Advanced calculus in R^n

The Numerical Solution of Parabolic and Elliptic Differential Equations

Assalamu’alaikum Wr. Wb. and Greetings.I am pleased and honored to welcome you at the First International Conference on Computer Science and Applied Mathematic (ICCSAM 2018), which was held this year by AMIK and STIKOM Tunas Bangsa Pematangsiantar in collaboration with the Indonesian Computer and Information Professional Association (IPKIN), Indonesian Mathematical Society (INDOMS) and Bank Muamalat. As Chair of the Foundation, I would like to convey a greeting Welcome to Parapat City Lake Toba to presenters from various countries and especially those I respect for the presence of scientists in the field of Computer and Mathematical Sciences and industry practitioners in the 2018 ICCSAM event.I see that this activity is designed to enhance the exchange of knowledge and new discoveries in computer science and mathematics and related fields in industry. I hope that scientists in the field of computer science and mathematics and those who work in the industry can share knowledge and work together as a team that has mutual relations with each other. I am very pleased to say that the theme of this conference, “Advancing Computability Innovation” is very much in line with the objectives of AMIK and STIKOM conferences and missions, namely “to become a Science and Technology based Study Program that meets industrial needs and functions as a research center in Information Data Science. The conference was held in response to output and aoutcame which had a significant contribution in the field of computer science and mathematics as an inseparable unit of science towards the development of local and global industries. It is our happiness and honor to welcome distinguished professors present to convey their expertise at this conference.I hope this meeting will enable the development of productive dialogue between participants from various countries. They also provide invaluable opportunities for networking among participants, institutions and industries. I also hope that diversity in these fields can reveal more opportunities for researchers and practitioners from all over the world to start a lot of research related to the industry in the future.I would like to congratulate AMIK and STIKOM Tunas Bangsa for starting this conference with a synergistic contribution from dedicated partners namely the USU Faculty of Mathematics and Natural Sciences, USU’s Faculty of Computer and Information Technology, the Indonesian Computer and Informatics Professional Association (IPKIN), Indonesian Mathematical Society (INDOMS), Bank Muamalat, Malaysia Pahang University (UMP), University of Essex, United Kingdom, Ankara, Turkey and Institute of Applied Mathematics Middle East Technical University to all delegates for their full support, cooperation and contribution to the 2018 ICCSAM. I also want to thank the Organizing Committee for their perseverance and extraordinary efforts. Various sponsors are also rewarded for their contributions. I really hope that all participants will get a pleasant stay here at NIAGARA HOTEL and bring back unforgettable experiences and valuable knowledge from this conference.Thanks.H. Ahmad Ridwansyah Putra

The division of inheritance it refers to the verses of inheritance turns out to date still leaves unresolved problems, such as the 2: 1 division between men and women who are considered gender biased. According Syahrur, inheritance legislation is time to change. Syahrur uses various methods in studying Islamic inheritance law, such as mathematical theory with reference to Newton's mathematical analysis theory. By the method of mathematical analysis, Syahrur formulated the boundaries of Allah's law which is termed with The Theory Of Limit. In thistheory, there is an understanding of the limits of Allah's provisions that should not be violated, but within it there is a flexible area of ijtihad. According to him, QS. AnNisa 'verse 11 which explains the male's doubling part is the maximum and can not be added, while the woman is the minimum limit, so under certain circumstances a woman potentially has more share. The Limit Theory intends to state that the Qur'anic verse, always relevant to every situation and condition, and Islam is the last and universal religion directed to all mankind.

The global Riemann problem for a nonstrictly hyperbolic system of conservation laws modeling polymer flooding is solved. In particular, the system contains a term that models adsorption effects.

An Algorithm for Least-Squares Estimation of Nonlinear Parameters

Typically in electrical engineering a network modelling approach for the simulation of devices and their surrounding circuitry is taken, where each device is considered by a voltage-to-current relation. For some applications, however, this simplification does not yield the required accuracy. In these cases, refined modelling can be performed, where a spatially distributed partial differential equation modelling the required physical quantity is coupled to the classic network equations. The resulting coupled system of equations often exhibits a multiscale, multirate and even multiphysical behaviour that is tackled with involved algorithms so as to efficiently simulate it. Its structural analysis is therefore important, to numerically treat the system appropriately and to ensure that the algorithms converge properly. This thesis deals with the mathematical analysis of these type of systems as well as their simulation. The systems of equations obtained from circuits with semidiscrete refined models are typically differential algebraic equations. Their numerical and analytical difficulties is studied in the context of their differential algebraic index. For that, three generalised circuit element definitions are given, that allow the classification of the refined models. Hereby, the index of the entire coupled system can be specified by means of topological properties of the circuit. Several approximations to Maxwell’s equations are classified with the generalised element definitions to obtain the index properties of the field-circuit coupled systems. For the simulation two algorithms are studied. First the co-simulation waveform relaxation method is analysed for field-circuit coupled systems arising from magnetoquasistatic fields with eddy current effects on superconducting coils. The convergence of the algorithm is sped up by means of optimised Schwarz methodologies. Here, the information exchange between both subsystems is improved by a linear combination of the coupling conditions. To further speed up simulation time, the parallel-in-time method Parareal is analysed. The algorithm is investigated in the context of differential algebraic equations by studying its applicability to nonlinear higher index systems arising e.g. from circuit simulation. Finally, two approaches are proposed for the combination of Parareal and waveform relaxation. One of them is specifically designed for field-circuit coupled systems and yields a micro-macro-like Parareal algorithm. However, the idea behind it can be applied to other type of coupled systems. Numerical tests of field-circuit coupled systems are made to underline the results obtained from the mathematical theory as well as test the efficiency of the proposed algorithms.

possesses properties (1.1), (1.2), and (1.3). In order to find the joint probability density function of (yo, yi , , yn), or of any n + 1 successive variates, it is necessary to invert the matrix Tn . In this paper, we derive an exact recursive procedure for the numerical inversion of an arbitrary positive definite Toeplitz matrix of finite order, which takes full advantage of the strong restrictions placed on its elements by (1.1), (1.2), and (1.3). The number of multiplications required for the inversion of an nth order Toeplitz matrix, using this procedure, is proportional to n2, rather than to n', as in the case of methods which are suitable for arbitrary Hermitian matrices. To the author's knowledge, this inversion algorithm is the first to be specifically designed to take advantage of the peculiar simplicity of the general Toeplitz matrix. In addition, the closing section of the paper is devoted to a statement of an algorithm for the inversion of lnon-Hernmitian matrices of the form (1.1).

A very general set of orthogonal polynomials with five free parameters is given explicitly, the orthogonality relation is proved and the three term recurrence relation is found.

Motivation Only 27% of computer and mathematical scientists in the United States and 18% of IT specialists in Europe are women. The under-representation of women in the field of Computer Science is, among other things, influenced by stereotypes of computer scientists. These stereotypes include being male, asocial and having an (obsessive) interest in computers. Even though stereotypical beliefs can develop at an early age, research on children’s stereotypes of computer scientists is sparse and inconclusive. Objectives Stereotypes we hold can be implicit or unconscious beliefs, or explicit or conscious beliefs. In this study, we focus on children’s implicit and explicit stereotypes regarding computer scientists’ gender, social skills and interests. We also study whether explaining what a computer scientist does affects these stereotypes. Method We study the implicit stereotypes through the reduced-length Child Implicit Association Test and the explicit stereotypes through self-reported absolute and relative Likert scale questions. We gathered data on 564 children between the age of 7 and 18 who were visiting a science museum. The participants in the experiment group (n=352) watch a video of either a man or woman explaining what a computer scientist does at the start of the study. Results We found weak implicit stereotypical beliefs on computer scientists’ social skills and moderate implicit stereotypical beliefs on computer scientists’ interests. We also found explicit stereotypes on computer scientists’ gender, social skills and interests. Measuring the effects of the intervention, we found significant differences between the control and experiment group in their explicit stereotypes on computer scientists’ social skills. Discussion The amount of scientific work on children’s stereotypes regarding computer scientists is still limited. Applying the reduced-length Child Implicit Association Test to measure children’s stereotypes on computer scientists has, to our knowledge, not been done before. Understanding children’s stereotypes and how to tackle them contributes to closing the gender gap in Computer Science.

Edited by Athanasios Migdalas, Panos M. Pardalos and Sverre Story, Kluwer Academic Publishers, Dordrecht, 1997, 585 pp., ISBN 0-7923-4583-5, $319.50 These two books, which have been published in almost the same time, are addressed to a relatively large audience. They may be of interest to people working on parallel optimization algorithms. The first book, in particular, may be of interest to readers involved in the real-life applications of optimization modeling. In addition, operations research and computer science students may benefit from them. Both books may be used as textbooks for graduate courses in those specializations. However, some background in mathematical analysis is necessary as the introductory requirement. In my opinion, those two books together constitute an ostensible state-of-the-art summary of parallel optimization. Book by Censor and Zenios is much more consistent and homogeneous and contains, among others, description of a relatively new approach based on the generalized projections. The second book is very carefully edited and contains the set of separate although well selected papers. The first book is devoted to a very important question how to use parallelism when solving large-scale optimization models. The authors consider two main approaches. The first, a relatively new one, relies on the sequential orthogonalization and its generalization based on the generalized Bregman's projections. Algorithms belonging to that group facilitate parallel computations due to the structure of their operations. The second approach exploits the structure of the model and some sparsity patterns often existing in the large-scale optimization models. Such structures arise, for instance, in a natural way in large spatial systems (in transportation or telecommunication problems). The authors have investigated decomposition algorithms based on the linearization or diagonal-quadratic approximations. In that way, they have obtained an algorithm with relatively simple coordinating (master) problem. Their third attempt to parallelize optimization algorithms concerns the primal-dual path-following algorithm (an example of the interior point algorithms). All interior point methods require at each step solution of a linear system of equations involving matrix AA T where A represents the linear constraints matrix in the linear or quadratic programming problem in question. The authors have shown how to exploit sparsity solving that system of linear equations in parallel. The book is a nice combination of a sound mathematical theory and applications. Part one of the book is devoted to the theory of generalized distances and projections and their use in proximal minimization applied to linear programming problems. It contains also some elements of penalty, barrier and augmented Lagrangian methods theory. Second part describes iterative projections algorithms, model decomposition algorithms and interior point algorithms developed on the theoretical basis from part one. Third part presents optimization models for such problems as matrix estimation problem, image recognition from projections, treatment planning in the radiation therapy, multicommodity network flow problems, planning under uncertainty. At the end, the reader finds discussion of the implementation issues and cited results of computations. The second book is in some sense complementary to the first one. Its range stretches from the theoretical models for parallel algorithms design and their complexity, vie of parallel computers through eyes of an experienced programmer, through sparse linear systems arising in various optimization problems. It contains even a paper devoted to the variational inequalities problem. However, it does not even touch optimization modeling and real life applications. This last feature is the strongest merit of the book written by Censor and Zenios, whose first theoretical part of the book is motivated by the applications considered in part two. Book edited by Migdalas, Pardalos and Story covers broader scope of optimization algorithms. For instance, discrete and stochastic optimization problems and variational inequalities, which are not represented in the first book (restricted practically to the linearly constrained continuous optimization problems). The first two chapters discuss the theoretical model for parallel algorithm design and for their complexity. Third chapter presents a survey on current high performance parallel computer architectures and discusses their performance bottlenecks. Fourth chapter is devoted to scalable parallel algorithms for sparse linear systems and the fifth one investigates automatic parallelization of the computation of the ordinary differential equations systems arising in the 2D-bearing mechanical problem. The next eight chapters are devoted to the optimization problems and methods. Chapter six contains a survey of parallel algorithms for network problems and a thorough discussion of the implementation of a parallel solver for the traffic assignment problem. In chapter seven one finds review on the sequential branch and bound method and a discussion of the problems connected with its parallelization. Chapter eight presents parallelizaton of heuristic methods for combinatorial optimization. Chapter nine contains analysis of decomposition algorithms for differentiable optimization. Chapter ten describes parallel algorithms for finite dimensional variational inequalities and chapter eleven parallel algorithms for stochastic programming. Chapter twelve deals with the heuristic algorithms for global optimization problems while chapter thirteen presents logarithmic barrier function algorithms for neural network training. The first book, in my opinion, would be a valuable supplement to a private library of any person, student, researcher or practitioner interested in operations research and various aspects of parallel optimization. The second book is almost four times as expensive as the first one. In my opinion, its content does not justify such big difference in price. Especially, since approximately one-third of its material may be found in general, much cheaper books on parallel computing.. Andrzej Stachurski Technical University of Warsaw

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients

Next article Singular Perturbation Theory and GeophysicsG. F. CarrierG. F. Carrierhttps://doi.org/10.1137/1012041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] W. Eckhaus and , E. M. de Jager, Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type, Arch. Rational Mech. Anal., 23 (1966), 26–86 10.1007/BF00281135 MR0206464 0151.15101 CrossrefISIGoogle Scholar[2] A. B. Vasil'eva, Asymptotic behaviour of solutions of certain problems for ordinary non-linear differential equations with a small parameter multiplying the highest derivatives, Uspehi Mat. Nauk, 18 (1963), 15–86, Russian Math. Surveys, 18 (1963), no. 3 MR0158137 0135.14001 Google Scholar[3] G. F. Carrier and , C. E. Pearson, Ordinary Differential Equations, Blaisdell, New York, 1968 0165.40601 Google Scholar[4] A. R. Robinson, The Wind Driven Ocean Circulation, Blaisdell, New York, 1963 Google Scholar[5] S. F. Feshchenko, , N. I. Shkil and , L. D. Nīkolenko, Asymptotic methods in the theory of linear differential equations, Translated from the Russian by Scripta Technica, Inc. Translation editor, Herbert Eagle. Modern Analytic and Computational Methods in Science and Mathematics, No. 10, American Elsevier Publishing Co., Inc., New York, 1967xvi+270 MR0221029 0153.40501 Google Scholar[6] S. Kaplun, Fluid mechanics and singular perturbations: A collection of papers by Saul Kaplun, Edited by Paco A. Lagerstrom, Louis N. Howard and Ching-shi Lin, Academic Press, New York, 1967xii+369 MR0214326 Google Scholar[7] Wolfgang Wasow, Asymptotic expansions for ordinary differential equations, Pure and Applied Mathematics, Vol. XIV, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1965ix+362 MR0203188 0133.35301 Google Scholar[8] R. E. O'Malley, Jr., Topics in singular perturbations, Advances in Mathematics, Vol. 2, Academic Press, New York, 1968, 365–470 Google Scholar[9A] L. E. Fraenkel, On the method of matched asymptotic expansions. I. A matching principle, Proc. Cambridge Philos. Soc., 65 (1969), 209–231 MR0237898 0187.24104 CrossrefISIGoogle Scholar[9B] L. E. Fraenkel, On the method of matched asymptotic expansions. II. Some applications of the composite series, Proc. Cambridge Philos. Soc., 65 (1969), 233–261 MR0237899 0187.24104 CrossrefISIGoogle Scholar[9C] L. E. Fraenkel, On the method of matched asymptotic expansions. III. Two boundary-value problems, Proc. Cambridge Philos. Soc., 65 (1969), 263–284 MR0237900 0187.24104 CrossrefISIGoogle Scholar[10] W. E. Exkhaus, On the foundations of the method of matched asymptotic approximationsMathematisch Instituut der Technische Hogeschool, Delft, Nederland, 1968 Google Scholar[11] Julian D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Co. 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Greenspan, The Theory of Rotating Fluids, Cambridge University Press, Cambridge, 1968 0182.28103 Google Scholar Next article FiguresRelatedReferencesCited byDetails A Numerical Approach for Singularly Perturbed Nonlinear Delay Differential Equations Using a Trigonometric SplineComputational and Mathematical Methods, Vol. 2022 Cross Ref A System of Singularly Perturbed Periodic Boundary Value Problem: Hybrid Difference Scheme28 May 2020 | International Journal of Applied and Computational Mathematics, Vol. 6, No. 3 Cross Ref A Numerical Technique for Solving Nonlinear Singularly Perturbed Delay Differential Equations12 February 2018 | Mathematical Modelling and Analysis, Vol. 23, No. 1 Cross Ref Analysis of Carrier's ProblemS. J. Chapman and P. E. Farrell13 June 2017 | SIAM Journal on Applied Mathematics, Vol. 77, No. 3AbstractPDF (4863 KB)Applications11 November 2014 Cross Ref Geometrical effects on western intensification of wind-driven ocean currents: The rotated-channel Stommel model, coastal orientation, and curvatureDynamics of Atmospheres and Oceans, Vol. 65 Cross Ref Two-Timing, Geometric, and Multi-scale Methods6 October 2014 Cross Ref Uniform asymptotic expansions of solutions of an inhomogeneous equationJournal of Differential Equations, Vol. 253, No. 3 Cross Ref Uniformly convergent second-order difference scheme for a singularly perturbed periodical boundary value problemInternational Journal of Computer Mathematics, Vol. 88, No. 1 Cross Ref Shallow-Water Equations and Related Topics Cross Ref On the Number of Solutions to Carrier's ProblemStudies in Applied Mathematics, Vol. 120, No. 3 Cross Ref Multi-bump solutions to Carrier's problemJournal of Mathematical Analysis and Applications, Vol. 277, No. 2 Cross Ref Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform GridsJournal of Optimization Theory and Applications, Vol. 114, No. 3 Cross Ref Numerical Solution of Singularly Perturbed Non-Linear Two Point Boundary Value Problems by Spline in Compression15 September 2010 | International Journal of Computer Mathematics, Vol. 79, No. 2 Cross Ref A Singular Perturbation Problem of Carrier and PearsonJournal of Mathematical Analysis and Applications, Vol. 255, No. 2 Cross Ref Parallel initial-value algorithms for singularly perturbed boundary-value problemsJournal of Optimization Theory and Applications, Vol. 73, No. 3 Cross Ref Numerical solution of second-order nonlinear singularly perturbed boundary-value problems by initial-value methodsJournal of Optimization Theory and Applications, Vol. 73, No. 2 Cross Ref The Quasi-Steady-State Assumption: A Case Study in PerturbationLee A. Segel and Marshall Slemrod18 July 2006 | SIAM Review, Vol. 31, No. 3AbstractPDF (3028 KB)Collocation for Singular Perturbation Problems III: Nonlinear Problems without Turning PointsU. Ascher and R. Weiss14 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 5, No. 4AbstractPDF (2185 KB)A Hybrid Asymptotic-Finite Element Method for Stiff Two-Point Boundary Value ProblemsR. C. Y. Chin and R. Krasny14 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 4, No. 2AbstractPDF (1502 KB)Singular Perturbation Techniques: A Comparison of the Method of Matched Asymptotic Expansions with that of Multiple ScalesDavid J. Wollkind18 July 2006 | SIAM Review, Vol. 19, No. 3AbstractPDF (1331 KB)Oceanic Morphogenesis Cross Ref The flow past a fixed sphere in a slowly rotating viscous fluidZeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 26, No. 4 Cross Ref The Multivariable Method in Singular Perturbation AnalysisDonald R. Smith18 July 2006 | SIAM Review, Vol. 17, No. 2AbstractPDF (4288 KB)A comparison of some numerical methods for two-point boundary value problems1 January 1974 | Mathematics of Computation, Vol. 28, No. 127 Cross Ref Applications of the Maximum Principle to Singular Perturbation ProblemsF. W. Dorr, S. V. Parter, and L. F. Shampine18 July 2006 | SIAM Review, Vol. 15, No. 1AbstractPDF (2993 KB)Multiple Asymptotic Expansions and Singular ProblemsKenneth D. Shere17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 3, No. 2AbstractPDF (649 KB)A collocation method for boundary value problemsNumerische Mathematik, Vol. 19, No. 1 Cross Ref Regular and singular perturbation expansions in the analysis of extensional vibrations of platesJournal of Sound and Vibration, Vol. 15, No. 4 Cross Ref Volume 12, Issue 2| 1970SIAM Review History Submitted:22 October 1969Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1012041Article page range:pp. 175-193ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

It is shown that when differencing analytic functions using the pseudospectral Fourier or Chebyshev methods, the error committed decays to zero at an exponential rate.

Relevance and expediency of introduction of a training course of computer mathematics for students of “Secondary Education (Computer Science)” is caused by necessity of use of computer equipment with the corresponding software almost in all areas of human activity; the fact that computer mathematics is one of priority directions of research work both in the field of mathematical sciences, and in the field of computer science. Computer mathematics is a field of applied computer science in which problems of development, implementation and use of information technologies for solving mathematical problems are studied. The purpose of teaching computer mathematics is to study and use computer mathematics systems by students to solve applied problems; to master the conceptual and terminological base of modern computer science as a fundamental science; to master theoretical fundamentals of computer science related to formal systems, knowledge bases and models of their representation, models and algorithms of decision making. Formulation of the problem. The study of computer mathematics by future computer science teachers and the use of modern systems of computer mathematics to solve applied problems, creates their system of professional competencies, in particular, informatics competencies in computer mathematics, informatics and mathematical competencies and skills to use modern information technology to analyze mathematical models of processes and phenomena from a variety of fields of knowledge and human activities. Materials and methods. To achieve this goal, the following research methods were used: analysis of scientific and pedagogical literature on the research topic; analysis of curricula, work programs and manuals on the subject "Computer Mathematics"; empirical methods (questionnaire, conversation, pedagogical observation, modeling). Results. This paper has built the model of building informatics competence within the professional competence of the future computer science teacher at the expense of integration of mathematical and information knowledge on the basis of mathematical modeling in environments of systems of computer mathematics, as these systems are an effective means of realization of inter-subject connections of computer science with other subjects of a natural-mathematical cycle. Conclusions. The study of "Computer Mathematics" courses by future computer science teachers, using computer mathematics systems, contributes to the formation of components of the information competence system in the field of information, mathematical and computer modeling.

The aim of this study was to analyze the current literature on the use of machine learning in glaucoma, comparing the characteristics and citations received by articles on computer science focus or medical focus. We performed a search using the Scopus database on 28th of January 2021 using appropriate keywords for journal articles and conference articles that discussed glaucoma in the context of machine and deep learning. We used Scopus-based field classification and compared different characteristics and citation metrics between articles classified as belonging to the computer science field, medical field, or both fields combined. A total of 858 documents resulted from the search. Upon comparing the mean citation received by publications in the computer science field and medical field, we found a significant difference (p = 0.013). The highest mean citation received was for articles in the combined fields with a mean of 26.2 (SD 41.7), and the least mean citations received by articles in computer science field with a mean of 13.7 (SD 34.6). Most articles related to machine learning assessment of glaucoma were classified as computer science articles. Articles that belong to medical or both fields combined received higher number of citations.