Applied Mathematical Sciences Research Articles

Improved rates for a space–time FOSLS of parabolic PDEs

We consider the first-order system space–time formulation of the heat equation introduced by Bochev and Gunzburger (in: Bochev and Gunzburger (eds) Applied mathematical sciences, vol 166, Springer, New York, 2009), and analyzed by Führer and Karkulik (Comput Math Appl 92:27–36, 2021) and Gantner and Stevenson (ESAIM Math Model Numer Anal 55(1):283–299 2021), with solution components (u1,u2)=(u,-∇xu)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(u_1,\ extbf{u}_2)=(u,-\ abla _\ extbf{x} u)$$\\end{document}. The corresponding operator is boundedly invertible between a Hilbert space U and a Cartesian product of L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_2$$\\end{document}-type spaces, which facilitates easy first-order system least-squares (FOSLS) discretizations. Besides L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_2$$\\end{document}-norms of ∇xu1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ abla _\ extbf{x} u_1$$\\end{document} and u2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{u}_2$$\\end{document}, the (graph) norm of U contains the L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_2$$\\end{document}-norm of ∂tu1+divxu2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial _t u_1 +{{\\,\ extrm{div}\\,}}_\ extbf{x} \ extbf{u}_2$$\\end{document}. When applying standard finite elements w.r.t. simplicial partitions of the space–time cylinder, estimates of the approximation error w.r.t. the latter norm require higher-order smoothness of u2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{u}_2$$\\end{document}. In experiments for both uniform and adaptively refined partitions, this manifested itself in disappointingly low convergence rates for non-smooth solutions u. In this paper, we construct finite element spaces w.r.t. prismatic partitions. They come with a quasi-interpolant that satisfies a near commuting diagram in the sense that, apart from some harmless term, the aforementioned error depends exclusively on the smoothness of ∂tu1+divxu2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial _t u_1 +{{\\,\ extrm{div}\\,}}_\ extbf{x} \ extbf{u}_2$$\\end{document}, i.e., of the forcing term f=(∂t-Δx)u\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f=(\\partial _t-\\Delta _x)u$$\\end{document}. Numerical results show significantly improved convergence rates.

Programmatic Strategies to Engage and Support Undergraduate Women in Applied Mathematics and Computer Science

This paper describes the implementation of a STEM scholarship program which utilized a holistic approach to providing a multi-dimensional student support system. The program has been successful in encouraging and supporting women in Applied Mathematics and Computer Science by offering a diverse suite of extracurricular opportunities, actively engaging them in organized events, research projects, and participation in STEM communities, and helping them achieve higher GPAs and shorter times to graduation. The supported women also benefitted from close mentoring relationships with the faculty mentors. The program emphasized the development of empowering settings for women’s engagement and achievement, which act to sustain and expand interest in mathematics and computing, and thereby help them to see themselves as future professionals in the field.

Use of Uncertain External Information in Statistical Estimation

Use of Uncertain External Information in Statistical Estimation by Sergey Tarima 1,* , Zhanna Zenkova 2 1 Medical College of Wisconsin, Division of Biostatistics, Institute for Health and Equity, Wauwatosa, Wisconsin, 53226, USA2 National Research Tomsk State University, Institute of Applied Mathematics and Computer Science, Tomsk, 634002, Russia * Author to whom correspondence should be

An Algebraic Specification/Schema for JSON

An Algebraic Specification/Schema for JSON by Konstantinos Barlas1,* , Petros Stefaneas2 1 Department of Informatics and Computer Engineering, University of West Attica, Athens, 12243, Greece2 School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, 15780, Greece * Author to whom correspondence should be addressed. Journal of Engineering Research and Sciences, Volume

Fundamental Approach to University Education and Training of IT Professionals

The paper is devoted to education and training of professionals in the IT field in classical universities in the context of the implementation of the Federal Project “Human Resources for the Digital Economy” of the National Program “Digital Economy of the Russian Federation”. The general approach, goals and content of fundamental education and specialized training of Bachelors, Masters and PhD-holders to complex, innovative and research activities have been determined. The structure of Bachelor, Master and PhD programs of the Institute of Applied Mathematics and Computer Science of Tomsk State University modernized on the basis of the above approach, is presented. The paper pays special attention to the training of T-Shaped specialists in IT in classical universities, dwells on the fundamental education of IT specialists. The results of the coordination of programs with employers and students are given.

Preface for International Conference on Recent Trends in Applied Research (ICoRTAR2021) Proceedings

The 2nd International Conference on Recent Trends in Applied Research (ICoRTAR2021) is a virtual conference based on enabling platforms to present research results relating to global issues. ICoRTAR2021 is hosted by ResearchAcad HUB with channels and human resources in India, Nigeria, Kenya, Mexico, Morocco, Ghana, and Cameroon. Thus, the conference was held virtually from October 08-09, 2021.The Theme of this second series (ICoRTAR2021) is ‘Effective Research Practices Amidst Covid-19 Pandemic’. ICoRTAR202 aims to bring together faculty members, leading scientists, academicians, research & graduate scholars, industrial professionals, and decision-makers to discuss current trends in research with implications on global phenomena such as COVID-19, economic growth & development, and so on. Basically, the ICORTAR2021 participants discussed extensively vital topics, recent trends, and issues in Applied Science, Mathematical Sciences, Computational Science, Engineering Science, Physics and Nanoscience, Financial Modeling, Artificial Intelligence, and Stochastic Dynamics. Five plenary sessions with different aspects of the ICORTAR2021 Theme were held successfully. The first keynote speaker, Professor Snehashish Chakraverty from the National Institute of Technology, Rourkela, INDIA, spoke on ‘Estimating Corona Positive Cases via Uncertainty Modeling.’ The second keynote speaker, Professor/Dr. Sannan khan, from the University Putra Malaysia, spoke on ‘Online Learning: A Panacea in the Time of COVID-19 Crisis.’List of editorial board/organizing committee are available in the pdf.

Applied mathematics and computer science educational program development in the context of the emerging digital economy

The article analyzes the digital part of the "Applied Mathematics and Computer Science" educational program competence model at different levels of education. The most popular competencies are identified and the digital economy competencies necessary for graduates of the educational program based on the analysis of the employers’ requirements are formulated, taking into account the level of education. The proposals for updating the educational process in applied mathematics and computer science are presented considering the current trends in the development of the digital economy.

A Statistician Teaches Deep Learning

Deep learning (DL) has gained much attention and become increasingly popular in modern data science. Computer scientists led the way in developing deep learning techniques, so the ideas and perspectives can seem alien to statisticians. Nonetheless, it is important that statisticians become involved—many of our students need this expertise for their careers. In this paper, developed as part of a program on DL held at the Statistical and Applied Mathematical Sciences Institute, we address this culture gap and provide tips on how to teach deep learning to statistics graduate students. After some background, we list ways in which DL and statistical perspectives differ, provide a recommended syllabus that evolved from teaching two iterations of a DL graduate course, offer examples of suggested homework assignments, give an annotated list of teaching resources, and discuss DL in the context of two research areas.

Self-similar Blow-Up Profiles for Slightly Supercritical Nonlinear Schrödinger Equations

We construct radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schrodinger equation $$\text {i}\partial _t u + \Delta u + |u|^{p-1}u=0$$ on $$\mathbb {R}^d$$ , close to the mass critical case and for any space dimension $$d\ge 1$$ . These profiles bifurcate from the ground-state solitary wave. The argument relies on the classical matched asymptotics method suggested in Sulem and Sulem (The nonlinear Schrodinger equation. Self-focusing and wave collapse. Applied mathematical sciences, 139, Springer, New York, 1999) which needs to be applied in a degenerate case due to the presence of exponentially small terms in the bifurcation equation related to the log–log blow-up law observed in the mass critical case.

On basic properties of relative Γ-ideals in Γ-near rings

The algebraic system Γ-near rings was introduced by Satyanarayana. Tamizh and Ganesan introduced the concept of bi-ideals in near-rings [On bi-ideals of near-rings, Indian J. Pure Appl. Math., 18(11), 1002-1005(1987)]. Tamizh and Meenakumari defined the concept of bi-ideals in Γ-near-rings and characterized Γ-near-fields [Bi-Ideals of Gamma Near-Rings, Southeast Asian Bulletin of Mathematics(2004), 27: 983-988]. Satyanarayana, Yahya, Basar and Kuncham studied abstract affine Γ-nearrings [Some Results on Abstract Affine Gamma-Near-Rings, International Journal of Pure and Applied Mathematical Sciences, 7(1) (2014), 43-49]. Recently, Basar, Satyanarayana, Kuncham, Kumar and Yahya studied some relative ideals in Γ-nearrings [A note on relative Γ-ideals in abstract affine Γ-nearrings, GIS Science Journal, 8(10)(2021), 9-13]. In this paper, we study relative quasi-Γ-ideals and relative bi-Γ-ideals in Γ-near rings. We also proved nice characterizations of Γ-near rings by these basic relative Γ-ideals.

Preface

International Conference on Recent Trends in Applied Mathematical Sciences (ICRTAMS-2020) On behalf of the organising committee, we would like to express our deep appreciation to all paper presenters, authors and participants of their participation in ICRTAMS-2020. This event was successfully organized by Arunai International Research Foundation, Department of Mathematics, University of Kerala In Association with (CERCOM) Universiti Tun Hussein Onn Malaysia on 26th and 27th September 2020, at Tiruvannamalai, Tamilnadu, India, (via online Mode)ICRTAMS-2020 is special platform that brings together researcher, engineer, and faculty of Applied Mathematical Science to discus and share the latest finding and future development in the Applied Mathematics and engineering fields, as well as collaboration Applied Mathematical research and Applied Physics. We wish ICRTAMS-2020 is filled with inspiring, mind-opening and enjoyable discoveries of latest research. We would like to thank all committee members for their valuable support and dedication in ensuring the success of ICRTAMS-2020. We should also like to thank the Keynote Speakers and reviewers for their unconditional support to assure the quality articles are produced for the IOP publications.List of titles Organizing Committee, Editorial Committee, Review Committee, Keynote Speakers, Organizing Institutions are available in the pdf

Preface

The International Conference on Mathematics & Data Science (ICMDS’20), was held on June 29-30, 2020 as a virtual conference due to the growing concerns over the coronavirus outbreak (COVID-19), and in order to protect the well-being of our attendees, partners, and staff as our number one priority. the ICMDS'20 event aims in its first edition to gather international and national researchers, interdisciplinary scientists, professors, students and professionals seeking to exchange and discuss their ideas and inspirations on Applied Mathematics and Data Science. Besides proclaiming knowledge in the fields of applied mathematics and data science, ICMDS'20 strives to promote scientific research and innovation among junior and senior researchers.This scientific event brings together more than 300 national and international researchers in mathematics and data sciences. On top of the local participants coming from different national universities, international participants are also registered from different countries, namely France, India, the United States, the Comoros, Senegal, Algeria and Iraq. The event has four plenary conferences and around 140 communications that span over four parallel sessions which are well balanced in content. At the end of the conference, 42 papers were selected to be published in the journal of physics conference series (JPCS).List of committees are available in this Pdf.

Building an Elliptic Curve Cryptography to Encode and Decode Vietnamese Texts

This article presents building an Elliptic curve cryptography and using it to encode and decode Vietnamese text. Here we have illustrated the prime number p = 151 in the future, which will use a large prime number. We consider an elliptic curve with a total score of 172 points. Encode and decode with standard Vietnamese text and combine with the special characters in ASCII code. The program is designed and installed and on the C# environment to give the correct result of the encryption algorithm.
 KeywordsData sequence, Decryption, Discrete logarithm, Elliptic curve, Elliptic curve cryptosystem, Encryption, Public key
 References[1] Koblitz, “Elliptic curve cryptosystems”, Mathematics of Computation”, 203 - 209, 1987.[2] Miller, “Uses of elliptic curves in cryptography, Advances in Cryptology - Crypto”, Lecture Notes in Computer Science, SpringerVerlag, 1986, pp. 417-426.[3] Sugantha Priya, Dr.M. Mohanraj, “A Review on Secure Elliptic Curve Cryptography (ECC) and Dynamic Secure Routing Link Path Detection Algorithm (DSRLP) Under Jamming Attack”, ISSN 68(30) (2020) 0474-9030.[4] Negin Dinarvand, Hamid Barati, “An efficient and secure RFID authentication protocol using ellipticcurvecryptography”,SpringerfScience+Business Media, LLC, 2017[5] Utku Gulen, Selcuk Baktir, “Elliptic Curve Cryptography for Wireless Sensor Networks Using the Number Theoretic Transform”, journal-sensors, Published: 9 March, 2020.[6] Sravana Kumar, C.H. Suneetha, A.R. Chandrasekh, “Encryption of Data Using Elliptic Curve Over Finite Fields”, International Journal of Distributed and Parallel Systems (IJDPS). 3(1) (2012) 301-308.[7] Amounas, E.H. El Kinani, ECC Encryption and Decryption with a Data Sequence, Applied Mathematical Sciences 6(101) (2012) 5039-5047.[8] Vu Thi Hai Ha, Dinh Thi Hang, Bui Dang Binh, “The influence of volume on the formant of vowels and the identification of Vietnamese speakers”, Vietnam Institute of Linguistics, 2015.[9] Enge, “Elliptic curves and their applications to cryptography”, Norwell, MA: Kulwer Academic publishers, 1999.[10] Neil Koblitz, “An Elliptic Curve implementation of the finite field digital signature algorithm”, in Advances in cryptology,(CRYPTO 1998), SpringerLecture Notes in computer science, 1462 (1998) 327-337.[11] S. Sandeep, Kumar, “Elliptic curve cryptography for constrained devices”, PhD thesis, Ruhr-University Bochum, June, 2006.

Experience in Teaching Mathematical Disciplines Using E-learning and Distance Learning Technologies during the COVID-19 Pandemic

The experience of e-learning (EL) with distance learning technologies (DLT) implementing for teaching of Numerical in the Mathematics and Computer Science department of V.I. Vernadsky Crimean Federal University during COVID-19 pandemic period from March to May 2020 is studied in the article. 107 students from third course that learn in the direction of 01.03.01 Mathematics, 01.03.02 Applied Mathematics and Computer science, 01.03.04 Applied Mathematics are participated in the experiment. As the main platform, the social network VKontakte (VK) with Discord, Youtube and HP Reveal platforms are used. The author's video lecture is the main type of educational content in the developed e-learning model. The students feedback is realized through discussion in the text and voice chats, video presentations of programming code for numerical methods realization, the tasks results demonstration in hand-written form (photo of problems decision) or in print format, in screenshots or video explanations including elements of the augmented reality technologies. The effectiveness of the developed methodological approach is confirmed by the results of students questionnaires (81,7% of the students that participate in the anonymous questionnaire estimate the quality of the numerical methods teaching as excellent) and the academic performance growth based on the tests results using the peer review method (the growth of the academic performance on average is 32,2%). It is confirmed that for e-learning organizing for mathematical disciplines teaching in the educational process planning, training contents and tests preparing the teachers need to use the interactive learning and multimodality principles, as well as web accessibility requirements. The best method of new learning content presentation is the author's screencast video lecture (the choice of 83,7% students) accompanied with subtitles and detailed explanations of the lecturer (audio descriptions) and text analogue (the lecture notes or verbatim report). The new e-learning model can be transferred to the MOOC format without significant logical changes or time costs.

A Conversation about COVID-19 with Economists, Sociologists, Statisticians, and Operations Researchers

The COVID-19 pandemic is causing economic and social change. Moderated by David Banks, the Director of the Statistical and Applied Mathematical Sciences Institute (SAMSI), six eminent scientists who study different aspects of social change and public policy came together to discuss the impacts of the COVID-19 pandemic on the U.S. and the world. The discussion took a range of quantitative perspectives on how to respond to the crisis and to forecast what challenges lie ahead. Specific topics include the role of data science, strategies for beginning to reopen the economy, the international impact of the disease, and its effect upon universities.

A Conversation about COVID-19 with Biostatisticians and Epidemiologists

The COVID-19 pandemic is an almost unprecedented challenge. Moderated by David Banks, Director of the Statistical and Applied Mathematical Sciences Institute (SAMSI), five leading biostatisticians and epidemiologists discuss the probable scope and duration of the pandemic, the kinds of medical responses that we need, and some of the impacts they foresee on the U.S. and on the world. They also discuss the pandemic’s likely effect on higher education.

Dynamics of G-processes

A G-process is briefly a process ([A. N. Carvalho, J. A. Langa and J. C. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Applied Mathematical Sciences, Vol. 182 (Springer, 2013)], [C. M. Dafermos, An invariance principle for compact processes, J. Differential Equations 9 (1971) 239–252], [P. E. Kloeden and M. Rasmussen, Nonautonomous Dynamical Systems, Mathematical Surveys and Monographs, Vol. 176 (Amer. Math. Soc., 2011)]) for which the role of evolution parameter is played by a general topological group [Formula: see text]. These processes are broad enough to include the [Formula: see text]-actions (characterized as autonomous [Formula: see text]-processes) and the two-parameter flows (where [Formula: see text]). We endow the space of [Formula: see text]-processes with a natural group structure. We introduce the notions of orbit, pseudo-orbit and shadowing property for [Formula: see text]-processes and analyze the relationship with the [Formula: see text]-processes group structure. We study the equicontinuous [Formula: see text]-processes and use it to construct nonautonomous [Formula: see text]-processes with the shadowing property. We study the global solutions of the [Formula: see text]-processes and the corresponding global shadowing property. We study the expansivity (global and pullback) of the [Formula: see text]-processes. We prove that there are nonautonomous expansive [Formula: see text]-processes and characterize the existence of expansive equicontinuous [Formula: see text]-processes. We define the topological stability for [Formula: see text]-processes and prove that every expansive [Formula: see text]-process with the shadowing property is topologically stable. Examples of nonautonomous topologically stable [Formula: see text]-processes are given.

A tutorial review of mathematical techniques for quantifying tumor heterogeneity.

Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at https://github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.

YSTEM OF COMPILING TESTS FOR ESP STUDENTS’ READING COMPETENCE ASSESSMENT AND METHODS OF THEIR APPLICATION

The article depicts various types of reading used at ESP lessons as well as the aims and the necessity of using evaluation system for the reading skill. As teaching ESP, students are implied working with texts most of the time of the lesson. Therefore, the developing students’ reading competence becomes vital. This denotes the usage of adequate evaluation system for ESP students’ reading skills. Moreover, based on ESP materials and taking into account different reading techniques various evaluation students’ foreign language reading competence techniques are described as well. Hence, to help teachers in compiling and using appropriate reading tests, some criteria for defining the level of ESP students’ reading competence and test designing are described with the examples of reading test exercises. Methods, described in the article, provide the reader with the information when and how to use the assessment material: at the beginning, in the middle or at the end of the course depending on the aims the teacher is targeting at. In addition, the article covers practical test results used at ESP lesson for the students of “Psychology” and “Applied Mathematics and Computer Science” faculties. Everything touched in the article could be valuable for other ESP teachers and scholars to implement in their further work with their students.

Highlights of the Inaugural Data Science Leadership Summit

On March 26, 2018, the Data Science Institute at Columbia University <https://datascience.columbia.edu/> hosted the inaugural Data Science Leadership Summit. It drew together a cross-section of academic researchers and administrators to discuss how university practices could best adapt to the emerging field of data science. The summit was co-funded by the National Science Foundation, the Gordon and Betty Moore Foundation, and the Alfred P. Sloan Foundation. This interview with Jeannette Wing, the Avanessians Director of the Data Science Institute at Columbia University and the author of The Data Life Cycle <https://hdsr.mitpress.mit.edu/pub/577rq08d> , discusses the motivation of the summit and summarizes its key findings. The interview was conducted by another experienced leader in data science, David Banks, the Director of the Statistical and Applied Mathematical Sciences Institute (SAMSI). <https://www.samsi.info/people/staff/> Keywords: data science institute, education units, inter-disciplinary, multi-disciplinary, university administration