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Wireless sensor networks are composed of many nodes distributed in a region of interest to monitor different environments and physical variables. In many cases, access to nodes is not easy or feasible. As such, the system lifetime is a primary design parameter to consider in the design of these networks. In this regard, for some applications, it is preferable to extend the system lifetime by actively reducing the number of packet transmissions and, thus, the number of reports. The system administrator can be aware of such reporting reduction to distinguish this final phase from a malfunction of the system or even an attack. Given this, we explore different mathematical functions that drastically reduce the number of packet transmissions when the residual energy in the system is low but still allow for an adequate number of transmissions. Indeed, in previous works, where the negative exponential distribution is used, the system reaches the point of zero transmissions extremely fast. Hence, we propose different dampening functions with different decreasing rates that present oscillations to allow for packet transmissions even at the end of the system lifetime. We compare the system performance under these mathematical functions, which, to the best of our knowledge, have never been used before, to find the most adequate transmission scheme for packet transmissions and system lifetime. We develop an analytical model based on a discrete-time Markov chain to show that a moderately decreasing function provides the best results. We also develop a discrete event simulator to validate the analytical results. [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 This may strike the logic-inclined philosopher as outdated given that there are now formal intensional logics designed to model meaning rather than reference.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]

First-principles calculations were performed to investigate the electronic and optical properties of small clusters of CH3NH3SnBr3. The reactive sites of the CH3NH3SnBr3 clusters were identified. The minimum values of electrostatic potential decreases monotonically with increasing cluster size from monomer to tetramer. The density of states (DOS) spectrum was obtained by convoluting molecular orbitals (MOs) with mathematical functions. The LUMO consists of Sn(5p), Br(4s), and Br(4p) orbitals, while the HOMO consists of Sn(5s), Sn(5p), and Br(4p) orbitals. The HOMO was observed to be more delocalized than the LUMO, likely due to the repulsion between the lone pair and the bonding pair. As "n" increases from 1 to 4, the HOMO–LUMO gap decreases. The HOMO–LUMO gap, optical gap, and wavelength corresponding to the absorption band maximum for the (CH3NH3SnBr3)n cluster (n → ∞) were modeled and found to be 3.622 eV, 3.091 eV, and 346.03 nm (3.5830 eV), respectively. The HOMO–LUMO gap of CH3NH3SnBr3 obtained from DOS was approximated to be 2.19 eV. [ABSTRACT FROM AUTHOR]

Purpose. To investigate the linearised mathematical model of a heater and identify the potential for lowering the order of the heater’s transfer functions for further synthesis of control systems and improvement in the efficiency and safe operation of a track heater. Methodology. After obtaining a linearised mathematical model of a heater with a transitory heat medium, the mathematical model equations are written in a standard format, followed by their Laplace transformation at zero initial conditions. With the help of the program product, an analytical study of the linearised model was performed, after which the Henkel singular values were used to simplify the order of the mathematical model transfer function from the seventh to the third and an assessment of the calculation accuracy loss after the function’s approximation was conducted, which showed that the accuracy loss was not significant. Findings. Having studied the linearised mathematical models of heaters with a transitory heat medium, it was determined that the transfer functions in the mathematical model are of the seventh order, which significantly complicates the creation of an automated heater control system. As a result, a simplified mathematical model with transfer functions of the third order is obtained, which significantly reduces the calculation complexity on modern microprocessors. Originality. Linearised mathematical models of an indirect heater were developed, based on the assumption of insignificant deviations of the output values from their baseline values. The studies of the linearised model showed that the transfer functions of the oil track heater are of the seventh order. Using Henkel singular values, it was possible to achieve transfer functions of the third order, which would reduce the complexity of creating automated control systems for indirect oil and gas condensate heaters. Practical value. Modern digital control systems for the oil heating process are created. Using the method for reducing the order of transfer functions by using Henkel singular values to three significantly facilitates the integration of these models into microprocessorbased controls. This helps to improve the efficiency and reliability of automatic control systems, ensuring a stable and safe oil heating process, which is critical for the smooth operation of technological processes. [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]

Stochastic differential equations (SDEs) are increasingly prevalent in a variety of fields. They have become routine in areas like pharmacokinetics and finance. Forestry applications, on the other hand, remain uncommon. This is an accessible introduction to the basic concepts and practical use of SDEs, with an emphasis on forest growth modeling. I begin by briefly discussing dynamical system ideas, describing rates of change in a state space instead of using functions of time directly. Rates of change can be specified by finite differences, but a formulation in continuous time with differential equations is often more convenient. Rational parameter estimation necessitates a stochastic representation of the error structure. Besides observation errors, process noise or environmental variability can be important. Both sources of variability can be taken into account with stochastic differential equations. Simple examples are demonstrated using R software. [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]

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 paper presents the implementation of a calculator of certain special mathematical functions in the form of an efficient web application with a simple and intuitive GUI (graphical user interface). This application aims to enable accurate numerical approximations of the most frequently used special mathematical functions in engineering and science, eliminating the need to acquire additional notational knowledge or programming language syntax experience. The investigation can be divided into three larger units. The initial section offers brief overview of the special mathematical functions of which numerical approximations are implemented in the subject application. For the time being, this application provides approximations for the following special mathematical functions: Bessel functions of the first kind, gamma and beta functions, and some orthogonal polynomials - Legendre, Laguerre, Hermite (physicist's and probabilist's) polynomials, Chebyshev polynomials of the first and the second kind, as well as Jacobi polynomials. The middle section presents a description of the computer implementation - an overview of the used technology and implemented algorithms, while the final section includes a discussion of the solution, as well as a comparison with existing software that provides the same features as the subject application. [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]

This introductory study suggests a formal basis for the interpretation of a continuous path in a connected matrix Lie group to be represented by the set of von Neumann ordinals which is a set-theoretical interpretation of natural numbers. In this study, it is aimed to relate the discrete recurrent structure of von Neumann ordinals to the exponential function. Since the Exponential function is fundamentally integrated into science and engineering literature this work aims to discover ties between the Exponential function and sets where, the Exponential function utilized in machine learning, loss functions; cryptography, key exchange and encryption algorithms; robotics, kinematics, trajectory planning; numerical analysis, discrete integration. Thus, the set theoretical interpretation of the exponential function has an interdisciplinary critical role. Throughout the article, necessary conjectures are postulated to interpret the rotations that form a smooth curve in terms of sets, namely von Neumann ordinals. Introduced formalizations covering Set existence axiom, unit element for set groups, interpretation of a smooth curve in terms of multiplication of exponentials, introduced a derivative operator to observe limited differentiable properties of the exponential function. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Qadisiyah Computer Science & Mathematics is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) 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.)

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]

This work proposes multiple variants of the Multiverse Optimizer Algorithm (MVO) with the use of Chaotic Maps and Fuzzy Logic. These variants come from the Fuzzy-Chaotic Multiverse Optimizer Algorithm (FCMVO), and the purpose is to analyze the behavior of the algorithm in some benchmark mathematical functions, to compare in which cases can perform best between the variants presented. The use of chaotic maps resides from some of the most used in the literature on optimization algorithms, and the main use is to adjust some of the parameters of behavior in the MVO algorithm; and other implementation is the use of Fuzzy Logic for dynamical adaptation of two parameters in the algorithm. In this study, we are presenting an extended comparison between the variants obtained from diverse chaotic maps, that in previous studies, we delimited to six variants which we called Elitist FCMVO. This comparison is done by evaluating the resulting variants from a set of three chaotic maps and comparing also with two different fuzzy inference systems (Mamdani and Sugeno types). The main objective is to present the obtained variants and compare which are the best chaotic maps in the FCMVO algorithm, to improve further in other study cases. [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]

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]

Copyright of Revista de Investigación en Educación is the property of Universidad de Vigo, Facultad de Ciencias de la Educacion y del Deporte 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.)

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]

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]

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]

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]

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 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]

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]

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.)

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]

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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]

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]

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]

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]

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]

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 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]

The primary aim of the current study was to develop a model capable of predicting the spatial distribution patterns of soil organic carbon (SOC) in mangrove forests (Avicennia marina) affected by camel grazing along the southern coast of the Red Sea. Four protected locations within mangrove forests were selected along the southern coast of the Saudi Red Sea, while eight other locations were selected under the influence of camel grazing. Three equations—allometric, exponential, and sigmoid—were employed on soil carbon data obtained from 40 soil cores, which equated to 600 soil samples. The goal was to develop models that could forecast how the cumulative SOC stocks (SOCc) and volumetric SOC densities (SOCv) would be distributed throughout the respective soil profiles in protected and grazed locations of mangroves, in order to predict how soil carbon changes when mangroves are under grazing stress. The sigmoid and exponential equations proved to be most effective in predicting SOCv distribution, with average R2 values of 0.956681 and 0.893894 for protected and grazed locations, respectively. For protected locations, all three equations effectively predicted the SOCc, with the sigmoid equation (R2 = 0.999942) exhibiting the best performance. In grazed locations, all equations were applicable, with the allometric equation demonstrating superior accuracy (R2 = 0.999910). The study found that grazing activities in mangrove forests resulted in a loss of SOC stock of 7.0 kg C/m2, accounting for 54% of the initial stock. These findings will significantly enhance our comprehension of SOC distribution in mangrove ecosystems under the grazing effect, allowing us to quantify the impact of camel grazing on SOC dynamics in coastal ecosystems.

Summary: It is well known that the function h (x) = x 1 x is strictly increasing on (0 , e ] and strictly decreasing on [ e , ∞) . This yields the conclusion that if e ≤ a < b , then b a < a b , and if 0 < a < b ≤ e , then b a > a b . Furthermore, if 0 < a < 1 < b , then b ln a < 0 < a ln b , which yields that a b < 1 < b a . However, it is difficult to compare ab and ba when 1 < a < e < b . For example, 2 3 < 3 2 , 2 4 = 4 2 , but 2 5 > 5 2 . In this note, we compare ab and ba completely when 0 < a < b . [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 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]