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This work presents a general framework that innovates and explores different mathematical aspects associated with special functions by utilizing the mathematical physics-based idea of monomiality. This study presents a unique family of multivariable Hermite polynomials that are closely related to Frobenius–Genocchi polynomials of Apostol type. The study’s deductions address the differential equation, generating expression, operational formalism, and other characteristics that define these polynomials. The affirmation of the controlling monomiality principle further confirms their mathematical foundations. In addition, the work proves recurrence relations, fractional operators, summation formulae, series representations, operational and symmetric identities, and so on, all of which contribute to our knowledge of these complex polynomials. [ABSTRACT FROM AUTHOR]

Functions are an essential concept in mathematics. The studies that have examined functions in advanced contexts have primarily focused on students' reasoning about specific types of functions (such as binary operations and isomorphisms) but not on the core characteristics of well-definedness and everywhere-definedness. Here, we report on a study in which we conducted task-based clinical interviews to gain insight into students' techniques for addressing "is the given relation a function?" tasks. We found that the techniques students employed necessarily extended far beyond those reported in the literature (such as the vertical line test) and relied on the previously undocumented notions of sameness, convention, and ambiguity (for well-defined) and notions of containment, existence, and set operations (for everywhere-defined). These techniques coordinated the domain, codomain, and rule, which previous research has highlighted the importance of but stopped short of directly investigating. Two contributions of this work include identifying successful techniques (as the landscape of functions literature predominantly focuses on challenges and difficulties) and identifying techniques for everywhere-definedness (which had not previously received any direct attention in the literature). [ABSTRACT FROM AUTHOR]

As technology rapidly advances and internet reliance grows for daily activities, the demand for robust and efficient cryptographic protocols is undeniable. Cryptography, the art of secret writing, uses symmetric mathematical functions to secure data in transit or at rest. Stream ciphers, unlike block ciphers, encrypt data sequentially, eliminating the need for padding with extra bits to complete a block. Rivest Cipher 4 (RC‐4) has been one of the most widely used stream ciphers. However, vulnerabilities exploited by attackers in 2014 led to its widespread replacement. In this paper, we introduce a modified version of RC‐4 designed to address and mitigate the security threats of traditional RC‐4. By incorporating negative numbers into the key generation schedule, our preliminary analysis shows promising results. This adaptation not only enhances RC‐4's security features but also revitalizes its applicability in modern cryptographic scenarios, potentially restoring its viability as a secure cryptographic tool. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms are stochastic-based search techniques widely used for solving different types of optimization problems. These methods mostly adjust their search behavior using pre-defined search pattern(s) regardless of the current problem specifications. Therefore, integrating them with logical auxiliary modules can significantly enhance their search efficiency by enabling them to dynamically adapt their search behavior. The present study introduces a novel decision-making approach that employs interval type-2 fuzzy logic to balance the search behavior during optimization process. The proposed approach, designed as a stand-alone module with the flexibility to be integrated into various algorithms, is incorporated into the Interactive Search Algorithm. The developed reinforced technique is named Type-2 Fuzzy Interactive Search Algorithm. Performance of the proposed method is tested on different unconstrained mathematical functions and constrained structural and mechanical optimization problems. The attained results are compared with standard ISA method and seven other metaheuristic techniques through a suite of numerical and statistical evaluations. Drawing from the obtained results, the integration of the type-2 fuzzy decision module significantly enhances the algorithm's search capability. This improvement is evident in terms of stability, accuracy, and computational cost. It is worth noting that the employed comparative performance index for the proposed method indicates improvements of 3.38, 13.09, 16.61, and 27.23 percent compared to the best solution found by the selected methods for engineering problems. [ABSTRACT FROM AUTHOR]

Mathematics, along with reading and writing, is a core academic subject in the school curriculum. The development of mathematical skills is influenced by various cognitive factors, with executive functions (EF) playing a central role. EF, which encompasses working memory, inhibitory control, and cognitive flexibility, is critical for supporting complex cognitive processes required for problem-solving and mathematical reasoning. Research consistently shows that children with stronger EF tend to achieve better academic outcomes, including in mathematics. The goal of the present study was to examine the relationships between the global EF and its three core components – working memory, inhibitory control, and cognitive flexibility – and their impact on mathematics achievement. The sample for this study consisted of 180 children, aged 8–11 years (mean age: 9.6, SD: 1.0 year; 83 girls, 97 boys). EF was assessed using the Yellow-Red test, while mathematics achievement was evaluated based on teachers’ evaluations of the child’s mathematics performance. The results indicated a statistically significant effect of global EF and its three components on mathematics achievement. Given the potential malleability of EFs, we conclude with recommendations for strategies to enhance EF development at an early school age. [ABSTRACT FROM AUTHOR]

The theory of inequalities is greatly influenced by interval‐valued concepts, and this contribution is explored from several perspectives and domains. The aim of this note is to develop several mathematical inequalities such as Hermite–Hadamard, Fejér, and the product version based on center radius CR‐order relations. Furthermore, we develop several nontrivial examples and remarks to support the main findings. [ABSTRACT FROM AUTHOR]

The current generation portfolio is obligated to incorporate zero-emissions energy sources, predominantly wind and solar, due to the depletion of fossil fuels and the alarming rate of global warming. In the current scenario, power engineers must devise a compromised solution that not only advocates for the adoption of renewable energy sources (RES) but also efficiently schedules all conventional power generation units to balance the increasing load demand while simultaneously minimizing fuel costs and harmful emissions that are currently addressed by Unit Commitment (UC) and Combined Economic Emission Dispatch (CEED) problem solutions. However, the integration of renewable energy resources (RES) further complicates the UC-CEED problem due to their intermittent nature. Recently, metaheuristic algorithms are acquiring momentum in resolving constrained UC-CEED problems due to their improved global solution ability, adaptability, and derivative-free construction. In this research, a computationally efficient binary hybrid version of crow search algorithm and improvised grey wolf optimization is proposed, namely Crow Search Improved Binary Grey Wolf Optimization Algorithm (CS-BIGWO) by inclusion of nonlinear control parameter, weight-based position updating, and mutation approach. Statistical results on standard mathematical functions prove the supremacy of the proposed algorithm over conventional algorithms. Further, a novel optimization strategy is devised by integrating enhanced lambda iteration with the CS-BIGWO algorithm (CS-BIGWO- λ ) to solve a day-ahead UC-CEED problem of the hybrid energy system incorporating cost functions of RES. For the model, a day-ahead forecast of wind power and solar photovoltaic power is obtained by using the Levy-Flight Chaotic Whale Optimization Algorithm optimized Extreme Learning Machines(LCWOA-ELM). The proposed algorithm is tested for the UC-CEED solution of an IEEE-39 bus system with two distinct cases: (1) without RES integration and (2) with RES integration. Several independent trial runs are executed, and the performance of the algorithms is assessed based on optimal UC schedules, fuel cost, emission quantization, convergence curve, and computational time. For case 1, the proposed algorithm resulted in a percentage reduction of 0.1021% in fuel cost and 0.7995% in emission. In contrast, for test case 2, it resulted in a percentage reduction of 0.12896% in fuel cost and 0.772% in emission with the proposed algorithm. The results validate the dominance of the proposed methodology over existing methods in terms of lower fuel costs and emissions. [ABSTRACT FROM AUTHOR]

We consider convex optimization problems with a possibly nonsmooth objective function in the form of a mathematical expectation. The proposed framework (AN-SPS) employs Sample Average Approximations (SAA) to approximate the objective function, which is either unavailable or too costly to compute. The sample size is chosen in an adaptive manner, which eventually pushes the SAA error to zero almost surely (a.s.). The search direction is based on a scaled subgradient and a spectral coefficient, both related to the SAA function. The step size is obtained via a nonmonotone line search over a predefined interval, which yields a theoretically sound and practically efficient algorithm. The method retains feasibility by projecting the resulting points onto a feasible set. The a.s. convergence of AN-SPS method is proved without the assumption of a bounded feasible set or bounded iterates. Preliminary numerical results on Hinge loss problems reveal the advantages of the proposed adaptive scheme. In addition, a study of different nonmonotone line search strategies in combination with different spectral coefficients within AN-SPS framework is also conducted, yielding some hints for future work. [ABSTRACT FROM AUTHOR]

This paper presents a new optimization technique based on the hybridization of two meta-heuristic methods, Jellyfish Search (JS) and Moth Flame Optimizer (MFO), to solve the Optimal Power Flow (OPF) problem. The JS algorithm offers good exploration capacity but lacks performance in its exploitation mechanism. To improve its efficiency, we combined it with the Moth Flame Optimizer, which has proven its ability to exploit good solutions in the search area. This hybrid algorithm combines the advantages of both algorithms. The performance and precision of the hybrid optimization approach (JS-MFO) were investigated by minimizing well-known mathematical benchmark functions and by solving the complex OPF problem. The OPF problem was solved by optimizing non-convex objective functions such as total fuel cost, total active transmission losses, total gas emission, total voltage deviation, and the voltage stability index. Two test systems, the IEEE 30-bus network and the Mauritanian RIM 27-bus transmission network, were considered for implementing the JS-MFO approach. Experimental tests of the JS, MFO, and JS-MFO algorithms on eight well-known benchmark functions, the IEEE 30-bus, and the Mauritanian RIM 27-bus system were conducted. For the IEEE 30-bus test system, the proposed hybrid approach provides a percent cost saving of 11.4028%, a percent gas emission reduction of 14.38%, and a percent loss saving of 50.60% with respect to the base case. For the RIM 27-bus system, JS-MFO achieved a loss percent saving of 50.67% and percent voltage reduction of 62.44% with reference to the base case. The simulation results using JS-MFO and obtained with the MATLAB 2009b software were compared with those of JS, MFO, and other well-known meta-heuristics cited in the literature. The comparison report proves the superiority of the JS-MFO method over JS, MFO, and other competing meta-heuristics in solving difficult OPF problems. [ABSTRACT FROM AUTHOR]

This investigation reveals the reasons behind severe shear distortion of carbon fiber towpreg observed during a series of winding sequences involving a geometry consisting of a hyperbolic hyperboloid attached to two cylinders at its open sides. The roving severely distorts at the transition zones, tending to slip and lose track, while the robust winding machine undergoes noticeable and unexpected vibrations. The DO IT 2 root cause analysis problem-solving method is applied to understand the failure mechanism using flow and causal diagrams, along with CNC data analysis. The winding angle at geometric transitions is measured using photographs. Additional data analysis involves evaluating the limits of mathematical functions used to construct the mandrel meridian profile, along with analyzing winder kinematics. The results reported here reveal numerical singularities that adversely affect solutions at all levels by impacting the mathematical definition of the meridian profile. This explains the shear-type distortion of the towpreg, speed changes surpassing ISO 10816-1 standards on mechanical vibration, alongside peaks in acceleration and jerk. Moreover, it is suggested that Coulomb's friction law may surpass its limits due to a viscous and tacky interface promoted by the non-rigid nature of the stranded towpreg. Preventive actions involve meeting the requirements of the Theory of Curves and Surfaces for mandrel meridian profile construction. Additionally, incorporating observed viscoelastic and shear strength phenomena into theoretical approaches is advised, alongside addressing discrepancies in measuring the filament winding angle and validating numerical solutions against CNC data. [ABSTRACT FROM AUTHOR]

The secretion of thyroid stimulating hormone (thyrotropin, TSH), is characterized by a marked circadian rhythm. Plasma or serum TSH values are significantly lower in the afternoon and in the evening as compared to the early morning. As in clinical practice, blood sampling time shows an important variation, a reliable assessment of thyroid status is often not an easy task for the clinician. The biological variation of TSH plays a major role in the intra-individual variability of TSH results in serum or plasma. The observed intra-day variation largely exceeds the reported inter-vendor variation and the coefficient of variation of clinical TSH assays. Therefore, a mathematical solution was sought for correcting interpretation of TSH results for sampling time.We have developed a cosinor model which allows to compensate TSH decision values for the fluctuating serum or plasma TSH concentrations throughout the day.The following mathematical function could be derived: corrected TSH cutoff_value (mIU/L)=0.40 + 0.24*cos(((π/12) *T) + 6) in which T represents the time (hours). This mathematical function can be easily implemented into a laboratory’s informatics system and furthermore allows a better tailored diagnosis of (subclinical) hyperthyroidism, regardless the blood sampling time.Implementing the corrected cut-off values result in a marked reduction of apparent (false positive) hyperthyroidism diagnosis, in particular in the afternoon. [ABSTRACT FROM AUTHOR]

A maximum likelihood estimator is guaranteed to exist, provided specific regularity conditions are met to ensure a well-defined likelihood function and achievable maximization. This paper considered the existence and uniqueness of the maximum likelihood estimates (MLE) of the exponentiated BurrXII Poisson (EBXIIP) distribution under some possible conditions. [ABSTRACT FROM AUTHOR]

Covert channel methods are techniques for improving privacy and security in network communications. These methods consist of embedding secret data within normal network channels, making it more difficult for unauthorized parties to detect such data. This paper presents a new approach for creating covert channels using the Message Queuing Telemetry Transport (MQTT) protocol, widely used in the context of the Internet of Things (IoT). The proposed method exploits storage channels by altering the field length of MQTT messages. Our solution leverages well-known one-way mathematical functions to ensure that data remain hidden from third parties observing the MQTT stream. In this way, we ensure that not only the content of the communication is preserved but also that the communication itself takes place. We conducted a security analysis to show that our solution offers the above-mentioned property even against severe threats, such as an adversary being able to observe all the messages exchanged in the network (even in the clear). Finally, we conducted an overhead analysis of our solution both in terms of the time required to perform the required operations and of the bytes to send. Our study shows that our solution adds no significant time overhead, and the additional overhead in terms of transmitted bytes remains within acceptable limits. [ABSTRACT FROM AUTHOR]

In information security, data encryption plays a crucial role in preventing unauthorized access. Traditional methods often fall short when faced with sophisticated cyber threats. This research presents a hybrid encryption technique that integrates a recently devised 5D chaotic system, effectively bolstering data security by encoding information in an intricate, puzzle-like structure. This approach thwarts easy access to sensitive data, thus safeguarding them from potential interception and exploitation. The proposed encryption method combines the Linear Encryption Algorithm (LEA) and the Advanced Encryption Standard (AES) to create the Parallel Improved LEA (PILEA), blending key components of both algorithms to enhance data security. By integrating AES's S-box, Shift Rounds, Mix Columns, and Add Round Key operations, the PILEA significantly raises the complexity of the encrypted data, making them more resistant to unauthorized decryption attempts. A key innovation of this system is the use of a chaotic system for key generation, resulting in a strong, nonlinear, and dynamic key stream. Furthermore, by operating the entire system in a parallel mode, the proposed approach aims to decrease the number of rounds in the encryption process and the overall execution time for encryption and decryption. These enhancements further strengthen the encryption system's resilience against infiltration by malicious entities. Experimental results show that the PILEA method can withstand various types of cryptographic attacks, provides reduced computation times, and produces a highly random keystream, as confirmed by the NIST statistical test suite for randomness. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new integral transform called the HK Transform and employ it to analytically solve the Volterra integral equations (VIE.) of the first kind. To achieve this First we derive the HK transform of basic algebraic and transcendental mathematical functions. The fundamental characteristics of the HK transform, which can be used to solve a variety of functional equations, including, we then discuss the fundamental properties, such as ordinary differential equations and integral equations, then we discover the exact solution for general first class V.I.E. To illustrate the applicability of the HK transform, numerical problems are examined and handled carefully step-by-step. The results show that the proposed HK Transform new integral transform produces accurate solutions for first-kind VIE. without requiring time-consuming computations. [ABSTRACT FROM AUTHOR]

This research uses a new method called the Modified Adolescent Identity Search Algorithm (MAISA) to solve optimization problems. The identity of a teenager is a different combination of thoughts, beliefs, and abilities that are obtained by him. He communicates with other people in society and tries to use the positive or negative feedback from these social interactions to shape his identity and become an independent person. Mathematical simulation of how adolescents' personality is formed during the mentioned process causes the emergence of this algorithm. The purpose of this research is to improve the performance of the AISA algorithm in the balance between exploration and exploitation. This algorithm isn't trapped in the optimal local points due to the appropriate convergence rate and reaches the universal optimal answer quickly. One of the features of this algorithm that we can mention is its simplicity and having few setting parameters. To show the effectiveness of this algorithm, results of solving two types of problems of mathematical functions and practical examples such as large-scale truss 120, 244, 942, and 72-bar truss, are measured by other similar algorithms. The results show that this algorithm has a good performance in the optimal solution of such problems, compared to other similar algorithms. [ABSTRACT FROM AUTHOR]

Rock mass classification is of great significance in guiding the design and construction of tunnels, which is often determined through single‐factor or multi‐factor classification methods based on some readily available rock indices, for example, dynamic elastic modulus, degree of tectonization, and so forth. Although these methods work reasonably well in some cases, they tend to lead to inaccurate classification results due to the pre‐selected main factor or function forms, especially for tunnels with complex geological conditions. Alternatively, the classification may be achieved with the aid of some machine learning (ML) methods, which are data‐driven, hence bypassing pre‐determination of the mathematical function forms of the main factor(s). Note although these ML methods perform well in the classification of surrounding rock mass, they generally employ all measurements of readily available rock indices as input variables, which might lead to excessive model complexity and a potential decrease in generalization performance. In this paper, a fully Bayesian Gaussian process classification (fB‐GPC) approach is proposed for probabilistic classification of surrounding rock mass, which is data‐driven and can select the optimal combination of main factors that affect rock mass classification. A real‐life example is used to illustrate and validate the proposed approach. Results show that the proposed fB‐GPC method performs very well in determination of the most important factor for classification of surrounding rock mass, with an area under the receiver operating characteristic curve (AUC) of around 0.98. A sensitivity study is also performed to systematically examine the accuracy and robustness of the proposed approach in this study. [ABSTRACT FROM AUTHOR]

Wind speed changes from one region to another due to several influencing variables. In this article, a software method has been proposed to determine the future wind speed at any time and under any conditions. Neural Networks were used with engineering data regarding the method of education, training algorithms, and different activation functions between the input and output layers, each according to the nature of the data that would be generated. Backpropagation Neural was used with three variables chosen to be the inputs for the learning and training network (wind speed, humidity, and time), which are considered the most important in determining the proposed or expected speed at the relevant time and place. The hidden layer consists of 10 neurons, which are determined according to the precision of output. After comparing the measurements from the weather system with the expected values, a very tiny percentage of error was found since these readings are regarded as acceptable and aid in the problem-solving process for running companies and researchers. The error rate recorded in this work ranged between (3 * 10-3 and 3 * 10-5), and the average number of attempts for the training and examination process reached 33 attempts, as it is known that neural networks carry out the training process based on specific mathematical functions and closed loops that depend on the lowest possible error rate. [ABSTRACT FROM AUTHOR]

Background: The study of growth traits is of interest to many animal scientists, regardless of specialization, due to the economic importance of growth rate, mature weight and other related traits. Objective: This study aimed to compare six non‐linear models for describing the growth of Lori‐Bakhtiari sheep. Methods: In order to collect weight data, 85 lambs (41 males and 44 females) were reared from birth to 140 days of age, and their growth patterns were recorded by measuring their body weight at 10‐day intervals. Various mathematical functions, including the negative exponential, Brody, Gompertz, Logistic, Morgan–Mercer–Flodin (MMF) and Weibull, were used to model the relationship between body weight records and age. Results: The results showed that the MMF and Gompertz models provided the best fit to the body weight data, whereas the negative exponential model exhibited the worst fit. In all models, the asymptotic weight of male lambs was higher than females. The research also revealed differences in growth patterns between male and female lambs. Overall, females had a lower absolute growth rate than males, but they reached their peak growth at an earlier period, and their growth rate declined faster. Conclusions: The differences in growth patterns between males and females indicate the importance of analysing male and female data separately when describing growth. As a result, Gompertz model can be recommended to Lori‐Bakhtiari female and male lamb breeders to determine more accurate growth traits. In addition, it should be considered that feeding male and female lambs separately according to absolute growth rate values may increase growth performance. [ABSTRACT FROM AUTHOR]

This study investigates when and how university students in first-semester introductory calculus interpret multiple representations of the same function. Specifically, it focuses on three tasks. The first task has students give their definitions of 'function sameness', the results of which suggests that many students understand a function as being determined by more than its points. The second has them assess the derivative of a piecewise-defined representation of a typical polynomial function, the results of which suggest that students see a piecewise function as two separate functions with the conditions as instructions. The third involves an instance of the fundamental theorem of calculus, the results of which suggest that students view (what we see as) the same function as two different functions. Taken together, these results suggest that many students see two functions where we as mathematicians see only one. In particular, students see various features of a function's analytic and graphical representations as being essential to the function's identity. [ABSTRACT FROM AUTHOR]

Suppose ε → B is a non-isotrivial elliptic surface defined over a number field, for smooth projective curve B. Let k denote the function field ℚ (B) and E the associated elliptic curve over k. In this article, we construct adelically metrized ℝ-divisors DX on the base curve B over a number field, for each X ∈ E(k) ⊗ ℝ. We prove non-degeneracy of the Arakelov-Zhang intersection numbers DX · DY, as a biquadratic form on E(k) ⊗ ℝ. As a consequence, we have the following Bogomolov-type statement for the Néron-Tate height functions on the fibers Et (ℚ) of ε over t ∈ B(ℚ): given points P1,..., Pm ∈ E(k) with m ≥ 2, there exist an infinite sequence {tn} C B(ℚ) and small-height perturbations P! t 2 Etn (Q) of specializations P... such that the set {P...',..., P...'} satisfies at least two independent linear relations for all n, if and only if the points P1,..., Pm are linearly dependent in E(k). This gives a new proof of results of Masser and Zannier (2010, 2012) and of Barroero and Capuano (2016) and extends our earlier 2020 results. In the Appendix, we prove an equidistribution theorem for adelically metrized ℝ-divisors on projective varieties (over a number field) using results of Moriwaki (2016), extending the equidistribution theorem of Yuan (2012). [ABSTRACT FROM AUTHOR]

Proxy signature schemes can be used in all the scenarios where a signer is not able to sign an important message. In some cases which involve a group of proxy signers, the anonymity of the proxy signer is required. We propose the first multivariate anonymous proxy signature scheme over finite field, and discuss all its security properties such as anonymity, unforgeability, verifiability, distinguishability, and undeniability. Additionally, we give a toy example to demonstrate the mathematical functioning of the proposed scheme. We compare our scheme with the existing post-quantum anonymous proxy signature scheme. [ABSTRACT FROM AUTHOR]

Copyright of Electronic Journal of Research in Educational Psychology is the property of Editorial of the University of Almeria (Spain) 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.)

The aim of the study is to obtain new binomial transforms for the κNarayana sequence. The first of these is the binomial transform, which is its normal form, and in the first step, after finding the recurrence relation of this new binomial transform, the generating function and Binet formula were obtained. Finally, Pascal's triangle was calculated. In the rest of the article, κbinomial transform was performed for the κNarayana sequence and the recurrence relation, generating function, Binet formula and Pascal's triangle were examined for the new sequence obtained. Then, by performing the falling binomial transform and the rising binomial transform, the features listed above were found again for these sequences. [ABSTRACT FROM AUTHOR]

Economic dispatch is an important issue in the management of power systems and is the current focus of specialists. In this paper, a new metaheuristic optimization algorithm is proposed, named Social Small Group Optimization (SSGO), inspired by the psychosocial processes that occur between members of small groups to solve real-life problems. The starting point of the SSGO algorithm is a philosophical conception similar to that of the social group optimization (SGO) algorithm. The novelty lies in the introduction of the small group concept and the modeling of individuals' evolution based on the social influence between two or more members of the small group. This conceptual framework has been mathematically mapped through a set of heuristics that are used to update the solutions, and the best solutions are retained by employing a greedy selection strategy. SSGO has been applied to solve the economic dispatch problem by considering some practical aspects, such as valve-point loading effects, sources with multiple fuel options, prohibited operating zones, and transmission line losses. The efficiency of the SSGO algorithm was tested on several mathematical functions (unimodal, multimodal, expanded, and composition functions) and on power systems of varying sizes (ranging from 10-units to 1280-units). The SSGO algorithm was compared with SGO and other algorithms belonging to various categories (such as: evolution-based, swarm-based, human behavior-based, hybrid algorithms, etc.), and the results indicated that SSGO outperforms other algorithms applied to solve the economic dispatch problem in terms of quality and stability of the solutions, as well as computation time. [ABSTRACT FROM AUTHOR]

The acquisition of biological signals like ECG includes the presence of noise from power line interference, muscle artefacts etc. Mathematical functions like Fourier Transform (FT) can be used to selectively eliminate specific noise frequencies from the signals. FT converts 1-D signals in their time-domain to frequency-domain. Subsequently, setting the amplitude of the noise frequency to zero, and applying the inverse FT function reconverts the signal back to its time-domain. This process removes the noise from the signals. In this paper we computationally demonstrate denoising the ECG signals using Fast Fourier Transform algorithm. [ABSTRACT FROM AUTHOR]

Due to the rapid development of a global navigation satellite system and the rapid growth of ships, the traditional control algorithms are not suitable; hence, the longitudinal rocking phenomenon generated by external disturbances is more serious when a ship is sailing. This paper takes a mathematical model of the super large oil tanker "KVLCC2"'s longitudinal motion as the controlled plant, establishing a multi-input multi-output instability control system, using the root trajectory shaping method and a weighting matrix to ensure the stability of its transfer function's mathematical model. An improved closed-loop gain-shaping algorithm is utilized to design a simple robust controller. And a dual nonlinear positive feedback control algorithm is added to the control system to further improve the controller's pitching stabilization performance and reduce the controller's output energy. In order to verify that the controller has a consistently strong robustness, simulation experiments are carried out by adding a level 6, 7 and 8 wind wave model and a perturbation link to the control system, respectively. The results show that when the value of the hysteresis constant is taken as 0.25, the output values of the heave displacement and the pitch angle are greatly reduced, and the longitudinal rocking phenomenon is significantly improved. The dual nonlinear positive feedback control algorithm enhances the ship's pitching stabilization control capability and further reduces the controller's output energy, which provides technical support for the smooth and efficient sailing of super large ships under changing sea conditions. Combined with a global navigation satellite system, this algorithm provides a new method for pitching stabilization control of super large ships. [ABSTRACT FROM AUTHOR]

In this paper, we collect some recent results on the approximation properties of generalized sampling operators and Kantorovich operators, focusing on pointwise and uniform convergence, rate of convergence, and Voronovskaya-type theorems in weighted spaces of functions. In the second part of the paper, we introduce a new generalization of sampling Durrmeyer operators including a special function ρ which satisfies certain assumptions. For the family of newly constructed operators, we obtain pointwise convergence, uniform convergence and rate of convergence for functions belonging to weighted spaces of functions. [ABSTRACT FROM AUTHOR]

This paper describes the development and optimization plans for the China Railway Express (CR Express). As a new type of international land transport organization, CR Express has emerged with the continuous expansion of China toward European investment and trade, and in particular, has expanded with the continuous progress of the One Belt and One Road (OBOR) initiative. In addition to improving the service quality of CR Express, the operating costs must be reduced for developing "smart railways" that serve "smart cities". We propose a dualobjective-based function mathematical optimization model; the satisfaction of the cargo owner is considered, and the timeliness, transportation capacity, and goods category constraints of CR Express transportation are designed. Moreover, we present the normalized equivalent method of the two-objective function of the model. Finally, a case study is conducted against the background of certain trains in the western corridor of CR Express to validate the effectiveness of the model and research methods proposed in this study. [ABSTRACT FROM AUTHOR]

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic (CCE) model. The underlying CCE model lacks a closed-form exact solution. Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model's necessary properties, such as positivity, boundedness, and feasibility. Therefore, the development of structure-preserving semi-analytical approaches is always necessary. This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model's physical properties by formulating an equivalent unconstrained optimization problem. Singularity-free safe Padé rational functions approximate the mathematical shape of state variables, while the model's physical requirements are treated as problem constraints. The primary model of the governing differential equations is imposed to minimize the error between approximate solutions. An evolutionary algorithm, the Genetic Algorithm with Multi-Parent Crossover (GA-MPC), executes the optimization task. The resulting method is the Evolutionary Safe Padé Approximation (ESPA) scheme. The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations. The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padé approximants. [ABSTRACT FROM AUTHOR]

In this study, the concept of C-class functions in the setup of Sb-metric spaces, and some common coupled fixed point theorems for these mappings in complete Sb-metric spaces that involve altering distance functions and ultra altering distance functions are established. A few instances are given to support our major findings. We also provided an application for integral equations as well as Homotopy. [ABSTRACT FROM AUTHOR]

Copyright of Humanitas: International Journal of Social Sciences / Uluslararasi Sosyal Bilimler Dergisi is the property of Humanitas: International Journal of Social 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.)

To enhance the performance of meta-heuristic algorithms, the development of new operators and the efficient combination of various optimization techniques are valuable strategies for discovering global optimal solutions. In this research endeavor, we introduce a novel optimization algorithm called PGS (Particle Swarm Optimization-GA-Sliding Surface). PGS combines the strengths of particle swarm optimization (PSO), genetic algorithm (GA), and sliding surface (SS) to tackle both mathematical test functions and real-world optimization problems. To achieve this, we adaptively tune the weighting function and learning coefficients of the PSO algorithm using the sliding mode control's SS relation. The global best particle discovered through the PSO method serves as one of the parents in the GA's crossover operation. This new crossover operator is then probabilistically integrated with an improved particle swarm optimization algorithm, enhancing convergence speed and facilitating escape from local optima. We evaluate the proposed algorithm's performance on both uni-modal and multi-modal mathematical test functions, considering un-rotated and rotated cases, thereby testing its effectiveness and efficiency against other prominent optimization techniques. Furthermore, we successfully implement the PGS algorithm in optimizing the state feedback controller for a nonlinear quadcopter system and determining the cross-section for an inelastic compression member. [ABSTRACT FROM AUTHOR]

Background and Objectives Previous researches have often used the Firefly Algorithm (FA) as a single-purpose operation of the reservoir. For example, Garousi-Nejad and Bozorg-haddad (2014) used FA for the first time in water science and reservoir operation, using ten-year statistical data of the Aidoghmoush reservoir located in East Azerbaijan province of Iran. They used it to meet the needs of downstream irrigation. In order to show the efficiency of FA, the results of this algorithm were compared with the global optimum results obtained from the nonlinear programming (NLP) method. The results showed that FA responses differed by less than one percent from NLP. Garousi-Nejad et al. (2016) used the FA to operate the reservoir and used the superiority of this algorithm over GA using five mathematical tests, the problem of reservoir operation for agricultural water supply, and the problem of reservoir operation to generate electricity. The results showed the superiority of FA performance in terms of global optimum convergence rate compared to GA results. Therefore, further investigating the capability and application of the multi-objective of this algorithm in the multi-purpose reservoir operation is necessary. In this study, first, the performance of the MOFA algorithm is compared with the well-known and common NSGA-II algorithm from three perspectives of execution time, generation distance, and distance metric in two mathematical test functions. After ensuring they perform correctly in the test functions, an evaluation is performed for a reservoir operation problem. Then, three reservoir operation policies are selected from the policy set and reviewed. Methodology Aidoghmoush dam is one of the dams built in East Azerbaijan Province, located at 19 km from Mianeh city. Aydoghmoush dam is located in the Sefidrood catchment area and Aidoghmoush sub-basin on the Aidoghmoush river. The structure of the dam is a clay-core rockfill. In this study, the Aidoghmoush reservoir's operation is examined from 1990 to 1996. The FA algorithm was developed by Yang (2008). This algorithm is based on the idealization of the behavior and flashing patterns of fireflies. The test functions used in the present study are (1) Schaffer test function (SCH) and (2) Fonesca test function (FON) (Coello et al. 2007). The MOFA algorithm was used to solve two multi-objective test functions, and its performance was compared with NSGA-II. The Generational Distance (GD) metric, introduced by Van Veldhuizen and Lamont (1998), was used to measure the proximity of the non-dominated solutions obtained to the true Pareto front (PFtrue) (Coello et al. 2007). The spacing (SP) metric introduced by Schott (1995) was also used to measure the distribution of the obtained non-dominated solutions. Findings In both test functions, the MOFA with good solution quality has a significant time difference in execution time compared to the NSGA-II algorithm; the MOFA is 30% faster in the SCH test function and 15% more quickly in the FON test function than the NSGA-II. Therefore, the MOFA can be a good algorithm for optimizing complex and time-consuming problems such as reservoir operation. The MOFA algorithm in two groups of parameters compared with the NSGA-II algorithm was evaluated in the problem of reservoir operation to maximize reservoir storage and minimize deficit. Extracted solutions from the MOFA algorithm improved by 11% compared to the NSGA-II algorithm by considering better parameter values in terms of proximity to the PFtrue. Also, the execution time of the MOFA algorithm was improved by 13% compared to the NSGA-II algorithm's execution time. Conclusion Nature-inspired meta-heuristic algorithms have been considered in recent decades due to their suitable ability to derive optimal reservoir operation policies compared to classical methods. In this research, the Multi- Objective Firefly Algorithm (MOFA) is compared with the widely-used Non-Dominated Genetic Algorithm (NSGA-II) in two test functions [Schaffer (SCH) and Fonseca (FON)]. These algorithms are then used to solve the optimizing the reservoir operation problem. Aidoghmoush reservoir, located in East Azerbaijan province, is used as a case study. Two conflicting objective functions are considered, including the first objective function of maximizing reservoir storage and the second objective function of minimizing deficiency. The algorithm runtime, generation distance, and Spacing matric are used to evaluate and compare the studied algorithms. The results showed that the execution time of the MOFA algorithm in the two test problems examined was, on average, 22% less than the execution time of the NSGA-II algorithm, and the quality of the answers could be better or worse than NSGA-II. The results obtained in the multi-objective operation of the reservoir showed that the set of solutions obtained from the MOFA algorithm became closer to the PFtrue averagely of 13% by considering the parameters α, β, and γ equal to 10, 1, and 0.1, instead of considering the parameters α, β, and γ equivalent to 0.25, 1 and 1, and the average execution time of the algorithm was improved by 3%. This improvement of the solution's quality and runtime was 13 and 11, respectively, compared to the NSGA-II algorithm. Since the MOFA algorithm is fast, the quality of the resulting set of answers can be improved by adjusting parameters, modifying, or integrating with other methods, such as different optimization algorithms or machine learning algorithms, and using it to Optimize real-time problems that are important in terms of computational time and burden. It is further suggested that the MOFA algorithm be developed for more complex models such as multi-purpose reservoir operation with more than two objectives of multi-reservoir systems, and its performance in reservoir operation management problems be compared with other meta-heuristic algorithms. [ABSTRACT FROM AUTHOR]

In this study, a broader class of rational functions r(u(z)) of degree mn, where u(z) is a polynomial of degree m is taken into consideration and obtain certain sharp compact generalization of well-known inequalities for rational functions. [ABSTRACT FROM AUTHOR]

The modified version of quasi-SMILES is studied. Unlike the previous ones, the new version allows building codes of experimental conditions in a user-friendly (easily interpreted) form. The quasi-SMILES can be a convenient basis for discussion between experimentalists and developers of models. The optimal descriptors for regression one-parameter models were calculated with the Monte Carlo method, using the vector of ideality of correlation. The vector of the ideality of correlation has two components: (i) the index of ideality of correlation (IIC) and (ii) the correlation intensity index (CII). Both the indices are components of the stochastic Monte Carlo process. The contribution of these indices is paradoxical: they improve the statistical quality of a model on the external validation set but to the detriment of the statistical quality of the model for the training set. Taking into account IIC and CII values for the Monte Carlo optimization gives an improvement of models of zeta potential of considered nanoparticles. The described approach is convenient for modelling the zeta potential of the considered nanoparticles. No less important is the universality of the use of quasi-SMILES as a means for studying the values of endpoints in the form of mathematical functions of not only the structures of the simulated objects (nanoparticles) but also the experimental conditions. [ABSTRACT FROM AUTHOR]

When there are some restrictions on the random variables of insurance risk model, it is impossible to calculate the exact value of ruin probabilities. For these cases, even finding a suitable approximation, is very important from a practical point of view. In the present paper, we consider the renewal insurance surplus model with light-tailed claim amount distributions and try to find some inequalities on the infinite time ruin probability depending on the amount of initial reserve using statistical and mathematical approaches if the assumption of net profit does not hold but there exist some other restrictions on the mathematical functions of random variables of model. The assertions depend on the amount of initial reserve, distribution of nonnegative claim occurrences times and successive claim amounts are obtained. Finally, to show the application and effectiveness of given theorems two examples are presented. Through these examples, the infinite time ruin probabilities are estimated using Monte Carlo simulation and give an intuitive way to understand the nature of ruin. [ABSTRACT FROM AUTHOR]

We study for each fixed integer $g \ge 2$ , for all primes $\ell $ and p with $\ell \neq p$ , finite regular directed graphs associated with the set of equivalence classes of $\ell $ -marked principally polarized superspecial abelian varieties of dimension g in characteristic p , and show that the adjacency matrices have real eigenvalues with spectral gaps independent of p. This implies a rapid mixing property of natural random walks on the family of isogeny graphs beyond the elliptic curve case and suggests a potential construction of the Charles–Goren–Lauter-type cryptographic hash functions for abelian varieties. We give explicit lower bounds for the gaps in terms of the Kazhdan constant for the symplectic group when $g \ge 2$. As a byproduct, we also show that the finite regular directed graphs constructed by Jordan and Zaytman also has the same property. [ABSTRACT FROM AUTHOR]

In What is Philosophy?, Deleuze and Guattari critique the relationship between formal logic and philosophy. They argue that since philosophy is the creation of concepts that are intensional, and formal logic reduces concepts to their extension, formal logic then has no special providence to decide philosophical questions. This may strike the logic-inclined philosopher as outdated given that there are now formal intensional logics designed to model meaning rather than reference. However, it will be shown that these logics too fail to express the concept in a way that preserves its philosophical import. Doing so requires contrasting Deleuze and Guattari's account of the concept with Frege's to show how the latter persists even in intensional logics in the form of mathematical functions that are ultimately referential. This then results in support for Deleuze and Guattari's claim that formal logic is a useful tool, but that it is incapable of adjudicating philosophical disputes. [ABSTRACT FROM AUTHOR]

This year is the 50th anniversary of Besag's classic auto‐models publication, a cornerstone in the development of modern‐day spatial statistics/econometrics. Besag struggled for nearly two decades to make his conceptualization collectively successful across a wide suite of random variables. But only his auto‐normal, and to a lesser degree his auto‐logistic/binomial, were workable. Others, like his auto‐Poisson, were effectively failures, whereas still others, such as potentials like an auto‐Weibull, defied even awkward mathematical incorporations of spatial lag terms. Besag circumvented this impediment by introducing an auto‐normal random effects components (within a Bayesian estimation context), building upon his single total success. This article describes an alternative approach, partly paralleling his reformulation while avoiding inserting spatial lag terms directly into probability density/mass functions, implanting spatial autocorrelation into cumulative distributions functions (CDFs), instead, via a spatially autocorrelated uniform distribution. The already existing probability integral transform and quantile function mathematical statistics theorems enable this mechanism to spatialize any random variable, with these new ones labeled sui‐models. [ABSTRACT FROM AUTHOR]

This study delves into special class of generalized p-trigonometric functions, examining their connection to the established counterparts like p-cosine and p-sine functions. We here explore the new class of functions called the p-versine, p-coversine, p-haversine, and p-hacovercosine, by providing comprehensive definitions and properties. Grounded in the characteristics of p-cosine and p-sine functions, the newly proposed functions offer unique mathematical insights. Our work contributes towards a thorough understanding of these new special functions, showcasing their potential applications in diverse scientific domains, from mathematical analysis to physics and engineering. This paper contributes as a valuable resource for future applied mathematics researchers, engaging with these new mathematical functions, enhancing the ability to model complex patterns from diverse real-world applications. [ABSTRACT FROM AUTHOR]

The aim of this research was to analyze the level of mathematical understanding based on the mathematical connections made by a group of Mexican High School students when solving mathematical tasks related to the concepts of equation and linear function. The study employed the thinking aloud method to collect data, whereby students verbalized their thought processes while solving three mathematical tasks, followed by answering some final questions. The collected data were analyzed using a simplified version of thematic analysis based on a preliminary framework adopted in this research. The findings revealed that students demonstrated different levels of mathematical understanding depending on the types of mathematical connections they made. Moreover, these outcomes facilitated the refinement of the preliminary framework, providing a more precise set of indicators for each tier of mathematical understanding. These indicators can be valuable resources for educators and researchers, offering guidance in developing instructional strategies aimed at promoting higher levels of mathematical understanding within the classroom. [ABSTRACT FROM AUTHOR]

Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three largely distinct velocity distributions, namely the Maxwell–Boltzmann distribution, the pathway distribution, and the Mittag-Leffler distribution. Moreover, a natural generalization of the Maxwell–Boltzmann velocity distribution is discussed. Furthermore, an explicit evaluation of the reaction rate integral in the high-energy cut-off case is carried out. Generalized special functions of mathematical physics like Meijer's G-function and Fox's H-functions and their utilization in mathematical physics are the prime focus of this paper. [ABSTRACT FROM AUTHOR]

The hydrocarbon extraction process is complex and involves numerous design variables and mitigating risk. Numerous time-consuming simulations are required to maximize objective functions such as NPV from a particular field while contemplating a significant representation of uncertainty scenarios and various production strategies. Production strategies searches may result in a high-dimensional search space which can yield sub-optimal reservoir economical exploration. As a solution, appropriate optimization algorithms selection and tuning may provide good solutions with lesser simulations. This paper presents a methodology to calibrate, develop, and select optimization algorithms for oil production strategy applications while quantifying the dimension and optimum location effects. Global optimum location altered the best method to be selected. It presents a novel algorithm (ASLHC) and a modification of the Nelder-Mead method (NMNS) to improve its high dimensionality performance. Performances of six pre-calibrated techniques were compared using novel normalized mathematical functions. Optimizations were limited to a 500 evaluation functions computational budget. The PSO, ASLHC, NMNS, and IDLHC were selected and implemented to perform production strategy improvements regarding two parameterizations of the reservoir management variables for a real reservoir model with restricted platform. Results showed the implemented algorithms successfully improved NPV by at least 8% at each of the 24 real-case optimizations. After upscaling the selected techniques for a 115 variable parameterization, the NMNS and IDLHC demonstrated good resilience against local convergence and each technique kept improving during all iterations of the process. An optimization method recommendation chart is presented based on the computational budget of the application. [ABSTRACT FROM AUTHOR]

An HFMD outbreak spread over the city of Hải Phòng from summer 2011 to autumn 2012. This epidemic was chosen because it was the very first HFMD epidemic in North Vietnam, eliminating thus interferences with previous outbreaks. This epidemic displayed three separate waves. A complete dataset was collected for more than 9500 patients during this period, which enabled us to analyze this epidemic at different scales. Access to the healthcare system was crucial during this period, which was possible due to a reorganization of the system in February–March 2012. An analysis at the commune level enabled us to track the epidemic along certain communication routes. The three-waves structure reveals a wide disparity at the district level. We developed a mathematical model showing high accuracy at the adjustment of data for both the total number of cases and for the number of cases per week. As a consequence, the model was able to accurately determine the dates of the beginning and end of each wave and to show that they overlapped. Using mathematical functions associated with this model, it was possible to calculate the probability for a patient to belong to a specific wave. [ABSTRACT FROM AUTHOR]

This study looks closely into the analysis of the variation of constants formula given by Φ (t) = S (t) Φ (0) + ∫ 0 t S (t − σ) F (σ , Φ (σ)) d σ , for t ∈ [ 0 , T ] , T > 0 , within the context of modular function spaces L ρ . Additionally, this research explores practical applications of the variation of constants formula in variable exponent Lebesgue spaces L p (·) . Specifically, the study examines these spaces under certain conditions applied to the exponent function p (·) and the functions F as well as the semigroup S (t) , utilizing the symmetry properties of the algebraic semigroup. This investigation sheds light on the intricate interplay between parameters and functions within these mathematical frameworks, offering valuable insights into their behavior and properties in L p (·) . [ABSTRACT FROM AUTHOR]

The objective of this case study was to identify the role of finger gestures in learning mathematics informally during play, especially in sociocultural settings. A mathematical activity involving addition was qualitatively analyzed at a Japanese preschool. We explored how the process of subjectification and objectification contributed to a mathematical activity at a Japanese preschool and how the role of preschoolers' finger gestures changed during the process of learning mathematics. We utilized Radford's theoretical construct of joint labor and analyzed Japanese preschool children's mathematical behaviors from a sociocultural perspective. The subjects were 15 Japanese preschool children and their teacher. We relied on both Radford's methodology and a microgenetic approach for the analysis. We found that subjectification and objectification proceeded in the scene of the conversations regarding addition; observing joint labor in a classroom activity offered valuable insights into these processes. In the activity, the children actively extended their practice of posing and answering quizzes, and learned how to resolve a conflict with the support of the teacher. Secondly, although the role of finger gestures was originally used to obtain correct answers to quizzes, it was reconstructed to solve the conflict between the children through the teacher's mediation. This showed that, even in an environment where children implicitly learn mathematics, they learn from one another, including the teacher, and that gestures in mathematical communications function well for developing mathematical thinking and skills. [ABSTRACT FROM AUTHOR]