Mathematical Model of the Process of Ultrasonic wave Propagation in a Relax Environment with its Given Profiles at three Time Moments

Nytrebych, Zinovii; Il’kiv, Volodymyr; Malanchuk, Oksana

Mathematical Model of the Process of Ultrasonic wave Propagation in a Relax Environment with its Given Profiles at three Time Moments

Zinovii Nytrebych¹, Volodymyr Il’kiv¹, Oksana Malanchuk^{2, *}

¹ Lviv Polytechnic National University, Lviv79013, Ukraine

² Danylo Halytskyi Lviv National Medical University, Lviv79017, Ukraine

Article Information

Identifiers and Pagination:

Year: 2021
Volume: 14
Issue: Suppl-M1
First Page: 87
Last Page: 92
Publisher ID: TOBIOIJ-14-87
DOI: 10.2174/1875036202114010087

Article History:

Received Date: 13/12/2020
Revision Received Date: 2/7/2021
Acceptance Date: 21/8/2021
Electronic publication date: 19/11/2021
Collection year: 2021

Article Metrics

CrossRef Citations:

Total Statistics:

Full-Text HTML Views: 1005
Abstract HTML Views: 535
PDF Downloads: 309
ePub Downloads: 195
Total Views/Downloads: 2044

Unique Statistics:

Full-Text HTML Views: 595
Abstract HTML Views: 298
PDF Downloads: 226
ePub Downloads: 140
Total Views/Downloads: 1259

© 2021 Nytrebych et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

^* Address correspondence to this author at Danylo Halytskyi Lviv National Medical University, Lviv 79017, Ukraine; Tel: +380982568494; E-mail: Oksana.Malan@gmail.com

Objective:

The process of ultrasound oscillations in a relaxed environment, provided that the profiles of the acoustic wave at three time moments are known, is modeled by a three-point problem for the partial differential equation of the third order in time. This equation as a partial case contains a hyperbolic equation of the third order, which is widely used in ultrasound diagnostics.

Methods:

The differential-symbol method is applied to study a three-point in-time problem. The advantage of this method is the possibility to obtain a solution of the problem only through operations of differentiation.

Results:

We propose the formula to construct the analytic solution of the problem, which describes the process of ultrasound oscillations propagation in a relax environment. Due to this, the profile of the ultrasonic wave is known at any time and at an arbitrary point of space. The class of quasi-polynomials is distinguished as a class of uniqueness solvability of a three-point problem.

Conclusion:

Using the proposed method, it is possible to analyze the influence of the main parameters of ultrasound diagnostics problems on the propagation of acoustic oscillations in a relaxed environment. The research example of a specific three-point problem is given.

Keywords: Mathematical model, Ultrasonic oscillations, Three-point in time problem, Differential-symbol method, Ultrasound diagnostics, Partial differential equation.

Previous Article View Fulltext HTML Download PDF Download ePub Next Article

Track Your Manuscript
Enter Correct Manuscript Reference Number:

Submit Reference Number
Published Contents
About the Editor
Feng Cheng
Department of Pharmaceutical Science
University of South Florida
Tampa, FL
USA
View Editorial Board
About the Journal
The Open Bioinformatics Journal
ISSN: 1875-0362
Volume: 17, 2024

Download Flyer
Processing Time: Average publication time is 18 days between the final acceptance of revised manuscript and its publication
READ MORE

Press Release
Bentham Open Welcomes Sultan Idris University of Education (UPSI) as Institutional Member

Description:
Bentham Open is pleased to welcome Sultan Idris University of Education (UPSI), Malaysia as Institutional Member. The partnership allows the researchers from the university to publish their research under an Open Access license with specified fee discounts. Bentham Open welcomes institutions and organizations from world over to join as Institutional Member and avail a host of benefits for their researchers.

Sultan Idris University of Education (UPSI) was established in 1922 and was known as the first Teacher Training College of Malaya. It is known as one of the oldest universities in Malaysia. UPSI was later upgraded to a full university institution on 1 May, 1997, an upgrade from their previous college status. Their aim to provide exceptional leadership in the field of education continues until today and has produced quality graduates to act as future educators to students in the primary and secondary level.

Bentham Open publishes a number of peer-reviewed, open access journals. These free-to-view online journals cover all major disciplines of science, medicine, technology and social sciences. Bentham Open provides researchers a platform to rapidly publish their research in a good-quality peer-reviewed journal. All peer-reviewed accepted submissions meeting high research and ethical standards are published with free access to all.

Ministry Of Health, Jordan joins Bentham Open as Institutional Member

Description:
Bentham Open is pleased to announce an Institutional Member partnership with the Ministry of Health, Jordan. The partnership provides the opportunity to the researchers, from the university, to publish their research under an Open Access license with specified fee concessions. Bentham Open welcomes institutions and organizations from the world over to join as Institutional Member and avail a host of benefits for their researchers.

The first Ministry of Health in Jordan was established in 1950. The Ministry began its duties in 1951, the beginning of the health development boom in Jordan. The first accomplishment was the establishment of six departments in the districts headed by a physician and under the central administration of the Ministry. The Ministry of Health undertakes all health affairs in the Kingdom and its accredited hospitals include AL-Basheer Hospital, Zarqa Governmental Hospital, University of Jordan Hospital, Prince Hashem Military Hospital and Karak Governmental Hospital.

Bentham Open publishes a number of peer-reviewed, open access journals. These free-to-view online journals cover all major disciplines of science, medicine, technology and social sciences. Bentham Open provides researchers a platform to rapidly publish their research in a good-quality peer-reviewed journal. All peer-reviewed, accepted submissions meeting high research and ethical standards are published with free access to all.

Porto University joins Bentham Open as Institutional Member

Description:
Bentham Open is pleased to announce an Institutional Member partnership with the Porto University, Faculty of Dental Medicine (FMDUP). The partnership provides the opportunity to the researchers, from the university, to publish their research under an Open Access license with specified fee concessions. Bentham Open welcomes institutions and organizations from world over to join as Institutional Member and avail a host of benefits for their researchers.

The Porto University was founded in 1911. Porto University create scientific, cultural and artistic knowledge, higher education training strongly anchored in research, the social and economic valorization of knowledge and active participation in the progress of the communities in which it operates.

Bentham Open publishes a number of peer-reviewed, open access journals. These free-to-view online journals cover all major disciplines of science, medicine, technology and social sciences. Bentham Open provides researchers a platform to rapidly publish their research in a good-quality peer-reviewed journal. All peer-reviewed accepted submissions meeting high research and ethical standards are published with free access to all.
Join Our Editorial Board

Description:
The Open Bioinformatics Journal is an Open Access online journal, which publishes research articles, reviews, letters, case reports and guest-edited single topic issues in all areas of bioinformatics and computational biology. Bentham Open ensures speedy peer review process and accepted papers are published within 2 weeks of final acceptance.

The Open Bioinformatics Journal is committed to ensuring high quality of research published. We believe that a dedicated and committed team of editors and reviewers make it possible to ensure the quality of the research papers. The overall standing of a journal is in a way, reflective of the quality of its Editor(s) and Editorial Board and its members.

The Open Bioinformatics Journal is seeking energetic and qualified researchers to join its editorial board team as Editorial Board Members or reviewers.

The essential criteria to become Editorial Board Members of The Open Bioinformatics Journal are as follows:
1. Experience in bioinformatics and computational biology with an academic degree.
2. At least 20 publication records of articles and /or books related to the field of bioinformatics and computational biology or in a specific research field.
3. Proficiency in English language.
The Roles of Editorial Board Member are to:
1. Offer advice on journals’ policy and scope.
2. Submit or solicit at least one article for the journal annually.
3. Contribute and/or solicit Guest Edited thematic issues to the journal in a hot area (at least one thematic issue every two years).
4. Peer-review of articles for the journal, which are in the area of expertise (2 to 3 times per year).
If you are interested in becoming our Editorial Board member, please submit the following information to info@benthamopen.net. We will respond to your inquiry shortly.

Email subject: Editorial Board Member Application
1. Your name
2. Email address
3. Telephone
4. City, State, Country
5. Name of your institution
6. Department or Division
7. Website of institution
8. Your title or position
9. Your highest degree
10. Complete list of publications and h-index
11. Interested field(s)
Testimonials

"Open access will revolutionize 21^st century knowledge work and accelerate the diffusion of ideas and evidence that support just in time learning and the evolution of thinking in a number of disciplines."
. —Daniel Pesut. (Indiana University School of Nursing, USA).

"It is important that students and researchers from all over the world can have easy access to relevant, high-standard and timely scientific information. This is exactly what Open Access Journals provide and this is the reason why I support this endeavor."
. —Jacques Descotes. (Centre Antipoison-Centre de Pharmacovigilance, France).

"Publishing research articles is the key for future scientific progress. Open Access publishing is therefore of utmost importance for wider dissemination of information, and will help serving the best interest of the scientific community."
. —Patrice Talaga. (UCB S.A., Belgium).

"Open access journals are a novel concept in the medical literature. They offer accessible information to a wide variety of individuals, including physicians, medical students, clinical investigators, and the general public. They are an outstanding source of medical and scientific information."
. —Jeffrey M. Weinberg. (St. Luke's-Roosevelt Hospital Center, USA).

"Open access journals are extremely useful for graduate students, investigators and all other interested persons to read important scientific articles and subscribe scientific journals. Indeed, the research articles span a wide range of area and of high quality. This is specially a must for researchers belonging to institutions with limited library facility and funding to subscribe scientific journals."
. —Debomoy K. Lahiri. (Indiana University School of Medicine, USA).

"Open access journals represent a major break-through in publishing. They provide easy access to the latest research on a wide variety of issues. Relevant and timely articles are made available in a fraction of the time taken by more conventional publishers. Articles are of uniformly high quality and written by the world's leading authorities."
. —Robert Looney. (Naval Postgraduate School, USA).

"Open access journals have transformed the way scientific data is published and disseminated: particularly, whilst ensuring a high quality standard and transparency in the editorial process, they have increased the access to the scientific literature by those researchers that have limited library support or that are working on small budgets."
. —Richard Reithinger. (Westat, USA).

"Not only do open access journals greatly improve the access to high quality information for scientists in the developing world, it also provides extra exposure for our papers."
. —J. Ferwerda. (University of Oxford, UK).

"Open Access 'Chemistry' Journals allow the dissemination of knowledge at your finger tips without paying for the scientific content."
. —Sean L. Kitson. (Almac Sciences, Northern Ireland).

"In principle, all scientific journals should have open access, as should be science itself. Open access journals are very helpful for students, researchers and the general public including people from institutions which do not have library or cannot afford to subscribe scientific journals. The articles are high standard and cover a wide area."
. —Hubert Wolterbeek. (Delft University of Technology, The Netherlands).

"The widest possible diffusion of information is critical for the advancement of science. In this perspective, open access journals are instrumental in fostering researches and achievements."
. —Alessandro Laviano. (Sapienza - University of Rome, Italy).

"Open access journals are very useful for all scientists as they can have quick information in the different fields of science."
. —Philippe Hernigou. (Paris University, France).

"There are many scientists who can not afford the rather expensive subscriptions to scientific journals. Open access journals offer a good alternative for free access to good quality scientific information."
. —Fidel Toldrá. (Instituto de Agroquimica y Tecnologia de Alimentos, Spain).

"Open access journals have become a fundamental tool for students, researchers, patients and the general public. Many people from institutions which do not have library or cannot afford to subscribe scientific journals benefit of them on a daily basis. The articles are among the best and cover most scientific areas."
. —M. Bendandi. (University Clinic of Navarre, Spain).

"These journals provide researchers with a platform for rapid, open access scientific communication. The articles are of high quality and broad scope."
. —Peter Chiba. (University of Vienna, Austria).

"Open access journals are probably one of the most important contributions to promote and diffuse science worldwide."
. —Jaime Sampaio. (University of Trás-os-Montes e Alto Douro, Portugal).

"Open access journals make up a new and rather revolutionary way to scientific publication. This option opens several quite interesting possibilities to disseminate openly and freely new knowledge and even to facilitate interpersonal communication among scientists."
. —Eduardo A. Castro. (INIFTA, Argentina).

"Open access journals are freely available online throughout the world, for you to read, download, copy, distribute, and use. The articles published in the open access journals are high quality and cover a wide range of fields."
. —Kenji Hashimoto. (Chiba University, Japan).

"Open Access journals offer an innovative and efficient way of publication for academics and professionals in a wide range of disciplines. The papers published are of high quality after rigorous peer review and they are Indexed in: major international databases. I read Open Access journals to keep abreast of the recent development in my field of study."
. —Daniel Shek. (Chinese University of Hong Kong, Hong Kong).

"It is a modern trend for publishers to establish open access journals. Researchers, faculty members, and students will be greatly benefited by the new journals of Bentham Science Publishers Ltd. in this category."
. —Jih Ru Hwu. (National Central University, Taiwan).

RESEARCH ARTICLE

Mathematical Model of the Process of Ultrasonic wave Propagation in a Relax Environment with its Given Profiles at three Time Moments

Article Information

Identifiers and Pagination:

Article History:

Article Metrics

CrossRef Citations:

Total Statistics:

Unique Statistics:

Abstract

Objective:

Methods:

Results:

Conclusion:

Track Your Manuscript

Published Contents

About the Editor

About the Journal

The Open Bioinformatics Journal

Press Release

Bentham Open Welcomes Sultan Idris University of Education (UPSI) as Institutional Member

Ministry Of Health, Jordan joins Bentham Open as Institutional Member

Porto University joins Bentham Open as Institutional Member

Join Our Editorial Board

Testimonials