Numerical calculation of multidimensional integrals depended on input information about the function in mathematical modelling of technical and economic processes

Nechuiviter, Olesia; Iarmosh, Olena Vit.; Kovalchuk, Kyrylo

doi:10.1088/1757-899x/1031/1/012059

Cited by 5 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Для обробки вищезазначеної інформації та побудови нових математичних моделей також можуть бути використані нові інформаційні оператори, які гарно себе зарекомендували при математичному моделюванні задач цифрової обробки сигналів і зображень [7][8][9][10].…”

Section: вступunclassified

Mathematical modeling of foreign bodies with different density in biological and non-biological models in the experiment

Khoroshun,

Nehoduiko,

Makarov

et al. 2024

ЕМ

View full text Add to dashboard Cite

Background. Modeling allows investigating both existing and predicted processes and is widely used in basic science and in many industries. The aim is to develop a mathematical model for determining the size of the foreign bodies (FB) and their radiographic density in non-biological and biological models to improve the results of diagnosis for gunshot ricochet wounds. Materials and methods. In the biological non-living model (a piece of pork) and non-biological models (polystyrene, foam rubber), we place the FB made of paper, leather, rubber, plastic, and lithium-ion batteries. The number of the FB is 9 of each type. Number of models is 3 each: pork, polystyrene, foam rubber. We measure the dimensions of the FB and models with a metric ruler. For each model, we select the FB, which we label with the study number. We immerse the FB to the same depth using a Billroth general surgical medium hemostatic clamp in the following sequence: paper, leather, rubber, plastic, and lithium-ion battery. Multislice computed tomography (MSCT) of the models is performed on the Revolution EVO (2021) apparatus with measurement of the sizes and radiographic density of the FB and models. Radiographic density was measured in conventional units on the Hounsfield scale. For each study group, the ratio of the actual sizes of the removed FB and according to MSCT data was determined in the MathCad 15 computer math software, depending on the radiological density of the FB and the model. Results. According to MSCT data, the radiographic density of the models on the Hounsfield scale is as follows: polystyrene — –990.0 ± 0.3 units; foam rubber — –985.0 ± 0.2 units; pork — 62.0 ± 0.3 units; radiographic density of the foreign bodies: paper — –743.0 ± 10.3 units, leather — –258.0 ± 14.2 units, rubber — –12.0 ± 2.6 units, plastic — 183.0 ± 14.6 units, lithium-ion batteries — 3071 units. Visualization of paper in non-biological and biological models and leather in non-biological models is problematic due to the similar radiographic density of the models and the inability to measure the dimensions. When the FB (rubber, plastic, battery) is immersed in polystyrene, the coefficient of length (CL) is 1.0612, the coefficient of width (CW) is 1.928; in foam rubber: CL is 0.9926, CW is 1.9641; in pork: CL is 0.8394, CW is 1.534. Comparing the average coefficients of the ratio (CL and CW), we find that the coefficient in a biological model is closest to 1. This means that the FB from rubber, plastic, and batteries are best detected in pork. Conclusions. The actual dimensions of the FB placed in biological and non-biological models differ from those obtained by MSCT. Data correction is performed through calculated coefficients for length and width. The radiographic density of the model affects the radial visualization of the FB. The use of mathematical modeling in determining the sizes and radiographic density allows reducing the measurement error and determine the structure of the FB.

show abstract

Section: вступunclassified

Mathematical modeling of foreign bodies with different density in biological and non-biological models in the experiment

Khoroshun,

Nehoduiko,

Makarov

et al. 2024

ЕМ

View full text Add to dashboard Cite

show abstract

“…Для наближеного обчислення інтегралу (1) в роботі [30] розглядалася та досліджувалася кубатурна формула…”

Section: постановка задачі для наближеного обчислення інтегралу від ф...unclassified

“…Питанню чисельного інтегрування подвійних та потрійних інтегралів з використанням нових інформаційних операторів приділено значно менше уваги. До таких досліджень можна віднести [28,29], де викладено алгоритм побудови кубатурних формул з використанням слідів функції на лініях (в тому числі на оптимально вибраних лініях), а також [30], де розглядалося питання наближеного обчислення потрійного інтегралу, у випадку, коли інформація про функцію задається на взаємно перпендикулярних площинах. Логічним продовженням досліджень в цьому напрямку є наближене обчислення потрійного інтегралу, у випадку, коли інформація про функцію задається на взаємно перпендикулярних лініях.…”

unclassified

New Information Operators in Problems of Numerical Integration of Functions of Three Variables

Nechuiviter¹,

Ivanov²,

Kovalchuk³

2023

MMTT

View full text Add to dashboard Cite

The rapid development and implementation of the latest information technologies in many fields of science and technology contribute to the rise of new methods in mathematical modeling of systems and processes. In particular, new mathematical theories have appeared that can be effectively used for building and improvement of existing mathematical models of various phenomena and objects. One of these theories is the theory of new information operators, authored by the Laureate of the State Prize of Ukraine in Science and Technology, doctor of physical and mathematical sciences, professor (думаю, это излишняя информация в аннотации) O. M. Lytvyn. New information operators have found their application in the digital processing of signals and images, namely in the numerical integration of rapidly oscillating functions of many variables. Cubature formulas were built that are optimal in the order of accuracy and use the value of the non-oscillating factor of the integrand function not only at points, but also on planes or lines. The article demonstrates the application of new information operators to the numerical integration of functions of many variables, namely, the issue of approximate calculation of the integral from functions of three variables is considered in the case when the information about the function is given by its traces on the lines. The cubature formula uses an interlineation operator built on the basis of an interflatation operator with auxiliary functions in the form of piecewise constant splines. An estimate of the approximation error of the proposed cubature formula on the class of differentiable functions was obtained. The results of the calculation experiment in the computer mathematics system Mathcad are presented. Numerical calculations confirm the theoretical statements of the study.

show abstract

API Design for Multidimensional Integration Library

Hernández-Rubio

Pescador-Rojas

Pérez

et al. 2021

HCI International 2021 - Posters

View full text Add to dashboard Cite

Numerical calculation of multidimensional integrals depended on input information about the function in mathematical modelling of technical and economic processes

Cited by 5 publications

References 8 publications

Mathematical modeling of foreign bodies with different density in biological and non-biological models in the experiment

Mathematical modeling of foreign bodies with different density in biological and non-biological models in the experiment

New Information Operators in Problems of Numerical Integration of Functions of Three Variables

API Design for Multidimensional Integration Library

Contact Info

Product

Resources

About