine samples were gathered and used for this investigation. The LIBS spectra of both diabetic and normal urine samples were captured using a LIBS spectrometer that was equipped with a laser that operated at the fundamental wavelength of 1064 nm. At particular elemental peaks in the LIBS spectra, significant intensity differences between the two (diseased and normal) groups were observed using principal component analysis (PCA) combined with a support vector classifier. In order to achieve linear separability, support vector machine has the ability to transform data that is linearly inseparable into a high-dimensional space using a mathematical function called a kernel. The SVM model was developed in this work and applied utilizing various kernel functions, notably the linear kernel, polynomial kernel, and Gaussian radial basis function, to distinguish between diseased samples and normal samples. Performance evaluation of the model was carried out using a k-fold cross-validation procedure with k = 10. Of all the kernel functions used in this investigation, the radial basis function (RBF) kernel produced the highest performance efficiency. The results of our study highlight the LIBS approach's potency as a quick and exceptional technique for real-time assessment of diabetes mellitus in clinical trials. [ABSTRACT FROM AUTHOR]

In order to mitigate the impact of temperature and irradiation variations on photovoltaic (PV) panels, it is crucial to employ the maximum power point tracking (MPPT) technique. This paper introduces a novel MPPT approach that provides a reference current, denoted as Iref, to extract the maximum power from the PV array. The difference between the input current Ipv, and Iref is then fed into a PID controller, which adjusts the duty cycle accordingly to control the Quadratic Boost Converter (QBC). The proposed MPPT approach is based on the analysis of measurement data obtained from PV panels. From this, a linear mathematical function between Iref and solar irradiation is achieved. To assess the performance of this approach, a comparative study is being carried out not only with conventional MPPT techniques such as P&O and INC-COND but also with modern techniques such as ANN, PSO, FLC, and improved P&O (IMP-P&O). The simulation results clearly demonstrate enhanced tracking performance under various test conditions, including the Step & Ropp test, as well as real profiles for both sunny and cloudy days. Certainly, the novel approach shows its ability to outperform both conventional and modern methods with a faster convergence speed (less than 2 milliseconds), the lowest steady-state oscillations (less than 0.25 Watts), and the highest tracking efficiency (greater than 99.79%). [ABSTRACT FROM AUTHOR]

A 305-d lactation followed by a 60-d dry period has traditionally been considered economically optimal, yet dairy cows in modern intensive dairy systems are frequently dried off while still producing significant quantities of milk. Managing cows for an extended lactation has reported production, welfare, and economic benefits, but not all cows are suitable for an extended lactation. Implementation of an extended lactation strategy on-farm could benefit from use of a decision support system, based on a mathematical lactation model, that can identify suitable cows during early lactation that have a high likelihood of producing above a target milk yield (MY) at 305 d in milk (DIM). Therefore, our objectives were (1) to compare the suitability of 3 commonly used lactation models for modeling extended lactations (Dijkstra, Wood, and Wilmink) in primiparous and multiparous cows under a variety of lactation lengths, and (2) to determine the amount of early-lactation daily MY data needed to accurately forecast MY at d 305 by using the most suitable model and determine whether this is sufficient for identifying cows suitable for an extended lactation before the end of a typical voluntary waiting period (50–90 d). Daily MY data from 467 individual Holstein-Friesian lactations (DIM >305 d; 379 ± 65-d lactation length [mean ± SD]) were fitted by the 3 lactation models using a nonlinear regression procedure. The parameter estimates of these models, lactation characteristics (peak yield, time to peak yield, and persistency), and goodness-of-fit were compared between parity and different lactation lengths. The models had similar performance, and differences between parity groups were consistent with previous literature. Then, data from only the first i DIM for each individual lactation, where i was incremented by 30 d from 30 to 150 DIM and by 50 d from 150 to 300 DIM, were fitted by each model to forecast MY at d 305. The Dijkstra model was selected for further analysis, as it had superior goodness-of-fit statistics for i = 30 and 60. The data set was fit twice by the Dijkstra model, with parameter bounds either unconstrained or constrained. The quality of predictions of MY at d 305 improved with increasing data availability for both models and assisting the model fitting procedure with more biologically relevant constraints on parameters improved the predictions, but neither was reliable enough for practical use on-farm due to the high uncertainty of forecasted predictions. Using 90 d of data, the constrained model correctly classified 66% of lactations as being above or below a target MY at d 305 of 25 kg/d, with a probability threshold of 0.95. The proportion of correct classifications became smaller at lower targets of MY at d 305 and became greater when using more lactation days. Overall, further work is required to develop a model that can forecast late-lactation MY with sufficient accuracy for practical use. We envisage that a hybridized machine learning and mechanistic model that incorporates additional historical and genetic information with early-lactation MY could produce meaningful lactation curve forecasts. [ABSTRACT FROM AUTHOR]

The firefly algorithm (FA) is a popular swarm intelligence optimization algorithm. The FA is used to solve various optimization problems, but it still has some deficiencies, such as high complexity, slow convergence rate, and low accuracy of the solution. This paper proposes a highly efficient quantum firefly algorithm with stochastic search strategies (QSSFA). In QSSFA, individuals are generated in the way of quantum angle coding by introducing the laws of quantum physics and quantum gates, and combined with the random neighborhood attraction model, an adaptive step size strategy is also introduced in the optimization. The complexity of the algorithm is greatly reduced, and the global search ability of the algorithm is optimized. The convergence speed of the algorithm, the ability to jump out of the local optimum, and the algorithm accuracy are improved. The proposed QSSFA's performance is tested on ten mathematical test functions. The obtained results show that the QSSFA algorithm is very competitive compared to the firefly algorithm and three other FA variants. [ABSTRACT FROM AUTHOR]

A special case of the Cauchy problem for two-dimensional equation with variable velocity is considered. The source of waves is localized. An approximate formula for the solution is derived. The formula contains derivatives of Hadamard's "elementary solution" of the wave equation and describes (in a linear approximation) tsunami wave from a localized source. [ABSTRACT FROM AUTHOR]

This article, titled "Historic Behavior in Nonautonomous Rock-Paper-Scissors Dynamics," explores the concept of historic behavior in dynamical systems. The author challenges the widely held belief that replicator equations in evolutionary game theory satisfy the "Folk Theorem of Evolutionary Game Theory." The paper proposes a class of replicator equations that exhibit historic behavior, where the time averages of the orbit do not converge. The article also presents some auxiliary results and provides a proof for the main theorem. The research was supported by ongoing institutional funding, and the author declares no conflicts of interest. [Extracted from the article]

Real-world optimization problems are ubiquitous across scientific domains, and many engineering challenges can be reimagined as optimization problems with relative ease. Consequently, researchers have focused on developing optimizers to tackle these challenges. The Snake Optimizer (SO) is an effective tool for solving complex optimization problems, drawing inspiration from snake patterns. However, the original SO requires the specification of six specific parameters to operate efficiently. In response to this, enhanced snake optimizers, namely ESO1 and ESO2, were developed in this study. In contrast to the original SO, ESO1 and ESO2 rely on a single set of parameters determined through sensitivity analysis when solving mathematical functions. This streamlined approach simplifies the application of ESOs for users dealing with optimization problems. ESO1 employs a logistic map to initialize populations, while ESO2 further refines ESO1 by integrating a Lévy flight to simulate snake movements during food searches. These enhanced optimizers were compared against the standard SO and 12 other established optimization methods to assess their performance. ESO1 significantly outperforms other algorithms in 15, 16, 13, 15, 21, 16, 24, 16, 19, 18, 13, 15, and 22 out of 24 mathematical functions. Similarly, ESO2 outperforms them in 16, 17, 18, 22, 23, 23, 24, 20, 19, 20, 17, 22, and 23 functions. Moreover, ESO1 and ESO2 were applied to solve complex structural optimization problems, where they outperformed existing methods. Notably, ESO2 generated solutions that were, on average, 1.16%, 0.70%, 2.34%, 3.68%, and 6.71% lighter than those produced by SO, and 0.79%, 0.54%, 1.28%, 1.70%, and 1.60% lighter than those of ESO1 for respective problems. This study pioneers the mathematical evaluation of ESOs and their integration with the finite element method for structural weight design optimization, establishing ESO2 as an effective tool for solving engineering problems. [ABSTRACT FROM AUTHOR]

This study aims to develop an Excel programming model to formulate feed for Nile tilapia (Oreochromis niloticus), mainly for small- and medium-sized fish feed manufacturers. The model allows users to formulate the least costly balanced diet of Nile tilapia species, giving them the ability to choose a specific ingredient in the formulation according to the realities of the local environment: space-temporary availability of ingredients, prices and nutritional quality. Computer programming of a database of 25 locally available feed components was carried out using the Excel Solver Add-in and Excel IF mathematical functions to incorporate/delete specific ingredients in real time in accordance with user objectives. The theoretical characteristics of the least-cost balanced diets performed were within the margin of the nutrients requirement of the target fish size with protein levels of 35 per cent (fry diet: $1.07/kg), 32 per cent (fingerlings diet: $0.48/kg), 29 per cent (growth diet: $0.43/kg) and 27.12 per cent (final diet: $0.39/kg). The digestible energy of these diets was between 3016.5 ± 93.8 kcal. In addition, the model shows that an increase in soya meal prices by 75 per cent led the local feed industry to rely on imported fish meals, as the number included reached 52.28 per cent. However, the cost of the diet margin did not vary significantly. Nevertheless, it would be important to test the balanced diet developed with the model before production and scaling. [ABSTRACT FROM AUTHOR]

This document discusses recent advances in special functions and their applications across various scientific and engineering disciplines. It highlights the importance of special functions in fields such as mathematics, physics, engineering, statistics, astronomy, computer science, economics, chemistry, biology, medicine, materials science, and environmental science. The document provides summaries of 13 articles that explore topics such as Fibonacci polynomials, Appell and Horn functions, generalized hypergeometric functions, Lagrange-based hypergeometric Bernoulli polynomials, hypergeometric series, Humbert functions, integral formulas, twisted Catalan numbers, incomplete gamma function, existence theorems, finite sum identities, Euler polynomials, and q-generalized tangent-based Apostol-type Frobenius-Euler polynomials. These articles contribute to the understanding and application of special functions in various research realms. [Extracted from the article]

Let 풜 be the class of normalized functions which are analytic in the open unit disc. Jakson q-derivative represented by convolution operator D q f (z) = 1 z { f (z) ★ z (1 - q z) (1 z) } , f ∈ 풜 , q ∈ (0 , 1) is used to introduce a unified class Mq(α, β, γ), α ≥ 0, β, γ ∈ [0, 1) and its various mapping properties are studied. For q → 1−1, β = γ = 0 and α = 1, this class reduces to the class K of close-to-convex univalent functions. A number of interesting results such as q-Bernardi integral operator and inclusion relations are included as part of this study. Applications are also pointed out as consequences of the main results. [ABSTRACT FROM AUTHOR]

General‐purpose mechanisms can perform a broad range of tasks but are usually rather heavy and expensive. If only particular movements need to be executed, more efficient special‐purpose mechanisms can be employed. However, they typically require an expert to design the system based on manual inspection of simulations and experimental results. This procedure is not only time‐consuming, but the outcome also depends on the expert's experience. Hence, the design process stems from subjective criteria while only a limited number of structurally different mechanisms can be considered. In contrast, a design assistant can consider a broad range of mechanisms and leverage multi‐objective optimization to retrieve optimal designs for the given task. Due to the systems being synthesized based on mathematical functions rather than individual experience, the assistant allows a more transparent development of optimal problem‐specific mechanisms compared to the conventional process. Experts can then fine‐tune and analyze the proposed designs to compose the final system. In recent years, neural networks have been utilized to directly learn the inverse mapping from a trajectory to a mechanism design. This requires some parameterization of the trajectory to be fed into the network. In this work, we evaluate various preprocessing methods for the trajectory on a simple mechanism design model problem. We assess multiple configurations such as different neural network sizes, applying input‐output normalization, and varying the number of features. Consequently, we investigate and compare the trends and robustness of the implemented methods. [ABSTRACT FROM AUTHOR]

As a mechanism to explore the role of environmental adaptation in establishing the optimal distribution of single nucleotide polymophisms (SNPs) within resident homeostatic populations, relationships between quantified environmental parameters and the frequencies of the variants are being explored. We have performed sequential double-blind scans on more than 30% of chromosome 3 in an attempt to discover possible relationships using simple mathematical functions that are indicative of "adaptive forces" on the variants due to specific quantified environmental agents. We have found an association of rs13071758 with rodent zoonotic diseases. This variant is within the FHIT gene, which spans the most fragile of the common fragile sites in human lymphoblasts. FHIT, which is highly sensitive to environmental carcinogens, is partially lost in most human cancers. This finding is consistent with other studies postulating an association between rodent zoonoses and cancer. We quantify the adaptive force on the T allele as 0.28 GEUs per unit of zoonotic rodent host richness. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of the modeling of FET power transistors made of gallium nitride offered by GaN Systems, Transphorm, and Nexperia. The considered devices have been available on the market since 2014. GaN-FETs are built as a cascade connection of a normally on gallium nitride HEMT and a normally off MOSFET made of silicon. On the manufacturer's sites, one can find models of these devices for like-SPICE tools in the text form. The main goal of this paper is to evaluate the model's accuracy by comparing calculation results obtained by the use of the considered models with the authors' measurement results and datasheet. It has been demonstrated that the GaN Systems model built on controlled sources described by a set of arbitrarily selected mathematical functions more accurately reproduces the basic characteristics of a transistor. On the other hand, the models from Transphorm and Nexperia, which are constructed based on built-in semiconductor device models, more precisely calculate the values of selected functional transistor parameters. [ABSTRACT FROM AUTHOR]

Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the cognitive skills required for success in mathematics have only considered the domain of arithmetic. We extended models of mathematical skills to consider how executive function skills play both a direct role in secondary-school-level mathematical achievement as well as an indirect role via algebra and geometry, alongside arithmetic. We found that verbal and visuospatial working memory were indirectly associated with mathematical achievement via number fact knowledge, calculation skills, algebra and geometry. Inhibition was also indirectly associated with mathematical achievement via number fact knowledge and calculation skills. These findings highlight that there are multiple mechanisms by which executive function skills may be involved in mathematics outcomes. Therefore, using specific measures of mathematical processes as well as context-rich assessments of mathematical achievement is important to understand these mechanisms. [ABSTRACT FROM AUTHOR]

Purpose: Kriging surrogate model has demonstrated a powerful ability to be applied to a variety of engineering challenges by emulating time-consuming simulations. However, when it comes to problems with high-dimensional input variables, it may be difficult to obtain a model with high accuracy and efficiency due to the curse of dimensionality. To meet this challenge, an improved high-dimensional Kriging modeling method based on maximal information coefficient (MIC) is developed in this work. Design/methodology/approach: The hyperparameter domain is first derived and the dataset of hyperparameter and likelihood function is collected by Latin Hypercube Sampling. MIC values are innovatively calculated from the dataset and used as prior knowledge for optimizing hyperparameters. Then, an auxiliary parameter is introduced to establish the relationship between MIC values and hyperparameters. Next, the hyperparameters are obtained by transforming the optimized auxiliary parameter. Finally, to further improve the modeling accuracy, a novel local optimization step is performed to discover more suitable hyperparameters. Findings: The proposed method is then applied to five representative mathematical functions with dimensions ranging from 20 to 100 and an engineering case with 30 design variables. Originality/value: The results show that the proposed high-dimensional Kriging modeling method can obtain more accurate results than the other three methods, and it has an acceptable modeling efficiency. Moreover, the proposed method is also suitable for high-dimensional problems with limited sample points. [ABSTRACT FROM AUTHOR]

This document from the College Mathematics Journal provides a collection of problems and solutions for college mathematics students and teachers. It encourages active participation by submitting solutions and proposing new problems. The document covers various mathematical topics, including integrals, triangle properties, equations, group theory, and summation. It also includes mathematical proofs, solutions to problems, and discussions on mathematical concepts such as functions, variables, partial orders, and isomorphism. [Extracted from the article]

In this article, a new multiobjective particle swarm optimization (MOPSO) algorithm is introduced to improve the performance of a sliding mode based robust fuzzy proportional–integral–derivative (PID) controller. In this regard, the non-dominated solution having minimum number of neighbors is considered as the global best position, while the sigma values of the members are employed to determine the personal best position. A modified multiple-crossover operator is combined with the operators of the particle swarm optimization to significantly increase the convergence speed of the algorithm. To limit the size of the archive, a dynamical elimination scheme defined in the Euclidean space is introduced. Besides, iteration-based linear relations are implemented to adaptively compute the inertia weight and learning coefficients. To evaluate the effectiveness of the introduced MOPSO algorithm, the requirements are conducted by means of three benchmark functions with regard to generational distance, spacing, and maximum spread metrics. This analysis demonstrates that the proposed algorithm operates better through comparison with well-known elitist multiobjective evolutionary algorithms. Moreover, the MOPSO algorithm is applied for optimal design of a hybrid robust fuzzy PID controller for a pneumatic system with two bellows. Conflicting objective functions are considered as the normalized values of overshoot and settling time of the displacement between the bellows that should be simultaneously minimized. The feasibility and efficiency of the strategy are assessed in comparison with the conventional controllers. [ABSTRACT FROM AUTHOR]

The collection of relevant information about the vulnerability of infrastructure damaged by landslides is not an easy task due to the existence of several compounding factors and uncertainties. This makes it difficult to quantitatively estimate their vulnerability to slow-moving landslides. This paper presents a new vulnerability assessment model for masonry buildings on slow-moving landslides based on physical models and field observations. A masonry building model is made of brick and concrete at a scale of 1:10 to physically simulate the damage in structures caused by ground tension cracks commonly developed on slow-moving landslides. The tension crack opening process is simulated through a load-controlled table with an aperture on which the building model is constructed. The strain on the wall and its foundation were measured, and the damage of the model (crack formation and evolution for each loading step) was collected, described, and analyzed. These data were used to develop failure criteria for masonry buildings in rural areas in China in terms of a quantitative vulnerability curve. The quantitative model of vulnerability for masonry structures was established based on fuzzy mathematics and the Weibull function applied on the test data and observations. The vulnerability curve is verified with field cases of masonry buildings damaged by ground tension cracks associated with slow-moving landslides in the Three Gorges Reservoir area. The results support further testing and use of vulnerability curve proposed. [ABSTRACT FROM AUTHOR]

The quantum-inspired genetic algorithm (QGA), which combines quantum mechanics concepts and GA to enhance search capability, has been popular and provides an efficient search mechanism. This paper proposes a modified QGA, called dynamic QGA (DQGA). The proposed algorithm utilizes a lengthening chromosome strategy for a balanced and smooth transition between exploration and exploitation phases to avoid local optima and premature convergence. Apart from that, a novel adaptive look-up table for rotation gates is presented to boost the algorithm's optimization abilities. To evaluate the effectiveness of these ideas, DQGA is tested by various mathematical benchmark functions as well as real-world constrained engineering problems against several well-known and state-of-the-art algorithms. The obtained results indicate the merits of the proposed algorithm and its superiority for solving multimodal benchmark functions and real-world constrained engineering problems. [ABSTRACT FROM AUTHOR]

A well known result in the theory of uniform distribution modulo 1 (which goes back to Fejér and Csillag) states that the fractional parts {nα} of the sequence (nα)n≥1 are uniformly distributed in the unit interval whenever α>0 is not an integer. For sharpening this knowledge to local statistics, the k-level correlation functions of the sequence ({nα})n≥1 ​ are of fundamental importance. We prove that for each k≥2, thek-level correlation function Rk is Poissonian for almost every α>4k² > 4k-1. [ABSTRACT FROM AUTHOR]