Mathematics and Computer Sciences

This paper explores the decomposition of pre-𝛽-irresolute (pre-𝛽-irr) maps and their connection to generalized closed sets (g-closed) in topological space (top. sp.). We provide the necessary background on top. sp., continuity, closed, and related concepts. We introduce the definitions of pre-𝛽-irr maps and g-closed and discuss their basic properties. The decomposition theorem is presented, stating that every pre-𝛽-irr map can be decomposed into a composition of a pre-𝛽-continuous (pre-𝛽-cont.) map and a b-irr map. Examples and applications are provided to illustrate the behavior of pre-𝛽-irr maps and the practical implications of the decomposition theorem. We examine the relationships between pre-𝛽-cont. maps and pre-𝛽-irr maps, exploring the conditions under which a pre-𝛽-irr map is also 𝑏-irr, and provide a proof for this relationship. The properties of pre-𝛽-cont. maps, 𝑏maps, g-pre-𝛽-cont. maps, and g-𝑏-cont. maps are discussed, along with proofs and examples to illustrate their applicability. This paper contributes to the understanding of pre-𝛽-irr maps, their decomposition, and their relationships with gclosed, providing a foundation for further research in top. sp. and map decompositions.

The study addresses the significant impact of artificial intelligence on three key areas: financial forecasting, medical
diagnosis, and marketing strategies. The objective is to provide tangible evidence of performance and accuracy
improvements in these domains facilitated by AI. The research method involves analyzing scientific and empirical
evidence, utilizing standard questionnaires, and conducting semi-structured interviews. The findings reveal that the
application of AI results in enhanced accuracy of financial forecasts, improved precision and speed in medical diagnostics, and
increased efficiency of marketing strategies. The results clearly demonstrate the positive influence of AI in boosting accuracy
and effectiveness across these sectors.

The purpose of this work is to investigate the Lane Emden equation by using Haar wavelet quasi-linearization approach defined over the interval [0,1]. The Lane Emden equation is widely studied and challenging equation in the theory of stellar structure for the gravitational potential of a self gravitating, spherically symmetric polytropic fluid which models the thermal behaviour of a spherical cloud of gas acting under the mutual attraction of its molecules and subject to the classical laws of thermodynamics.The proposed method is based on the replacement of unknown function through a truncated series of Haar wavelet series of the function. The method is shown to be very reliable for any finite polytropic index p and for other linear and nonlinear cases of Lane Emden equations.

The objective of this work is the evaluation, through computational simulation, of the performance and behavior of the PUMA 560 robot under different types of motion controllers. Nominal models for control design were obtained through linearization of the robot dynamic model considering selected points of operation through Denavit-Hartenberg (DH) modeling and convention. In addition to a PID joint decentralized control law and a computed torque control law that had already been implemented in the simulator, it was implemented a predictive control law and a robust control law as well. Tuning of the parameters of these control laws were performed for the Puma 560 robot and each control system was evaluated through simulation. Results about the controller design and the control system simulation were collected and discussed. Completing this study aimed to analyzing a six degree of freedom robot manipulator motion control taking in account performance and robustness aspects, it was chosen a particular structure and introduced a force control loop; this controller design and simulator extension allowed an evaluation of some force control aspects and digital twin.

Abstract---This paper compared the efficiency of Simpson’s 1/3 and 3/8 rules for the numerical solution of first order Volterra integro-differential equations. In developing the solution, collocation approximation method was adopted using the shifted Legendre polynomial as basis function. A block method approach is preferred to the predictor corrector method for being self-starting. Experimental results confirmed that the Simpson’s 3/8 rule is more efficient than the Simpson’s 1/3 rule.

A numerical procedure is developed to obtain the solution of a mathematical model for capillary formation in tumor angiogenesis. The proposed method is based on the shifted Legendre tau technique. Our approach consists of reducing the problem to a set of algebraic equations by expanding the approximate solution as a shifted Legendre polynomial with unknown coefficients. The operational matrices of integral and derivative together with the tau method are then utilized to evaluate the unknown coefficients of shifted Legendre polynomials. Illustrative example is included to demonstrate the validity and applicability of the presented technique.

Lane-Emden equation is also of fundamental importance in mathematical physics, celestial mechanics, and computer science. It can be used to describe stellar structures, equilibrium density distribution in polytrophic isothermal gas, thermal behavior in mutual attraction of its molecules. An improved numerical method is developed for solving Lane-Emden type differential equations. The method is based on power series solutions of differential equations and Maclaurin series expansion. A python program is written to carry out numerical calculations. Five examples are solved and shown in this paper, the solutions obtained by the program are compared with the exact solutions of differential equation, an excellent agreement is found between them. The present method improves runtime.

In this paper, we consider the Lane-Emden equation of the first kind which arises in the study of stellar structures. We use multiple algorithms, based on Homotopy Analysis Method (HAM) to find the convergent series solutions to the singular, non-linear, initial value problem. It is found that the radius of convergence for the solutions is affected by three factors: the choice of initial value, the order and type of non-linearity, and the linear operator used. We then compare analytical results to the 20 th order series solution, the Pade approximant to the series, and the approximate solution obtained via the Runge-Kutta-Fehlberg method (RKF45).

Lane-Emden equation is also of fundamental importance in mathematical physics, celestial mechanics, and computer science. It can be used to describe stellar structures, equilibrium density distribution in polytrophic isothermal gas, thermal behavior in mutual attraction of its molecules. An improved numerical method is developed for solving Lane-Emden type differential equations. The method is based on power series solutions of differential equations and Maclaurin series expansion. A python program is written to carry out numerical calculations. Five examples are solved and shown in this paper, the solutions obtained by the program are compared with the exact solutions of differential equation, an excellent agreement is found between them. The present method improves runtime.

An all new technique has been devised to solve non-linear Lane-Emden type equations. This novel technique is based on the Perturbation Iteration Algorithm. In this paper, a few examples are presented for the illustration of the power and wide usability of the proposed method. Moreover, a compare and contrast with the actual solution is provided. It has been evaluated that by employment of this method, the construction of perturbation solutions converging swiftly to the true solutions usually becomes easy, by giving us room to exactly demonstrate how ε-terms influence linearized equations. This swift convergence of the method gives solutions that are accurate quantitatively through relatively little iteration.

In this paper, we consider the Lane-Emden equation of the first kind which arises in the study of stellar structures. We use multiple algorithms, based on Homotopy Analysis Method (HAM) to find the convergent series solutions to the singular, non-linear, initial value problem. It is found that the radius of convergence for the solutions is affected by three factors: the choice of initial value, the order and type of non-linearity, and the linear operator used. We then compare analytical results to the 20 th order series solution, the Pade approximant to the series, and the approximate solution obtained via the Runge-Kutta-Fehlberg method (RKF45).

This paper presents a computational method to solve nonlinear boundary value problems with multi-point boundary conditions. These problems have important applications in the theoretical physics and engineering problems. The method is based on reproducing kernel Hilbert spaces operational matrices and an iterative technique is used to overcome the nonlinearity of the problem. Furthermore, a rigorous convergence analysis is provided and some numerical tests reveal the high efficiency and versatility of the proposed method. The results of numerical experiments are compared with analytical solutions and the best results reported in the literature to confirm the good accuracy of the presented method.

Wind and solar energy technologies offer clean and renewable energy sources, and are essential components of sustainable energy future. The current paper presents a new methodology for size optimization of stand-alone Wind/PV energy systems. The principal objective of this study is to maximize the electricity match rate between demand and supplies, able to accomplish the energy requirements of a given load distribution, for a specific site. Mathematical models of hybrid components are exploited to estimate the total output power using solar radiation, temperature and wind speed data, collected on the site of Zabol, located in Sistan and Baluchestan, Iran. Then, a new methodology has been proposed which can obtain the optimal size of each hybrid component. The objective functions are considered based on supply/demand match evaluation criteria, minimizing the inequality coefficient (IC) and also maximizing the correlation coefficient (CC), simultaneously. The elitist non-dominated sorting genetic algorithm (NSGA-II), which is one of the multi-objective evolutionary algorithm (MOEA), have been employed for a hybrid stand-alone renewable energy power system (Wind/PV) to find the optimal size of each components. The Pareto-optimal solution is obtained in order to have higher-level decision. The designers can select the best configuration among the Pareto set which fits their desire.

The book presents an expanded excursion into the creative activities of the Tallinn Research Group during 1970–2022 with a focus on researches and development in such main fields as mainframes, personal computers, general statistics theory, issues of parallel information processing and computing, computer mathematics systems (Maple, Mathematica), programming, automated control systems, mathematical developmental biology, some mathematical problems in the cellular automata theory with a focus on our standpoint on the main stages of formation of the cellular automata theory. The book may be of certain interest as a retrospective standpoint on development of the above areas in the USSR (primarily in the ESSR) and the republics of the former USSR. The book is equipped with a fairly extensive bibliography on the issues under consideration.

The paper represents Maple library containing more than 400 procedures expanding possibilities of the Maple package of releases 6,7 and 8. The library is structurally organized similarly to the main Maple library. The process of the library installing is simple enough as a result of which the above library will be logically linked with the main Maple library, supporting access to software located in it equally with standard Maple software. The demo library is delivered free of charge at request to addresses mentioned above.

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off-grid points to obtain two different four discrete schemes, each of order (5,5,5,5) T , which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.

Generally, huge data of any organization possess data redundancy, noise and data inconsistency. To eliminate, Data preprocessing should be performed on raw data, then sorting technique is applied on it. Data preprocessing includes many methods such as data cleaning, data integration, data transformation and data reduction. Depending on the complexity of given data, these methods are taken and applied on raw data in order to produce quality of data. Then, external sorting is applied. The proposed external sorting now takes the number of passes less than actual passes log B (N/M) + 1 for the traditional B – way external merge sorting. Also, the number of Input / Outputs of proposed method is less than 2*N* (log B (N/M) + 1) of Input / Outputs than traditional method, and also proposed method consume least number of runs compared to actual basic external sorting.

paper presents external sorting using data preprocessing. Generally, huge data of any organization possess data redundancy, noise and data inconsistency. To eliminate, Data preprocessing should be performed on raw data, then sorting technique is applied on it. Data preprocessing includes many methods such as data cleaning, data integration, data transformation and data reduction. Depending on the complexity of given data, these methods are taken and applied on raw data in order to produce quality of data. Then, external sorting is applied. The external sorting now takes the number of passes less than actual passes log B (N/M) + 1 for B – way external merge sorting, and number of Input / Outputs less than 2*N* (log B (N/M) + 1) of Input / Outputs and also involve least number of runs compared to actual basic external sorting