• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.433-444
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• 2024

Our study explores the connection between the Pythagorean theorem and the Fixed-point theorem in metric spaces. Both of which center around the concepts of distance transformations and point relationships. The Pythagorean theorem deals with right triangles in Euclidean space, emphasizing distances between points. In contrast, fixed-point theorems pertain to the points that remain unchanged under specific transformations thereby preserving distances. The article delves into the intrinsic correlation between these concepts and presents a novel study in Euclidean metric spaces, examining the relationship between contraction mapping and Pythagorean Right Triangles. Practical applications are also discussed particularly in the context of image compression. Here, the integration of the Pythagorean right triangle paradigm with contraction mappings results in efficient data representation and the preservation of visual data relation-ships. This illustrates the practical utility of seemingly abstract theories in addressing real-world challenges.

• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.235-246
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• 2024

In high-dimensional data analysis, sufficient dimension reduction (SDR) has been considered as an attractive tool for reducing the dimensionality of predictors while preserving regression information. The principal support vector machine (PSVM) (Li et al., 2011) offers a unified approach for both linear and nonlinear SDR. This article comprehensively explores a variety of SDR methods based on the PSVM, which we call principal machines (PM) for SDR. The PM achieves SDR by solving a sequence of convex optimizations akin to popular supervised learning methods, such as the support vector machine, logistic regression, and quantile regression, to name a few. This makes the PM straightforward to handle and extend in both theoretical and computational aspects, as we will see throughout this article.

• Computers and Concrete
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• v.33 no.4
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• pp.409-423
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• 2024

Using an extensive database, a sensitivity analysis across fifteen machine learning (ML) classifiers was conducted to evaluate the impact of various data manipulation techniques, evaluation metrics, and explainability tools. The results of this sensitivity analysis reveal that the examined models can achieve an accuracy ranging from 72-93% in predicting the fire-induced spalling of concrete and denote the light gradient boosting machine, extreme gradient boosting, and random forest algorithms as the best-performing models. Among such models, the six key factors influencing spalling were maximum exposure temperature, heating rate, compressive strength of concrete, moisture content, silica fume content, and the quantity of polypropylene fiber. Our analysis also documents some conflicting results observed with the deep learning model. As such, this study highlights the necessity of selecting suitable models and carefully evaluating the presence of possible outcome biases.

• Steel and Composite Structures
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• v.51 no.4
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• pp.407-416
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• 2024

The main objective of the present paper is to investigate the nonlinear vibration of buckled beams fixed at both ends and made of Aluminium allay (Al-alloy) reinforced with randomly dispersed Single Walled Carbon Nanotube (SWNT). The Mori-Tanak (M-T) micromechanical approach is selected to predict the homogenized material properties of the beams. The differential equation of motion governing the nonlinear behavior of the Euler-Bernoulli homogeneous beam is solved using an analytical method. The influences of diverse parameters including axial load, vibration amplitude, SWNT volume fraction, SWNT aspect ratio and beam slenderness ratio on the nonlinear frequency are studied.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.435-450
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• 2024

This study depends on the modified conformable fractional derivative definition to generalize and proves some theorems of the classical power series into the fractional power series. Furthermore, a comprehensive formulation of the generalized Taylor's series is derived within this context. As a result, a new technique is introduced for the fractional power series. The efficacy of this new technique has been substantiated in solving some fractional differential equations.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.461-475
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• 2024

The concept of an extension α-F-contraction and it's modified counterpart represents an advancement in the theory of metric space contractions. Through our study of the contraction principles and it's relationship to extension and modified extension, we found different conditions somewhat lengthy. In our paper, we create a development of the conditions for the extension of α-F-contraction and a modified α-F-contraction by reducing the conditions and make them easier. Our propose conditions are notably simple and effective. They serve as the foundation for proving theorems and solving examples that belong to our study. Moreover, they have remarkable significance in the condition of mathematical analysis and problem-solving. Thus, we find that these new conditions that we mention in the definitions achieve what is require and through them, we choose λ = 1 and we choose λ ∈ (0, 1) to clarify our ideas.

• Computers and Concrete
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• v.34 no.1
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• pp.63-77
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• 2024

In this research, we considered fractional order optimal control models for cancer, HIV treatment and glucose.These models are based on fractional order differential equations that describe the dynamics underlying the disease.It is formulated in term of left and right Caputo fractional derivative. Pontryagin's Maximum Principle is used as a necessary condition to find the optimal curve for the respective controls over fixed time period. The formulated problems are numerically solved using forward backward sweep method with generalized Euler scheme.

• International Journal of Computer Science & Network Security
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• v.24 no.9
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• pp.50-62
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• 2024

The decision to integrate mobile cloud computing (MCC) in higher education without first defining suitable usage scenarios is a global issue as the usage of such services becomes extensive. Consequently, this study investigates the security determinants of the educational use of mobile cloud computing among universities' students. This study proposes and develops a theoretical model by adopting and modifying the Protection Motivation Theory (PMT). The study's findings show that a significant amount of variance in MCC adoption was explained by the proposed model. MCC adoption intention was shown to be highly influenced by threat appraisal and coping appraisal factors. Perceived severity alone explains 37.8% of students "Intention" to adopt MCC applications, which indicates the student's perception of the degree of harm that would happen can hinder them from using MCC. It encompasses concerns about data security, privacy breaches, and academic integrity issues. Response cost, perceived vulnerability and response efficacy also have significant influence on students "intention" by 18.8%, 17.7%, and 6.7%, respectively.

• International Journal of Computer Science & Network Security
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• v.24 no.9
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• pp.85-92
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• 2024

Information Security is the foremost concern for IoT (Internet of things) devices and applications. Since the advent of IoT, its applications and devices have experienced an exponential increase in numerous applications which are utilized. Nowadays we people are becoming smart because we started using smart devices like a smartwatch, smart TV, smart home appliances. These devices are part of the IoT devices. The IoT device differs widely in capacity storage, size, computational power, and supply of energy. With the rapid increase of IoT devices in different IoT fields, information security, and privacy are not addressed well. Most IoT devices having constraints in computational and operational capabilities are a threat to security and privacy, also prone to cyber-attacks. This study presents a CIA triad-based information security implementation for the four-layer architecture of the IoT devices. An overview of layer-wise threats to the IoT devices and finally suggest CIA triad-based security techniques for securing the IoT devices..Make sure that the abstract is written as one paragraph.

• Steel and Composite Structures
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• v.52 no.2
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• pp.183-197
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• 2024

Not all structural columns maintain a vertical orientation. Several contemporary building structures have inclined columns, introducing distinct challenges, particularly in buckling behavior. This study examines the buckling behavior of inclined, thin-walled steel bundled columns, differing from typical vertical columns. Using specimens with three tubes welded to plates linearly aligned at the top and triangularly at the bottom, tests indicated that buckling capacity increases with tube wall thickness and diameter but decreases with column height. Inclined tubes in bundled columns showed improved buckling resistance over vertical ones. Results were verified against standard steel design guidelines to assess their predictive accuracy.