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Sample records for single ordinary differential

  1. Solving Ordinary Differential Equations

    Science.gov (United States)

    Krogh, F. T.

    1987-01-01

    Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

  2. Introduction to ordinary differential equations

    CERN Document Server

    Rabenstein, Albert L

    1966-01-01

    Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutio

  3. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  4. Dichotomies for generalized ordinary differential equations and applications

    Science.gov (United States)

    Bonotto, E. M.; Federson, M.; Santos, F. L.

    2018-03-01

    In this work we establish the theory of dichotomies for generalized ordinary differential equations, introducing the concepts of dichotomies for these equations, investigating their properties and proposing new results. We establish conditions for the existence of exponential dichotomies and bounded solutions. Using the correspondences between generalized ordinary differential equations and other equations, we translate our results to measure differential equations and impulsive differential equations. The fact that we work in the framework of generalized ordinary differential equations allows us to manage functions with many discontinuities and of unbounded variation.

  5. Schwarz maps of algebraic linear ordinary differential equations

    Science.gov (United States)

    Sanabria Malagón, Camilo

    2017-12-01

    A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

  6. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  7. Design of TIR collimating lens for ordinary differential equation of extended light source

    Science.gov (United States)

    Zhan, Qianjing; Liu, Xiaoqin; Hou, Zaihong; Wu, Yi

    2017-10-01

    The source of LED has been widely used in our daily life. The intensity angle distribution of single LED is lambert distribution, which does not satisfy the requirement of people. Therefore, we need to distribute light and change the LED's intensity angle distribution. The most commonly method to change its intensity angle distribution is the free surface. Generally, using ordinary differential equations to calculate free surface can only be applied in a point source, but it will lead to a big error for the expand light. This paper proposes a LED collimating lens based on the ordinary differential equation, combined with the LED's light distribution curve, and adopt the method of calculating the center gravity of the extended light to get the normal vector. According to the law of Snell, the ordinary differential equations are constructed. Using the runge-kutta method for solution of ordinary differential equation solution, the curve point coordinates are gotten. Meanwhile, the edge point data of lens are imported into the optical simulation software TracePro. Based on 1mm×1mm single lambert body for light conditions, The degrees of collimating light can be close to +/-3. Furthermore, the energy utilization rate is higher than 85%. In this paper, the point light source is used to calculate partial differential equation method and compared with the simulation of the lens, which improve the effect of 1 degree of collimation.

  8. Monograph - The Numerical Integration of Ordinary Differential Equations.

    Science.gov (United States)

    Hull, T. E.

    The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…

  9. Ordinary differential equations with applications in molecular biology.

    Science.gov (United States)

    Ilea, M; Turnea, M; Rotariu, M

    2012-01-01

    Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances

  10. Inverse problems in ordinary differential equations and applications

    CERN Document Server

    Llibre, Jaume

    2016-01-01

    This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.

  11. Numerical analysis of systems of ordinary and stochastic differential equations

    CERN Document Server

    Artemiev, S S

    1997-01-01

    This text deals with numerical analysis of systems of both ordinary and stochastic differential equations. It covers numerical solution problems of the Cauchy problem for stiff ordinary differential equations (ODE) systems by Rosenbrock-type methods (RTMs).

  12. Ordinary differential equations

    CERN Document Server

    Cox, William

    1995-01-01

    Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further

  13. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

    Institute of Scientific and Technical Information of China (English)

    WANG; Shunjin; ZHANG; Hua

    2006-01-01

    The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.

  14. Ordinary differential equation for local accumulation time.

    Science.gov (United States)

    Berezhkovskii, Alexander M

    2011-08-21

    Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

  15. A Unified Introduction to Ordinary Differential Equations

    Science.gov (United States)

    Lutzer, Carl V.

    2006-01-01

    This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

  16. FORSIM, Solution of Ordinary or Partial Differential Equation with Initial Conditions

    International Nuclear Information System (INIS)

    Carver, M.B.

    1985-01-01

    1 - Description of problem or function: FORSIM is a FORTRAN oriented simulation program which automates the continuous transient solution of systems of ordinary and/or partial differential equations. The user writes his equations in a FORTRAN subroutine, following prescribed rules, and loads this routine along with the executive routines. The executive routines then read in initial data supplied by the user and proceed with the integration. 2 - Method of solution: Partial differential equations are converted to coupled ordinary differential equations by suitable discretization formulae. Integration is done by variable order, variable step-size error controlled algorithms. 3 - Restrictions on the complexity of the problem - Maximum of: 1000 ordinary differential equations

  17. Differential equation analysis in biomedical science and engineering ordinary differential equation applications with R

    CERN Document Server

    Schiesser, William E

    2014-01-01

    Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-worldODE problems that are found in a variety of fields, including chemistry, physics, biology,and physiology. The book provides readers with the necessary knowledge to reproduce andextend the comp

  18. A course in ordinary differential equations

    CERN Document Server

    Swift, Randall J

    2014-01-01

    Praise for the First Edition:"A Course in Ordinary Differential Equations deserves to be on the MAA's Basic Library List … the book with its layout, is very student friendly-it is easy to read and understand; every chapter and explanations flow smoothly and coherently … the reviewer would recommend this book highly for undergraduate introductory differential equation courses." -Srabasti Dutta, College of Saint Elizabeth, MAA Online, July 2008"An important feature is that the exposition is richly accompanied by computer algebra code (equally distributed between MATLAB, Mathematica, and Maple). The major part of the book is devoted to classical theory (both for systems and higher order equations). The necessary material from linear algebra is also covered. More advanced topics include numerical methods, stability of equilibria, bifurcations, Laplace transforms, and the power series method."-EMS Newsletter, June 2007"This is a delightful textbook for a standard one-semester undergraduate course in ordinary d...

  19. A textbook on ordinary differential equations

    CERN Document Server

    Ahmad, Shair

    2015-01-01

    This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, whic...

  20. Ordinary differential equations introduction to the theory of ordinary differential equations in the real domain

    CERN Document Server

    Kurzweil, J

    1986-01-01

    The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Car

  1. Time-course window estimator for ordinary differential equations linear in the parameters

    NARCIS (Netherlands)

    Vujacic, Ivan; Dattner, Itai; Gonzalez, Javier; Wit, Ernst

    In many applications obtaining ordinary differential equation descriptions of dynamic processes is scientifically important. In both, Bayesian and likelihood approaches for estimating parameters of ordinary differential equations, the speed and the convergence of the estimation procedure may

  2. (Ln-bar, g)-spaces. Ordinary and tensor differentials

    International Nuclear Information System (INIS)

    Manoff, S.; Dimitrov, B.

    1998-01-01

    Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces

  3. Network Reconstruction From High-Dimensional Ordinary Differential Equations.

    Science.gov (United States)

    Chen, Shizhe; Shojaie, Ali; Witten, Daniela M

    2017-01-01

    We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.

  4. Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations

    International Nuclear Information System (INIS)

    Khan, Junaid Ali; Raja, Muhammad Asif Zahoor; Qureshi, Ijaz Mansoor

    2011-01-01

    We present an evolutionary computational approach for the solution of nonlinear ordinary differential equations (NLODEs). The mathematical modeling is performed by a feed-forward artificial neural network that defines an unsupervised error. The training of these networks is achieved by a hybrid intelligent algorithm, a combination of global search with genetic algorithm and local search by pattern search technique. The applicability of this approach ranges from single order NLODEs, to systems of coupled differential equations. We illustrate the method by solving a variety of model problems and present comparisons with solutions obtained by exact methods and classical numerical methods. The solution is provided on a continuous finite time interval unlike the other numerical techniques with comparable accuracy. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed. (general)

  5. Lie group classification of first-order delay ordinary differential equations

    Science.gov (United States)

    Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

    2018-05-01

    A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

  6. Solutions manual to accompany Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  7. Differential equations a dynamical systems approach ordinary differential equations

    CERN Document Server

    Hubbard, John H

    1991-01-01

    This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.

  8. Symmetries, Integrals and Solutions of Ordinary Differential ...

    Indian Academy of Sciences (India)

    Second-and third-order scalar ordinary differential equations of maximal symmetry in the traditional sense of point, respectively contact, symmetry are examined for the mappings they produce in solutions and fundamental first integrals. The properties of the `exceptional symmetries', i.e. those not considered to be generic to ...

  9. From ordinary to partial differential equations

    CERN Document Server

    Esposito, Giampiero

    2017-01-01

    This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

  10. Numerical solutions of ordinary and partial differential equations in the frequency domain

    International Nuclear Information System (INIS)

    Hazi, G.; Por, G.

    1997-01-01

    Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)

  11. A new numerical approximation of the fractal ordinary differential equation

    Science.gov (United States)

    Atangana, Abdon; Jain, Sonal

    2018-02-01

    The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

  12. Numerical Integration of Stiff System of Ordinary Differential ...

    African Journals Online (AJOL)

    The goal of this work is to develop, analyse and implement a K-step Implicit Rational Runge-Kutta schemes for Integration of Stiff system of Ordinary differential Equations. Its development adopted Taylor and Binomial series expansion Techniques to generate its parameters. The analysis of its basic properties adopted ...

  13. KRYSI, Ordinary Differential Equations Solver with Sdirk Krylov Method

    International Nuclear Information System (INIS)

    Hindmarsh, A.C.; Norsett, S.P.

    2001-01-01

    1 - Description of program or function: KRYSI is a set of FORTRAN subroutines for solving ordinary differential equations initial value problems. It is suitable for both stiff and non-stiff systems. When solving the implicit stage equations in the stiff case, KRYSI uses a Krylov subspace iteration method called the SPIGMR (Scaled Preconditioned Incomplete Generalized Minimum Residual) method. No explicit Jacobian storage is required, except where used in pre- conditioning. A demonstration problem is included with a description of two pre-conditioners that are natural for its solution by KRYSI. 2 - Method of solution: KRYSI uses a three-stage, third-order singly diagonally implicit Runge-Kutta (SDIRK) method. In the stiff case, a preconditioned Krylov subspace iteration within a (so-called) inexact Newton iteration is used to solve the system of nonlinear algebraic equations

  14. Generalized Ordinary Differential Equation Models.

    Science.gov (United States)

    Miao, Hongyu; Wu, Hulin; Xue, Hongqi

    2014-10-01

    Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.

  15. Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations

    Directory of Open Access Journals (Sweden)

    Rutwig Campoamor-Stursberg

    2016-03-01

    Full Text Available A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems.

  16. Ordinary differential equations principles and applications

    CERN Document Server

    Nandakumaran, A K; George, Raju K

    2017-01-01

    Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.

  17. Hojman's theorem of the third-order ordinary differential equation

    International Nuclear Information System (INIS)

    Hong-Sheng, Lü; Hong-Bin, Zhang; Shu-Long, Gu

    2009-01-01

    This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results. (general)

  18. Generation and Identification of Ordinary Differential Equations of Maximal Symmetry Algebra

    Directory of Open Access Journals (Sweden)

    J. C. Ndogmo

    2016-01-01

    Full Text Available An effective method for generating linear ordinary differential equations of maximal symmetry in their most general form is found, and an explicit expression for the point transformation reducing the equation to its canonical form is obtained. New expressions for the general solution are also found, as well as several identification and other results and a direct proof of the fact that a linear ordinary differential equation is iterative if and only if it is reducible to the canonical form by a point transformation. New classes of solvable equations parameterized by an arbitrary function are also found, together with simple algebraic expressions for the corresponding general solution.

  19. On oscillation of second-order linear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, A.; Šremr, Jiří

    2011-01-01

    Roč. 54, - (2011), s. 69-81 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear second-order ordinary differential equation * Kamenev theorem * oscillation Subject RIV: BA - General Mathematics http://www.rmi.ge/jeomj/memoirs/vol54/abs54-4.htm

  20. Quantifying uncertainty, variability and likelihood for ordinary differential equation models

    LENUS (Irish Health Repository)

    Weisse, Andrea Y

    2010-10-28

    Abstract Background In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well-known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.

  1. Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations

    Directory of Open Access Journals (Sweden)

    2009-02-01

    Full Text Available We consider a second-order ordinary differential equation with antiperiodic boundary conditions and impulses. By using Schaefer's fixed-point theorem, some existence results are obtained.

  2. Ordinary differential equations a graduate text

    CERN Document Server

    Bhamra, K S

    2015-01-01

    ORDINARY DIFFERENTIAL EQUATIONS: A Graduate Text presents a systematic and comprehensive introduction to ODEs for graduate and postgraduate students. The systematic organized text on differential inequalities, Gronwall's inequality, Nagumo's theorems, Osgood's criteria and applications of different equations of first order is dealt with in a greater depth. The book discusses qualitative and quantitative aspects of the Strum - Liouville problems, Green's function, integral equations, Laplace transform and is supported by a number of worked-out examples in each lesson to make the concepts clear. A lot of stress on stability theory is laid down, especially on Lyapunov and Poincare stability theory. A numerous figures in various lessons (in particular lessons dealing with stability theory) have been added to clarify the key concepts in DE theory. Nonlinear oscillation in conservative systems and Hamiltonian systems highlights basic nature of the systems considered. Perturbation techniques lesson deals in fairly d...

  3. Algorithmic Verification of Linearizability for Ordinary Differential Equations

    KAUST Repository

    Lyakhov, Dmitry A.

    2017-07-19

    For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a linear one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra. The second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation. The implementation of both algorithms is discussed and their application is illustrated using several examples.

  4. VODE, Variable Coefficient Ordinary Differential Equations (ODE) Solver

    International Nuclear Information System (INIS)

    Brown, P.N.; Hindmarsh, A.C.; Byrne, G.D.

    2002-01-01

    1 - Description of program or function: VODE is a package of subroutines for the numerical solution of the initial-value problem for systems of first-order ordinary differential equations. The package can be used for either stiff or non-stiff systems. In the stiff case, the Jacobian matrix is treated as full or banded. An algorithm is included for saving and reusing the Jacobian matrix under certain conditions. If storage is limited, this option may be suppressed. 2 - Method of solution - VODE uses the variable-order, variable- coefficient Adams-Moulton method for non-stiff systems and the variable-order, fixed-leading-coefficient Backward Differentiation Formula (BDF) method for stiff systems

  5. Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations

    Science.gov (United States)

    Radhakrishnan, Krishnan; Hindmarsh, Alan C.

    1993-01-01

    LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user can easily switch methods to increase computational efficiency for problems that change character. For both methods a variety of corrector iteration techniques is included in the code. Also, to minimize computational work, both the step size and method order are varied dynamically. This report presents complete descriptions of the code and integration methods, including their implementation. It also provides a detailed guide to the use of the code, as well as an illustrative example problem.

  6. Solving (2 + 1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

    International Nuclear Information System (INIS)

    Ka-Lin, Su; Yuan-Xi, Xie

    2010-01-01

    By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. (general)

  7. Ordinary Differential Equation Models for Adoptive Immunotherapy.

    Science.gov (United States)

    Talkington, Anne; Dantoin, Claudia; Durrett, Rick

    2018-05-01

    Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor.

  8. Symmetries of th-Order Approximate Stochastic Ordinary Differential Equations

    OpenAIRE

    Fredericks, E.; Mahomed, F. M.

    2012-01-01

    Symmetries of $n$ th-order approximate stochastic ordinary differential equations (SODEs) are studied. The determining equations of these SODEs are derived in an Itô calculus context. These determining equations are not stochastic in nature. SODEs are normally used to model nature (e.g., earthquakes) or for testing the safety and reliability of models in construction engineering when looking at the impact of random perturbations.

  9. Error estimation in the neural network solution of ordinary differential equations.

    Science.gov (United States)

    Filici, Cristian

    2010-06-01

    In this article a method of error estimation for the neural approximation of the solution of an Ordinary Differential Equation is presented. Some examples of the application of the method support the theory presented. Copyright 2010. Published by Elsevier Ltd.

  10. Approximate analytical methods for solving ordinary differential equations

    CERN Document Server

    Radhika, TSL; Rani, T Raja

    2015-01-01

    Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods.The book is suitable not only for mathematicians and engineers but also for biologists, physicists, and economists. It gives a complete descripti

  11. From Ordinary Differential Equations to Structural Causal Models: the deterministic case

    NARCIS (Netherlands)

    Mooij, J.M.; Janzing, D.; Schölkopf, B.; Nicholson, A.; Smyth, P.

    2013-01-01

    We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of

  12. Solving Second-Order Ordinary Differential Equations without Using Complex Numbers

    Science.gov (United States)

    Kougias, Ioannis E.

    2009-01-01

    Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…

  13. Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

    Science.gov (United States)

    Rosenbaum, J. S.

    1971-01-01

    Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

  14. An introduction to linear ordinary differential equations using the impulsive response method and factorization

    CERN Document Server

    Camporesi, Roberto

    2016-01-01

    This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

  15. EXISTENCE OF POSITIVE SOLUTION TO TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.

  16. Using trees to compute approximate solutions to ordinary differential equations exactly

    Science.gov (United States)

    Grossman, Robert

    1991-01-01

    Some recent work is reviewed which relates families of trees to symbolic algorithms for the exact computation of series which approximate solutions of ordinary differential equations. It turns out that the vector space whose basis is the set of finite, rooted trees carries a natural multiplication related to the composition of differential operators, making the space of trees an algebra. This algebraic structure can be exploited to yield a variety of algorithms for manipulating vector fields and the series and algebras they generate.

  17. Extending the Constant Coefficient Solution Technique to Variable Coefficient Ordinary Differential Equations

    Science.gov (United States)

    Mohammed, Ahmed; Zeleke, Aklilu

    2015-01-01

    We introduce a class of second-order ordinary differential equations (ODEs) with variable coefficients whose closed-form solutions can be obtained by the same method used to solve ODEs with constant coefficients. General solutions for the homogeneous case are discussed.

  18. A Simple Method to Find out when an Ordinary Differential Equation Is Separable

    Science.gov (United States)

    Cid, Jose Angel

    2009-01-01

    We present an alternative method to that of Scott (D. Scott, "When is an ordinary differential equation separable?", "Amer. Math. Monthly" 92 (1985), pp. 422-423) to teach the students how to discover whether a differential equation y[prime] = f(x,y) is separable or not when the nonlinearity f(x, y) is not explicitly factorized. Our approach is…

  19. Numerical integration of asymptotic solutions of ordinary differential equations

    Science.gov (United States)

    Thurston, Gaylen A.

    1989-01-01

    Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

  20. Identifying and Exploring Relationships between Contextual Situations and Ordinary Differential Equations

    Science.gov (United States)

    Camacho-Machín, M.; Guerrero-Ortiz, C.

    2015-01-01

    The aim of this paper is to present and discuss some of the evidence regarding the resources that students use when they establish relationships between a contextual situation and an ordinary differential equation (ODE). We present research results obtained from work by seven students in a graduate level course in mathematics education, where they…

  1. Consistency of direct integral estimator for partially observed systems of ordinary differential equations

    NARCIS (Netherlands)

    Vujačić, Ivan; Dattner, Itai

    In this paper we use the sieve framework to prove consistency of the ‘direct integral estimator’ of parameters for partially observed systems of ordinary differential equations, which are commonly used for modeling dynamic processes.

  2. Ordinary differential equations basics and beyond

    CERN Document Server

    Schaeffer, David G

    2016-01-01

    This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text. Given its many applications, the book may be used comfortably in sc...

  3. Universal formats for nonlinear ordinary differential systems

    International Nuclear Information System (INIS)

    Kerner, E.H.

    1981-01-01

    It is shown that very general nonlinear ordinary differential systems (embracing all that arise in practice) may, first, be brought down to polynomial systems (where the nonlinearities occur only as polynomials in the dependent variables) by introducing suitable new variables into the original system; second, that polynomial systems are reducible to ''Riccati systems,'' where the nonlinearities are quadratic at most; third, that Riccati systems may be brought to elemental universal formats containing purely quadratic terms with simple arrays of coefficients that are all zero or unity. The elemental systems have representations as novel types of matrix Riccati equations. Different starting systems and their associated Riccati systems differ from one another, at the final elemental level, in order and in initial data, but not in format

  4. A variational approach to parameter estimation in ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Kaschek Daniel

    2012-08-01

    Full Text Available Abstract Background Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters. Results The approach presented in this work is able to deal with course estimation for extrinsic system inputs or intrinsic reactants, both not being constrained by the reaction network itself. Our method is based on variational calculus which is carried out analytically to derive an augmented system of differential equations including the unconstrained components as ordinary state variables. Finally, conventional parameter estimation is applied to the augmented system resulting in a combined estimation of courses and parameters. Conclusions The combined estimation approach takes the uncertainty in input courses correctly into account. This leads to precise parameter estimates and correct confidence intervals. In particular this implies that small motifs of large reaction networks can be analysed independently of the rest. By the use of variational methods, elements from control theory and statistics are combined allowing for future transfer of methods between the two fields.

  5. A variational approach to parameter estimation in ordinary differential equations.

    Science.gov (United States)

    Kaschek, Daniel; Timmer, Jens

    2012-08-14

    Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters. The approach presented in this work is able to deal with course estimation for extrinsic system inputs or intrinsic reactants, both not being constrained by the reaction network itself. Our method is based on variational calculus which is carried out analytically to derive an augmented system of differential equations including the unconstrained components as ordinary state variables. Finally, conventional parameter estimation is applied to the augmented system resulting in a combined estimation of courses and parameters. The combined estimation approach takes the uncertainty in input courses correctly into account. This leads to precise parameter estimates and correct confidence intervals. In particular this implies that small motifs of large reaction networks can be analysed independently of the rest. By the use of variational methods, elements from control theory and statistics are combined allowing for future transfer of methods between the two fields.

  6. Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

    Science.gov (United States)

    Camporesi, Roberto

    2011-01-01

    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

  7. Runge-Kutta Methods for Linear Ordinary Differential Equations

    Science.gov (United States)

    Zingg, David W.; Chisholm, Todd T.

    1997-01-01

    Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

  8. Random ordinary differential equations and their numerical solution

    CERN Document Server

    Han, Xiaoying

    2017-01-01

    This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs).   RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems.  They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor ...

  9. The qualitative theory of ordinary differential equations an introduction

    CERN Document Server

    Brauer, Fred

    1989-01-01

    ""This is a very good book ... with many well-chosen examples and illustrations."" - American Mathematical MonthlyThis highly regarded text presents a self-contained introduction to some important aspects of modern qualitative theory for ordinary differential equations. It is accessible to any student of physical sciences, mathematics or engineering who has a good knowledge of calculus and of the elements of linear algebra. In addition, algebraic results are stated as needed; the less familiar ones are proved either in the text or in appendixes.The topics covered in the first three chapters a

  10. A textbook on ordinary differential equations

    CERN Document Server

    Ahmad, Shair

    2014-01-01

    The book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises; the reader will also find a set of solutions of selected exercises. The book contains many interesting examples as well (like the equations for the electric circuits, the pendium equation, the logistic equation, the Lotka-Volterra system, and many other) which introduce the reader to some interesting aspects of the theory and its applications. The work is mainly addressed to students of Mathematics, Physics, Engineering, Statistics, Computer Sciences, with  knowledge of Calculus and Linear Algebra, and contains more advanced topics for further developments, such as Laplace transform; Stability theory and existence of solutions to Boundary Value problems. The authors are preparing a complete solutions manual, containing solutions to all the exercises published in the book. The manual will be available Summer 2014. Instructors who wish to adopt the book may request the manual by writing...

  11. Numerical solution of ordinary differential equations

    CERN Document Server

    Fox, L

    1987-01-01

    Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numeri...

  12. Exploring Students' Understanding of Ordinary Differential Equations Using Computer Algebraic System (CAS)

    Science.gov (United States)

    Maat, Siti Mistima; Zakaria, Effandi

    2011-01-01

    Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…

  13. Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

    Science.gov (United States)

    Gainetdinova, A A; Gazizov, R K

    2017-01-01

    We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

  14. Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.

    Science.gov (United States)

    Ding, A Adam; Wu, Hulin

    2014-10-01

    We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.

  15. Contact symmetries of general linear second-order ordinary differential equations: letter to the editor

    NARCIS (Netherlands)

    Martini, Ruud; Kersten, P.H.M.

    1983-01-01

    Using 1-1 mappings, the complete symmetry groups of contact transformations of general linear second-order ordinary differential equations are determined from two independent solutions of those equations, and applied to the harmonic oscillator with and without damping.

  16. Numerical methods for the solution of ordinary differential equations

    International Nuclear Information System (INIS)

    Azeem, M.

    1999-01-01

    The ode 113 code solves non-stiff differential equations and is a fully variable step, variable order, PECE implementation in terms of modified divided differences of Adams-Bashforth-Moulton family of formulas of order 1-12. The main objectives of this project were to modify PECE mode of ode 113 into PEC mode, study the variable step size and variable order strategy of both the modes and finally, develop the switching strategy between both PECE and PEC modes to minimize the cost of solving the ordinary differential equations. Using some test problems (including stiff, mild stiff and non-stiff), it was found that the PEC mode was more efficient for non-stiff problems at crude and intermediate tolerances and the PECE mode for all problems at the stringent tolerance. An automatic switching strategy was developed using the results observed from the step size and order plots of all the test problems for both the modes and gave the optimum results. (author)

  17. The relationship among the solutions of two auxiliary ordinary differential equations

    International Nuclear Information System (INIS)

    Liu Xiaoping; Liu Chunping

    2009-01-01

    In a recent article [Phys. Lett. A 356 (2006) 124], Sirendaoreji extended their auxiliary equation method by introducing a new auxiliary ordinary differential equation (NAODE) and its 14 solutions. Then the author studied some nonlinear evolution equations (NLEEs) and got more exact travelling wave solutions. In this paper, we will show that the 14 solutions of the NAODE are actually the same as the solutions obtained by original auxiliary equation method, and they are only different in the form.

  18. On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Yoshitsugu Takei

    2015-01-01

    Full Text Available Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.

  19. Constructive Development of the Solutions of Linear Equations in Introductory Ordinary Differential Equations

    Science.gov (United States)

    Mallet, D. G.; McCue, S. W.

    2009-01-01

    The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to…

  20. On method of solving third-order ordinary differential equations directly using Bernstein polynomials

    Science.gov (United States)

    Khataybeh, S. N.; Hashim, I.

    2018-04-01

    In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

  1. Comparative numerical solutions of stiff Ordinary differential equations using magnus series expansion method

    Directory of Open Access Journals (Sweden)

    SURE KÖME

    2014-12-01

    Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.

  2. Blow up of solutions to ordinary differential equations arising in nonlinear dispersive problems

    Directory of Open Access Journals (Sweden)

    Milena Dimova

    2018-03-01

    Full Text Available We study a new class of ordinary differential equations with blow up solutions. Necessary and sufficient conditions for finite blow up time are proved. Based on the new differential equation, a revised version of the concavity method of Levine is proposed. As an application we investigate the non-existence of global solutions to the Cauchy problem of Klein-Gordon, and to the double dispersive equations. We obtain necessary and sufficient condition for finite time blow up with arbitrary positive energy. A very general sufficient condition for blow up is also given.

  3. New results for exponential synchronization of linearly coupled ordinary differential systems

    International Nuclear Information System (INIS)

    Tong Ping; Chen Shi-Hua

    2017-01-01

    This paper investigates the exponential synchronization of linearly coupled ordinary differential systems. The intrinsic nonlinear dynamics may not satisfy the QUAD condition or weak-QUAD condition. First, it gives a new method to analyze the exponential synchronization of the systems. Second, two theorems and their corollaries are proposed for the local or global exponential synchronization of the coupled systems. Finally, an application to the linearly coupled Hopfield neural networks and several simulations are provided for verifying the effectiveness of the theoretical results. (paper)

  4. LSODE, 1. Order Stiff or Non-Stiff Ordinary Differential Equations System Initial Value Problems

    International Nuclear Information System (INIS)

    Hindmarsh, A.C.; Petzold, L.R.

    2005-01-01

    1 - Description of program or function: LSODE (Livermore Solver for Ordinary Differential Equations) solves stiff and non-stiff systems of the form dy/dt = f. In the stiff case, it treats the Jacobian matrix df/dy as either a dense (full) or a banded matrix, and as either user-supplied or internally approximated by difference quotients. It uses Adams methods (predictor-corrector) in the non-stiff case, and Backward Differentiation Formula (BDF) methods (the Gear methods) in the stiff case. The linear systems that arise are solved by direct methods (LU factor/solve). The LSODE source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available. 2 - Methods: It is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. LSODE contains two variable-order, variable- step (with interpolatory step-changing) integration methods. The first is the implicit Adams or non-stiff method, of orders one through twelve. The second is the backward differentiation or stiff method (or BDF method, or Gear's method), of orders one through five. 3 - Restrictions on the complexity of the problem: The differential equations must be given in explicit form, i.e., dy/dt = f(y,t). Problems with intermittent high-speed transients may cause inefficient or unstable performance

  5. Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.

    Science.gov (United States)

    Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M

    2013-01-01

    Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.

  6. A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

    NARCIS (Netherlands)

    Bochev, Mikhail A.

    2013-01-01

    We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of

  7. On one two-point BVP for the fourth order linear ordinary differential equation

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Manjikashvili, M.

    2017-01-01

    Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077. xml

  8. On periodic bounded and unbounded solutions of second order nonlinear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander

    2017-01-01

    Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009. xml

  9. On periodic bounded and unbounded solutions of second order nonlinear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander

    2017-01-01

    Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009.xml

  10. On one two-point BVP for the fourth order linear ordinary differential equation

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Manjikashvili, M.

    2017-01-01

    Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077.xml

  11. SAHYB-2, Solution of Ordinary Differential Equation with User-Supplied Subroutine

    International Nuclear Information System (INIS)

    Hoop, H. d'; Monterosso, R.

    1967-01-01

    1 - Nature of physical problem solved: SAHYB-2 is a general purpose programme for the solution of ordinary differential equations. These are written in a user-supplied subroutine called DER, which uses notations very close to mathematical formulas. Special mathematical functions are included in the programme, as: Function generation, delay generation, steps, ramps and pulses, as well as a simplified standard output procedure - boundary value problems or parametric optimisation may be handled by iterations adding a subroutine called REPEAT. 2 - Method of solution: Integration is carried out by constant step fourth-order Runge-Kutta method, or by a fixed or variable step Adams-Moulton predictor corrector method. 3 - Restrictions on the complexity of the problem: Maximum 150 differential equations of the first order. Maximum 30 tables for function generator or delay lines

  12. On the coupling of systems of hyperbolic conservation laws with ordinary differential equations

    International Nuclear Information System (INIS)

    Borsche, Raul; Colombo, Rinaldo M; Garavello, Mauro

    2010-01-01

    Motivated by applications to the piston problem, to a manhole model, to blood flow and to supply chain dynamics, this paper deals with a system of conservation laws coupled with a system of ordinary differential equations. The former is defined on a domain with boundary and the coupling is provided by the boundary condition. For each of the examples considered, numerical integrations are provided

  13. Optical solver for a system of ordinary differential equations based on an external feedback assisted microring resonator.

    Science.gov (United States)

    Hou, Jie; Dong, Jianji; Zhang, Xinliang

    2017-06-15

    Systems of ordinary differential equations (SODEs) are crucial for describing the dynamic behaviors in various systems such as modern control systems which require observability and controllability. In this Letter, we propose and experimentally demonstrate an all-optical SODE solver based on the silicon-on-insulator platform. We use an add/drop microring resonator to construct two different ordinary differential equations (ODEs) and then introduce two external feedback waveguides to realize the coupling between these ODEs, thus forming the SODE solver. A temporal coupled mode theory is used to deduce the expression of the SODE. A system experiment is carried out for further demonstration. For the input 10 GHz NRZ-like pulses, the measured output waveforms of the SODE solver agree well with the calculated results.

  14. Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors.

    Science.gov (United States)

    Sun, Mengyang; Cheng, Xianrui; Socolar, Joshua E S

    2013-06-01

    A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

  15. Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

    Science.gov (United States)

    Hunt, L. R.; Villarreal, Ramiro

    1987-01-01

    System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

  16. Conservation properties of numerical integration methods for systems of ordinary differential equations

    Science.gov (United States)

    Rosenbaum, J. S.

    1976-01-01

    If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

  17. Analytical approaches for the approximate solution of a nonlinear fractional ordinary differential equation

    International Nuclear Information System (INIS)

    Basak, K C; Ray, P C; Bera, R K

    2009-01-01

    The aim of the present analysis is to apply the Adomian decomposition method and He's variational method for the approximate analytical solution of a nonlinear ordinary fractional differential equation. The solutions obtained by the above two methods have been numerically evaluated and presented in the form of tables and also compared with the exact solution. It was found that the results obtained by the above two methods are in excellent agreement with the exact solution. Finally, a surface plot of the approximate solutions of the fractional differential equation by the above two methods is drawn for 0≤t≤2 and 1<α≤2.

  18. A Fresh Look at Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

    Science.gov (United States)

    Camporesi, Roberto

    2016-01-01

    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

  19. Robust estimation for ordinary differential equation models.

    Science.gov (United States)

    Cao, J; Wang, L; Xu, J

    2011-12-01

    Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a nonparametric function, which is a linear combination of basis functions. The nonparametric function is estimated by a robust penalized smoothing method. The penalty term is defined with the parametric ODE model, which controls the roughness of the nonparametric function and maintains the fidelity of the nonparametric function to the ODE model. The basis coefficients and ODE parameters are estimated in two nested levels of optimization. The coefficient estimates are treated as an implicit function of ODE parameters, which enables one to derive the analytic gradients for optimization using the implicit function theorem. Simulation studies show that the robust method gives satisfactory estimates for the ODE parameters from noisy data with outliers. The robust method is demonstrated by estimating a predator-prey ODE model from real ecological data. © 2011, The International Biometric Society.

  20. VCODE, Ordinary Differential Equation Solver for Stiff and Non-Stiff Problems

    International Nuclear Information System (INIS)

    Cohen, Scott D.; Hindmarsh, Alan C.

    2001-01-01

    1 - Description of program or function: CVODE is a package written in ANSI standard C for solving initial value problems for ordinary differential equations. It solves both stiff and non stiff systems. In the stiff case, it includes a variety of options for treating the Jacobian of the system, including dense and band matrix solvers, and a preconditioned Krylov (iterative) solver. 2 - Method of solution: Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by functional iteration or Newton iteration. For the solution of linear systems within Newton iteration, users can select a dense solver, a band solver, a diagonal approximation, or a preconditioned Generalized Minimal Residual (GMRES) solver. In the dense and band cases, the user can supply a Jacobian approximation or let CVODE generate it internally. In the GMRES case, the pre-conditioner is user-supplied

  1. Nonlinear ordinary differential equations analytical approximation and numerical methods

    CERN Document Server

    Hermann, Martin

    2016-01-01

    The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

  2. Cause and cure of sloppiness in ordinary differential equation models.

    Science.gov (United States)

    Tönsing, Christian; Timmer, Jens; Kreutz, Clemens

    2014-08-01

    Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.

  3. Cause and cure of sloppiness in ordinary differential equation models

    Science.gov (United States)

    Tönsing, Christian; Timmer, Jens; Kreutz, Clemens

    2014-08-01

    Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objective function covering orders of magnitudes was observed and has been termed as sloppiness. In this work, we investigate the origin of sloppiness from structures in the sensitivity matrix arising from the properties of the model topology and the experimental design. Furthermore, we present strategies using optimal experimental design methods in order to circumvent the sloppiness issue and present nonsloppy designs for a benchmark model.

  4. SIVA/DIVA- INITIAL VALUE ORDINARY DIFFERENTIAL EQUATION SOLUTION VIA A VARIABLE ORDER ADAMS METHOD

    Science.gov (United States)

    Krogh, F. T.

    1994-01-01

    The SIVA/DIVA package is a collection of subroutines for the solution of ordinary differential equations. There are versions for single precision and double precision arithmetic. These solutions are applicable to stiff or nonstiff differential equations of first or second order. SIVA/DIVA requires fewer evaluations of derivatives than other variable order Adams predictor-corrector methods. There is an option for the direct integration of second order equations which can make integration of trajectory problems significantly more efficient. Other capabilities of SIVA/DIVA include: monitoring a user supplied function which can be separate from the derivative; dynamically controlling the step size; displaying or not displaying output at initial, final, and step size change points; saving the estimated local error; and reverse communication where subroutines return to the user for output or computation of derivatives instead of automatically performing calculations. The user must supply SIVA/DIVA with: 1) the number of equations; 2) initial values for the dependent and independent variables, integration stepsize, error tolerance, etc.; and 3) the driver program and operational parameters necessary for subroutine execution. SIVA/DIVA contains an extensive diagnostic message library should errors occur during execution. SIVA/DIVA is written in FORTRAN 77 for batch execution and is machine independent. It has a central memory requirement of approximately 120K of 8 bit bytes. This program was developed in 1983 and last updated in 1987.

  5. Mathematical modelling of tissue formation on the basis of ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Maxim N. Nazarov

    2017-10-01

    Full Text Available A mathematical model is proposed for describing the population dynamics of cellular clusters on the basis of systems of the first-order ordinary differential equations. The main requirement for the construction of model equations was to obtain a formal biological justification for their derivation, as well as proof of their correctness. In addition, for all the parameters involved in the model equations, the presence of biological meaning was guaranteed, as well as the possibility of evaluating them either during the experiment or by using models of intracellular biochemistry. In the desired model the intercellular exchange of a special signal molecules was chosen as the main mechanism for coordination of the tissue growth and new types selection during cell division. For simplicity, all signalling molecules that can create cells of the same type were not considered separately in the model, but were instead combined in a single complex of molecules: a ‘generalized signal’. Such an approach allows us to eventually assign signals as a functions of cell types and introduce their effects in the form of matrices in the models, where the rows are responsible for the types of cells receiving the signals, and the columns for the types of cells emitting signals.

  6. The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

    Science.gov (United States)

    Estabrook, F. B.; Wahlquist, H. D.

    1975-01-01

    The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

  7. Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells.

    Science.gov (United States)

    Sundnes, J; Lines, G T; Tveito, A

    2001-08-01

    The contraction of the heart is preceded and caused by a cellular electro-chemical reaction, causing an electrical field to be generated. Performing realistic computer simulations of this process involves solving a set of partial differential equations, as well as a large number of ordinary differential equations (ODEs) characterizing the reactive behavior of the cardiac tissue. Experiments have shown that the solution of the ODEs contribute significantly to the total work of a simulation, and there is thus a strong need to utilize efficient solution methods for this part of the problem. This paper presents how an efficient implicit Runge-Kutta method may be adapted to solve a complicated cardiac cell model consisting of 31 ODEs, and how this solver may be coupled to a set of PDE solvers to provide complete simulations of the electrical activity.

  8. Finding higher order Darboux polynomials for a family of rational first order ordinary differential equations

    Science.gov (United States)

    Avellar, J.; Claudino, A. L. G. C.; Duarte, L. G. S.; da Mota, L. A. C. P.

    2015-10-01

    For the Darbouxian methods we are studying here, in order to solve first order rational ordinary differential equations (1ODEs), the most costly (computationally) step is the finding of the needed Darboux polynomials. This can be so grave that it can render the whole approach unpractical. Hereby we introduce a simple heuristics to speed up this process for a class of 1ODEs.

  9. The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

    Directory of Open Access Journals (Sweden)

    Hasan Bulut

    2013-01-01

    Full Text Available We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM to some interesting nonhomogeneous fractional ordinary differential equations (FODEs. Finally, we use the solutions to form two-dimensional (2D graphs, by using the symbolic algebra package Mathematica Program 7.

  10. Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Winfried Auzinger

    2006-01-01

    Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.

  11. Assessment of available integration algorithms for initial value ordinary differential equations

    International Nuclear Information System (INIS)

    Carver, M.B.; Stewart, D.G.

    1979-11-01

    There exists an extremely large number of algorithms designed for the ordinary differential equation initial value problem. The integration is normally done by a finite sum at time intervals which are chosen dynamically to satisfy an imposed error tolerance. This report describes the basic logistics of the integration process, identifies common areas of difficulty, and establishes a comprehensive test profile for integration algorithms. A number of algorithms are described, and selected published subroutines are evaluated using the test profile. It concludes that an effective library for general use need have only two such routines. The two selected are versions of the well-known Gear and Runge-Kutta-Fehlberg algorithms. Full documentation and listings are included. (auth)

  12. Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

    Science.gov (United States)

    Sánchez Pérez, J F; Conesa, M; Alhama, I; Alhama, F; Cánovas, M

    2017-01-01

    Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

  13. Nonchaoticity of Ordinary Differential Equations Describing Autonomous Transcriptional Regulatory Circuits

    International Nuclear Information System (INIS)

    Li Pengfei; Hu Gang; Chen Runsheng

    2008-01-01

    Gene transcriptional regulation (TR) processes are often described by coupled nonlinear ordinary differential equations (ODEs). When the dimension of TR circuits is high (e.g. n ≥ 3) the motions of the corresponding ODEs may, very probably, show self-sustained oscillations and chaos. On the other hand, chaoticity may be harmful for the normal biological functions of TR processes. In this letter we numerically study the dynamics of 3-gene TR ODEs in great detail, and investigate many 4-, 5-, and 10-gene TR systems by randomly choosing figures and parameters in the conventionally accepted ranges. And we find that oscillations are very seldom and no chaotic motion is observed, even if the dimension of systems is sufficiently high (n ≥ 3). It is argued that the observation of nonchaoticity of these ODEs agrees with normal functions of actual TR processes

  14. An accurate scheme by block method for third order ordinary ...

    African Journals Online (AJOL)

    problems of ordinary differential equations is presented in this paper. The approach of collocation approximation is adopted in the derivation of the scheme and then the scheme is applied as simultaneous integrator to special third order initial value problem of ordinary differential equations. This implementation strategy is ...

  15. Particle Swarm Optimization Based on Local Attractors of Ordinary Differential Equation System

    Directory of Open Access Journals (Sweden)

    Wenyu Yang

    2014-01-01

    Full Text Available Particle swarm optimization (PSO is inspired by sociological behavior. In this paper, we interpret PSO as a finite difference scheme for solving a system of stochastic ordinary differential equations (SODE. In this framework, the position points of the swarm converge to an equilibrium point of the SODE and the local attractors, which are easily defined by the present position points, also converge to the global attractor. Inspired by this observation, we propose a class of modified PSO iteration methods (MPSO based on local attractors of the SODE. The idea of MPSO is to choose the next update state near the present local attractor, rather than the present position point as in the original PSO, according to a given probability density function. In particular, the quantum-behaved particle swarm optimization method turns out to be a special case of MPSO by taking a special probability density function. The MPSO methods with six different probability density functions are tested on a few benchmark problems. These MPSO methods behave differently for different problems. Thus, our framework not only gives an interpretation for the ordinary PSO but also, more importantly, provides a warehouse of PSO-like methods to choose from for solving different practical problems.

  16. Ordinary differential equations and Boolean networks in application to modelling of 6-mercaptopurine metabolism.

    Science.gov (United States)

    Lavrova, Anastasia I; Postnikov, Eugene B; Zyubin, Andrey Yu; Babak, Svetlana V

    2017-04-01

    We consider two approaches to modelling the cell metabolism of 6-mercaptopurine, one of the important chemotherapy drugs used for treating acute lymphocytic leukaemia: kinetic ordinary differential equations, and Boolean networks supplied with one controlling node, which takes continual values. We analyse their interplay with respect to taking into account ATP concentration as a key parameter of switching between different pathways. It is shown that the Boolean networks, which allow avoiding the complexity of general kinetic modelling, preserve the possibility of reproducing the principal switching mechanism.

  17. Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

    Science.gov (United States)

    Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

    2014-04-02

    The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

  18. A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

    Science.gov (United States)

    Camporesi, Roberto

    2016-01-01

    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

  19. The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions

    Directory of Open Access Journals (Sweden)

    Mehmet Tarik Atay

    2013-01-01

    Full Text Available The Variational Iteration Method (VIM and Modified Variational Iteration Method (MVIM are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM and the Modified Variational Iteration Method (MVIM are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.

  20. A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects.

    Science.gov (United States)

    Chow, Sy-Miin; Bendezú, Jason J; Cole, Pamela M; Ram, Nilam

    2016-01-01

    Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay & Silverman, 2005 ), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, & Peel, 2010 ), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 ). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children's self-regulation.

  1. Calculus & ordinary differential equations

    CERN Document Server

    Pearson, David

    1995-01-01

    Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.

  2. Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries

    Science.gov (United States)

    Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

    2018-05-01

    A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.

  3. Higher derivative discontinuous solutions to linear ordinary differential equations: a new route to complexity?

    International Nuclear Information System (INIS)

    Datta, Dhurjati Prasad; Bose, Manoj Kumar

    2004-01-01

    We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of higher derivative discontinuous solutions as well. The discontinuity can occur only for a subset of even order derivatives, viz., 2nd, 4th, 8th, 16th,.... The solutions are shown to break the discrete parity (reflection) symmetry of the underlying equation. These results are expected to gain significance in the contemporary search of a new dynamical principle for understanding complex phenomena in nature

  4. Solving ordinary differential equations by electrical analogy: a multidisciplinary teaching tool

    Science.gov (United States)

    Sanchez Perez, J. F.; Conesa, M.; Alhama, I.

    2016-11-01

    Ordinary differential equations are the mathematical formulation for a great variety of problems in science and engineering, and frequently, two different problems are equivalent from a mathematical point of view when they are formulated by the same equations. Students acquire the knowledge of how to solve these equations (at least some types of them) using protocols and strict algorithms of mathematical calculation without thinking about the meaning of the equation. The aim of this work is that students learn to design network models or circuits in this way; with simple knowledge of them, students can establish the association of electric circuits and differential equations and their equivalences, from a formal point of view, that allows them to associate knowledge of two disciplines and promote the use of this interdisciplinary approach to address complex problems. Therefore, they learn to use a multidisciplinary tool that allows them to solve these kinds of equations, even students of first course of engineering, whatever the order, grade or type of non-linearity. This methodology has been implemented in numerous final degree projects in engineering and science, e.g., chemical engineering, building engineering, industrial engineering, mechanical engineering, architecture, etc. Applications are presented to illustrate the subject of this manuscript.

  5. Dimensional analysis to transform the differential equations in partial derivates in the theory of heat transmission into ordinary ones

    International Nuclear Information System (INIS)

    Diaz Sanchidrian, C.

    1989-01-01

    The present paper applies dimensional analysis with spatial discrimination to transform the differential equations in partial derivatives developed in the theory of heat transmission into ordinary ones. The effectivity of the method is comparable to that methods based in transformations of uni or multiparametric groups, with the advantage of being more direct and simple. (Author)

  6. A first course in ordinary differential equations analytical and numerical methods

    CERN Document Server

    Hermann, Martin

    2014-01-01

    This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed t...

  7. Mathematical Methods for Engineers and Scientists 2 Vector Analysis, Ordinary Differential Equations and Laplace Transforms

    CERN Document Server

    Tang, Kwong-Tin

    2007-01-01

    Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

  8. ODEPACK, Initial Value Problems of Ordinary Differential Equation System

    International Nuclear Information System (INIS)

    Hindmarsh, A.C.; Petzold, L.R.

    2005-01-01

    I - Description of program or function: ODEPACK is a collection of Fortran solvers for the initial value problem for ordinary differential equation systems. It consists of nine solvers, namely a basic solver called LSODE and eight variants of it -- LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS. The collection is suitable for both stiff and non-stiff systems. It includes solvers for systems given in explicit form, dy/dt = f(t,y), and also solvers for systems given in linearly implicit form, A(t,y) dy/dt = g(t,y). Two of the solvers use general sparse matrix solvers for the linear systems that arise. Two others use iterative (preconditioned Krylov) methods instead of direct methods for these linear systems. The most recent addition is LSODIS, which solves implicit problems with general sparse treatment of all matrices involved. The ODEPACK solvers are written in standard Fortran 77, with a few exceptions, and with minimal machine dependencies. There are separate double and single precision versions of ODEPACK. The actual solver names are those given above with a prefix of D- or S- for the double or single precision version, respectively, i.e. DLSODE/SLSODE, etc. Each solver consists of a main driver subroutine having the same name as the solver and some number of subordinate routines. For each solver, there is also a demonstration program, which solves one or two simple problems in a somewhat self-checking manner. A. Solvers for explicitly given systems. For each of the following solvers, it is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. 1. LSODE (Livermore Solver for Ordinary Differential Equations) is the basic solver of the collection. It solves stiff and non-stiff systems of the form dy/dt = f. In the stiff case, it treats the Jacobian matrix df/dy as either a dense (full) or a banded matrix, and as

  9. FORSIM-6, Automatic Solution of Coupled Differential Equation System

    International Nuclear Information System (INIS)

    Carver, M.B.; Stewart, D.G.; Blair, J.M.; Selander, W.N.

    1983-01-01

    1 - Description of problem or function: The FORSIM program is a versatile package which automates the solution of coupled differential equation systems. The independent variables are time, and up to three space coordinates, and the equations may be any mixture of partial and/or ordinary differential equations. The philosophy of the program is to provide a tool which will solve a system of differential equations for a user who has basic but unspecialized knowledge of numerical analysis and FORTRAN. The equations to be solved, together with the initial conditions and any special instructions, may be specified by the user in a single FORTRAN subroutine, although he may write a number of routines if this is more suitable. These are then loaded with the control routines, which perform the solution and any requested input and output. 2 - Method of solution: Partial differential equations are automatically converted into sets of coupled ordinary differential equations by variable order discretization in the spatial dimensions. These and other ordinary differential equations are integrated continuously in time using efficient variable order, variable step, error-controlled algorithms

  10. ODEion--a software module for structural identification of ordinary differential equations.

    Science.gov (United States)

    Gennemark, Peter; Wedelin, Dag

    2014-02-01

    In the systems biology field, algorithms for structural identification of ordinary differential equations (ODEs) have mainly focused on fixed model spaces like S-systems and/or on methods that require sufficiently good data so that derivatives can be accurately estimated. There is therefore a lack of methods and software that can handle more general models and realistic data. We present ODEion, a software module for structural identification of ODEs. Main characteristic features of the software are: • The model space is defined by arbitrary user-defined functions that can be nonlinear in both variables and parameters, such as for example chemical rate reactions. • ODEion implements computationally efficient algorithms that have been shown to efficiently handle sparse and noisy data. It can run a range of realistic problems that previously required a supercomputer. • ODEion is easy to use and provides SBML output. We describe the mathematical problem, the ODEion system itself, and provide several examples of how the system can be used. Available at: http://www.odeidentification.org.

  11. Fast integration-based prediction bands for ordinary differential equation models.

    Science.gov (United States)

    Hass, Helge; Kreutz, Clemens; Timmer, Jens; Kaschek, Daniel

    2016-04-15

    To gain a deeper understanding of biological processes and their relevance in disease, mathematical models are built upon experimental data. Uncertainty in the data leads to uncertainties of the model's parameters and in turn to uncertainties of predictions. Mechanistic dynamic models of biochemical networks are frequently based on nonlinear differential equation systems and feature a large number of parameters, sparse observations of the model components and lack of information in the available data. Due to the curse of dimensionality, classical and sampling approaches propagating parameter uncertainties to predictions are hardly feasible and insufficient. However, for experimental design and to discriminate between competing models, prediction and confidence bands are essential. To circumvent the hurdles of the former methods, an approach to calculate a profile likelihood on arbitrary observations for a specific time point has been introduced, which provides accurate confidence and prediction intervals for nonlinear models and is computationally feasible for high-dimensional models. In this article, reliable and smooth point-wise prediction and confidence bands to assess the model's uncertainty on the whole time-course are achieved via explicit integration with elaborate correction mechanisms. The corresponding system of ordinary differential equations is derived and tested on three established models for cellular signalling. An efficiency analysis is performed to illustrate the computational benefit compared with repeated profile likelihood calculations at multiple time points. The integration framework and the examples used in this article are provided with the software package Data2Dynamics, which is based on MATLAB and freely available at http://www.data2dynamics.org helge.hass@fdm.uni-freiburg.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e

  12. Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

    Energy Technology Data Exchange (ETDEWEB)

    Moryakov, A. V., E-mail: sailor@orc.ru [National Research Centre Kurchatov Institute (Russian Federation)

    2016-12-15

    An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

  13. Shooting method for third order simultaneous ordinary differential equations with application to magnetohydrodynamic boundary layer

    International Nuclear Information System (INIS)

    Srivastava, A.C.; Hazarika, G.C.

    1990-01-01

    An algorithm based on the shooting method has been developed for the solution of a two-point boundary value problem consisting of a system of third order simultaneous ordinary differential equations. The Falkner-Skan equations for electrically conducting viscous fluid with applied magnetic field has been solved by using this algorithm for various values of the wedge angle and magnetic parameters. The shooting method seems to be well convergent for a system as the results are in good agreement with those obtained by other methods. It is observed that both viscous boundary layer and magnetic boundary layer decrease while velocity as well as magnetic field increase with the increase of the wedge angle. (author). 6 tabs., 7 refs

  14. All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator.

    Science.gov (United States)

    Yang, Ting; Dong, Jianji; Lu, Liangjun; Zhou, Linjie; Zheng, Aoling; Zhang, Xinliang; Chen, Jianping

    2014-07-04

    Photonic integrated circuits for photonic computing open up the possibility for the realization of ultrahigh-speed and ultra wide-band signal processing with compact size and low power consumption. Differential equations model and govern fundamental physical phenomena and engineering systems in virtually any field of science and engineering, such as temperature diffusion processes, physical problems of motion subject to acceleration inputs and frictional forces, and the response of different resistor-capacitor circuits, etc. In this study, we experimentally demonstrate a feasible integrated scheme to solve first-order linear ordinary differential equation with constant-coefficient tunable based on a single silicon microring resonator. Besides, we analyze the impact of the chirp and pulse-width of input signals on the computing deviation. This device can be compatible with the electronic technology (typically complementary metal-oxide semiconductor technology), which may motivate the development of integrated photonic circuits for optical computing.

  15. Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order

    International Nuclear Information System (INIS)

    Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M

    2011-01-01

    In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)

  16. Stabilization of chromium salt in ordinary portland cement

    Indian Academy of Sciences (India)

    Ordinary Portland cement (OPC) samples containing the chromium salt have been investigated using differential microcalorimetry, conductometry and Fourier transform infrared spectroscopic analysis. The effect of chromium on OPC hydration was evaluated by continuous observing of early hydration.

  17. Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

    Directory of Open Access Journals (Sweden)

    M. P. Markakis

    2010-01-01

    Full Text Available Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1 equations. Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1 equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.

  18. Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

    KAUST Repository

    Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin

    2012-01-01

    Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.

  19. The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

    International Nuclear Information System (INIS)

    Lima, M.L.; Mignaco, J.A.

    1985-01-01

    It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

  20. Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

    Science.gov (United States)

    Hasegawa, Chihiro; Duffull, Stephen B

    2018-02-01

    Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

  1. Numerical solution of ordinary differential equations. For classical, relativistic and nano systems

    International Nuclear Information System (INIS)

    Greenspan, D.

    2006-01-01

    An up-to-date survey on numerical solutions with theory, intuition and applications. Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses. Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved. This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic and nano systems. The examples are carefully explained and compiled into an algorithm, each of which is presented generically, independent of a specific programming language, while each chapter is rounded off with exercises. The text meets the demands of MA200 courses and of the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, as well as for physicists, mathematicians, engineers, and electrical engineers. From the Contents - Euler's Method - Runge-Kutta Methods - The Method of Taylor Expansions - Large Second Order Systems with Application to Nano Systems - Completely Conservative, Covariant Numerical Methodology - Instability - Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems - Approximate Solution of Boundary Value Problems - Special Relativistic Motion - Special Topics - Appendix: Basic Matrix Operations - Bibliography. (orig.) (orig.)

  2. The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

    International Nuclear Information System (INIS)

    Lima, M.L.; Mignaco, J.A.

    1985-01-01

    It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

  3. Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology.

    Science.gov (United States)

    Bonin, Carla Rezende Barbosa; Fernandes, Guilherme Cortes; Dos Santos, Rodrigo Weber; Lobosco, Marcelo

    2017-02-01

    New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus.

  4. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

    Science.gov (United States)

    Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

    2015-01-01

    Background There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). Methodology We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δkm=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value of the prediction errors for methadone’s extraction and throughput were less than 2%. Conclusion ODE/PDE modeling of methadone’s hemodialysis is a new approach to study methadone’s removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone’s mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model

  5. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis.

    Science.gov (United States)

    Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

    2015-01-01

    There is a need to have a model to study methadone's losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone's overall intradialytic mass transfer rate coefficient, km ; and, methadone's removal rate, j ME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. The ODE/PDE model revealed a significant increase in the change of methadone's mass transfer with increased dialysate flow rate, %Δkm =18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone's mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone's removal during dialysis. The absolute value of the prediction errors for methadone's extraction and throughput were less than 2%. ODE/PDE modeling of methadone's hemodialysis is a new approach to study methadone's removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone's mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans.

  6. LIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION

    Directory of Open Access Journals (Sweden)

    Decio Levi

    2013-10-01

    Full Text Available We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the “first differential approximation” is invariant under the same Lie group as the original ordinary differential equation.

  7. An algorithm for solving initial value problems of third order ordinary ...

    African Journals Online (AJOL)

    Abstract. We propose an implicit multi-step method for the solution of initial value problems (IVPs) of third order ordinary differential equations (ODE) which does not require reducing the ODE to first order before solving. The development of the method is based on collocation of the differential system and interpolation of the ...

  8. A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy.

    Science.gov (United States)

    Tao, Youshan; Guo, Qian; Aihara, Kazuyuki

    2014-10-01

    Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.

  9. A Bayesian approach to estimating hidden variables as well as missing and wrong molecular interactions in ordinary differential equation-based mathematical models.

    Science.gov (United States)

    Engelhardt, Benjamin; Kschischo, Maik; Fröhlich, Holger

    2017-06-01

    Ordinary differential equations (ODEs) are a popular approach to quantitatively model molecular networks based on biological knowledge. However, such knowledge is typically restricted. Wrongly modelled biological mechanisms as well as relevant external influence factors that are not included into the model are likely to manifest in major discrepancies between model predictions and experimental data. Finding the exact reasons for such observed discrepancies can be quite challenging in practice. In order to address this issue, we suggest a Bayesian approach to estimate hidden influences in ODE-based models. The method can distinguish between exogenous and endogenous hidden influences. Thus, we can detect wrongly specified as well as missed molecular interactions in the model. We demonstrate the performance of our Bayesian dynamic elastic-net with several ordinary differential equation models from the literature, such as human JAK-STAT signalling, information processing at the erythropoietin receptor, isomerization of liquid α -Pinene, G protein cycling in yeast and UV-B triggered signalling in plants. Moreover, we investigate a set of commonly known network motifs and a gene-regulatory network. Altogether our method supports the modeller in an algorithmic manner to identify possible sources of errors in ODE-based models on the basis of experimental data. © 2017 The Author(s).

  10. A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

    Science.gov (United States)

    Bartels, Robert E.

    2002-01-01

    A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

  11. Phase integral approximation for coupled ordinary differential equations of the Schroedinger type

    International Nuclear Information System (INIS)

    Skorupski, Andrzej A.

    2008-01-01

    Four generalizations of the phase integral approximation (PIA) to sets of ordinary differential equations of Schroedinger type [u j '' (x)+Σ k=1 N R jk (x)u k (x)=0, j=1,2,...,N] are described. The recurrence relations for higher order corrections are given in a form valid to arbitrary order and for the matrix R(x)[≡(R jk (x))] either Hermitian or non-Hermitian. For Hermitian and negative definite R(x) matrices, a Wronskian conserving PIA theory is formulated, which generalizes Fulling's current conserving theory pertinent to positive definite R(x) matrices. The idea of a modification of the PIA, which is well known for one equation [u '' (x)+R(x)u(x)=0], is generalized to sets. A simplification of Wronskian or current conserving theories is proposed which in each order eliminates one integration from the formulas for higher order corrections. If the PIA is generated by a nondegenerate eigenvalue of the R(x) matrix, the eliminated integration is the only one present. In that case, the simplified theory becomes fully algorithmic and is generalized to non-Hermitian R(x) matrices. The general theory is illustrated by a few examples automatically generated by using the author's program in MATHEMATICA published in e-print arXiv:0710.5406 [math-ph

  12. NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations.

    Science.gov (United States)

    Prague, Mélanie; Commenges, Daniel; Guedj, Jérémie; Drylewicz, Julia; Thiébaut, Rodolphe

    2013-08-01

    Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

  13. The mixed BVP for second order nonlinear ordinary differential equation at resonance

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    2017-01-01

    Roč. 290, 2-3 (2017), s. 393-400 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : mixed problem at resonance * nonlinear ordinary differencial equation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.742, year: 2016

  14. Modeling and Prediction Using Stochastic Differential Equations

    DEFF Research Database (Denmark)

    Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp

    2016-01-01

    Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...

  15. Model Selection and Risk Estimation with Applications to Nonlinear Ordinary Differential Equation Systems

    DEFF Research Database (Denmark)

    Mikkelsen, Frederik Vissing

    eective computational tools for estimating unknown structures in dynamical systems, such as gene regulatory networks, which may be used to predict downstream eects of interventions in the system. A recommended algorithm based on the computational tools is presented and thoroughly tested in various......Broadly speaking, this thesis is devoted to model selection applied to ordinary dierential equations and risk estimation under model selection. A model selection framework was developed for modelling time course data by ordinary dierential equations. The framework is accompanied by the R software...... package, episode. This package incorporates a collection of sparsity inducing penalties into two types of loss functions: a squared loss function relying on numerically solving the equations and an approximate loss function based on inverse collocation methods. The goal of this framework is to provide...

  16. On the selection of ordinary differential equation models with application to predator-prey dynamical models.

    Science.gov (United States)

    Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J

    2015-03-01

    We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso. We show the resulting method, here called the LSA method, to be an (asymptotically) oracle model selection method. The finite sample performance of the proposed LSA method is investigated with Monte Carlo simulations, in which we examine the percentage of selecting true ODE models, the efficiency of the parameter estimation compared to simply using the full and true models, and coverage probabilities of the estimated confidence intervals for ODE parameters, all of which have satisfactory performances. Our method is also demonstrated by selecting the best predator-prey ODE to model a lynx and hare population dynamical system among some well-known and biologically interpretable ODE models. © 2014, The International Biometric Society.

  17. From differential to difference equations for first order ODEs

    Science.gov (United States)

    Freed, Alan D.; Walker, Kevin P.

    1991-01-01

    When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE.

  18. Theoretical Analysis of Fas Ligand-Induced Apoptosis with an Ordinary Differential Equation Model.

    Science.gov (United States)

    Shi, Zhimin; Li, Yan; Liu, Zhihai; Mi, Jun; Wang, Renxiao

    2012-12-01

    Upon the treatment of Fas ligand, different types of cells exhibit different apoptotic mechanisms, which are determined by a complex network of biological pathways. In order to derive a quantitative interpretation of the cell sensitivity and apoptosis pathways, we have developed an ordinary differential equation model. Our model is intended to include all of the known major components in apoptosis pathways mediated by Fas receptor. It is composed of 29 equations using a total of 49 rate constants and 13 protein concentrations. All parameters used in our model were derived through nonlinear fitting to experimentally measured concentrations of four selected proteins in Jurkat T-cells, including caspase-3, caspase-8, caspase-9, and Bid. Our model is able to correctly interpret the role of kinetic parameters and protein concentrations in cell sensitivity to FasL. It reveals the possible reasons for the transition between type-I and type-II pathways and also provides some interesting predictions, such as the more decisive role of Fas over Bax in apoptosis pathway and a possible feedback mechanism between type-I and type-II pathways. But our model failed in predicting FasL-induced apoptotic mechanism of NCI-60 cells from their gene-expression levels. Limitations in our model are also discussed. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  19. Studies of neutrino asymmetries generated by ordinary-sterile neutrino oscillations in the early Universe and implications for big bang nucleosynthesis bounds

    Energy Technology Data Exchange (ETDEWEB)

    Foot, R.; Volkas, R.R. [Research Centre for High Energy Physics, School of Physics, University of Melbourne, Parkville, 3052 (Australia)

    1997-04-01

    Ordinary-sterile neutrino oscillations can generate a significant lepton number asymmetry in the early Universe. We study this phenomenon in detail. We show that the dynamics of ordinary-sterile neutrino oscillations in the early Universe can be approximately described by a single integrodifferential equation which we derive from both the density matrix and Hamiltonian formalisms. This equation reduces to a relatively simple ordinary first-order differential equation if the system is sufficiently smooth (static limit). We study the conditions for which the static limit is an acceptable approximation. We also study the effect of the thermal distribution of neutrino momenta on the generation of lepton number. We apply these results to show that it is possible to evade (by many orders of magnitude) the big bang nucleosynthesis (BBN) bounds on the mixing parameters {delta}m{sup 2} and sin{sup 2}2{theta}{sub 0} describing ordinary-sterile neutrino oscillations. We show that the large angle or maximal vacuum oscillation solution to the solar neutrino problem does not significantly modify BBN for most of the parameter space of interest, provided that the {tau} and/or {mu} neutrinos have masses greater than about 1 eV. We also show that the large angle or maximal ordinary-sterile neutrino oscillation solution to the atmospheric neutrino anomaly does not significantly modify BBN for a range of parameters. {copyright} {ital 1997} {ital The American Physical Society}

  20. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

    Directory of Open Access Journals (Sweden)

    Linares OA

    2015-07-01

    Full Text Available Oscar A Linares,1 William E Schiesser,2 Jeffrey Fudin,3–6 Thien C Pham,6 Jeffrey J Bettinger,6 Roy O Mathew,6 Annemarie L Daly7 1Translational Genomic Medicine Lab, Plymouth Pharmacokinetic Modeling Study Group, Plymouth, MI, 2Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA, 3University of Connecticut School of Pharmacy, Storrs, CT, 4Western New England College of Pharmacy, Springfield, MA, 5Albany College of Pharmacy and Health Sciences, Albany, NY, 6Stratton VA Medical Center, Albany, NY, 7Grace Hospice of Ann Arbor, Ann Arbor, MI, USA Background: There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim: To build a one-dimensional (1-D, hollow-fiber geometry, ordinary differential equation (ODE and partial differential equation (PDE countercurrent hemodialyzer model (ODE/PDE model. Methodology: We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results: The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δ km=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11. This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11. The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value

  1. Solar-Based Boost Differential Single Phase Inverter | Eya | Nigerian ...

    African Journals Online (AJOL)

    Solar-Based Boost Differential Single Phase Inverter. ... Solar-based boost differential inverter is reduced down to 22.37% in closed loop system with the aid of Proportional –integral-Differential (PID) ... The dc power source is photovoltaic cell.

  2. A perturbative solution to metadynamics ordinary differential equation

    Science.gov (United States)

    Tiwary, Pratyush; Dama, James F.; Parrinello, Michele

    2015-12-01

    Metadynamics is a popular enhanced sampling scheme wherein by periodic application of a repulsive bias, one can surmount high free energy barriers and explore complex landscapes. Recently, metadynamics was shown to be mathematically well founded, in the sense that the biasing procedure is guaranteed to converge to the true free energy surface in the long time limit irrespective of the precise choice of biasing parameters. A differential equation governing the post-transient convergence behavior of metadynamics was also derived. In this short communication, we revisit this differential equation, expressing it in a convenient and elegant Riccati-like form. A perturbative solution scheme is then developed for solving this differential equation, which is valid for any generic biasing kernel. The solution clearly demonstrates the robustness of metadynamics to choice of biasing parameters and gives further confidence in the widely used method.

  3. A perturbative solution to metadynamics ordinary differential equation.

    Science.gov (United States)

    Tiwary, Pratyush; Dama, James F; Parrinello, Michele

    2015-12-21

    Metadynamics is a popular enhanced sampling scheme wherein by periodic application of a repulsive bias, one can surmount high free energy barriers and explore complex landscapes. Recently, metadynamics was shown to be mathematically well founded, in the sense that the biasing procedure is guaranteed to converge to the true free energy surface in the long time limit irrespective of the precise choice of biasing parameters. A differential equation governing the post-transient convergence behavior of metadynamics was also derived. In this short communication, we revisit this differential equation, expressing it in a convenient and elegant Riccati-like form. A perturbative solution scheme is then developed for solving this differential equation, which is valid for any generic biasing kernel. The solution clearly demonstrates the robustness of metadynamics to choice of biasing parameters and gives further confidence in the widely used method.

  4. An ordinary differential equation model for full thickness wounds and the effects of diabetes.

    Science.gov (United States)

    Bowden, L G; Maini, P K; Moulton, D E; Tang, J B; Wang, X T; Liu, P Y; Byrne, H M

    2014-11-21

    Wound healing is a complex process in which a sequence of interrelated phases contributes to a reduction in wound size. For diabetic patients, many of these processes are compromised, so that wound healing slows down. In this paper we present a simple ordinary differential equation model for wound healing in which attention focusses on the dominant processes that contribute to closure of a full thickness wound. Asymptotic analysis of the resulting model reveals that normal healing occurs in stages: the initial and rapid elastic recoil of the wound is followed by a longer proliferative phase during which growth in the dermis dominates healing. At longer times, fibroblasts exert contractile forces on the dermal tissue, the resulting tension stimulating further dermal tissue growth and enhancing wound closure. By fitting the model to experimental data we find that the major difference between normal and diabetic healing is a marked reduction in the rate of dermal tissue growth for diabetic patients. The model is used to estimate the breakdown of dermal healing into two processes: tissue growth and contraction, the proportions of which provide information about the quality of the healed wound. We show further that increasing dermal tissue growth in the diabetic wound produces closure times similar to those associated with normal healing and we discuss the clinical implications of this hypothesised treatment. Copyright © 2014 Elsevier Ltd. All rights reserved.

  5. An analytical approximation scheme to two-point boundary value problems of ordinary differential equations

    International Nuclear Information System (INIS)

    Boisseau, Bruno; Forgacs, Peter; Giacomini, Hector

    2007-01-01

    A new (algebraic) approximation scheme to find global solutions of two-point boundary value problems of ordinary differential equations (ODEs) is presented. The method is applicable for both linear and nonlinear (coupled) ODEs whose solutions are analytic near one of the boundary points. It is based on replacing the original ODEs by a sequence of auxiliary first-order polynomial ODEs with constant coefficients. The coefficients in the auxiliary ODEs are uniquely determined from the local behaviour of the solution in the neighbourhood of one of the boundary points. The problem of obtaining the parameters of the global (connecting) solutions, analytic at one of the boundary points, reduces to find the appropriate zeros of algebraic equations. The power of the method is illustrated by computing the approximate values of the 'connecting parameters' for a number of nonlinear ODEs arising in various problems in field theory. We treat in particular the static and rotationally symmetric global vortex, the skyrmion, the Abrikosov-Nielsen-Olesen vortex, as well as the 't Hooft-Polyakov magnetic monopole. The total energy of the skyrmion and of the monopole is also computed by the new method. We also consider some ODEs coming from the exact renormalization group. The ground-state energy level of the anharmonic oscillator is also computed for arbitrary coupling strengths with good precision. (fast track communication)

  6. Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

    Science.gov (United States)

    Pratt, D. T.

    1984-01-01

    Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

  7. Applications of Parameterized Nonlinear Ordinary Differential Equations and Dynamic Systems: An Example of the Taiwan Stock Index

    Directory of Open Access Journals (Sweden)

    Meng-Rong Li

    2018-01-01

    Full Text Available Considering the phenomenon of the mean reversion and the different speeds of stock prices in the bull market and in the bear market, we propose four dynamic models each of which is represented by a parameterized ordinary differential equation in this study. Based on existing studies, the models are in the form of either the logistic growth or the law of Newton’s cooling. We solve the models by dynamic integration and apply them to the daily closing prices of the Taiwan stock index, Taiwan Stock Exchange Capitalization Weighted Stock Index. The empirical study shows that some of the models fit the prices well and the forecasting ability of the best model is acceptable even though the martingale forecasts the prices slightly better. To increase the forecasting ability and to broaden the scope of applications of the dynamic models, we will model the coefficients of the dynamic models in the future. Applying the models to the market without the price limit is also our future work.

  8. Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

    Science.gov (United States)

    Wu, Hulin; Xue, Hongqi; Kumar, Arun

    2012-06-01

    Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

  9. Pure soliton solutions of some nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Fuchssteiner, B.

    1977-01-01

    A general approach is given to obtain the system of ordinary differential equations which determines the pure soliton solutions for the class of generalized Korteweg-de Vries equations. This approach also leads to a system of ordinary differential equations for the pure soliton solutions of the sine-Gordon equation. (orig.) [de

  10. Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation

    OpenAIRE

    Tarun Kumar Rawat; Abhirup Lahiri; Ashish Gupta

    2008-01-01

    In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parame...

  11. Calculation of similarity solutions of partial differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1980-08-01

    When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/

  12. [Extension of cardiac monitoring function by used of ordinary ECG machine].

    Science.gov (United States)

    Chen, Zhencheng; Jiang, Yong; Ni, Lili; Wang, Hongyan

    2002-06-01

    This paper deals with a portable monitor system on liquid crystal display (LCD) based on this available ordinary ECG machine, which is low power and suitable for China's specific condition. Apart from developing the overall scheme of the system, this paper also has completed the design of the hardware and the software. The 80c196 single chip microcomputer is taken as the central microprocessor and real time electrocardiac single is data treated and analyzed in the system. With the performance of ordinary monitor, this machine also possesses the following functions: five types of arrhythmia analysis, alarm, freeze, and record of automatic pappering, convenient in carrying, with alternate-current (AC) or direct-current (DC) powered. The hardware circuit is simplified and the software structure is optimized in this paper. Multiple low power designs and LCD unit design are adopted and completed in it. Popular in usage, low in cost price, the portable monitor system will have a valuable influence on China's monitor system field.

  13. PSsolver: A Maple implementation to solve first order ordinary differential equations with Liouvillian solutions

    Science.gov (United States)

    Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.

    2012-10-01

    We present a set of software routines in Maple 14 for solving first order ordinary differential equations (FOODEs). The package implements the Prelle-Singer method in its original form together with its extension to include integrating factors in terms of elementary functions. The package also presents a theoretical extension to deal with all FOODEs presenting Liouvillian solutions. Applications to ODEs taken from standard references show that it solves ODEs which remain unsolved using Maple's standard ODE solution routines. New version program summary Program title: PSsolver Catalogue identifier: ADPR_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADPR_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2302 No. of bytes in distributed program, including test data, etc.: 31962 Distribution format: tar.gz Programming language: Maple 14 (also tested using Maple 15 and 16). Computer: Intel Pentium Processor P6000, 1.86 GHz. Operating system: Windows 7. RAM: 4 GB DDR3 Memory Classification: 4.3. Catalogue identifier of previous version: ADPR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 144 (2002) 46 Does the new version supersede the previous version?: Yes Nature of problem: Symbolic solution of first order differential equations via the Prelle-Singer method. Solution method: The method of solution is based on the standard Prelle-Singer method, with extensions for the cases when the FOODE contains elementary functions. Additionally, an extension of our own which solves FOODEs with Liouvillian solutions is included. Reasons for new version: The program was not running anymore due to changes in the latest versions of Maple. Additionally, we corrected/changed some bugs/details that were hampering the smoother functioning of the routines. Summary

  14. Automatic differentiation bibliography

    Energy Technology Data Exchange (ETDEWEB)

    Corliss, G.F. [comp.

    1992-07-01

    This is a bibliography of work related to automatic differentiation. Automatic differentiation is a technique for the fast, accurate propagation of derivative values using the chain rule. It is neither symbolic nor numeric. Automatic differentiation is a fundamental tool for scientific computation, with applications in optimization, nonlinear equations, nonlinear least squares approximation, stiff ordinary differential equation, partial differential equations, continuation methods, and sensitivity analysis. This report is an updated version of the bibliography which originally appeared in Automatic Differentiation of Algorithms: Theory, Implementation, and Application.

  15. Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

    Science.gov (United States)

    Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

    2016-01-01

    Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

  16. On the relation between elementary partial difference equations and partial differential equations

    NARCIS (Netherlands)

    van den Berg, I.P.

    1998-01-01

    The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential

  17. Algorithmic Verification of Linearizability for Ordinary Differential Equations

    KAUST Repository

    Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Michels, Dominik L.

    2017-01-01

    one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra. The second algorithm exploits the differential

  18. Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

    Science.gov (United States)

    Ding, Xiao-Li; Nieto, Juan J.

    2017-11-01

    In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

  19. Non-instantaneous impulses in differential equations

    CERN Document Server

    Agarwal, Ravi; O'Regan, Donal

    2017-01-01

    This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses. It aims to equip the reader with mathematical models and theory behind real life processes in physics, biology, population dynamics, ecology and pharmacokinetics. The authors examine a wide scope of differential equations with non-instantaneous impulses through three comprehensive chapters, providing an all-rounded and unique presentation on the topic, including: - Ordinary differential equations with non-instantaneous impulses (scalar and n-dimensional case) - Fractional differential equa tions with non-instantaneous impulses (with Caputo fractional derivatives of order q ϵ (0, 1)) - Ordinary differential equations with non-instantaneous impulses occurring at random moments (with exponential, Erlang, or Gamma distribution) Each chapter focuses on theory, proofs and examples, and contains numerous graphs to enrich the reader’s understanding. Additionally, a carefully selected bibliogr...

  20. 7 CFR 28.407 - Good Ordinary Color.

    Science.gov (United States)

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Good Ordinary Color. 28.407 Section 28.407 Agriculture..., TESTING, AND STANDARDS Standards Official Cotton Standards of the United States for the Color Grade of American Upland Cotton § 28.407 Good Ordinary Color. Good Ordinary Color is color which is within the range...

  1. Transmission of neutrons in serpentine mixed and ordinary concrete a comparative study

    International Nuclear Information System (INIS)

    Ravishankar, R.; Bhattacharyya, Sarmishtha; Bandyopadhyay, Tapas; Sarkar, P.K.

    2002-01-01

    Full text: In particle accelerator facilities, for radiation shielding, concrete is commonly used for its effectiveness in attenuating neutrons in addition to its good structural and mechanical properties. Neutron attenuation depends largely on the water content in the concrete. Serpentine mixed concrete is reported to retain better water content than ordinary concrete. Experiments have been carried out to compare neutron attenuation properties of Serpentine mixed concrete slabs and ordinary concrete slabs of different thickness. Transmission of neutrons from a 185 GBq Pu-Be neutron source has been studied using NE-213 liquid scintillator detector, along with the associated electronics to discriminate neutron from gamma using pulse shape discrimination techniques. The energy differential neutron spectra transmitted through the concrete slabs and the corresponding dose have been obtained by unfolding the pulse height spectra using the FERDOR-U computer code and proper response matrix data of the NE-213 detector. The neutron transmission factors through both Serpentine and Ordinary concrete slabs have been studied. The results show serpentine mixed concrete slabs can attenuate more neutrons of varying energies compared to ordinary concrete slabs of equal dimensions. From the trend, it has been found out, with the increase in slab thickness, the gain in neutron attenuation increases. This is due to increase in quantity of serpentine with the increase in thickness of, concrete. A Monte Carlo simulation carried out, for theoretical analysis of the results, has been found to be in order

  2. Transmission of neutrons in serpentine mixed and ordinary concrete- a comparative study

    International Nuclear Information System (INIS)

    Ravishankar, R.; Bhattacharyya, Sarmishtha; Bandyopadhyay, Tapas; Sarkar, P. K.

    2002-01-01

    In particle accelerator facilities, for radiation shielding, concrete is commonly used for its effectiveness in attenuating neutrons in addition to its good structural and mechanical properties. Neutron attenuation depends largely on the water content in the concrete. Serpentine mixed concrete is reported to retain better water content than ordinary concrete. Experiments have been carried out to compare neutron attenuation properties of Serpentine mixed concrete slabs and ordinary concrete slabs of different thickness. Transmission of neutrons from a 185 GBq Pu-Be neutron source has been studied using NE-213 liquid scintillator detector, along with the associated electronics to discriminate neutron from gamma using pulse shape discrimination techniques. The energy differential neutron spectra transmitted through the concrete slabs and the corresponding dose have been obtained by unfolding the pulse height spectra using the FERDOR-U computer code and proper response matrix data of the NE-213 detector. The neutron transmission factors through both Serpentine and Ordinary concrete slabs have been studied. The results show serpentine mixed concrete slabs can attenuate more neutrons of varying energies compared to ordinary concrete slabs of equal dimensions. From the trend, it has been found out, with the increase in slab thickness, the gain in neutron attenuation increases. This is due to increase in quantity of serpentine with the increase in thickness of concrete. A Monte Carlo simulation carried out, for theoretical analysis of the results, has been found to be in order

  3. Generalized ordinary differential equations not absolutely continuous solutions

    CERN Document Server

    Kurzweil, Jaroslav

    2012-01-01

    This book provides a systematic treatment of the Volterra integral equation by means of a modern integration theory which extends considerably the field of differential equations. It contains many new concepts and results in the framework of a unifying theory. In particular, this new approach is suitable in situations where fast oscillations occur.

  4. Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation

    International Nuclear Information System (INIS)

    Liu Chengshi

    2007-01-01

    Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.

  5. A single-to-differential low-noise amplifier with low differential output imbalance

    International Nuclear Information System (INIS)

    Duan Lian; Ma Chengyan; He Xiaofeng; Ye Tianchun; Huang Wei; Jin Yuhua

    2012-01-01

    This paper presents a single-ended input differential output low-noise amplifier intended for GPS applications. We propose a method to reduce the gain/amplitude and phase imbalance of a differential output exploiting the inductive coupling of a transformer or center-tapped differential inductor. A detailed analysis of the theory of imbalance reduction, as well as a discussion on the principle of choosing the dimensions of a transformer, are given. An LNA has been implemented using TSMC 0.18 μm technology with ESD-protected. Measurement on board shows a voltage gain of 24.6 dB at 1.575 GHz and a noise figure of 3.2 dB. The gain imbalance is below 0.2 dB and phase imbalance is less than 2 degrees. The LNA consumes 5.2 mA from a 1.8 V supply. (semiconductor integrated circuits)

  6. Vibration modes of a single plate with general boundary conditions

    Directory of Open Access Journals (Sweden)

    Phamová L.

    2016-06-01

    Full Text Available This paper deals with free flexural vibration modes and natural frequencies of a thin plate with general boundary conditions — a simply supported plate connected to its surroundings with torsional springs. Vibration modes were derived on the basis of the Rajalingham, Bhat and Xistris approach. This approach was originally used for a clamped thin plate, so its adaptation was needed. The plate vibration function was usually expressed as a single partial differential equation. This partial differential equation was transformed into two ordinary differential equations that can be solved in the simpler way. Theoretical background of the computations is briefly described. Vibration modes of the supported plate with torsional springs are presented graphically and numerically for three different values of stiffness of torsional springs.

  7. Differential equations from the algebraic standpoint

    CERN Document Server

    Ritt, Joseph Fels

    1932-01-01

    This book can be viewed as a first attempt to systematically develop an algebraic theory of nonlinear differential equations, both ordinary and partial. The main goal of the author was to construct a theory of elimination, which "will reduce the existence problem for a finite or infinite system of algebraic differential equations to the application of the implicit function theorem taken with Cauchy's theorem in the ordinary case and Riquier's in the partial." In his 1934 review of the book, J. M. Thomas called it "concise, readable, original, precise, and stimulating", and his words still rema

  8. A new class of scale free solutions to linear ordinary differential equations and the universality of the golden mean (Radical radicand 5 -1)/2=0.618033...

    CERN Document Server

    Datta, D P

    2003-01-01

    A new class of finitely differentiable scale free solutions to the simplest class of ordinary differential equations is presented. Consequently, the real number set gets replaced by an extended physical set, each element of which is endowed with an equivalence class of infinitesimally separated neighbours in the form of random fluctuations. We show how a sense of time and evolution is intrinsically defined by the infinite continued fraction of the golden mean irrational number (Radical radicand 5 -1)/2, which plays a key role in this extended SL(2,R) formalism of calculus analogous to El Naschie's theory of E sup ( supinfinity sup ) spacetime manifold. Time may thereby undergo random inversions generating well defined random scales, thus allowing a dynamical system to evolve self similarly over the set of multiple scales. The late time stochastic fluctuations of a dynamical system enjoys the generic 1/f spectrum. A universal form of the related probability density is also derived. We prove that the golden mea...

  9. Ordinary Least Squares and Quantile Regression: An Inquiry-Based Learning Approach to a Comparison of Regression Methods

    Science.gov (United States)

    Helmreich, James E.; Krog, K. Peter

    2018-01-01

    We present a short, inquiry-based learning course on concepts and methods underlying ordinary least squares (OLS), least absolute deviation (LAD), and quantile regression (QR). Students investigate squared, absolute, and weighted absolute distance functions (metrics) as location measures. Using differential calculus and properties of convex…

  10. Pod systems: an equivariant ordinary differential equation approach to dynamical systems on a spatial domain

    International Nuclear Information System (INIS)

    Elmhirst, Toby; Stewart, Ian; Doebeli, Michael

    2008-01-01

    We present a class of systems of ordinary differential equations (ODEs), which we call 'pod systems', that offers a new perspective on dynamical systems defined on a spatial domain. Such systems are typically studied as partial differential equations, but pod systems bring the analytic techniques of ODE theory to bear on the problems, and are thus able to study behaviours and bifurcations that are not easily accessible to the standard methods. In particular, pod systems are specifically designed to study spatial dynamical systems that exhibit multi-modal solutions. A pod system is essentially a linear combination of parametrized functions in which the coefficients and parameters are variables whose dynamics are specified by a system of ODEs. That is, pod systems are concerned with the dynamics of functions of the form Ψ(s, t) = y 1 (t) φ(s; x 1 (t)) + ··· + y N (t) φ(s; x N (t)), where s in R n is the spatial variable and φ: R n × R d → R. The parameters x i in R d and coefficients y i in R are dynamic variables which evolve according to some system of ODEs, x-dot i = G i (x, y) and y-dot i = H i (x, y), for i = 1, ..., N. The dynamics of Ψ in function space can then be studied through the dynamics of the x and y in finite dimensions. A vital feature of pod systems is that the ODEs that specify the dynamics of the x and y variables are not arbitrary; restrictions on G i and H i are required to guarantee that the dynamics of Ψ in function space are well defined (that is, that trajectories are unique). One important restriction is symmetry in the ODEs which arises because Ψ is invariant under permutations of the indices of the (x i , y i ) pairs. However, this is not the whole story, and the primary goal of this paper is to determine the necessary structure of the ODEs explicitly to guarantee that the dynamics of Ψ are well defined

  11. CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR ...

    African Journals Online (AJOL)

    This paper describes a new nonlinear backward differentiation schemes for the numerical solution of nonlinear initial value problems of first order ordinary differential equations. The schemes are based on rational interpolation obtained from canonical polynomials. They are A-stable. The test problems show that they give ...

  12. Differential equations methods and applications

    CERN Document Server

    Said-Houari, Belkacem

    2015-01-01

    This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .

  13. Fuchs indices and the first integrals of nonlinear differential equations

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.

    2005-01-01

    New method of finding the first integrals of nonlinear differential equations in polynomial form is presented. Basic idea of our approach is to use the scaling of solution of nonlinear differential equation and to find the dimensions of arbitrary constants in the Laurent expansion of the general solution. These dimensions allows us to obtain the scalings of members for the first integrals of nonlinear differential equations. Taking the polynomials with unknown coefficients into account we present the algorithm of finding the first integrals of nonlinear differential equations in the polynomial form. Our method is applied to look for the first integrals of eight nonlinear ordinary differential equations of the fourth order. The general solution of one of the fourth order ordinary differential equations is given

  14. Introduction to partial differential equations with applications

    CERN Document Server

    Zachmanoglou, E C

    1988-01-01

    This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

  15. Differential equations

    CERN Document Server

    Barbu, Viorel

    2016-01-01

    This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

  16. Differentiation of real functions

    CERN Document Server

    Bruckner, Andrew

    1994-01-01

    Topics related to the differentiation of real functions have received considerable attention during the last few decades. This book provides an efficient account of the present state of the subject. Bruckner addresses in detail the problems that arise when dealing with the class \\Delta ' of derivatives, a class that is difficult to handle for a number of reasons. Several generalized forms of differentiation have assumed importance in the solution of various problems. Some generalized derivatives are excellent substitutes for the ordinary derivative when the latter is not known to exist; others are not. Bruckner studies generalized derivatives and indicates "geometric" conditions that determine whether or not a generalized derivative will be a good substitute for the ordinary derivative. There are a number of classes of functions closely linked to differentiation theory, and these are examined in some detail. The book unifies many important results from the literature as well as some results not previously pub...

  17. 7 CFR 28.406 - Strict Good Ordinary Color.

    Science.gov (United States)

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Good Ordinary Color. 28.406 Section 28.406... for the Color Grade of American Upland Cotton § 28.406 Strict Good Ordinary Color. Strict Good Ordinary Color is color which is within the range represented by a set of samples in the custody of the...

  18. Porting Ordinary Applications to Blue Gene/Q Supercomputers

    Energy Technology Data Exchange (ETDEWEB)

    Maheshwari, Ketan C.; Wozniak, Justin M.; Armstrong, Timothy; Katz, Daniel S.; Binkowski, T. Andrew; Zhong, Xiaoliang; Heinonen, Olle; Karpeyev, Dmitry; Wilde, Michael

    2015-08-31

    Efficiently porting ordinary applications to Blue Gene/Q supercomputers is a significant challenge. Codes are often originally developed without considering advanced architectures and related tool chains. Science needs frequently lead users to want to run large numbers of relatively small jobs (often called many-task computing, an ensemble, or a workflow), which can conflict with supercomputer configurations. In this paper, we discuss techniques developed to execute ordinary applications over leadership class supercomputers. We use the high-performance Swift parallel scripting framework and build two workflow execution techniques-sub-jobs and main-wrap. The sub-jobs technique, built on top of the IBM Blue Gene/Q resource manager Cobalt's sub-block jobs, lets users submit multiple, independent, repeated smaller jobs within a single larger resource block. The main-wrap technique is a scheme that enables C/C++ programs to be defined as functions that are wrapped by a high-performance Swift wrapper and that are invoked as a Swift script. We discuss the needs, benefits, technicalities, and current limitations of these techniques. We further discuss the real-world science enabled by these techniques and the results obtained.

  19. The Euler’s Graphical User Interface Spreadsheet Calculator for Solving Ordinary Differential Equations by Visual Basic for Application Programming

    Science.gov (United States)

    Gaik Tay, Kim; Cheong, Tau Han; Foong Lee, Ming; Kek, Sie Long; Abdul-Kahar, Rosmila

    2017-08-01

    In the previous work on Euler’s spreadsheet calculator for solving an ordinary differential equation, the Visual Basic for Application (VBA) programming was used, however, a graphical user interface was not developed to capture users input. This weakness may make users confuse on the input and output since those input and output are displayed in the same worksheet. Besides, the existing Euler’s spreadsheet calculator is not interactive as there is no prompt message if there is a mistake in inputting the parameters. On top of that, there are no users’ instructions to guide users to input the derivative function. Hence, in this paper, we improved previous limitations by developing a user-friendly and interactive graphical user interface. This improvement is aimed to capture users’ input with users’ instructions and interactive prompt error messages by using VBA programming. This Euler’s graphical user interface spreadsheet calculator is not acted as a black box as users can click on any cells in the worksheet to see the formula used to implement the numerical scheme. In this way, it could enhance self-learning and life-long learning in implementing the numerical scheme in a spreadsheet and later in any programming language.

  20. On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra

    Science.gov (United States)

    Ndogmo, J. C.

    2017-06-01

    Although every iterative scalar linear ordinary differential equation is of maximal symmetry algebra, the situation is different and far more complex for systems of linear ordinary differential equations, and an iterative system of linear equations need not be of maximal symmetry algebra. We illustrate these facts by examples and derive families of vector differential operators whose iterations are all linear systems of equations of maximal symmetry algebra. Some consequences of these results are also discussed.

  1. Workshop on Numerical Methods for Ordinary Differential Equations

    CERN Document Server

    Gear, Charles; Russo, Elvira

    1989-01-01

    Developments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay integral and integro-differential equations, stability properties, continuous extensions (interpolants for Runge-Kutta methods and their applications, effective stepsize control, parallel algorithms for small- and large-scale parallel architectures). The resulting proceedings address many of these topics in both research and survey papers.

  2. Solving Differential Equations in R: Package deSolve

    Science.gov (United States)

    In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

  3. Introduction to differentiable manifolds

    CERN Document Server

    Auslander, Louis

    2009-01-01

    The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary diff

  4. Single-cell entropy for accurate estimation of differentiation potency from a cell's transcriptome

    Science.gov (United States)

    Teschendorff, Andrew E.; Enver, Tariq

    2017-01-01

    The ability to quantify differentiation potential of single cells is a task of critical importance. Here we demonstrate, using over 7,000 single-cell RNA-Seq profiles, that differentiation potency of a single cell can be approximated by computing the signalling promiscuity, or entropy, of a cell's transcriptome in the context of an interaction network, without the need for feature selection. We show that signalling entropy provides a more accurate and robust potency estimate than other entropy-based measures, driven in part by a subtle positive correlation between the transcriptome and connectome. Signalling entropy identifies known cell subpopulations of varying potency and drug resistant cancer stem-cell phenotypes, including those derived from circulating tumour cells. It further reveals that expression heterogeneity within single-cell populations is regulated. In summary, signalling entropy allows in silico estimation of the differentiation potency and plasticity of single cells and bulk samples, providing a means to identify normal and cancer stem-cell phenotypes. PMID:28569836

  5. Solution of differential equations by application of transformation groups

    Science.gov (United States)

    Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

    1968-01-01

    Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

  6. Solving Differential Equations in R: Package deSolve

    NARCIS (Netherlands)

    Soetaert, K.E.R.; Petzoldt, T.; Setzer, R.W.

    2010-01-01

    In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The

  7. Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

    Science.gov (United States)

    Kennedy, Christopher A.; Carpenter, Mark H.

    2016-01-01

    A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.

  8. Ordinary General Assembly

    CERN Multimedia

    Staff Association

    2011-01-01

    Tuesday 12 April at 14.00 Council Chamber, Bldg 503 In conformity with the Statutes of the Staff Association, an ordinary General Assembly is organized once a year (article IV.2.1). Agenda   Adoption of the Agenda Approval of the Draft Minutes of the Ordinary General Assembly of 20 April 2010 Presentation and approval of the Activity Report 2010 Presentation and approval of the Financial Report 2010 Presentation and approval of the Auditors Report 2010 Programme for 2011 Presentation et and approval of the draft budget and subscription rate 2012 Election of the Election Committee Election of the Board of Auditors Miscellaneous We remind members of article IV.3.4 in the Statutes of the Association which reads: “After having dealt with all the items on the agenda, the members may, with the consent of the Assembly, have other matters discussed, but decisions may be taken only on the items listed on the agenda. Nevertheless, the Assembly ma...

  9. Ordinary General Assembly

    CERN Multimedia

    Association du personnel

    2010-01-01

    Tuesday 20 April at 10.00 Council Chamber, Bldg 503 In conformity with the Statutes of the Staff Association, an ordinary General Assembly is organized once a year (article IV.2.1). Agenda Adoption of the Agenda Approval of the Draft Minutes of the Ordinary General Assembly of 12 May 2009 Presentation and approval of the Activity Report 2009 Presentation and approval of the Financial Report 2009 Presentation and approval of the Auditors Report 2009 Programme for 2010 Presentation et and approval of the draft budget and subscription rate 2010 Modifications to the statutes of the association Election of the Election Committee Election of the Board of Auditors Miscellaneous We remind members of article IV.3.4 in the Statutes of the Association which reads: “After having dealt with all the items on the agenda, the members may, with the consent of the Assembly, have other matters discussed, but decisions may be taken only on the items listed on the agenda...

  10. Ordinary General Assembly

    CERN Multimedia

    Staff Association

    2011-01-01

    Tuesday 12 April at 14.00 Council Chamber, Bldg 503 In conformity with the Statutes of the Staff Association, an ordinary General Assembly is organized once a year (article IV.2.1). Agenda   Adoption of the Agenda Approval of the Draft Minutes of the Ordinary General Assembly of 20 April 2010 Presentation and approval of the Activity Report 2010 Presentation and approval of the Financial Report 2010 Presentation and approval of the Auditors Report 2010 Programme for 2011 Presentation and approval of the draft budget and subscription rate 2012 Election of the Election Committee Election of the Board of Auditors Miscellaneous We remind members of article IV.3.4 in the Statutes of the Association which reads: “After having dealt with all the items on the agenda, the members may, with the consent of the Assembly, have other matters discussed, but decisions may be taken only on the items listed on the agenda. Nevertheless, the Assembly may r...

  11. Ordinary General Assembly

    CERN Multimedia

    Staff Association

    2010-01-01

    Tuesday 20 April at 10.00 Council Chamber, Bldg 503 In conformity with the Statutes of the Staff Association, an ordinary General Assembly is organized once a year (article IV.2.1). Agenda   Adoption of the Agenda Approval of the Draft Minutes of the Ordinary General Assembly of 12 May 2009 Presentation and approval of the Activity Report 2009 Presentation and approval of the Financial Report 2009 Presentation and approval of the Auditors Report 2009 Programme for 2010 Presentation et and approval of the draft budget and subscription rate 2010 Election of the Election Committee Election of the Board of Auditors Miscellaneous We remind members of article IV.3.4 in the Statutes of the Association which reads: “After having dealt with all the items on the agenda, the members may, with the consent of the Assembly, have other matters discussed, but decisions may be taken only on the items listed on the agenda. Nevertheless, the Assembly may require t...

  12. The Bessel polynomials and their differential operators

    International Nuclear Information System (INIS)

    Onyango Otieno, V.P.

    1987-10-01

    Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs

  13. The Numerical Solution of an Abelian Ordinary Differential Equation ...

    African Journals Online (AJOL)

    In this paper we present a relatively new technique call theNew Hybrid of Adomian decomposition method (ADM) for solution of an Abelian Differential equation. The numerical results of the equation have been obtained in terms of convergent series with easily computable component. These methods are applied to solve ...

  14. Differential-algebraic solutions of the heat equation

    OpenAIRE

    Buchstaber, Victor M.; Netay, Elena Yu.

    2014-01-01

    In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of a special form. The ansatz for such solutions is called the $n$-ansatz, where $n+1$ is the order of the differential equation.

  15. Single-cell RNA sequencing reveals metallothionein heterogeneity during hESC differentiation to definitive endoderm

    Directory of Open Access Journals (Sweden)

    Junjie Lu

    2018-04-01

    Full Text Available Differentiation of human pluripotent stem cells towards definitive endoderm (DE is the critical first step for generating cells comprising organs such as the gut, liver, pancreas and lung. This in-vitro differentiation process generates a heterogeneous population with a proportion of cells failing to differentiate properly and maintaining expression of pluripotency factors such as Oct4. RNA sequencing of single cells collected at four time points during a 4-day DE differentiation identified high expression of metallothionein genes in the residual Oct4-positive cells that failed to differentiate to DE. Using X-ray fluorescence microscopy and multi-isotope mass spectrometry, we discovered that high intracellular zinc level corresponds with persistent Oct4 expression and failure to differentiate. This study improves our understanding of the cellular heterogeneity during in-vitro directed differentiation and provides a valuable resource to improve DE differentiation efficiency. Keywords: hPSC, Differentiation, Definitive endoderm, Heterogeneity, Single cell, RNA sequencing

  16. Functional differential equations—a reciprocity principle

    Directory of Open Access Journals (Sweden)

    Lloyd K. Williams

    1986-01-01

    Full Text Available The functional differential equations proposed for solution here are mainly ordinary differential equations with fairly general argument deviations. Included among them are equations with involutions and some with reflections of the argument. Solutions will be obtained by quadratures in terms of implicitly defined functions. They have a wide range of applicability from the stability theory of differential-difference equations to electrodynamics and biological models.

  17. Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

    Science.gov (United States)

    DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.

    2008-06-01

    For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).

  18. Tailored parameter optimization methods for ordinary differential equation models with steady-state constraints.

    Science.gov (United States)

    Fiedler, Anna; Raeth, Sebastian; Theis, Fabian J; Hausser, Angelika; Hasenauer, Jan

    2016-08-22

    Ordinary differential equation (ODE) models are widely used to describe (bio-)chemical and biological processes. To enhance the predictive power of these models, their unknown parameters are estimated from experimental data. These experimental data are mostly collected in perturbation experiments, in which the processes are pushed out of steady state by applying a stimulus. The information that the initial condition is a steady state of the unperturbed process provides valuable information, as it restricts the dynamics of the process and thereby the parameters. However, implementing steady-state constraints in the optimization often results in convergence problems. In this manuscript, we propose two new methods for solving optimization problems with steady-state constraints. The first method exploits ideas from optimization algorithms on manifolds and introduces a retraction operator, essentially reducing the dimension of the optimization problem. The second method is based on the continuous analogue of the optimization problem. This continuous analogue is an ODE whose equilibrium points are the optima of the constrained optimization problem. This equivalence enables the use of adaptive numerical methods for solving optimization problems with steady-state constraints. Both methods are tailored to the problem structure and exploit the local geometry of the steady-state manifold and its stability properties. A parameterization of the steady-state manifold is not required. The efficiency and reliability of the proposed methods is evaluated using one toy example and two applications. The first application example uses published data while the second uses a novel dataset for Raf/MEK/ERK signaling. The proposed methods demonstrated better convergence properties than state-of-the-art methods employed in systems and computational biology. Furthermore, the average computation time per converged start is significantly lower. In addition to the theoretical results, the

  19. Differential Single-Capture Cross Sections for Fast Alpha–Helium Collisions

    International Nuclear Information System (INIS)

    Ghanbari-Adivi, Ebrahim; Ghavaminia, Hoda

    2014-01-01

    A four-body theoretical study of the single charge transfer process in collision of energetic alpha ions with helium atoms in their ground states is presented. The model utilizes the Coulomb–Born distorted wave approximation with correct boundary conditions to calculate the single-electron capture differential and integral cross sections. The influence of the dynamic and static electron correlations on the capture probability is investigated. The results of the calculations are compared with the recent experimental measurements for differential cross sections and with the other theoretical manipulations. The results for scattering at extreme forward angles are in good agreement with the experimental measurements, but in other scattering angles the agreement is poor. However, the present four-body results for integral cross sections are in excellent agreement with the experimental data. (author)

  20. Variable-mesh method of solving differential equations

    Science.gov (United States)

    Van Wyk, R.

    1969-01-01

    Multistep predictor-corrector method for numerical solution of ordinary differential equations retains high local accuracy and convergence properties. In addition, the method was developed in a form conducive to the generation of effective criteria for the selection of subsequent step sizes in step-by-step solution of differential equations.

  1. Solving polynomial differential equations by transforming them to linear functional-differential equations

    OpenAIRE

    Nahay, John Michael

    2008-01-01

    We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

  2. A Line-Tau Collocation Method for Partial Differential Equations ...

    African Journals Online (AJOL)

    This paper deals with the numerical solution of second order linear partial differential equations with the use of the method of lines coupled with the tau collocation method. The method of lines is used to convert the partial differential equation (PDE) to a sequence of ordinary differential equations (ODEs) which is then ...

  3. Selective Disparity of Ordinary Chondritic Precursors in Micrometeorite Flux

    Science.gov (United States)

    Rudraswami, N. G.; Fernandes, D.; Naik, A. K.; Shyam Prasad, M.; Carrillo-Sánchez, J. D.; Plane, J. M. C.; Feng, W.; Taylor, S.

    2018-01-01

    All known extraterrestrial dust (micrometeoroids) entering the Earth’s atmosphere is anticipated to have a significant contribution from ordinary chondritic precursors, as seen in meteorites, but this is an apparent contradiction that needs to be addressed. Ordinary chondrites represent a minor contribution to the overall meteor influx compared to carbonaceous chondrites, which are largely dominated by CI and/or CM chondrites. However, the near-Earth asteroid population presents a scenario with sufficient scope for generation of dust-sized debris from ordinary chondritic sources. The bulk chemical composition of 3255 micrometeorites (MMs) collected from Antarctica and deep-sea sediments has shown Mg/Si largely dominated by carbonaceous chondrites, and less than 10% having ordinary chondritic precursors. The chemical ablation model is combined with different initial chondritic compositions (CI, CV, L, LL, H), and the results clearly indicate that high-density (≥2.8 g cm‑3) precursors, such as CV and ordinary chondrites in the size range 100–700 μm and zenith angle 0°–70°, ablate at much faster rates and lose their identity even before reaching the Earth’s surface and hence are under-represented in our collections. Moreover, their ability to survive as MMs remains grim for high-velocity micrometeoroids (>16 km s‑1). The elemental ratio for CV and ordinary chondrites are also similar to each other irrespective of the difference in the initial chemical composition. In conclusion, MMs belonging to ordinary chondritic precursors’ concentrations may not be insignificant in thermosphere, as they are found on Earth’s surface.

  4. Evidence from the Semarkona ordinary chondrite for 26Al heating of small planets

    International Nuclear Information System (INIS)

    Hutcheon, I.D.

    1989-01-01

    We report the first observation of radiogenic 26 Mg in non-refractory meteoritic material, a plagio-clase-bearing, olivine-pyroxene clast chondrule in the Semarkona ordinary chondrite. The inferred initial abundance of 26 Al is sufficient to produce incipient melting in well insulated bodies of chondritic composition. We conclude that planetary accretion and differentiation must have begun on a timescale comparable to the half life of 26 Al and that, even if widespread melting did not occur, 26 Al heating played a significant role in thermal metamorphism on small planets. (author)

  5. First order linear ordinary differential equations in associative algebras

    Directory of Open Access Journals (Sweden)

    Gordon Erlebacher

    2004-01-01

    Full Text Available In this paper, we study the linear differential equation $$ frac{dx}{dt}=sum_{i=1}^n a_i(t x b_i(t + f(t $$ in an associative but non-commutative algebra $mathcal{A}$, where the $b_i(t$ form a set of commuting $mathcal{A}$-valued functions expressed in a time-independent spectral basis consisting of mutually annihilating idempotents and nilpotents. Explicit new closed solutions are derived, and examples are presented to illustrate the theory.

  6. Lie symmetries in differential equations

    International Nuclear Information System (INIS)

    Pleitez, V.

    1979-01-01

    A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt

  7. Linear measure functional differential equations with infinite delay

    OpenAIRE

    Monteiro, G. (Giselle Antunes); Slavík, A.

    2014-01-01

    We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.

  8. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  9. Nonlinear differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

  10. Elements of partial differential equations

    CERN Document Server

    Sneddon, Ian Naismith

    1957-01-01

    Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

  11. On a quaternionic generalisation of the Riccati differential equation

    OpenAIRE

    Kravchenko, Viktor; Kravchenko, Vladislav; Williams, Benjamin

    2001-01-01

    A quaternionic partial differential equation is shown to be a generalisation of the Riccati ordinary differential equation and its relationship with the Schrodinger equation is established. Various approaches to the problem of finding particular solutions are explored, and the generalisations of two theorems of Euler on the Riccati differential equation, which correspond to the quaternionic equation, are given.

  12. Reduced minimax filtering by means of differential-algebraic equations

    NARCIS (Netherlands)

    V. Mallet; S. Zhuk (Sergiy)

    2011-01-01

    htmlabstractA reduced minimax state estimation approach is proposed for high-dimensional models. It is based on the reduction of the ordinary differential equation with high state space dimension to the low-dimensional Differential-Algebraic Equation (DAE) and on the subsequent application of the

  13. Non-diagonal processes of singlet and ordinary quark production

    International Nuclear Information System (INIS)

    Bejlin, V.A.; Vereshkov, G.M.; Kuksa, V.I.

    1995-01-01

    Non-diagonal processes of singlet and ordinary quark production are analyzed in the model where the down singlet quark mixes with the ordinary ones. The possibility of experimental selection of h-quark effects is demonstrated

  14. Differential equations, mechanics, and computation

    CERN Document Server

    Palais, Richard S

    2009-01-01

    This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.

  15. Solving Differential Equations Analytically. Elementary Differential Equations. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 335.

    Science.gov (United States)

    Goldston, J. W.

    This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…

  16. Linear measure functional differential equations with infinite delay

    Czech Academy of Sciences Publication Activity Database

    Monteiro, Giselle Antunes; Slavík, A.

    2014-01-01

    Roč. 287, 11-12 (2014), s. 1363-1382 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : measure functional differential equations * generalized ordinary differential equations * Kurzweil-Stieltjes integral Subject RIV: BA - General Mathematics Impact factor: 0.683, year: 2014 http://onlinelibrary.wiley.com/doi/10.1002/mana.201300048/abstract

  17. Partial differential equations for scientists and engineers

    CERN Document Server

    Farlow, Stanley J

    1993-01-01

    Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th

  18. Legendre-tau approximations for functional differential equations

    Science.gov (United States)

    Ito, K.; Teglas, R.

    1986-01-01

    The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

  19. Lie symmetries and differential galois groups of linear equations

    NARCIS (Netherlands)

    Oudshoorn, W.R.; Put, M. van der

    2002-01-01

    For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In

  20. Topological Higgs mechanism with ordinary Higgs mechanism

    International Nuclear Information System (INIS)

    Oda Ichiro; Yahikozawa Shigeaki.

    1989-12-01

    Topological Higgs mechanism in higher dimensions is analyzed when ordinary Higgs potential exists. It is shown that if one-form B-field becomes massive by the ordinary Higgs mechanism, another D-2 form C-field also becomes massive through topological term in addition to the topological mass generation by the topological Higgs mechanism. Moreover we investigate this mechanism in three dimensional theories, that is to say, Chern-Simons theory and more general theory. (author). 10 refs

  1. Iterative Splitting Methods for Differential Equations

    CERN Document Server

    Geiser, Juergen

    2011-01-01

    Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

  2. Doubly differential single and multiple ionization of krypton by electron impact

    International Nuclear Information System (INIS)

    Lucio, O. G. de; Gavin, J.; DuBois, R. D.

    2007-01-01

    Differential measurements for single and multiple ionization of Kr by 240 and 500 eV electron impact are presented. Using a pulsed extraction field, Kr + , Kr 2+ , and Kr 3+ ions were measured in coincidence with scattered electrons for energy losses up to 120 eV and scattering angles between 16 degree sign and 90 degree sign . Scaling properties of the doubly differential cross sections (DDCS) are investigated as a function of energy loss, scattering angle, and momentum transfer. It is shown that scaling the DDCS as outlined by Kim and Inokuti and plotting them versus a parameter consisting of the momentum transfer divided by the square root of the impact energy times 1-cos(θ), where θ is the scattering angle, yielded similar curves, but with different magnitudes, for single and multiple ionization. Normalizing these curves together produced two universal curves, one appropriate for single and multiple electron emission at larger scattering angles (θ≥30 degree sign ) and one appropriate for small scattering angles (θ<30 degree sign )

  3. A new class of scale free solutions to linear ordinary differential equations and the universality of the golden mean (Radical radicand 5 -1)/2=0.618033.

    International Nuclear Information System (INIS)

    Datta, Dhurjati Prasad

    2003-01-01

    A new class of finitely differentiable scale free solutions to the simplest class of ordinary differential equations is presented. Consequently, the real number set gets replaced by an extended physical set, each element of which is endowed with an equivalence class of infinitesimally separated neighbours in the form of random fluctuations. We show how a sense of time and evolution is intrinsically defined by the infinite continued fraction of the golden mean irrational number (Radical radicand 5 -1)/2, which plays a key role in this extended SL(2,R) formalism of calculus analogous to El Naschie's theory of E (∞) spacetime manifold. Time may thereby undergo random inversions generating well defined random scales, thus allowing a dynamical system to evolve self similarly over the set of multiple scales. The late time stochastic fluctuations of a dynamical system enjoys the generic 1/f spectrum. A universal form of the related probability density is also derived. We prove that the golden mean number is intrinsically random, letting all measurements in the physical universe fundamentally uncertain. The present analysis offers an explanation of the universal occurrence of the golden mean in diverse natural and biological processes as well as the mass spectrum of high energy particle physics

  4. Test of numerical methods for the integration of kinetic equations in tropospheric chemistry; Confronto di metodi numerici per l'integrazione di sistemi di equazioni differenziali ordinarie di tipo STIFF inserite nel modello fotochimico Calgrid

    Energy Technology Data Exchange (ETDEWEB)

    Lorenzini, R.; Passoni, L. [ENEA, Centro Ricerche Ezio Clementel, Bologna (Italy). Dipt. Ambiente

    1999-07-01

    The integration of ordinary differential equations systems (ODEs) is of significant concern to tropospheric and stratospheric chemistry modelers. The solution of the ODEs requires a large computational effort because of their stiff nature; in a three-dimensional photochemical model the solution of the ODEs required at least 70% of the total CPU time. Several numerical integration techniques exist which attempt to provide accurate and computationally efficient solutions. In this work it is presented a comparison of some of the techniques in terms of solution accuracy and required computational time. It has been compared the Hybrid Solver (Young and Boris, 1977), the Quasi Steady-State Approximation method (Hesstvedt et al., 1978) and the Chemical Solver for Ordinary Differential Equations (Aro, 1996), by using the CALGRID photochemical model. The accuracy is evaluated by comparing the results of every method with the solutions obtained by the Livermore Solver for Ordinary Differential Equations (Hindmarsh, 1980). The comparison has been made varing the parameters of the error tolerances, and taking into account the trade-off between solution accuracy and computational efficiency. [Italian] L'integrazione di sistemi di equazioni differenziali ordinarie (ODEs), e' un problema significativo per i modellisti della chimica troposferica e stratosferica. A causa della loro natura stiff la soluzione degli ODEs richiese un notevole sforzo computazionale; in un modello fotochimico tridimensionale la soluzione degli ODEs richiede almeno il 70% del tempo totale di CPU. Esistono diverse tecniche di integrazione numerica che possono fornire soluzioni accurate e computazionalmente efficienti: in questo lavoro presentiamo un confronto fra alcune tecniche in termini di accuratezza della soluzione e tempo computazionale richiesto. Si sono confrontati il Solver Ibrido (Young and Boris, 1977), il metodo Quasi Steady-State Approximation (Hesstvedt et al., 1978) ed il Chemical

  5. Evidence from the Semarkona ordinary chondrite for /sup 26/Al heating of small planets

    Energy Technology Data Exchange (ETDEWEB)

    Hutcheon, I D; Hutchison, R

    1989-01-19

    We report the first observation of radiogenic /sup 26/Mg in non-refractory meteoritic material, a plagio-clase-bearing, olivine-pyroxene clast chondrule in the Semarkona ordinary chondrite. The inferred initial abundance of /sup 26/Al is sufficient to produce incipient melting in well insulated bodies of chondritic composition. We conclude that planetary accretion and differentiation must have begun on a timescale comparable to the half life of /sup 26/Al and that, even if widespread melting did not occur, /sup 26/Al heating played a significant role in thermal metamorphism on small planets.

  6. Selected papers on analysis and differential equations

    CERN Document Server

    Society, American Mathematical

    2010-01-01

    This volume contains translations of papers that originally appeared in the Japanese journal Sūgaku. These papers range over a variety of topics in ordinary and partial differential equations, and in analysis. Many of them are survey papers presenting new results obtained in the last few years. This volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.

  7. On a complex differential Riccati equation

    International Nuclear Information System (INIS)

    Khmelnytskaya, Kira V; Kravchenko, Vladislav V

    2008-01-01

    We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schroedinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation such as the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical 'one-dimensional' results, we discuss new features of the considered equation including an analogue of the Cauchy integral theorem

  8. Differential equations inverse and direct problems

    CERN Document Server

    Favini, Angelo

    2006-01-01

    DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMSSOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMSFOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITIONSTUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACESDEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONSCONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY ASYMPTOTIC BEHA

  9. Lectures on differential Galois theory

    CERN Document Server

    Magid, Andy R

    1994-01-01

    Differential Galois theory studies solutions of differential equations over a differential base field. In much the same way that ordinary Galois theory is the theory of field extensions generated by solutions of (one variable) polynomial equations, differential Galois theory looks at the nature of the differential field extension generated by the solutions of differential equations. An additional feature is that the corresponding differential Galois groups (of automorphisms of the extension fixing the base and commuting with the derivation) are algebraic groups. This book deals with the differential Galois theory of linear homogeneous differential equations, whose differential Galois groups are algebraic matrix groups. In addition to providing a convenient path to Galois theory, this approach also leads to the constructive solution of the inverse problem of differential Galois theory for various classes of algebraic groups. Providing a self-contained development and many explicit examples, this book provides ...

  10. Lectures on the practical solution of differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1979-11-01

    This report comprises lectures on the practical solution of ordinary and partial differential equations given in the In-Hours Continuing Education Program for Scientific and Technical Personnel at Oak Ridge National Laboratory

  11. POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.

  12. Introduction to numerical methods for time dependent differential equations

    CERN Document Server

    Kreiss, Heinz-Otto

    2014-01-01

    Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the t

  13. 7 CFR 28.426 - Strict Good Ordinary Spotted Color.

    Science.gov (United States)

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Strict Good Ordinary Spotted Color. 28.426 Section 28.426 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards... Spotted Color. Strict Good Ordinary Spotted Color is color which is within the range represented by a set...

  14. A single-cell resolution map of mouse hematopoietic stem and progenitor cell differentiation.

    Science.gov (United States)

    Nestorowa, Sonia; Hamey, Fiona K; Pijuan Sala, Blanca; Diamanti, Evangelia; Shepherd, Mairi; Laurenti, Elisa; Wilson, Nicola K; Kent, David G; Göttgens, Berthold

    2016-08-25

    Maintenance of the blood system requires balanced cell fate decisions by hematopoietic stem and progenitor cells (HSPCs). Because cell fate choices are executed at the individual cell level, new single-cell profiling technologies offer exciting possibilities for mapping the dynamic molecular changes underlying HSPC differentiation. Here, we have used single-cell RNA sequencing to profile more than 1600 single HSPCs, and deep sequencing has enabled detection of an average of 6558 protein-coding genes per cell. Index sorting, in combination with broad sorting gates, allowed us to retrospectively assign cells to 12 commonly sorted HSPC phenotypes while also capturing intermediate cells typically excluded by conventional gating. We further show that independently generated single-cell data sets can be projected onto the single-cell resolution expression map to directly compare data from multiple groups and to build and refine new hypotheses. Reconstruction of differentiation trajectories reveals dynamic expression changes associated with early lymphoid, erythroid, and granulocyte-macrophage differentiation. The latter two trajectories were characterized by common upregulation of cell cycle and oxidative phosphorylation transcriptional programs. By using external spike-in controls, we estimate absolute messenger RNA (mRNA) levels per cell, showing for the first time that despite a general reduction in total mRNA, a subset of genes shows higher expression levels in immature stem cells consistent with active maintenance of the stem-cell state. Finally, we report the development of an intuitive Web interface as a new community resource to permit visualization of gene expression in HSPCs at single-cell resolution for any gene of choice. © 2016 by The American Society of Hematology.

  15. Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE

    Science.gov (United States)

    Ansmann, Gerrit

    2018-04-01

    We present a family of Python modules for the numerical integration of ordinary, delay, or stochastic differential equations. The key features are that the user enters the derivative symbolically and it is just-in-time-compiled, allowing the user to efficiently integrate differential equations from a higher-level interpreted language. The presented modules are particularly suited for large systems of differential equations such as those used to describe dynamics on complex networks. Through the selected method of input, the presented modules also allow almost complete automatization of the process of estimating regular as well as transversal Lyapunov exponents for ordinary and delay differential equations. We conceptually discuss the modules' design, analyze their performance, and demonstrate their capabilities by application to timely problems.

  16. Pythagoras, Binomial, and de Moivre Revisited Through Differential Equations

    OpenAIRE

    Singh, Jitender; Bajaj, Renu

    2018-01-01

    The classical Pythagoras theorem, binomial theorem, de Moivre's formula, and numerous other deductions are made using the uniqueness theorem for the initial value problems in linear ordinary differential equations.

  17. Cellular network entropy as the energy potential in Waddington's differentiation landscape

    Science.gov (United States)

    Banerji, Christopher R. S.; Miranda-Saavedra, Diego; Severini, Simone; Widschwendter, Martin; Enver, Tariq; Zhou, Joseph X.; Teschendorff, Andrew E.

    2013-01-01

    Differentiation is a key cellular process in normal tissue development that is significantly altered in cancer. Although molecular signatures characterising pluripotency and multipotency exist, there is, as yet, no single quantitative mark of a cellular sample's position in the global differentiation hierarchy. Here we adopt a systems view and consider the sample's network entropy, a measure of signaling pathway promiscuity, computable from a sample's genome-wide expression profile. We demonstrate that network entropy provides a quantitative, in-silico, readout of the average undifferentiated state of the profiled cells, recapitulating the known hierarchy of pluripotent, multipotent and differentiated cell types. Network entropy further exhibits dynamic changes in time course differentiation data, and in line with a sample's differentiation stage. In disease, network entropy predicts a higher level of cellular plasticity in cancer stem cell populations compared to ordinary cancer cells. Importantly, network entropy also allows identification of key differentiation pathways. Our results are consistent with the view that pluripotency is a statistical property defined at the cellular population level, correlating with intra-sample heterogeneity, and driven by the degree of signaling promiscuity in cells. In summary, network entropy provides a quantitative measure of a cell's undifferentiated state, defining its elevation in Waddington's landscape. PMID:24154593

  18. Applications of differential algebra to single-particle dynamics in storage rings

    International Nuclear Information System (INIS)

    Yan, Y.

    1991-09-01

    Recent developments in the use of differential algebra to study single-particle beam dynamics in charged-particle storage rings are the subject of this paper. Chapter 2 gives a brief review of storage rings. The concepts of betatron motion and synchrotron motion, and their associated resonances, are introduced. Also introduced are the concepts of imperfections, such as off-momentum, misalignment, and random and systematic errors, and their associated corrections. The chapter concludes with a discussion of numerical simulation principles and the concept of one-turn periodic maps. In Chapter 3, the discussion becomes more focused with the introduction of differential algebras. The most critical test for differential algebraic mapping techniques -- their application to long-term stability studies -- is discussed in Chapter 4. Chapter 5 presents a discussion of differential algebraic treatment of dispersed betatron motion. The paper concludes in Chapter 6 with a discussion of parameterization of high-order maps

  19. Modified Chebyshev Collocation Method for Solving Differential Equations

    Directory of Open Access Journals (Sweden)

    M Ziaul Arif

    2015-05-01

    Full Text Available This paper presents derivation of alternative numerical scheme for solving differential equations, which is modified Chebyshev (Vieta-Lucas Polynomial collocation differentiation matrices. The Scheme of modified Chebyshev (Vieta-Lucas Polynomial collocation method is applied to both Ordinary Differential Equations (ODEs and Partial Differential Equations (PDEs cases. Finally, the performance of the proposed method is compared with finite difference method and the exact solution of the example. It is shown that modified Chebyshev collocation method more effective and accurate than FDM for some example given.

  20. Asymptotic behavior and stability of second order neutral delay differential equations

    NARCIS (Netherlands)

    Chen, G.L.; van Gaans, O.W.; Verduyn Lunel, Sjoerd

    2014-01-01

    We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed

  1. Nonlinear differential equations with exact solutions expressed via the Weierstrass function

    NARCIS (Netherlands)

    Kudryashov, NA

    2004-01-01

    A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear

  2. Hybrid modeling of the crosstalk between signaling and transcriptional networks using ordinary differential equations and multi-valued logic.

    Science.gov (United States)

    Khan, Faiz M; Schmitz, Ulf; Nikolov, Svetoslav; Engelmann, David; Pützer, Brigitte M; Wolkenhauer, Olaf; Vera, Julio

    2014-01-01

    A decade of successful results indicates that systems biology is the appropriate approach to investigate the regulation of complex biochemical networks involving transcriptional and post-transcriptional regulations. It becomes mandatory when dealing with highly interconnected biochemical networks, composed of hundreds of compounds, or when networks are enriched in non-linear motifs like feedback and feedforward loops. An emerging dilemma is to conciliate models of massive networks and the adequate description of non-linear dynamics in a suitable modeling framework. Boolean networks are an ideal representation of massive networks that are humble in terms of computational complexity and data demand. However, they are inappropriate when dealing with nested feedback/feedforward loops, structural motifs common in biochemical networks. On the other hand, models of ordinary differential equations (ODEs) cope well with these loops, but they require enormous amounts of quantitative data for a full characterization of the model. Here we propose hybrid models, composed of ODE and logical sub-modules, as a strategy to handle large scale, non-linear biochemical networks that include transcriptional and post-transcriptional regulations. We illustrate the construction of this kind of models using as example a regulatory network centered on E2F1, a transcription factor involved in cancer. The hybrid modeling approach proposed is a good compromise between quantitative/qualitative accuracy and scalability when considering large biochemical networks with a small highly interconnected core, and module of transcriptionally regulated genes that are not part of critical regulatory loops. This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications. Guest Editor: Yudong Cai. Copyright © 2013 Elsevier B.V. All rights reserved.

  3. Conventional hamiltonian for first-order differential systems

    International Nuclear Information System (INIS)

    Farias, J.R.

    1984-01-01

    Lagrangian systems corresponding to a given set of 2n first-order ordinary differential equations are singular ones. In despite this, it is shown that these systems can be put into a Hamiltonian form in the usual manner. (Author) [pt

  4. Solving Nonlinear Coupled Differential Equations

    Science.gov (United States)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  5. Subroutine for series solutions of linear differential equations

    International Nuclear Information System (INIS)

    Tasso, H.; Steuerwald, J.

    1976-02-01

    A subroutine for Taylor series solutions of systems of ordinary linear differential equations is descriebed. It uses the old idea of Lie series but allows simple implementation and is time-saving for symbolic manipulations. (orig.) [de

  6. Single particle detecting telescope system

    International Nuclear Information System (INIS)

    Yamamoto, I.; Tomiyama, T.; Iga, Y.; Komatsubara, T.; Kanada, M.; Yamashita, Y.; Wada, T.; Furukawa, S.

    1981-01-01

    We constructed the single particle detecting telescope system for detecting a fractionally charged particle. The telescope consists of position detecting counters, wall-less multi-cell chambers, single detecting circuits and microcomputer system as data I/0 processor. Especially, a frequency of double particle is compared the case of the single particle detecting with the case of an ordinary measurement

  7. Stability analysis of impulsive functional differential equations

    CERN Document Server

    Stamova, Ivanka

    2009-01-01

    This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equationsis under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied research

  8. Exponentially Convergent Algorithms for Abstract Differential Equations

    CERN Document Server

    Gavrilyuk, Ivan; Vasylyk, Vitalii

    2011-01-01

    This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for the practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as the partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which

  9. Auxiliary equation method for solving nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Sirendaoreji,; Jiong, Sun

    2003-01-01

    By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

  10. Praying "Online": The Ordinary Theology of Prayer Intentions Posted on the Internet

    Science.gov (United States)

    ap Sion, Tania; Edwards, Owen

    2012-01-01

    Astley's construct of ordinary theology takes seriously listening to the religious expression and experience of ordinary people, both churched and unchurched. One method by which this has already been achieved is through the empirical analysis of the content of ordinary people's intercessory prayer requests left in hospitals and churches. Building…

  11. Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations

    DEFF Research Database (Denmark)

    Tornøe, Christoffer Wenzel; Overgaard, Rune Viig; Agerso, H.

    2005-01-01

    of noise: a measurement and a system noise term. The measurement noise represents uncorrelated error due to, for example, assay error while the system noise accounts for structural misspecifications, approximations of the dynamical model, and true random physiological fluctuations. Since the system noise...... degarelix. Conclusions. The EKF-based algorithm was successfully implemented in NONMEM for parameter estimation in population PK/PD models described by systems of SDEs. The example indicated that it was possible to pinpoint structural model deficiencies, and that valuable information may be obtained......Purpose. The objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling. Methods. The intra-individual variability in nonlinear mixed-effects models based on SDEs is decomposed into two types...

  12. Sobolev gradients and differential equations

    CERN Document Server

    Neuberger, J W

    2010-01-01

    A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair p...

  13. Complex centers of polynomial differential equations

    Directory of Open Access Journals (Sweden)

    Mohamad Ali M. Alwash

    2007-07-01

    Full Text Available We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.

  14. Differential recurrence formulae for orthogonal polynomials

    Directory of Open Access Journals (Sweden)

    Anton L. W. von Bachhaus

    1995-11-01

    Full Text Available Part I - By combining a general 2nd-order linear homogeneous ordinary differential equation with the three-term recurrence relation possessed by all orthogonal polynomials, it is shown that sequences of orthogonal polynomials which satisfy a differential equation of the above mentioned type necessarily have a differentiation formula of the type: gn(xY'n(x=fn(xYn(x+Yn-1(x. Part II - A recurrence formula of the form: rn(xY'n(x+sn(xY'n+1(x+tn(xY'n-1(x=0, is derived using the result of Part I.

  15. Neural network error correction for solving coupled ordinary differential equations

    Science.gov (United States)

    Shelton, R. O.; Darsey, J. A.; Sumpter, B. G.; Noid, D. W.

    1992-01-01

    A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.

  16. Algorithms For Integrating Nonlinear Differential Equations

    Science.gov (United States)

    Freed, A. D.; Walker, K. P.

    1994-01-01

    Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

  17. Physiological differentiation within a single-species biofilm fueled by serpentinization.

    Science.gov (United States)

    Brazelton, William J; Mehta, Mausmi P; Kelley, Deborah S; Baross, John A

    2011-01-01

    Carbonate chimneys at the Lost City hydrothermal field are coated in biofilms dominated by a single phylotype of archaea known as Lost City Methanosarcinales. In this study, we have detected surprising physiological complexity in single-species biofilms, which is typically indicative of multispecies biofilm communities. Multiple cell morphologies were visible within the biofilms by transmission electron microscopy, and some cells contained intracellular membranes that may facilitate methane oxidation. Both methane production and oxidation were detected at 70 to 80°C and pH 9 to 10 in samples containing the single-species biofilms. Both processes were stimulated by the presence of hydrogen (H(2)), indicating that methane production and oxidation are part of a syntrophic interaction. Metagenomic data included a sequence encoding AMP-forming acetyl coenzyme A synthetase, indicating that acetate may play a role in the methane-cycling syntrophy. A wide range of nitrogen fixation genes were also identified, many of which were likely acquired via lateral gene transfer (LGT). Our results indicate that cells within these single-species biofilms may have differentiated into multiple physiological roles to form multicellular communities linked by metabolic interactions and LGT. Communities similar to these Lost City biofilms are likely to have existed early in the evolution of life, and we discuss how the multicellular characteristics of ancient hydrogen-fueled biofilm communities could have stimulated ecological diversification, as well as unity of biochemistry, during the earliest stages of cellular evolution. Our previous work at the Lost City hydrothermal field has shown that its carbonate chimneys host microbial biofilms dominated by a single uncultivated "species" of archaea. In this paper, we integrate evidence from these previous studies with new data on the metabolic activity and cellular morphology of these archaeal biofilms. We conclude that the archaeal biofilm

  18. Single ionization of Ne, Ar and Kr by proton impact: Single differential distributions in energy and angle

    Energy Technology Data Exchange (ETDEWEB)

    Otranto, S [CONICET and Dto. de Fisica, Universidad Nacional del Sur, 8000 BahIa Blanca (Argentina); Miraglia, J E [Instituto de AstronomIa y Fisica del Espacio, CONICET and Universidad de Buenos Aires C1428EGA (Argentina); Olson, R E, E-mail: sotranto@uns.edu.a [Physics Department, Missouri University of Science and Technology, Rolla MO 65409 (United States)

    2009-11-01

    In this work we present a theoretical study of singly differential cross sections in energy and angle for the single ionization of neon, argon and krypton by proton impact. Theoretical results obtained by means of the Continuum Distorted Wave-Eikonal initial state (CDW-EIS) model are compared to those provided by the First Born Approximation (FBA) and the classical trajectory Monte Carlo (CTMC) method as well as to experimental data from several laboratories. We note in particular for argon, that the CDW-EIS model does not reproduce the experimental data as accurately as expected, while the CTMC instead is in very good agreement.

  19. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

    Science.gov (United States)

    Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

    2016-01-01

    This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

  20. The Local Brewery: A Project for Use in Differential Equations Courses

    Science.gov (United States)

    Starling, James K.; Povich, Timothy J.; Findlay, Michael

    2016-01-01

    We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…

  1. Do Wage Subsidies Reduce Ordinary Employment?

    DEFF Research Database (Denmark)

    Azhar, Hussain; Rasmussen, Martin

    Applying administrative register data information for Danish firms in 1999, 2000, and 2001, this paper investigate how the employment of wage subsidized labour affects ordinary employment at the firm level. Descriptive statistics as well as econometric estimations are presented. Descriptive...

  2. Distinct gene expression signatures in human embryonic stem cells differentiated towards definitive endoderm at single-cell level

    DEFF Research Database (Denmark)

    Norrman, Karin; Strömbeck, Anna; Semb, Henrik

    2013-01-01

    for the three activin A based protocols applied. Our data provide novel insights in DE gene expression at the cellular level of in vitro differentiated human embryonic stem cells, and illustrate the power of using single-cell gene expression profiling to study differentiation heterogeneity and to characterize...... of anterior definitive endoderm (DE). Here, we differentiated human embryonic stem cells towards DE using three different activin A based treatments. Differentiation efficiencies were evaluated by gene expression profiling over time at cell population level. A panel of key markers was used to study DE...... formation. Final DE differentiation was also analyzed with immunocytochemistry and single-cell gene expression profiling. We found that cells treated with activin A in combination with sodium butyrate and B27 serum-free supplement medium generated the most mature DE cells. Cell population studies were...

  3. Integration of differential equations by the pseudo-linear (PL) approximation

    International Nuclear Information System (INIS)

    Bonalumi, Riccardo A.

    1998-01-01

    A new method of integrating differential equations was originated with the technique of approximately calculating the integrals called the pseudo-linear (PL) procedure: this method is A-stable. This article contains the following examples: 1st order ordinary differential equations (ODEs), 2nd order linear ODEs, stiff system of ODEs (neutron kinetics), one-dimensional parabolic (diffusion) partial differential equations. In this latter case, this PL method coincides with the Crank-Nicholson method

  4. Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces

    Institute of Scientific and Technical Information of China (English)

    LI Shoufu

    2005-01-01

    A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.

  5. Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC.

    Directory of Open Access Journals (Sweden)

    Zachary F Phillips

    Full Text Available We present a new technique for quantitative phase and amplitude microscopy from a single color image with coded illumination. Our system consists of a commercial brightfield microscope with one hardware modification-an inexpensive 3D printed condenser insert. The method, color-multiplexed Differential Phase Contrast (cDPC, is a single-shot variant of Differential Phase Contrast (DPC, which recovers the phase of a sample from images with asymmetric illumination. We employ partially coherent illumination to achieve resolution corresponding to 2× the objective NA. Quantitative phase can then be used to synthesize DIC and phase contrast images or extract shape and density. We demonstrate amplitude and phase recovery at camera-limited frame rates (50 fps for various in vitro cell samples and c. elegans in a micro-fluidic channel.

  6. 24 April 2018: Ordinary General Assembly of the Staff Association!

    CERN Multimedia

    Staff Association

    2018-01-01

    In the first semester of each year, the Staff Association (SA) invites its members to attend and participate in the Ordinary General Assembly (OGA). This year the OGA will be held on Tuesday, 24 April 2018 from 14.00 to 16.00, Main Auditorium, Meyrin (500-1-001). During the Ordinary General Assembly, the activity and financial reports of the SA are presented and submitted for approval to the members. This is the occasion to get a global view on the activities of the SA, its management, and an opportunity to express your opinion, particularly by taking part in votes. Other items are listed on the agenda, as proposed by the Staff Council. Who can vote? Ordinary members (MPE) of the SA can take part in all votes. Associated members (MPA) of the SA and/or affiliated pensioners have a right to vote on those topics that are of direct interest to them. Who can give their opinion, and how? The Ordinary General Assembly is also the opportunity for members of the SA to express themselves through the addition of discus...

  7. 24 April 2018: Ordinary General Assembly of the Staff Association!

    CERN Multimedia

    Staff Association

    2018-01-01

    In the first semester of each year, the Staff Association (SA) invites its members to attend and participate in the Ordinary General Assembly (OGA). This year the OGA will be held on Thursday, 24 April 2018 from 14.00 to 16.00, Main Auditorium, Meyrin (500-1-001). During the Ordinary General Assembly, the activity and financial reports of the SA are presented and submitted for approval to the members. This is the occasion to get a global view on the activities of the SA, its management, and an opportunity to express your opinion, particularly by taking part in votes. Other items are listed on the agenda, as proposed by the Staff Council. Who can vote? Ordinary members (MPE) of the SA can take part in all votes. Associated members (MPA) of the SA and/or affiliated pensioners have a right to vote on those topics that are of direct interest to them. Who can give their opinion, and how? The Ordinary General Assembly is also the opportunity for members of the SA to express themselves through the addition of disc...

  8. Plasticity of marrow mesenchymal stem cells from human first-trimester fetus: from single-cell clone to neuronal differentiation.

    Science.gov (United States)

    Zhang, Yihua; Shen, Wenzheng; Sun, Bingjie; Lv, Changrong; Dou, Zhongying

    2011-02-01

    Recent results have shown that bone marrow mesenchymal stem cells (BMSCs) from human first-trimester abortus (hfBMSCs) are closer to embryonic stem cells and perform greater telomerase activity and faster propagation than mid- and late-prophase fetal and adult BMSCs. However, no research has been done on the plasticity of hfBMSCs into neuronal cells using single-cell cloned strains without cell contamination. In this study, we isolated five single cells from hfBMSCs and obtained five single-cell cloned strains, and investigated their biological property and neuronal differentiation potential. We found that four of the five strains showed similar expression profile of surface antigen markers to hfBMSCs, and most of them differentiated into neuron-like cells expressing Nestin, Pax6, Sox1, β-III Tubulin, NF-L, and NSE under induction. One strain showed different expression profile of surface antigen markers from the four strains and hfBMSCs, and did not differentiate toward neuronal cells. We demonstrated for the first time that some of single-cell cloned strains from hfBMSCs can differentiate into nerve tissue-like cell clusters under induction in vitro, and that the plasticity of each single-cell cloned strain into neuronal cells is different.

  9. Trilinear Higgs coupling determination via single-Higgs differential measurements at the LHC

    Energy Technology Data Exchange (ETDEWEB)

    Maltoni, Fabio; Shivaji, Ambresh; Zhao, Xiaoran [Universite Catholique de Louvain, Centre for Cosmology, Particle Physics and Phenomenology (CP3), Louvain-la-Neuve (Belgium); Pagani, Davide [Technische Universitaet Muenchen, Garching (Germany)

    2017-12-15

    We study one-loop effects induced by an anomalous Higgs trilinear coupling on total and differential rates for the H → 4l decay and some of the main single-Higgs production channels at the LHC, namely, VBF, VH, t anti tH and tHj. Our results are based on a public code that calculates these effects by simply reweighting samples of Standard-Model-like events for a given production channel. For VH and t anti tH production, where differential effects are particularly relevant, we include Standard Model electroweak corrections, which have similar sizes but different kinematic dependences. Finally, we study the sensitivity of future LHC runs to determine the trilinear coupling via inclusive and differential measurements, considering also the case where the Higgs couplings to vector bosons and the top quark is affected by new physics. We find that the constraints on the couplings and the relevance of differential distributions critically depend on the expected experimental and theoretical uncertainties. (orig.)

  10. Trilinear Higgs coupling determination via single-Higgs differential measurements at the LHC

    Science.gov (United States)

    Maltoni, Fabio; Pagani, Davide; Shivaji, Ambresh; Zhao, Xiaoran

    2017-12-01

    We study one-loop effects induced by an anomalous Higgs trilinear coupling on total and differential rates for the H→ 4ℓ decay and some of the main single-Higgs production channels at the LHC, namely, VBF, VH, t{\\bar{t}}H and tHj. Our results are based on a public code that calculates these effects by simply reweighting samples of Standard-Model-like events for a given production channel. For VH and t{\\bar{t}}H production, where differential effects are particularly relevant, we include Standard Model electroweak corrections, which have similar sizes but different kinematic dependences. Finally, we study the sensitivity of future LHC runs to determine the trilinear coupling via inclusive and differential measurements, considering also the case where the Higgs couplings to vector bosons and the top quark is affected by new physics. We find that the constraints on the couplings and the relevance of differential distributions critically depend on the expected experimental and theoretical uncertainties.

  11. Measuring metamorphic history of unequilibrated ordinary chondrites

    International Nuclear Information System (INIS)

    Sears, D.W.; Grossman, J.N.; Melcher, C.L.; Ross, L.M.; Mills, A.A.

    1980-01-01

    A thermoluminescence sensitivity technique is used to give a new measurement of the degree of metamorphism of unequilibrated ordinary chondrites. Consequently the petrological assignment of these meteorites is modified. (author)

  12. Functional analysis in the study of differential and integral equations

    International Nuclear Information System (INIS)

    Sell, G.R.

    1976-01-01

    This paper illustrates the use of functional analysis in the study of differential equations. Our particular starting point, the theory of flows or dynamical systems, originated with the work of H. Poincare, who is the founder of the qualitative theory of ordinary differential equations. In the qualitative theory one tries to describe the behaviour of a solution, or a collection of solutions, without ''solving'' the differential equation. As a starting point one assumes the existence, and sometimes the uniqueness, of solutions and then one tries to describe the asymptotic behaviour, as time t→+infinity, of these solutions. We compare the notion of a flow with that of a C 0 -group of bounded linear operators on a Banach space. We shall show how the concept C 0 -group, or more generally a C 0 -semigroup, can be used to study the behaviour of solutions of certain differential and integral equations. Our main objective is to show how the concept of a C 0 -group and especially the notion of weak-compactness can be used to prove the existence of an invariant measure for a flow on a compact Hausdorff space. Applications to the theory of ordinary differential equations are included. (author)

  13. Developing concepts of ordinary and extraordinary communication.

    Science.gov (United States)

    Lane, Jonathan D; Evans, E Margaret; Brink, Kimberly A; Wellman, Henry M

    2016-01-01

    We examine how understandings of ordinary and extraordinary communication develop. Three- to 10-year-old children and adults (N = 183) were given scenarios in which a protagonist wanted help from a human (their parent) or from God. Scenarios varied in whether protagonists expressed their desires aloud (by asking) or silently (by hoping), whether (for human scenarios) parents were nearby or far away, and whether (for God scenarios) protagonists expressed desires through ordinary means (asking or hoping) or more extraordinary means (praying). Following each scenario, participants were asked whether the recipient (either the parent or God) was aware of the protagonist's desire. Children as young as 3 to 4 years old understood that both loudness and distance limit the effectiveness of human communication, reporting that humans would most likely be aware of desires when they were expressed both aloud and nearby. As well, by this age children reported that God would more often be aware of desires than would humans, but children of all ages often reported that God (like humans) would be more aware of desires expressed aloud (rather than silently). These concepts of ordinary and extraordinary communication continued to be refined through middle childhood. Children's performance on standard theory-of-mind tasks and participants' religious background predicted whether they attributed awareness to God. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

  14. A practical course in differential equations and mathematical modeling

    CERN Document Server

    Ibragimov , Nail H

    2009-01-01

    A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame

  15. Differential cross sections for single ionization of H2 by 75keV proton impact

    International Nuclear Information System (INIS)

    Chowdhury, U; Schulz, M; Madison, D H

    2012-01-01

    We have calculated Triply differential cross sections (TDCS) and doubly differential cross sections (DDCS) for single ionization of H 2 by 75 keV proton impact using the molecular 3 body distorted wave Eikonal initial state (M3DW-EIS) approach. Previously published measured DDCS-P (differential in the projectile scattering angle and integrated over the ejected electron angles) found pronounced structures at relatively large angles which were interpreted as an interference resulting from the two-centered potential of the molecule.

  16. On nonlinear differential equation with exact solutions having various pole orders

    International Nuclear Information System (INIS)

    Kudryashov, N.A.

    2015-01-01

    We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed

  17. Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Ahmet Bekir

    2013-01-01

    Full Text Available The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

  18. The ATOMFT integrator - Using Taylor series to solve ordinary differential equations

    Science.gov (United States)

    Berryman, Kenneth W.; Stanford, Richard H.; Breckheimer, Peter J.

    1988-01-01

    This paper discusses the application of ATOMFT, an integration package based on Taylor series solution with a sophisticated user interface. ATOMFT has the capabilities to allow the implementation of user defined functions and the solution of stiff and algebraic equations. Detailed examples, including the solutions to several astrodynamics problems, are presented. Comparisons with its predecessor ATOMCC and other modern integrators indicate that ATOMFT is a fast, accurate, and easy method to use to solve many differential equation problems.

  19. Population stochastic modelling (PSM)-An R package for mixed-effects models based on stochastic differential equations

    DEFF Research Database (Denmark)

    Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode

    2009-01-01

    are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE1 approximation......The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model...... development, J. Pharmacokinet. Pharmacodyn. 32 (February(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8...

  20. Stream Kriging: Incremental and recursive ordinary Kriging over spatiotemporal data streams

    Science.gov (United States)

    Zhong, Xu; Kealy, Allison; Duckham, Matt

    2016-05-01

    Ordinary Kriging is widely used for geospatial interpolation and estimation. Due to the O (n3) time complexity of solving the system of linear equations, ordinary Kriging for a large set of source points is computationally intensive. Conducting real-time Kriging interpolation over continuously varying spatiotemporal data streams can therefore be especially challenging. This paper develops and tests two new strategies for improving the performance of an ordinary Kriging interpolator adapted to a stream-processing environment. These strategies rely on the expectation that, over time, source data points will frequently refer to the same spatial locations (for example, where static sensor nodes are generating repeated observations of a dynamic field). First, an incremental strategy improves efficiency in cases where a relatively small proportion of previously processed spatial locations are absent from the source points at any given iteration. Second, a recursive strategy improves efficiency in cases where there is substantial set overlap between the sets of spatial locations of source points at the current and previous iterations. These two strategies are evaluated in terms of their computational efficiency in comparison to ordinary Kriging algorithm. The results show that these two strategies can reduce the time taken to perform the interpolation by up to 90%, and approach average-case time complexity of O (n2) when most but not all source points refer to the same locations over time. By combining the approaches developed in this paper with existing heuristic ordinary Kriging algorithms, the conclusions indicate how further efficiency gains could potentially be accrued. The work ultimately contributes to the development of online ordinary Kriging interpolation algorithms, capable of real-time spatial interpolation with large streaming data sets.

  1. Multifunction Voltage-Mode Filter Using Single Voltage Differencing Differential Difference Amplifier

    Directory of Open Access Journals (Sweden)

    Chaichana Amornchai

    2017-01-01

    Full Text Available In this paper, a voltage mode multifunction filter based on single voltage differencing differential difference amplifier (VDDDA is presented. The proposed filter with three input voltages and single output voltage is constructed with single VDDDA, two capacitors and two resistors. Its quality factor can be adjusted without affecting natural frequency. Also, the natural frequency can be electronically tuned via adjusting of bias current. The filter can offer five output responses, high-pas (HP, band-pass (BP, band-reject (BR, low-pass (LP and all-ass (AP functions in the same circuit topology. The output response can be selected by choosing the suitable input voltage without the component matching condition and the requirement of additional double gain voltage amplifier. PSpice simulation results to confirm an operation of the proposed filter correspond to the theory.

  2. Processes of aesthetic transformation in ordinary landscapes

    DEFF Research Database (Denmark)

    Krarup, Jonna Majgaard

    2004-01-01

    it was distributed systematically as an almost industrially produced landscape element. Windbreaks are now regarded as a traditional element in the Danish agricultural landscape. As a landscape element it is an international phenomenon known and used in Germany, France, England etc. Originally local farming...... practices, natural conditions, techniques and national legislation in the respective countries, formed the aesthetic expression. In this respect one could speak of the impact of northern nature on the aesthetic expression of the Danish windbreaks, as well as the impact from national phenomena....... These features determined the specific aesthetic and architectural identity of ordinary Danish, i.e. Nordic, landscapes. Contemporary cultural changes such as the aesthetification of everyday life and of ordinary landscape, i.e. farming landscape, are now manifest in the way the windbreaks are motivated...

  3. International Conference on Differential and Difference Equations with Applications

    CERN Document Server

    Došlá, Zuzana; Došlý, Ondrej; Kloeden, Peter

    2016-01-01

    Aimed at the community of mathematicians working on ordinary and partial differential equations, difference equations, and functional equations, this book contains selected papers based on the presentations at the International Conference on Differential and Difference Equations and Applications (ICDDEA) 2015, dedicated to the memory of Professor Georg Sell. Contributions include new trends in the field of differential and difference equations, applications of differential and difference equations, as well as high-level survey results. The main aim of this recurring conference series is to promote, encourage, cooperate, and bring together researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with special emphasis on applications.

  4. Symmetries of stochastic differential equations: A geometric approach

    Energy Technology Data Exchange (ETDEWEB)

    De Vecchi, Francesco C., E-mail: francesco.devecchi@unimi.it; Ugolini, Stefania, E-mail: stefania.ugolini@unimi.it [Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy); Morando, Paola, E-mail: paola.morando@unimi.it [DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)

    2016-06-15

    A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.

  5. Solving differential equations with unknown constitutive relations as recurrent neural networks

    Energy Technology Data Exchange (ETDEWEB)

    Hagge, Tobias J.; Stinis, Panagiotis; Yeung, Enoch H.; Tartakovsky, Alexandre M.

    2017-12-08

    We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and use a recurrent neural network to “learn” the reaction rate from this data. This is achieved by including discretized ordinary differential equations as part of a recurrent neural network training problem. We extend TensorFlow’s recurrent neural network architecture to create a simple but scalable and effective solver for the unknown functions, and apply it to a fedbatch bioreactor simulation problem. Use of techniques from recent deep learning literature enables training of functions with behavior manifesting over thousands of time steps. Our networks are structurally similar to recurrent neural networks, but differ in purpose, and require modified training strategies.

  6. Modified Differential Transform Method for Two Singular Boundary Values Problems

    Directory of Open Access Journals (Sweden)

    Yinwei Lin

    2014-01-01

    Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

  7. Ordinary or peculiar men? Comparing the customers of prostitutes with a nationally representative sample of men.

    Science.gov (United States)

    Monto, Martin A; Milrod, Christine

    2014-07-01

    Recent media attention implies that prostitution seeking is widespread, an "ordinary" aspect of masculine sexual behavior. Other accounts suggest that customers are "peculiar," characterized by distinct qualities, perversions, or psychological impairments. Using the nationally representative General Social Survey (GSS), this study demonstrates that prostitution seeking is relatively uncommon. Only about 14% of men in the United States report having ever paid for sex, and only 1% report having done so during the previous year. Furthermore, this study dissects whether customers are ordinary or peculiar by comparing a new sample of active customers who solicit sex on the Internet with an older sample of arrested customers, a sample of customers from the GSS, and a nationally representative sample of noncustomers. The customers of Internet sexual service providers differed greatly from men in general and also from other customers. The remaining samples of customers differed slightly from noncustomers in general. We argue for a balanced perspective that recognizes the significant variety among customers. There is no evidence of a peculiar quality that differentiates customers in general from men who have not paid for sex. © The Author(s) 2013.

  8. On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

    Science.gov (United States)

    Savoye, Philippe

    2009-01-01

    In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

  9. Differentiation of a bipotential glial progenitor cell in a single cell microculture.

    Science.gov (United States)

    Temple, S; Raff, M C

    Although it is known that most cells of the vertebrate central nervous system (CNS) are derived from the neuroepithelial cells of the neural tube, the factors determining whether an individual neuroepithelial cell develops into a particular type of neurone or glial cell remain unknown. A promising model for studying this problem is the bipotential glial progenitor cell in the developing rat optic nerve; this cell differentiates into a particular type of astrocyte (a type-2 astrocyte) if cultured in 10% fetal calf serum (FCS) and into an oligodendrocyte if cultured in serum-free medium. As the oligodendrocyte-type-2 astrocyte (0-2A) progenitor cell can differentiate along either glial pathway in neurone-free cultures, living axons clearly are not required for its differentiation, at least in vitro. However, the studies on 0-2A progenitor cells were carried out in bulk cultures of optic nerve, and so it was possible that other cell-cell interactions were required for differentiation in culture. We show here that 0-2A progenitor cells can differentiate into type-2 astrocytes or oligodendrocytes when grown as isolated cells in microculture, indicating that differentiation along either glial pathway in vitro does not require signals from other CNS cells, apart from the signals provided by components of the culture medium. We also show that single 0-2A progenitor cells can differentiate along either pathway without dividing, supporting our previous studies using 3H-thymidine and suggesting that DNA replication is not required for these cells to choose between the two differentiation programmes.

  10. Fast and quantitative differentiation of single-base mismatched DNA by initial reaction rate of catalytic hairpin assembly.

    Science.gov (United States)

    Li, Chenxi; Li, Yixin; Xu, Xiao; Wang, Xinyi; Chen, Yang; Yang, Xiaoda; Liu, Feng; Li, Na

    2014-10-15

    The widely used catalytic hairpin assembly (CHA) amplification strategy generally needs several hours to accomplish one measurement based on the prevailingly used maximum intensity detection mode, making it less practical for assays where high throughput or speed is desired. To make the best use of the kinetic specificity of toehold domain for circuit reaction initiation, we developed a mathematical model and proposed an initial reaction rate detection mode to quantitatively differentiate the single-base mismatch. Using the kinetic mode, assay time can be reduced substantially to 10 min for one measurement with the comparable sensitivity and single-base mismatch differentiating ability as were obtained by the maximum intensity detection mode. This initial reaction rate based approach not only provided a fast and quantitative differentiation of single-base mismatch, but also helped in-depth understanding of the CHA system, which will be beneficial to the design of highly sensitive and specific toehold-mediated hybridization reactions. Copyright © 2014 Elsevier B.V. All rights reserved.

  11. A procedure to construct exact solutions of nonlinear fractional differential equations.

    Science.gov (United States)

    Güner, Özkan; Cevikel, Adem C

    2014-01-01

    We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

  12. Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations

    International Nuclear Information System (INIS)

    Mokhtari, R.; Toodar, A. Samadi; Chegini, N.G.

    2011-01-01

    The aim of this paper is to obtain numerical solutions of the one-dimensional, two-dimensional and coupled Burgers' equations through the generalized differential quadrature method (GDQM). The polynomial-based differential quadrature (PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta (TVD-RK) method. The numerical solutions are satisfactorily coincident with the exact solutions. The method can compete against the methods applied in the literature. (general)

  13. Functional Determinants for Radially Separable Partial Differential Operators

    Directory of Open Access Journals (Sweden)

    G. V. Dunne

    2007-01-01

    Full Text Available Functional determinants of differential operators play a prominent role in many fields of theoretical and mathematical physics, ranging from condensed matter physics, to atomic, molecular and particle physics. They are, however, difficult to compute reliably in non-trivial cases. In one dimensional problems (i.e. functional determinants of ordinary differential operators, a classic result of Gel’fand and Yaglom greatly simplifies the computation of functional determinants. Here I report some recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators, with applications in quantum field theory. 

  14. Pyroelectric effect in tryglicyne sulphate single crystals - Differential measurement method

    Science.gov (United States)

    Trybus, M.

    2018-06-01

    A simple mathematical model of the pyroelectric phenomenon was used to explain the electric response of the TGS (triglycine sulphate) samples in the linear heating process in ferroelectric and paraelectric phases. Experimental verification of mathematical model was realized. TGS single crystals were grown and four electrode samples were fabricated. Differential measurements of the pyroelectric response of two different regions of the samples were performed and the results were compared with data obtained from the model. Experimental results are in good agreement with model calculations.

  15. An implementation of Kovacic's algorithm for solving ordinary differential equations in FORMAC

    International Nuclear Information System (INIS)

    Zharkov, A.Yu.

    1987-01-01

    An implementation of Kovacic's algorithm for finding Liouvillian solutions of the differential equations y'' + a(x)y' + b(x)y = 0 with rational coefficients a(x) and b(x) in the Computer Algebra System FORMAC is described. The algorithm description is presented in such a way that one can easily implement it in a suitable Computer Algebra System

  16. Samples of noncommutative products in certain differential equations

    International Nuclear Information System (INIS)

    Legare, M

    2010-01-01

    A set of associative noncommutative products is considered in different differential equations of the ordinary and partial types. A method of separation of variables is considered for a large set of those systems. The products involved include for example some * products and some products based on Nijenhuis tensors, which are embedded in the differential equations of the Laplace/Poisson, Lax and Schroedinger styles. A comment on the *-products of Reshetikhin-Jambor-Sykora type is also given in relation to *-products of Vey type.

  17. A Second-Year Undergraduate Course in Applied Differential Equations.

    Science.gov (United States)

    Fahidy, Thomas Z.

    1991-01-01

    Presents the framework for a chemical engineering course using ordinary differential equations to solve problems with the underlying strategy of concisely discussing the theory behind each solution technique without extensions to formal proofs. Includes typical class illustrations, student responses to this strategy, and reaction of the…

  18. On Robust Stability of Systems of Differential-Algebraic Equations

    Directory of Open Access Journals (Sweden)

    A. Shcheglova

    2016-06-01

    The sufficient conditions of robust stability for index-one and index-two systems are obtained. We use the values of real and complex stability radii obtained for system of ordinary differential equations solved with respect to the derivatives. We consider the example illustrating the obtained results.

  19. Ordinary Social Interaction and the Main Effect Between Perceived Support and Affect.

    Science.gov (United States)

    Lakey, Brian; Vander Molen, Randy J; Fles, Elizabeth; Andrews, Justin

    2016-10-01

    Relational regulation theory hypothesizes that (a) the main effect between perceived support and mental health primarily reflects ordinary social interaction rather than conversations about stress and how to cope with it, and (b) the extent to which a provider regulates a recipient's mental health primarily reflects the recipient's personal taste (i.e., is relational), rather than the provider's objective supportiveness. In three round-robin studies, participants rated each other on supportiveness and the quality of ordinary social interaction, as well as their own affect when interacting with each other. Samples included marines about to deploy to Afghanistan (N = 100; 150 dyads), students sharing apartments (N = 64; 96 dyads), and strangers (N = 48; 72 dyads). Perceived support and ordinary social interaction were primarily relational, and most of perceived support's main effect on positive affect was redundant with ordinary social interaction. The main effect between perceived support and affect emerged among strangers after brief text conversations, and these links were partially verified by independent observers. Findings for negative affect were less consistent with theory. Ordinary social interaction appears to be able to explain much of the main effect between perceived support and positive affect. © 2015 Wiley Periodicals, Inc.

  20. The non-ordinary Regge behavior of the K{sup *}{sub 0}(800) or κ-meson versus the ordinary K{sup *}{sub 0}(1430)

    Energy Technology Data Exchange (ETDEWEB)

    Pelaez, J.R.; Rodas, A. [Universidad Complutense de Madrid, Departamento de Fisica Teorica II and UPARCOS, Madrid (Spain)

    2017-06-15

    The Regge trajectory of an elastic resonance can be calculated from dispersion theory, instead of fitted phenomenologically, using only its pole parameters as input. This also provides a correct treatment of resonance widths in Regge trajectories, essential for very wide resonances. In this work we first calculate the K{sup *}{sub 0}(1430) Regge trajectory, finding the ordinary almost real and linear behavior, typical of q anti q resonances. In contrast, for the K{sup *}{sub 0}(800) meson, the resulting Regge trajectory is non-linear and has a much smaller slope than ordinary resonances, being remarkably similar to that of the f{sub 0}(500) or σ meson. The slope of these unusual Regge trajectories seems to scale with the meson masses rather than with scales typical of quark degrees of freedom. We also calculate the range of the interaction responsible for the formation of these resonances. Our results strongly support a non-ordinary, predominantly meson-meson-like, interpretation for the lightest strange and non-strange resonances. (orig.)

  1. Introductory course on differential equations

    CERN Document Server

    Gorain, Ganesh C

    2014-01-01

    Introductory Course on DIFFERENTIAL EQUATIONS provides an excellent exposition of the fundamentals of ordinary and partial differential equations and is ideally suited for a first course of undergraduate students of mathematics, physics and engineering. The aim of this book is to present the elementary theories of differential equations in the forms suitable for use of those students whose main interest in the subject are based on simple mathematical ideas. KEY FEATURES: Discusses the subject in a systematic manner without sacrificing mathematical rigour. A variety of exercises drill the students in problem solving in view of the mathematical theories explained in the book. Worked out examples illustrated according to the theories developed in the book with possible alternatives. Exhaustive collection of problems and the simplicity of presentation differentiate this book from several others. Material contained will help teachers as well as aspiring students of different competitive examinations.

  2. Communication: Surface-facilitated softening of ordinary and vapor-deposited glasses

    Science.gov (United States)

    Cubeta, Ulyana; Bhattacharya, Deepanjan; Sadtchenko, Vlad

    2017-08-01

    A common distinction between the ordinary glasses formed by melt cooling and the stable amorphous films formed by vapor deposition is the apparent mechanism of their devitrification. Using quasi-adiabatic, fast scanning calorimetry that is capable of heating rates in excess of 105 K s-1, we have investigated the softening kinetics of micrometer-scale, ordinary glass films of methylbenzene and 2-propanol. At the limit of high heating rates, the transformation mechanism of ordinary glasses is identical to that of their stable vapor-deposited counterparts. In both cases, softening is likely to begin at the sample surface and progress into its bulk via a transformation front. Furthermore, such a surface-facilitated mechanism complies with zero-order, Arrhenius rate law. The activation energy barriers for the softening transformation imply that the kinetics must be defined, at least in part, by the initial thermodynamic and structural state of the samples.

  3. Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes

    Science.gov (United States)

    Seaman, Brian; Osler, Thomas J.

    2004-01-01

    A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

  4. Third-order ordinary differential equations Y”' = f(x, y, y'', y′”) with ...

    African Journals Online (AJOL)

    dimensional symmetry algebra. Mathematics Subject Classication (2010): 34A05, 34A25, 53A55, 76M60. Key words: Linearization, third order ODEs, point transformation, contact transformation, Lie symmetries, relative differential invariants.

  5. Image charge effects in single-molecule junctions: Breaking of symmetries and negative-differential resistance in a benzene single-electron transistor

    DEFF Research Database (Denmark)

    Kaasbjerg, Kristen; Flensberg, K.

    2011-01-01

    and molecular symmetries remain unclear. Using a theoretical framework developed for semiconductor-nanostructure-based single-electron transistors (SETs), we demonstrate that the image charge interaction breaks the molecular symmetries in a benzene-based single-molecule transistor operating in the Coulomb...... blockade regime. This results in the appearance of a so-called blocking state, which gives rise to negative-differential resistance (NDR). We show that the appearance of NDR and its magnitude in the symmetry-broken benzene SET depends in a complicated way on the interplay between the many-body matrix...

  6. Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method

    International Nuclear Information System (INIS)

    Bekir Ahmet; Güner Özkan

    2013-01-01

    In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations

  7. Partial differential operators of elliptic type

    CERN Document Server

    Shimakura, Norio

    1992-01-01

    This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics.

  8. Differential cross sections for single-electron capture in He{sup 2+}-D collisions

    Energy Technology Data Exchange (ETDEWEB)

    Bordenave-Montesquieu, D.; Dagnac, R. [Centre National de la Recherche Scientifique (CNRS), 31 - Toulouse (France)]|[Toulouse-3 Univ., 31 (France)

    1995-06-14

    A translational energy spectroscopy technique was used to study single-electron capture into the He{sup +} (n = 2) and He{sup +} (n 3) states in He{sup 2+}-D collisions. Differential cross sections were determined at 4, 6 and 8 keV in the angular range 5`-1{sup o}30` (laboratory frame). As expected, single-electron capture into the n = 2 state was found to be the dominant process; total cross sections for capture into the He{sup +} (n = 3) state were compared to other experimental and theoretical results. (author).

  9. Trends in differential equations and applications

    CERN Document Server

    Neble, María; Galván, José

    2016-01-01

    This work collects the most important results presented at the Congress on Differential Equations and Applications/Congress on Applied Mathematics (CEDYA/CMA) in Cádiz (Spain) in 2015. It supports further research in differential equations, numerical analysis, mechanics, control and optimization. In particular, it helps readers gain an overview of specific problems of interest in the current mathematical research related to different branches of applied mathematics. This includes the analysis of nonlinear partial differential equations, exact solutions techniques for ordinary differential equations, numerical analysis and numerical simulation of some models arising in experimental sciences and engineering, control and optimization, and also trending topics on numerical linear Algebra, dynamical systems, and applied mathematics for Industry. This volume is mainly addressed to any researcher interested in the applications of mathematics, especially in any subject mentioned above. It may be also useful to PhD s...

  10. The crux of the method: assumptions in ordinary least squares and logistic regression.

    Science.gov (United States)

    Long, Rebecca G

    2008-10-01

    Logistic regression has increasingly become the tool of choice when analyzing data with a binary dependent variable. While resources relating to the technique are widely available, clear discussions of why logistic regression should be used in place of ordinary least squares regression are difficult to find. The current paper compares and contrasts the assumptions of ordinary least squares with those of logistic regression and explains why logistic regression's looser assumptions make it adept at handling violations of the more important assumptions in ordinary least squares.

  11. Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations.

    Science.gov (United States)

    Tornøe, Christoffer W; Overgaard, Rune V; Agersø, Henrik; Nielsen, Henrik A; Madsen, Henrik; Jonsson, E Niclas

    2005-08-01

    The objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling. The intra-individual variability in nonlinear mixed-effects models based on SDEs is decomposed into two types of noise: a measurement and a system noise term. The measurement noise represents uncorrelated error due to, for example, assay error while the system noise accounts for structural misspecifications, approximations of the dynamical model, and true random physiological fluctuations. Since the system noise accounts for model misspecifications, the SDEs provide a diagnostic tool for model appropriateness. The focus of the article is on the implementation of the Extended Kalman Filter (EKF) in NONMEM for parameter estimation in SDE models. Various applications of SDEs in population PK/PD modeling are illustrated through a systematic model development example using clinical PK data of the gonadotropin releasing hormone (GnRH) antagonist degarelix. The dynamic noise estimates were used to track variations in model parameters and systematically build an absorption model for subcutaneously administered degarelix. The EKF-based algorithm was successfully implemented in NONMEM for parameter estimation in population PK/PD models described by systems of SDEs. The example indicated that it was possible to pinpoint structural model deficiencies, and that valuable information may be obtained by tracking unexplained variations in parameters.

  12. [INFLUENCE OF INHIBITION OF ACTIN POLYMERIZATION ON ADIPOGENIC DIFFERENTIATION OF RAT Achilles-DERIVED TENDON STEM CELLS IN VITRO].

    Science.gov (United States)

    Chen, Bo; Tang, Kanglai; Zhang, Jiqiang; Guo, Yupeng; Liu, Xiangzhou; Shi, Youxin

    2015-02-01

    To investigate the effect of cytoskeleton modification on the adipogenic differentiation of rat Achilles-derived tendon stem cells (TSCs) in vitro. TSCs were isolated from the tendon tissue of male Sprague Dawley rats (aged 3 weeks) by enzymatic digestion method and cultured for 3 passages. After the 3rd passage cells were cultured with DMEM medium containing 15% fetal bovine serum and cytochalasin D (CYD) at the concentrations of 0, 50, 100, 500, and 1 000 ng/mL, the cell survival condition and morphology changes were observed by inverted phase contrast microscope, the cytoskeleton was observed through fibrous actin (F-actin) staining, and the ratio of F-actin/ soluble globular actin (G-actin) was detected and calculated through Western blot. According to the above results, the effective concentration of CYD was selected and used for next experiments. After TSCs were cultured for 3 and 7 days respectively with adipogenic induction media (induction group), adipogenic induction media containing CYD (CYD+induction group), ordinary medium (ordinary group), and ordinary medium containing CYD (CYD+ordinary group), the real-time quantitative PCR (qRT-PCR) and Western blot were carried out to measure the mRNA and protein expressions of adipogenic differentiation-related markers, including peroxisome proliferator-activated receptor y (PPARγ), lipoprotein lipase (LPL), and fatty acid binding protein (aP2). The final CYD concentration of 100 ng/mL can inhibit effectively G-actin polymerization into F-actin, but could not affect TSCs survival, which was used for next experiments. qRT-PCR and Western blot suggested that the mRNA expressions of PPARγ, LPL, and aP2 and the protein expressions of PPARγ and aP2 were increased significantly in the CYD+induction group at 3 and 7 days when compared with the induction group (P < 0.05). In the CYD+ordinary group, there still was a significant increase in the mRNA expressions of PPARγ, LPL, and aP2 when compared with the ordinary

  13. Ordinary Dark Matter versus Mysterious Dark Matter in Galactic Rotation

    Science.gov (United States)

    Gallo, C. F.; Feng, James

    2008-04-01

    To theoretically describe the measured rotational velocity curves of spiral galaxies, there are two different approaches and conclusions. (1) ORDINARY DARK MATTER. We assume Newtonian gravity/dynamics and successfully find (via computer) mass distributions in bulge/disk configurations that duplicate the measured rotational velocities. There is ordinary dark matter within the galactic disk towards the cooler periphery which has lower emissivity/opacity. There are no mysteries in this scenario based on verified physics. (2) MYSTERIOUS DARK MATTER. Others INaccurately assume the galactic mass distributions follow the measured light distributions, and then the measured rotational velocity curves are NOT duplicated. To alleviate this discrepancy, speculations are invoked re ``Massive Peripheral Spherical Halos of Mysterious Dark Matter.'' But NO matter has been detected in this UNtenable Halo configuration. Many UNverified ``Mysteries'' are invoked as necessary and convenient. CONCLUSION. The first approach utilizing Newtonian gravity/dynamics and searching for the ordinary mass distributions within the galactic disk simulates reality and agrees with data.

  14. Effect of fast freeze-thaw cycles on mechanical properties of ordinary-air-entrained concrete.

    Science.gov (United States)

    Shang, Huai-shuai; Cao, Wei-qun; Wang, Bin

    2014-01-01

    Freezing-thawing resistance is a very significant characteristic for concrete in severe environment (such as cold region with the lowest temperature below 0°C). In this study, ordinary-air-entrained (O-A-E) concrete was produced in a laboratory environment; the compressive strength, cubic compressive strength of C50, C40, C30, C25, and C20 ordinary-air-entrained concrete, tensile strength, and cleavage strength of C30 ordinary-air-entrained concrete were measured after fast freeze-thaw cycles. The effects of fast freeze-thaw cycles on the mechanical properties (compressive strength and cleavage strength) of ordinary-air-entrained concrete materials are investigated on the basis of the experimental results. And the concise mathematical formula between mechanical behavior and number of fast freeze-thaw cycles was established. The experiment results can be used as a reference in design, maintenance, and life prediction of ordinary-air-entrained concrete structure (such as dam, offshore platform, etc.) in cold regions.

  15. Modelling Evolutionary Algorithms with Stochastic Differential Equations.

    Science.gov (United States)

    Heredia, Jorge Pérez

    2017-11-20

    There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.

  16. Dielectric metasurfaces solve differential and integro-differential equations.

    Science.gov (United States)

    Abdollahramezani, Sajjad; Chizari, Ata; Dorche, Ali Eshaghian; Jamali, Mohammad Vahid; Salehi, Jawad A

    2017-04-01

    Leveraging subwavelength resonant nanostructures, plasmonic metasurfaces have recently attracted much attention as a breakthrough concept for engineering optical waves both spatially and spectrally. However, inherent ohmic losses concomitant with low coupling efficiencies pose fundamental impediments over their practical applications. Not only can all-dielectric metasurfaces tackle such substantial drawbacks, but also their CMOS-compatible configurations support both Mie resonances that are invariant to the incident angle. Here, we report on a transmittive metasurface comprising arrayed silicon nanodisks embedded in a homogeneous dielectric medium to manipulate phase and amplitude of incident light locally and almost independently. By taking advantage of the interplay between the electric/magnetic resonances and employing general concepts of spatial Fourier transformation, a highly efficient metadevice is proposed to perform mathematical operations including solution of ordinary differential and integro-differential equations with constant coefficients. Our findings further substantiate dielectric metasurfaces as promising candidates for miniaturized, two-dimensional, and planar optical analog computing systems that are much thinner than their conventional lens-based counterparts.

  17. Differential pseudoconnections and field theories

    International Nuclear Information System (INIS)

    Modugno, Marco; Ragionieri, Rodolfo; Stefani, Gianna

    1981-01-01

    Several general field theories have been successful in describing fundamental physical fields by a unique schema. Our purpose is to present the first step of an attempt based on differential pseudoconnections on jet bundles. In this paper we are dealing with the essential elements of such an approach and with the testing of a certain number of important examples. We define a 'differential pseudoconnection of order k' on a bundle p:E→M as a translation morphism on the affine bundle. Such concept is a generalization of usual connections. Then we study in the framework of jet spaces several important differential operators used in physics. In this context an interest arises naturally for the second order affine differential equations, called 'special'. Particular cases of special equations are both the geodesics equation (an ordinary equation) and any Kind of Laplace equation (a partial equation) even modified by the addition of physical terms. So special equations are candidate to fit a lot of fundamental physical fields

  18. 29th June 2017 – Ordinary General Assembly of the Staff Association!

    CERN Document Server

    Staff Association

    2017-01-01

    In the first semester of each year, the Staff Association (SA) invites its members to attend and participate in the Ordinary General Assembly (OGA). This year the OGA will be held on Thursday, 29 June 2017 from 15.30 to 17.30, Main Auditorium, Meyrin (500-1-001). During the Ordinary General Assembly, the activity and financial reports of the SA are presented and submitted for approval to the members. This is the occasion to get a global view on the activities of the SA, its management, and an opportunity to express your opinion, particularly by taking part in votes. Other items are listed on the agenda, as proposed by the Staff Council. Who can vote? Ordinary members (MPE) of the SA can take part in all votes. Associated members (MPA) of the SA and/or affiliated pensioners have a right to vote on those topics that are of direct interest to them. Who can give their opinion, and how? The Ordinary General Assembly is also the opportunity for members of the SA to express themselves through the addition of disc...

  19. Operator overloading as an enabling technology for automatic differentiation

    International Nuclear Information System (INIS)

    Corliss, G.F.; Griewank, A.

    1993-01-01

    We present an example of the science that is enabled by object-oriented programming techniques. Scientific computation often needs derivatives for solving nonlinear systems such as those arising in many PDE algorithms, optimization, parameter identification, stiff ordinary differential equations, or sensitivity analysis. Automatic differentiation computes derivatives accurately and efficiently by applying the chain rule to each arithmetic operation or elementary function. Operator overloading enables the techniques of either the forward or the reverse mode of automatic differentiation to be applied to real-world scientific problems. We illustrate automatic differentiation with an example drawn from a model of unsaturated flow in a porous medium. The problem arises from planning for the long-term storage of radioactive waste

  20. Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

    Science.gov (United States)

    Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

    2009-06-01

    The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

  1. Composition between mecd and runge-Kutta algorithm method for large system of second order differential equations

    International Nuclear Information System (INIS)

    Supriyono; Miyoshi, T.

    1997-01-01

    NECD Method and runge-Kutta method for large system of second order ordinary differential equations in comparing algorithm. The paper introduce a extrapolation method used for solving the large system of second order ordinary differential equation. We call this method the modified extrapolated central difference (MECD) method. for the accuracy and efficiency MECD method. we compare the method with 4-th order runge-Kutta method. The comparison results show that, this method has almost the same accuracy as the 4-th order runge-Kutta method, but the computation time is about half of runge-Kutta. The MECD was declare by the author and Tetsuhiko Miyoshi of the Dept. Applied Science Yamaguchi University Japan

  2. Linear program differentiation for single-channel speech separation

    DEFF Research Database (Denmark)

    Pearlmutter, Barak A.; Olsson, Rasmus Kongsgaard

    2006-01-01

    Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver....... For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied...... to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of over complete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single...

  3. Surveys in differential-algebraic equations IV

    CERN Document Server

    Reis, Timo

    2017-01-01

    The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs) which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - History of DAEs - DAE aspects of mechanical multibody systems - Model reduction of DAEs - Observability for DAEs - Numerical Analysis for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

  4. Surveys in differential-algebraic equations III

    CERN Document Server

    Reis, Timo

    2015-01-01

    The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Flexibility of DAE formulations - Reachability analysis and deterministic global optimization - Numerical linear algebra methods - Boundary value problems The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

  5. A differential Michelson interferometer with orthogonal single frequency laser for nanometer displacement measurement

    International Nuclear Information System (INIS)

    Yan, Liping; Chen, Benyong; Wang, Bin

    2017-01-01

    A novel differential Michelson laser interferometer is proposed to eliminate the influence of environmental fluctuations for nanometer displacement measurement. This differential interferometer consists of two homodyne interferometers in which two orthogonal single frequency beams share common reference arm and partial measurement arm. By modulating the displacement of the common reference arm with a piezoelectric transducer, the common-mode displacement drift resulting from the environmental disturbances can be well suppressed and the measured displacement as differential-mode displacement signal is achieved. In addition, a phase difference compensation method is proposed for accurately determining the phase difference between interference signals by correcting the time interval according to the average speed in one cycle of interference signal. The nanometer displacement measurement experiments were performed to demonstrate the effectiveness and feasibility of the proposed interferometer and show that precision displacement measurement with standard deviation less than 1 nm has been achieved. (paper)

  6. Regarding on the exact solutions for the nonlinear fractional differential equations

    Directory of Open Access Journals (Sweden)

    Kaplan Melike

    2016-01-01

    Full Text Available In this work, we have considered the modified simple equation (MSE method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW and the modified equal width (mEW equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

  7. WKB: an interactive code for solving differential equations using phase integral methods

    International Nuclear Information System (INIS)

    White, R.B.

    1978-01-01

    A small code for the analysis of ordinary differential equations interactively through the use of Phase Integral Methods (WKB) has been written for use on the DEC 10. This note is a descriptive manual for those interested in using the code

  8. A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

    NARCIS (Netherlands)

    Dorren, H.J.S.

    1998-01-01

    It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of

  9. Olig2 and Hes regulatory dynamics during motor neuron differentiation revealed by single cell transcriptomics.

    Directory of Open Access Journals (Sweden)

    Andreas Sagner

    2018-02-01

    Full Text Available During tissue development, multipotent progenitors differentiate into specific cell types in characteristic spatial and temporal patterns. We addressed the mechanism linking progenitor identity and differentiation rate in the neural tube, where motor neuron (MN progenitors differentiate more rapidly than other progenitors. Using single cell transcriptomics, we defined the transcriptional changes associated with the transition of neural progenitors into MNs. Reconstruction of gene expression dynamics from these data indicate a pivotal role for the MN determinant Olig2 just prior to MN differentiation. Olig2 represses expression of the Notch signaling pathway effectors Hes1 and Hes5. Olig2 repression of Hes5 appears to be direct, via a conserved regulatory element within the Hes5 locus that restricts expression from MN progenitors. These findings reveal a tight coupling between the regulatory networks that control patterning and neuronal differentiation and demonstrate how Olig2 acts as the developmental pacemaker coordinating the spatial and temporal pattern of MN generation.

  10. Developing Concepts of Ordinary and Extraordinary Communication

    Science.gov (United States)

    Lane, Jonathan D.; Evans, E. Margaret; Brink, Kimberly A.; Wellman, Henry M.

    2016-01-01

    We examine how understandings of ordinary and extraordinary communication develop. Three- to 10-year-old children and adults (N = 183) were given scenarios in which a protagonist wanted help from a human (their parent) or from God. Scenarios varied in whether protagonists expressed their desires aloud (by asking) or silently (by hoping), whether…

  11. Response of an oscillatory differential delay equation to a single stimulus.

    Science.gov (United States)

    Mackey, Michael C; Tyran-Kamińska, Marta; Walther, Hans-Otto

    2017-04-01

    Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are able to completely characterize the perturbed response to a pulse of positive amplitude and duration with onset at different points in the limit cycle. We determine the perturbed minima and maxima and period of the limit cycle and show how the pulse modifies these from the unperturbed case.

  12. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  13. Differential equation for genus-two characters in arbitrary rational conformal field theories

    International Nuclear Information System (INIS)

    Mathur, S.D.; Sen, A.

    1989-01-01

    We develop a general method for deriving ordinary differential equations for the genus-two ''characters'' of an arbitrary rational conformal field theory using the hyperelliptic representation of the genus-two moduli space. We illustrate our method by explicitly deriving the character differential equations for k=1 SU(2), G 2 , and F 4 WZW models. Our method provides an intrinsic definition of conformal field theories on higher genus Riemann surfaces. (orig.)

  14. Ordinary Share Price Behaviour Around 'C' Share Issues by Investment Trusts

    OpenAIRE

    Adams, Andrew T; Szakacs, M

    1995-01-01

    This paper examines the "C" share issue, a method of issuing shares which is peculiar to the UK investment trust industry. In particular, we analyse abnormal returns and discount/premium to net asset value behaviour of the ordinary shares both before and after the announcement of "C" share issues. The research was conducted using event study methodology and an innovative approach to the analysis of discount/premium movements. The results suggest a tendency for the ordinary shares to outperfor...

  15. Multiple and fast: The accretion of ordinary chondrite parent bodies

    International Nuclear Information System (INIS)

    Vernazza, P.; Barge, P.; Zanda, B.; Hewins, R.; Binzel, R. P.; DeMeo, F. E.; Lockhart, M.; Hiroi, T.; Birlan, M.; Ricci, L.

    2014-01-01

    Although petrologic, chemical, and isotopic studies of ordinary chondrites and meteorites in general have largely helped establish a chronology of the earliest events of planetesimal formation and their evolution, there are several questions that cannot be resolved via laboratory measurements and/or experiments alone. Here, we propose the rationale for several new constraints on the formation and evolution of ordinary chondrite parent bodies (and, by extension, most planetesimals) from newly available spectral measurements and mineralogical analysis of main-belt S-type asteroids (83 objects) and unequilibrated ordinary chondrite meteorites (53 samples). Based on the latter, we suggest that spectral data may be used to distinguish whether an ordinary chondrite was formed near the surface or in the interior of its parent body. If these constraints are correct, the suggested implications include that: (1) large groups of compositionally similar asteroids are a natural outcome of planetesimal formation and, consequently, meteorites within a given class can originate from multiple parent bodies; (2) the surfaces of large (up to ∼200 km) S-type main-belt asteroids mostly expose the interiors of the primordial bodies, a likely consequence of impacts by small asteroids (D < 10 km) in the early solar system; (3) the duration of accretion of the H chondrite parent bodies was likely short (instantaneous or in less than ∼10 5 yr, but certainly not as long as 1 Myr); (4) LL-like bodies formed closer to the Sun than H-like bodies, a possible consequence of the radial mixing and size sorting of chondrules in the protoplanetary disk prior to accretion.

  16. Single Parenthood and Children's Reading Performance in Asia

    Science.gov (United States)

    Park, Hyunjoon

    2007-01-01

    Using the data from Program for International Student Assessment, I examine the gap in reading performance between 15-year-old students in single-parent and intact families in 5 Asian countries in comparison to the United States. The ordinary least square regression analyses show negligible disadvantages of students with a single parent in Hong…

  17. A direct algebraic method applied to obtain complex solutions of some nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Zhang Huiqun

    2009-01-01

    By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.

  18. Analytical approach for the Floquet theory of delay differential equations.

    Science.gov (United States)

    Simmendinger, C; Wunderlin, A; Pelster, A

    1999-05-01

    We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincaré-Lindstedt and the Shohat expansions, which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows us to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions.

  19. Differentiation of drug and non-drug Cannabis using a single nucleotide polymorphism (SNP) assay.

    Science.gov (United States)

    Rotherham, D; Harbison, S A

    2011-04-15

    Cannabis sativa is both an illegal drug and a legitimate crop. The differentiation of illegal drug Cannabis from non-drug forms of Cannabis is relevant in the context of the growth of fibre and seed oil varieties of Cannabis for commercial purposes. This differentiation is currently determined based on the levels of tetrahydrocannabinol (THC) in adult plants. DNA based methods have the potential to assay Cannabis material unsuitable for analysis using conventional means including seeds, pollen and severely degraded material. The purpose of this research was to develop a single nucleotide polymorphism (SNP) assay for the differentiation of "drug" and "non-drug"Cannabis plants. An assay was developed based on four polymorphisms within a 399 bp fragment of the tetrahydrocannabinolic acid (THCA) synthase gene, utilising the snapshot multiplex kit. This SNP assay was tested on 94 Cannabis plants, which included 10 blind samples, and was able to differentiate between "drug" and "non-drug"Cannabis in all cases, while also differentiating between Cannabis and other species. Non-drug plants were found to be homozygous at the four sites assayed while drug Cannabis plants were either homozygous or heterozygous. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

  20. Geometric approach to the (BRS-) differential algebras of supersymmetric YM-theories

    International Nuclear Information System (INIS)

    Gieres, F.

    1987-01-01

    The (BRS-) differential algebra of susy YM-theories is defined in terms of superfields and forms on rigid U(N)-superspace. For d = 4 and N = 1.2 we show that it projects to the ''BRS-component field algebra in the WZ-gauge'' without any supergauge fixing. In this process the supergeometry is destroyed with the result that the final algebra becomes a prototype for a differential algebra which cannot be associated with an ordinary Lie algebra

  1. Simultaneous determination of ordinary and extraordinary refractive index dispersions of nematic liquid crystals in the visible and near-infrared regions from an interference spectrum

    Science.gov (United States)

    Ozaki, Ryotaro; Nishi, Koji; Kan, Takayuki; Kadowaki, Kazunori

    2016-10-01

    An improved interference method is proposed to determine ordinary and extraordinary refractive index dispersions of nematic liquid crystals (LCs). In this method, an LC cell coated with a thin metal layer is used as a Fabry-Perot interferometer, which shows us a sharp transmission fringe. To ensure high reliability, the wavelength dispersion of the refractive index of the metal is taken into account in fitting calculation. In spite of measuring ordinary and extraordinary components, the LC cell, polarizers, and other equipment are not rotated during the experiment. The index evaluation from a single spectrum avoids errors depending on the measurement position owing to non-uniformities of molecular orientation and cell thickness because we can obtain the two indices at exactly the same position. This system can adapt to a wide frequency range and does not require any specific wavelength light source or laser. We demonstrate the determination of ordinary and extraordinary refractive index dispersions of a nematic liquid crystal in the visible and near-infrared regions. Furthermore, we quantitatively reproduce the measured spectrum by calculation using the measured refractive indices.

  2. Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations

    Directory of Open Access Journals (Sweden)

    Josef Diblík

    2013-01-01

    dimension of the set of initial data generating such solutions is estimated. An asymptotic behavior of solutions is determined as well and relevant asymptotic formulas are derived. The method of functions defined implicitly and the topological method (Ważewski's method are used in the proofs. The results generalize some previous ones on singular initial value problems for differential equations.

  3. Onset of chaos in a single-phase power electronic inverter

    DEFF Research Database (Denmark)

    Avrutin, Viktor; Mosekilde, Erik; Zhusubaliyev, Zhanybai T.

    2015-01-01

    derived from a non-autonomous ordinary differential equation with discontinuous right-hand side. By construction, this stroboscopic map has a high number of border points. It is shown that the onset of chaos occurs stepwise, via irregular cascades of different border collisions, some of which lead...

  4. Numerical methods for differential equations and applications

    International Nuclear Information System (INIS)

    Ixaru, L.G.

    1984-01-01

    This book is addressed to persons who, without being professionals in applied mathematics, are often faced with the problem of numerically solving differential equations. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations: multistep methods; one-step methods; and piecewise perturbation methods. The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations, with a section devoted to the Schroedinger equation. In the fifth chapter the eigenvalue problem for the radial Schroedinger equation is solved in several ways, with computer programs included. (Auth.)

  5. A comparison of flashbacks and ordinary autobiographical memories of trauma: content and language.

    Science.gov (United States)

    Hellawell, Steph J; Brewin, Chris R

    2004-01-01

    We investigated hypotheses derived from the dual representation theory of posttraumatic stress disorder, which proposes that flashbacks and ordinary memories of trauma are supported by different types of representation. Sixty-two participants meeting diagnostic criteria for posttraumatic stress disorder completed a detailed written trauma narrative, and afterwards identified those sections in the narrative that had been written in flashback and ordinary memory periods. As predicted, flashback periods were characterised by greater use of detail, particularly perceptual detail, by more mentions of death, more use of the present tense, and more mention of fear, helplessness, and horror. In contrast, ordinary memory sections were characterised by more mention of secondary emotions such as guilt and anger.

  6. LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration with Root-finding

    International Nuclear Information System (INIS)

    Hindmarsh, A.C.; Petzold, L.R.

    2005-01-01

    1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, The nonlinear iteration method-switching differs from the method-switching in LSODA and LSODAR, but provides similar savings by using the cheaper method in the non-stiff regions of the problem. c) LSODKR includes the ability to find roots of given functions of the solution during the integration. d) LSODKR also improves on the Krylov methods in LSODPK by offering the option to save and reuse the approximate Jacobian data underlying the pre-conditioner. The LSODKR source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available. 2 - Methods: It is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user

  7. Molecular hierarchy in neurons differentiated from mouse ES cells containing a single human chromosome 21.

    Science.gov (United States)

    Wang, Chi Chiu; Kadota, Mitsutaka; Nishigaki, Ryuichi; Kazuki, Yasuhiro; Shirayoshi, Yasuaki; Rogers, Michael Scott; Gojobori, Takashi; Ikeo, Kazuho; Oshimura, Mitsuo

    2004-02-06

    Defects in neurogenesis and neuronal differentiation in the fetal brain of Down syndrome (DS) patients lead to the apparent neuropathological abnormalities and contribute to the phenotypic characters of mental retardation, and premature development of Alzheimer's disease, those being the most common phenotype in DS. In order to understand the molecular mechanism underlying the cause of phenotypic abnormalities in the DS brain, we have utilized an in vitro model of TT2F mouse embryonic stem cells containing a single human chromosome 21 (hChr21) to study neuron development and neuronal differentiation by microarray containing 15K developmentally expressed cDNAs. Defective neuronal differentiation in the presence of extra hChr21 manifested primarily the post-transcriptional and translational modification, such as Mrpl10, SNAPC3, Srprb, SF3a60 in the early neuronal stem cell stage, and Mrps18a, Eef1g, and Ubce8 in the late differentiated stage. Hierarchical clustering patterned specific expression of hChr21 gene dosage effects on neuron outgrowth, migration, and differentiation, such as Syngr2, Dncic2, Eif3sf, and Peg3.

  8. Novel driver method to improve ordinary CCD frame rate for high-speed imaging diagnosis

    Energy Technology Data Exchange (ETDEWEB)

    Luo, Tong-Ding, E-mail: snuohui@126.com; Li, Bin-Kang; Yang, Shao-Hua; Guo, Ming-An; Yan, Ming

    2016-06-21

    The use of ordinary Charge-coupled-Device (CCD) imagers for the analysis of fast physical phenomenon is restricted because of the low-speed performance resulting from their long output times. Even though the form of Intensified-CCD (ICCD), coupled with a gated image intensifier, has extended their use for high speed imaging, the deficiency remains to be solved that ICDD could record only one image in a single shot. This paper presents a novel driver method designed to significantly improve the ordinary interline CCD burst frame rate for high-speed photography. This method is based on the use of vertical registers as storage, so that a small number of additional frames comprised of reduced-spatial-resolution images obtained via a specific sampling operation can be buffered. Hence, the interval time of the received series of images is related to the exposure and vertical transfer times only and, thus, the burst frame rate can be increased significantly. A prototype camera based on this method is designed as part of this study, exhibiting a burst rate of up to 250,000 frames per second (fps) and a capacity to record three continuous images. This device exhibits a speed enhancement of approximately 16,000 times compared with the conventional speed, with a spatial resolution reduction of only 1/4.

  9. A New Factorisation of a General Second Order Differential Equation

    Science.gov (United States)

    Clegg, Janet

    2006-01-01

    A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…

  10. Relative boundedness and compactness theory for second-order differential operators

    Directory of Open Access Journals (Sweden)

    Don B. Hinton

    1997-01-01

    Full Text Available The problem considered is to give necessary and sufficient conditions for perturbations of a second-order ordinary differential operator to be either relatively bounded or relatively compact. Such conditions are found for three classes of operators. The conditions are expressed in terms of integral averages of the coefficients of the perturbing operator.

  11. New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

    International Nuclear Information System (INIS)

    Yao Ruo-Xia; Wang Wei; Chen Ting-Hua

    2014-01-01

    Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. (general)

  12. Proximity-based differential single cell analysis of the niche to identify stem/progenitor cell regulators

    Science.gov (United States)

    Silberstein, Lev; Goncalves, Kevin A; Kharchenko, Peter V; Turcotte, Raphael; Kfoury, Youmna; Mercier, Francois; Baryawno, Ninib; Severe, Nicolas; Bachand, Jacqueline; Spencer, Joel; Papazian, Ani; Lee, Dongjun; Chitteti, Brahmananda Reddy; Srour, Edward F; Hoggatt, Jonathan; Tate, Tiffany; Celso, Cristina Lo; Ono, Noriaki; Nutt, Stephen; Heino, Jyrki; Sipilä, Kalle; Shioda, Toshihiro; Osawa, Masatake; Lin, Charles P; Hu, Guo-fu; Scadden, David T

    2016-01-01

    SUMMARY Physiological stem cell function is regulated by secreted factors produced by niche cells. In this study, we describe an unbiased approach based on differential single-cell gene expression analysis of mesenchymal osteolineage cells close to and further removed from hematopoietic stem/progenitor cells to identify candidate niche factors. Mesenchymal cells displayed distinct molecular profiles based on their relative location. Amongst the genes which were preferentially expressed in proximal cells, we functionally examined three secreted or cell surface molecules not previously connected to HSPC biology: the secreted RNase Angiogenin, the cytokine IL18 and the adhesion molecule Embigin and discovered that all of these factors are HSPC quiescence regulators. Our proximity-based differential single cell approach therefore reveals molecular heterogeneity within niche cells and can be used to identify novel extrinsic stem/progenitor cell regulators. Similar approaches could also be applied to other stem cell/niche pairs to advance understanding of microenvironmental regulation of stem cell function. PMID:27524439

  13. A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

    Science.gov (United States)

    Benhammouda, Brahim; Vazquez-Leal, Hector

    2016-01-01

    This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

  14. Solution of linear ordinary differential equations by means of the method of variation of arbitrary constants

    DEFF Research Database (Denmark)

    Mejlbro, Leif

    1997-01-01

    An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians.......An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....

  15. 3D Laser Scanning Assisted by Ordinary Plane Mirror for Non-direct Viewing Area

    Directory of Open Access Journals (Sweden)

    ZHANG Fan

    2017-12-01

    Full Text Available Terrestrial 3D laser scanning is one of principal methods to get the geometric information of object surface,and the integrity of the scanned object is a basic requirement in data acquisition. In order to solve the missing point cloud problem due to the scanning dead angle caused by confined working space,this paper proposes a method using ordinary plane mirror to obtain laser scanning data for non-direct viewing area according to the plane mirror reflection principle,analyzes the influence mechanism of the ordinary plane mirror on the propagation path and distance of laser beam,deduces the coordinate equation of the object point corresponding to the image point reflected by ordinary plane mirror in laser scanning. Given the laser scanning characteristic,this paper introduces a mirror reflection system included target balls and ordinary plane mirror,and expounds the system construction,system calibration and constructing method of system coordinate system. The feasibility and precision of the method are verified by experiments.

  16. Learning to Compute: Computerization and Ordinary, Everyday Life

    Science.gov (United States)

    Sullivan, Joseph F.

    2009-01-01

    This study utilizes the basic framework of classical sociology as a foundation for examining the intersection of the structural history of the computer revolution with ordinary, everyday life. Just as the classical forefathers of modern sociology--Marx, Durkheim, and Weber--attempted to understand their eras of structural transformation, this…

  17. X-ray diffractometry of steam cured ordinary Portland and blast-furnace-slag cements

    International Nuclear Information System (INIS)

    Camarini, G.; Djanikian, J.G.

    1994-01-01

    This work studies some aspects of the phases produced by hydration of ordinary and blast-furnace-slag cements, at normal conditions and steam cured (60 and 95 0 C), using an X-ray diffraction technique. The blast-furnace-slag cement was a mixture of 50% of ordinary Portland cement and 50% of blast-furnace-slag (separately grinding). After curing the X-ray diffraction reveals that, in relation to ordinary Portland cement, the main phases in blast-furnace-slag cement are hydrated silicates and aluminates, hydro garnet, etringitte and mono sulphate. After steam curing the hydration of blast-furnace-slag cement proceeds. This is a result of the slag activation by the curing temperature. (author). 8 refs., 3 figs., 1 tab

  18. Differential cross sections for single ionization of H2 by 75-keV proton impact

    International Nuclear Information System (INIS)

    Chowdhury, U.; Schulz, M.; Madison, D. H.

    2011-01-01

    We have calculated triply differential cross sections (TDCS) and doubly differential cross sections (DDCS) for single ionization of H 2 by 75-keV proton impact using the molecular three-body distorted-wave-eikonal initial-state (M3DW-EIS) approach. Previously published measured DDCS (differential in the projectile scattering angle and integrated over the ejected electron angles) found pronounced structures at relatively large angles that were interpreted as an interference resulting from the two-centered potential of the molecule. Theory treating H 2 as atomic H multiplied by a molecular interference factor only predicts the observed structure when assumptions are made about the molecular orientation. Here we apply the M3DW-EIS method, which does not rely on such an ad hoc approach, but rather treats the interference from first principles.

  19. Partial differential equations & boundary value problems with Maple

    CERN Document Server

    Articolo, George A

    2009-01-01

    Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple''s animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations.  Maple files can be found on the books website. Ancillary list: Maple files- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747327  Provides a quick overview of the software w/simple commands needed to get startedIncludes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equationsIncorporates an early introduction to Sturm-L...

  20. The utility of diffusion-weighted MR imaging for differentiating uterine sarcomas from benign leiomyomas

    International Nuclear Information System (INIS)

    Tamai, Ken; Saga, Tsuneo; Morisawa, Nobuko; Fujimoto, Koji; Togashi, Kaori; Koyama, Takashi; Mikami, Yoshiki

    2008-01-01

    The usefulness of diffusion-weighted (DW) magnetic resonance (MR) imaging for the diagnosis of uterine sarcomas was investigated, as well as whether DW images and quantitative measurement of apparent diffusion coefficient (ADC) values can facilitate differentiating uterine sarcomas from benign leiomyomas. MR images including DW images were obtained in 43 surgically treated patients with 58 myometrial tumors, including seven uterine sarcomas (five leiomyosarcomas and two endometrial stromal sarcomas) and 51 benign leiomyomas (43 ordinary leiomyomas, two cellular leiomyomas and six degenerated leiomyomas). Qualitative analysis of non-enhanced and postcontrast MR images and DW images and quantitative measurement of ADC values were performed for each myometrial tumor. Both uterine sarcomas and cellular leiomyomas exhibited high signal intensity on DW images, whereas ordinary leiomyomas and most degenerated leiomyomas showed low signal intensity. The mean ADC value (10 -3 mm 2 /s) of sarcomas was 1.17 ± 0.15, which was lower than those of the normal myometrium (1.62 ± 0.11) and degenerated leiomyomas (1.70 ± 0.11) without any overlap; however, they were overlapped with those of ordinary leiomyomas and cellular leiomyomas. In addition to morphological features on nonenhanced and postcontrast MR sequences, DW imaging and ADC measurement may have a potential ability to differentiate uterine sarcomas from benign leiomyomas. (orig.)

  1. "E pluribus unum" or How to Derive Single-equation Descriptions for Output-quantities in Nonlinear Circuits using Differential Algebra

    OpenAIRE

    Gerbracht, Eberhard H. -A.

    2008-01-01

    In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear algebra to the system of differential equations which is used to model the analog circuit. For nonlinear circuits and their corresponding nonlinear differential equations, we show how to employ computer algebra tools implemented in Maple, which are based on diff...

  2. Nanodiamonds and silicate minerals in ordinary chondrites as determined by micro-Raman spectroscopy

    Science.gov (United States)

    Saikia, Bhaskar J.; Parthasarathy, Gopalakrishnarao; Borah, Rashmi R.

    2017-06-01

    We present here the Raman spectroscopic study of silicate and carbonaceous minerals in three ordinary chondrites with the aim to improve our understanding the impact process including the peak metamorphic pressures present in carbon-bearing ordinary chondites. The characteristic Raman vibrational peaks of olivines, pyroxenes, and plagioclase have been determined on three ordinary chondrites from India, Dergaon (H5), Mahadevpur (H4/5), and Kamargaon (L6). The Raman spectra of these meteorite samples show the presence of nanodiamonds at 1334-1345 cm-1 and 1591-1619 cm-1. The full-width at half maximum (FWHM) of Raman peaks for Mahadevpur and Dergaon reflect the nature of shock metamorphism in these meteorites. The frequency shift in Raman spectra might be because of shock effects during the formation of the diamond/graphite grains.

  3. Giant Pulse Studies of Ordinary and Recycled Pulsars with NICER

    Science.gov (United States)

    Lewandowska, Natalia; Arzoumanian, Zaven; Gendreau, Keith C.; Enoto, Teruaki; Harding, Alice; Lommen, Andrea; Ray, Paul S.; Deneva, Julia; Kerr, Matthew; Ransom, Scott M.; NICER Team

    2018-01-01

    Radio Giant Pulses are one of the earliest discovered form of anomalous single pulse emission from pulsars. Known for their non-periodical occurrence, restriction to certain phase ranges, power-law intensity distributions, pulse widths ranging from microseconds to nanoseconds and very high brightness temperatures, they stand out as an individual form of pulsar radio emission.Discovered originally in the case of the Crab pulsar, several other pulsars have been observed to emit radio giant pulses, the most promising being the recycled pulsar PSR B1937+21 and also the Vela pulsar.Although radio giant pulses are apparently the result of a coherent emission mechanism, recent studies of the Crab pulsar led to the discovery of an additional incoherent component at optical wavelengths. No such component has been identified for recycled pulsars, or Vela yet.To provide constraints on possible emission regions in their magnetospheres and to search for differences between giant pulses from ordinary and recycled pulsars, we present the progress of the correlation study of PSR B1937+21 and the Vela pulsar carried out with NICER and several radio observatories.

  4. Analysis and differentiation of mineral dust by single particle laser mass spectrometry

    International Nuclear Information System (INIS)

    Gallavardin, S. J.; Lohmann, U.; Cziczo, Daniel J.

    2008-01-01

    This study evaluates the potential of single particle laser desorption/ionization mass spectrometry for the analysis of atmospherically relevant mineral dusts. Samples of hematite, goethite, calcium carbonate, calcium sulfate, silica, quartz, montmorrillonite, kaolinite, illite, hectorite, wollastonite and nephelinsyenit were investigated in positive and negative ion mode with a monopolar time-of-flight mass spectrometer where the desorption/ionization step was performed with a 193 nm excimer laser (∼10 9 W/cm 2 ). Particle size ranged from 500 nm to 3 (micro)m. Positive mass spectra mainly provide elemental composition whereas negative ion spectra provide information on element speciation and of a structural nature. The iron oxide, calcium-rich and aluminosilicate nature of particles is established in positive ion mode. The differentiation of calcium materials strongly relies on the calcium counter-ions in negative mass spectra. Aluminosilicates can be differentiated in both positive and negative ion mode using the relative abundance of various aluminum and silicon ions

  5. Sustainability in a Differential Equations Course: A Case Study of Easter Island

    Science.gov (United States)

    Koss, Lorelei

    2011-01-01

    Easter Island is a fascinating example of resource depletion and population collapse, and its relatively short period of human habitation combined with its isolation lends itself well to investigation by students in a first-semester ordinary differential equations course. This article describes curricular materials for a semester-long case study…

  6. An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi -GBM Detection of GRB 170817A

    Energy Technology Data Exchange (ETDEWEB)

    Goldstein, A.; Roberts, O. J.; Connaughton, V. [Science and Technology Institute, Universities Space Research Association, Huntsville, AL 35805 (United States); Veres, P.; Briggs, M. S.; Hamburg, R.; Preece, R. D.; Poolakkil, S. [Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, 320 Sparkman Drive, Huntsville, AL 35899 (United States); Burns, E.; Racusin, J.; Canton, T. Dal [NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States); Kocevski, D.; Wilson-Hodge, C. A.; Hui, C. M.; Littenberg, T. [Astrophysics Office, ST12, NASA/Marshall Space Flight Center, Huntsville, AL 35812 (United States); Kienlin, A. von [Max-Planck-Institut für extraterrestrische Physik, Giessenbachstrasse 1, D-85748 Garching (Germany); Christensen, N.; Broida, J. [Physics and Astronomy, Carleton College, MN 55057 (United States); Siellez, K. [Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332 (United States); Blackburn, L., E-mail: Adam.M.Goldstein@nasa.gov [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); and others

    2017-10-20

    On 2017 August 17 at 12:41:06 UTC the Fermi Gamma-ray Burst Monitor (GBM) detected and triggered on the short gamma-ray burst (GRB) 170817A. Approximately 1.7 s prior to this GRB, the Laser Interferometer Gravitational-wave Observatory triggered on a binary compact merger candidate associated with the GRB. This is the first unambiguous coincident observation of gravitational waves and electromagnetic radiation from a single astrophysical source and marks the start of gravitational-wave multi-messenger astronomy. We report the GBM observations and analysis of this ordinary short GRB, which extraordinarily confirms that at least some short GRBs are produced by binary compact mergers.

  7. Accounting for technical noise in differential expression analysis of single-cell RNA sequencing data.

    Science.gov (United States)

    Jia, Cheng; Hu, Yu; Kelly, Derek; Kim, Junhyong; Li, Mingyao; Zhang, Nancy R

    2017-11-02

    Recent technological breakthroughs have made it possible to measure RNA expression at the single-cell level, thus paving the way for exploring expression heterogeneity among individual cells. Current single-cell RNA sequencing (scRNA-seq) protocols are complex and introduce technical biases that vary across cells, which can bias downstream analysis without proper adjustment. To account for cell-to-cell technical differences, we propose a statistical framework, TASC (Toolkit for Analysis of Single Cell RNA-seq), an empirical Bayes approach to reliably model the cell-specific dropout rates and amplification bias by use of external RNA spike-ins. TASC incorporates the technical parameters, which reflect cell-to-cell batch effects, into a hierarchical mixture model to estimate the biological variance of a gene and detect differentially expressed genes. More importantly, TASC is able to adjust for covariates to further eliminate confounding that may originate from cell size and cell cycle differences. In simulation and real scRNA-seq data, TASC achieves accurate Type I error control and displays competitive sensitivity and improved robustness to batch effects in differential expression analysis, compared to existing methods. TASC is programmed to be computationally efficient, taking advantage of multi-threaded parallelization. We believe that TASC will provide a robust platform for researchers to leverage the power of scRNA-seq. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

  8. Aiming for the ordinary

    DEFF Research Database (Denmark)

    Offersen, Sara Marie Hebsgaard

    that the Danes are encouraged to be alert to still earlier and vaguer bodily signs of potential cancer and seek care ‘in time’. With biomedical constructions such as ‘cancer awareness’ and ‘alarm symptoms of cancer’ and the retrospectively oriented definition of life before symptoms-based healthcare seeking...... and articulation of bodily sensations, and how decisions about healthcare seeking are established in this context. This dissertation aims to explore these matters from the perspective of the Danish middle class, mainly focusing on how sensations are ascribed meaning as symptoms and how they are evoked...... on a continuum between what is locally considered ordinary and extraordinary. Overall, the dissertation argues that inquiries into morality and potentiality provide valuable insights into healthcare seeking practices and the making and management of symptoms in everyday life. The dissertation is based on 18...

  9. On the asymptotic expansions of solutions of an nth order linear differential equation with power coefficients

    International Nuclear Information System (INIS)

    Paris, R.B.; Wood, A.D.

    1984-11-01

    The asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n, containing a factor zsup(m) multiplying the lower order derivatives, are investigated for large values of z in the complex plane. Four classes of solutions are considered which exhibit the following behaviour as /z/ → infinity in certain sectors: (i) solutions whose behaviour is either exponentially large or algebraic (involving p ( < n) algebraic expansions), (ii) solutions which are exponentially small (iii) solutions with a single algebraic expansion and (iv) solutions which are even and odd functions of z whenever n+m is even. The asymptotic expansions of these solutions in a full neigbourhood of the point at infinity are obtained by means of the theory of the solutions in the case m=O developed in a previous paper

  10. W-transform for exponential stability of second order delay differential equations without damping terms.

    Science.gov (United States)

    Domoshnitsky, Alexander; Maghakyan, Abraham; Berezansky, Leonid

    2017-01-01

    In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.

  11. Proximity-Based Differential Single-Cell Analysis of the Niche to Identify Stem/Progenitor Cell Regulators.

    Science.gov (United States)

    Silberstein, Lev; Goncalves, Kevin A; Kharchenko, Peter V; Turcotte, Raphael; Kfoury, Youmna; Mercier, Francois; Baryawno, Ninib; Severe, Nicolas; Bachand, Jacqueline; Spencer, Joel A; Papazian, Ani; Lee, Dongjun; Chitteti, Brahmananda Reddy; Srour, Edward F; Hoggatt, Jonathan; Tate, Tiffany; Lo Celso, Cristina; Ono, Noriaki; Nutt, Stephen; Heino, Jyrki; Sipilä, Kalle; Shioda, Toshihiro; Osawa, Masatake; Lin, Charles P; Hu, Guo-Fu; Scadden, David T

    2016-10-06

    Physiological stem cell function is regulated by secreted factors produced by niche cells. In this study, we describe an unbiased approach based on the differential single-cell gene expression analysis of mesenchymal osteolineage cells close to, and further removed from, hematopoietic stem/progenitor cells (HSPCs) to identify candidate niche factors. Mesenchymal cells displayed distinct molecular profiles based on their relative location. We functionally examined, among the genes that were preferentially expressed in proximal cells, three secreted or cell-surface molecules not previously connected to HSPC biology-the secreted RNase angiogenin, the cytokine IL18, and the adhesion molecule Embigin-and discovered that all of these factors are HSPC quiescence regulators. Therefore, our proximity-based differential single-cell approach reveals molecular heterogeneity within niche cells and can be used to identify novel extrinsic stem/progenitor cell regulators. Similar approaches could also be applied to other stem cell/niche pairs to advance the understanding of microenvironmental regulation of stem cell function. Copyright © 2016 Elsevier Inc. All rights reserved.

  12. Modeling Group Differences in OLS and Orthogonal Regression: Implications for Differential Validity Studies

    Science.gov (United States)

    Kane, Michael T.; Mroch, Andrew A.

    2010-01-01

    In evaluating the relationship between two measures across different groups (i.e., in evaluating "differential validity") it is necessary to examine differences in correlation coefficients and in regression lines. Ordinary least squares (OLS) regression is the standard method for fitting lines to data, but its criterion for optimal fit…

  13. Operational method of solution of linear non-integer ordinary and partial differential equations.

    Science.gov (United States)

    Zhukovsky, K V

    2016-01-01

    We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.

  14. New Ideas: Ordinary is Extraordinary

    Directory of Open Access Journals (Sweden)

    Antonio Jose

    2004-06-01

    Full Text Available Abstract With the initial issue of this journal, a new challenge has been offered tothe world of sports nutrition: initiate "team oriented" research and clinical trials in order to make dynamic progress in terms of understandingand applying nutrition principals to the field of competitive sports. It is our further challenge that these teams think "outside the box" in terms of their approach to elucidating new concepts through which nutritional interventions might play a role in the regulation of muscle growth and repair, athletic performance and endurance, and mental acuity. What was once thought of as extraordinary might now be approached as ordinary, if the correct composition of "teams" were formed.

  15. Filtering informal learning in everyday life: invoking ordinariness and moving to civic engagement

    OpenAIRE

    Grummell, Bernie

    2010-01-01

    This article explores the role of informal learning from television as it is anchored within the ordinariness of daily life. It examines the consequences for pedagogy and civic engagement, questioning how informal learning from television can enhance civic engagement. For many, this learning was localized through personalized and interpersonal relations of everyday life. Learning was not viewed as a distant institutional force, but as an embedded part of an ordinary life. The invoking of ordi...

  16. Performance Evaluation of the Ordinary Least Square (OLS) and ...

    African Journals Online (AJOL)

    Nana Kwasi Peprah

    1Deparment of Geomatic Engineering, University of Mines and Technology, ... precise, accurate and can be used to execute any engineering works due to ..... and Ordinary Least Squares Methods”, Journal of Geomatics and Planning, Vol ... Technology”, Unpublished BSc Project Report, University of Mines and Technology ...

  17. Families of null surfaces in the Minkowski tri dimensional space-time and its associated differential equations

    International Nuclear Information System (INIS)

    Silva O, G.; Garcia G, P.

    2004-01-01

    In this work we describe the procedure to obtain all the family of third order ordinary differential equations connected by a contact transformation such that in their spaces of solutions is defined a conformal three dimensional Minkowski metric. (Author)

  18. Ridge regression estimator: combining unbiased and ordinary ridge regression methods of estimation

    Directory of Open Access Journals (Sweden)

    Sharad Damodar Gore

    2009-10-01

    Full Text Available Statistical literature has several methods for coping with multicollinearity. This paper introduces a new shrinkage estimator, called modified unbiased ridge (MUR. This estimator is obtained from unbiased ridge regression (URR in the same way that ordinary ridge regression (ORR is obtained from ordinary least squares (OLS. Properties of MUR are derived. Results on its matrix mean squared error (MMSE are obtained. MUR is compared with ORR and URR in terms of MMSE. These results are illustrated with an example based on data generated by Hoerl and Kennard (1975.

  19. Delay differential equations for mode-locked semiconductor lasers.

    Science.gov (United States)

    Vladimirov, Andrei G; Turaev, Dmitry; Kozyreff, Gregory

    2004-06-01

    We propose a new model for passive mode locking that is a set of ordinary delay differential equations. We assume a ring-cavity geometry and Lorentzian spectral filtering of the pulses but do not use small gain and loss and weak saturation approximations. By means of a continuation method, we study mode-locking solutions and their stability. We find that stable mode locking can exist even when the nonlasing state between pulses becomes unstable.

  20. Total and single differential cross sections for the electron impact ionization of the ground state of helium

    International Nuclear Information System (INIS)

    Singh, T.S.C.; Choudhury, K.B.; Singh, M.B.; Deb, N.C.; Mukherjee, S.C.; Mazumdar, P.S.

    1997-01-01

    Total cross sections (TCS) and single differential cross sections (SDCS) have been computed for the single ionization of the ground state of helium by electron impact in a distorted wave formalism which takes into account the effects of the initial and final channel distortions. The present TCS and SDCS results are in fair agreement with the measured values and other theoretical predictions for the incident electron energy E i > 150 eV. (orig.)

  1. Stability with respect to initial time difference for generalized delay differential equations

    Directory of Open Access Journals (Sweden)

    Ravi Agarwal

    2015-02-01

    Full Text Available Stability with initial data difference for nonlinear delay differential equations is introduced. This type of stability generalizes the known concept of stability in the literature. It gives us the opportunity to compare the behavior of two nonzero solutions when both initial values and initial intervals are different. Several sufficient conditions for stability and for asymptotic stability with initial time difference are obtained. Lyapunov functions as well as comparison results for scalar ordinary differential equations are employed. Several examples are given to illustrate the theory.

  2. Insights on the Nature of Intelligence from Ordinary Discourse.

    Science.gov (United States)

    Derr, Richard L.

    1989-01-01

    The use of "intelligence" in ordinary discourse is analyzed to glean hypotheses that may resolve the debate among psychologists regarding the nature of intelligence. Intelligence is conceived as an innate intellectual capacity, and a sharp conceptual distinction is made between intelligence and intelligent behavior. (Author/TJH)

  3. Stanley Cavell, Classical Hollywood and the Constitution of the Ordinary (With Notes on Billy Wilder

    Directory of Open Access Journals (Sweden)

    Tatjana Jukić

    2016-04-01

    Full Text Available When in his Tanner lectures Stanley Cavell sets out to define Ordinary Language Philosophy or – rather – to explain how it demarcates philosophy as such, he takes up psychoanalytic literary criticism in order to articulate the terms of this task. Yet the constitution of the ordinary, in Cavell, is never quite accessed from within psychoanalysis-cum-literature alone; instead, it takes another relation, that of psychoanalysis and literature to classical Hollywood, for Cavell to address the ordinary in terms of its constitution. I propose to discuss this complex using two films by Billy Wilder as a passageway to Cavell’s analytic procedure.

  4. Ordinary and extraordinary means.

    Science.gov (United States)

    Gillon, R

    1986-01-25

    The Roman Catholic doctrine of ordinary and extraordinary means in patient care decisions is the subject of this essay in Gillon's series on medical ethics. He briefly traces the Church history of this doctrine, which holds that saving life is not obligatory if doing so would be excessively burdensome or disproportionate in relation to the expected benefits. The burdens and benefits are to be weighed in the context of "circumstances of persons, places, times, and cultures," and factors such as the costs and risks of undergoing a proposed treatment may be considered. Gillon also notes the disagreement among Roman Catholic commentators over whether it is ever permissible to discontinue feeding as a burdensome, extraordinary treatment. He concludes that, despite different weightings of harms and benefits, Roman Catholic and non-Catholic thinkers are in accord over the appropriate moral approach to deciding when treatment is not obligatory.

  5. Periodic solutions of nonautonomous differential systems modeling obesity population

    International Nuclear Information System (INIS)

    Arenas, Abraham J.; Gonzalez-Parra, Gilberto; Jodar, Lucas

    2009-01-01

    In this paper we study the periodic behaviour of the solutions of a nonautonomous model for obesity population. The mathematical model represented by a nonautonomous system of nonlinear ordinary differential equations is used to model the dynamics of obese populations. Numerical simulations suggest periodic behaviour of subpopulations solutions. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained using a continuation theorem based on coincidence degree theory.

  6. Periodic solutions of nonautonomous differential systems modeling obesity population

    Energy Technology Data Exchange (ETDEWEB)

    Arenas, Abraham J. [Departamento de Matematicas y Estadistica, Universidad de Cordoba Monteria (Colombia)], E-mail: aarenas@sinu.unicordoba.edu.co; Gonzalez-Parra, Gilberto [Departamento de Calculo, Universidad de los Andes, Merida (Venezuela, Bolivarian Republic of)], E-mail: gcarlos@ula.ve; Jodar, Lucas [Instituto de Matematica Multidisciplinar, Universidad Politecnica de Valencia Edificio 8G, 2o, 46022 Valencia (Spain)], E-mail: ljodar@imm.upv.es

    2009-10-30

    In this paper we study the periodic behaviour of the solutions of a nonautonomous model for obesity population. The mathematical model represented by a nonautonomous system of nonlinear ordinary differential equations is used to model the dynamics of obese populations. Numerical simulations suggest periodic behaviour of subpopulations solutions. Sufficient conditions which guarantee the existence of a periodic positive solution are obtained using a continuation theorem based on coincidence degree theory.

  7. Interpreting experimental data on egg production--applications of dynamic differential equations.

    Science.gov (United States)

    France, J; Lopez, S; Kebreab, E; Dijkstra, J

    2013-09-01

    This contribution focuses on applying mathematical models based on systems of ordinary first-order differential equations to synthesize and interpret data from egg production experiments. Models based on linear systems of differential equations are contrasted with those based on nonlinear systems. Regression equations arising from analytical solutions to linear compartmental schemes are considered as candidate functions for describing egg production curves, together with aspects of parameter estimation. Extant candidate functions are reviewed, a role for growth functions such as the Gompertz equation suggested, and a function based on a simple new model outlined. Structurally, the new model comprises a single pool with an inflow and an outflow. Compartmental simulation models based on nonlinear systems of differential equations, and thus requiring numerical solution, are next discussed, and aspects of parameter estimation considered. This type of model is illustrated in relation to development and evaluation of a dynamic model of calcium and phosphorus flows in layers. The model consists of 8 state variables representing calcium and phosphorus pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. Experiments that measure Ca and P uptake in layers fed different calcium concentrations during shell-forming days are used to evaluate the model. In addition to providing a useful management tool, such a simulation model also provides a means to evaluate feeding strategies aimed at reducing excretion of potential pollutants in poultry manure to the environment.

  8. The Reduction of Chazy Classes and Other Third-Order Differential Equations Related to Boundary Layer Flow Models

    International Nuclear Information System (INIS)

    Fakhar, K.; Kara, A. H.

    2012-01-01

    We study the symmetries, conservation laws and reduction of third-order equations that evolve from a prior reduction of models that arise in fluid phenomena. These could be the ordinary differential equations (ODEs) that are reductions of partial differential equations (PDEs) or, alternatively, PDEs related to given ODEs. In this class, the analysis includes the well-known Blasius, Chazy, and other associated third-order ODEs. (general)

  9. Moyal star product of μ-holomorphic j-differentials

    International Nuclear Information System (INIS)

    Kachkachi, K.

    2007-08-01

    It was shown only for scalar conformal fields, that the Moyal-Weyl star product can introduce the quantum effect as the phase factor to the ordinary product. In this paper we show that, even on the same complex structure, the Moyal-Weyl star product of two j-differentials (conformal fields of weights (j, 0)) does not vanish but it generates the quantum effect at the first order of its perturbative series. More generally, we get the explicit expression of the Moyal-Weyl star product of j-differentials defined on any complex structure of a bi-dimensional Riemann surface Σ. We show that the star product of two j-differentials is not a j-differential and does not preserve the conformal covariance character. This can shed some light on the Moyal-Weyl deformation quantization procedure connection's with the deformation of complex structures on a Riemann surface. Hence, the situation might relate the star products to the Moduli and Teichmuller spaces of Riemann surfaces. (author)

  10. Dynamic data analysis modeling data with differential equations

    CERN Document Server

    Ramsay, James

    2017-01-01

    This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...

  11. Implementing Families of Implicit Chebyshev Methods with Exact Coefficients for the Numerical Integration of First- and Second-Order Differential Equations

    National Research Council Canada - National Science Library

    Mitchell, Jason

    2002-01-01

    A method is presented for the generation of exact numerical coefficients found in two families of implicit Chebyshev methods for the numerical integration of first- and second-order ordinary differential equations...

  12. Numerical Simulation of Coupled Nonlinear Schrödinger Equations Using the Generalized Differential Quadrature Method

    International Nuclear Information System (INIS)

    Mokhtari, R.; Toodar, A. Samadi; Chegini, N. G.

    2011-01-01

    We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrödinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge—Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out. (general)

  13. Comunidades de atingidos, o comum e o dom expandido Affected communities, the ordinary and the expanded gift

    Directory of Open Access Journals (Sweden)

    Antonio Lafuente

    2011-07-01

    Full Text Available Este artigo examina a relação entre a tecnologia e os bens comuns e, a partir daí, propõe uma nova valência para o comum. O novo comum deve ser entendido como uma economia do dom que assiste, a cada novo ciclo de relações assimétricas, ao surgimento de uma questão que preocupa uma comunidade de afeto ou de atingidos. A economia do dom expandido retém a produtividade conceitual da famosa teoria do dom de Marcel Mauss, mas é adaptada a um mundo em que quem doa e quem recebe tendem a permanecer anônimos e as expectativas de retribuição, indefinidas. Finalmente, o artigo defende a noção de um dom expandido, cuja economia de reciprocidade possa, em um único gesto, fazer aparecer novas formas de comunidade e inaugurar protocolos inovadores de mobilização social.The article investigates the relationship between technology and ordinary goods in order to propose a new valence for the ordinary. The new ordinary should be understood as a gift economy that witnesses, within every new cycle of asymmetrical relations, the rise of a matter that regards a community of shared affections, or affected community. The expanded gift economy retains the conceptual productivity of Marcel Mauss’s famous theory about the gift, except that it is adapted to a world in which giver and receiver tend to remain anonymous, and the retribution expectations, undefined. At long last, the article argues for a notion of an expanded gift, whose reciprocity economy may - in a single gesture - make appear new forms of community and launch innovative social mobilization protocols.

  14. Comparative study of the properties of ordinary portland cement ...

    African Journals Online (AJOL)

    The study explored metakaolin as alternative material to cement. It compares the properties of Ordinary Portland Cement (OPC) concrete and binary concrete containing metakaolin as partial replacement of OPC. Two set of concrete samples; one with 10% Metakaolin (MK) replacing OPC by weight, and the other without ...

  15. Sports for learners with physical disabilities in ordinary public ...

    African Journals Online (AJOL)

    No adapted sport was offered specifically for these learners. Most learners wanted to participate in swimming. Fewer types of sports were offered in ordinary schools than in special schools. Barriers to participation included poor teacher preparation and inadequate financial support. The shortage of support from school staff, ...

  16. ON ASYMTOTIC APPROXIMATIONS OF FIRST INTEGRALS FOR DIFFERENTIAL AND DIFFERENCE EQUATIONS

    Directory of Open Access Journals (Sweden)

    W.T. van Horssen

    2007-04-01

    Full Text Available In this paper the concept of integrating factors for differential equations and the concept of invariance factors for difference equations to obtain first integrals or invariants will be presented. It will be shown that all integrating factors have to satisfya system of partial differential equations, and that all invariance factors have to satisfy a functional equation. In the period 1997-2001 a perturbation method based on integrating vectors was developed to approximate first integrals for systems of ordinary differential equations. This perturbation method will be reviewed shortly. Also in the paper the first results in the development of a perturbation method for difference equations based on invariance factors will be presented.

  17. On the use of the Lie group technique for differential equations with a small parameter: Approximate solutions and integrable equations

    International Nuclear Information System (INIS)

    Burde, G.I.

    2002-01-01

    A new approach to the use of the Lie group technique for partial and ordinary differential equations dependent on a small parameter is developed. In addition to determining approximate solutions to the perturbed equation, the approach allows constructing integrable equations that have solutions with (partially) prescribed features. Examples of application of the approach to partial differential equations are given

  18. Observation of negative differential resistance and single-electron tunneling in electromigrated break junctions

    International Nuclear Information System (INIS)

    Noguchi, Yutaka; Ueda, Rieko; Kubota, Tohru; Kamikado, Toshiya; Yokoyama, Shiyoshi; Nagase, Takashi

    2008-01-01

    We observed a negative differential resistance (NDR) along with single-electron tunneling (SET) in the electron transport of electromigrated break junctions with metal-free tetraphenylporphyrin (H 2 BSTBPP) at a temperature of 11 K. The NDR strongly depended on the applied gate voltages, and appeared only in the electron tunneling region of the Coulomb diamond. We could explain the mechanism of this new type of electron transport by a model assuming a molecular Coulomb island and local density of states of the source and the drain electrodes

  19. "Solid All the Way Through": Margaret Mahy's Ordinary Witches

    Science.gov (United States)

    Waller, Alison

    2004-01-01

    In "The Haunting," "The Changeover," and "The Tricksters," Margaret Mahy fuses supernatural iconography of witchcraft and magic with images of ordinary and domestic adolescence. This article argues that Mahy's "fantastic realism" illuminates aspects of female teenage experience through a blend of myth, fairy tale, folklore and history, as well as…

  20. Signs in Architecture: Beauty in the Ordinary

    OpenAIRE

    Suzuki, Akiko

    2004-01-01

    In Japan, the basics of living are described as three main elements; clothing, food, and shelter. These elements involve simple daily activities such as changing clothes in the morning, eating lunch, and sleeping at night. It may easily become a mundane topic since they are woven into our daily routines. Nevertheless, a moment in one's day may become joyful when we reconsider and play with the ordinary. The first trace of a dwelling in Japan is a pit shelter. People dug a circular ...

  1. Discrete variational derivative method a structure-preserving numerical method for partial differential equations

    CERN Document Server

    Furihata, Daisuke

    2010-01-01

    Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer

  2. Radiative transitions from the psi (3095) to ordinary hadrons

    Energy Technology Data Exchange (ETDEWEB)

    Scharre, D.L.

    1980-05-01

    Preliminary results from the Mark II and Crystal Ball experiments on radiative transitions from the psi to ordinary hadrons are presented. In additon to the previously observed transitions to the eta, eta'(958), and f(1270), both groups observe a transition to a state which is tentatively identified as the E(1420).

  3. Mix design proposal for structural concrete using messobo ordinary ...

    African Journals Online (AJOL)

    Hessebo Ordinary Portland Cement (OPC). Realizing the various factors contributing to the quality of concrete, 43 trial batches of different mix designs were investigated. Based on the test results, equations were derived to relate compressive strength to w/c and to predict the 28 days compressive strength from the 7 days ...

  4. Fractal-Based Methods and Inverse Problems for Differential Equations: Current State of the Art

    Directory of Open Access Journals (Sweden)

    Herb E. Kunze

    2014-01-01

    Full Text Available We illustrate, in this short survey, the current state of the art of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. We review several methods based on the Collage Theorem and its extensions. We also discuss two innovative applications: the first one is related to a vibrating string model while the second one considers a collage-based approach for solving inverse problems for partial differential equations on a perforated domain.

  5. Robust optimal control design using a differential game approach for open-loop linear quadratic descriptor systems

    NARCIS (Netherlands)

    Musthofa, M.W.; Salmah, S.; Engwerda, Jacob; Suparwanto, A.

    This paper studies the robust optimal control problem for descriptor systems. We applied differential game theory to solve the disturbance attenuation problem. The robust control problem was converted into a reduced ordinary zero-sum game. Within a linear quadratic setting, we solved the problem for

  6. A NEW FRACTIONAL MODEL OF SINGLE DEGREE OF FREEDOM SYSTEM, BY USING GENERALIZED DIFFERENTIAL TRANSFORM METHOD

    Directory of Open Access Journals (Sweden)

    HASHEM SABERI NAJAFI

    2016-07-01

    Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.

  7. Simple Adaptive Single Differential Coherence Detection of BPSK Signals in IEEE 802.15.4 Wireless Sensor Networks.

    Science.gov (United States)

    Zhang, Gaoyuan; Wen, Hong; Wang, Longye; Xie, Ping; Song, Liang; Tang, Jie; Liao, Runfa

    2017-12-26

    In this paper, we propose an adaptive single differential coherent detection (SDCD) scheme for the binary phase shift keying (BPSK) signals in IEEE 802.15.4 Wireless Sensor Networks (WSNs). In particular, the residual carrier frequency offset effect (CFOE) for differential detection is adaptively estimated, with only linear operation, according to the changing channel conditions. It was found that the carrier frequency offset (CFO) and chip signal-to-noise ratio (SNR) conditions do not need a priori knowledge. This partly benefits from that the combination of the trigonometric approximation sin - 1 ( x ) ≈ x and a useful assumption, namely, the asymptotic or high chip SNR, is considered for simplification of the full estimation scheme. Simulation results demonstrate that the proposed algorithm can achieve an accurate estimation and the detection performance can completely meet the requirement of the IEEE 802.15.4 standard, although with a little loss of reliability and robustness as compared with the conventional optimal single-symbol detector.

  8. PKPD model of interleukin-21 effects on thermoregulation in monkeys - Application and evaluation of stochastic differential equations

    DEFF Research Database (Denmark)

    Overgaard, Rune Viig; Holford, Nick; Rytved, K. A.

    2007-01-01

    Purpose To describe the pharmacodynamic effects of recombinant human interleukin-21 (IL-21) on core body temperature in cynomolgus monkeys using basic mechanisms of heat regulation. A major effort was devoted to compare the use of ordinary differential equations (ODEs) with stochastic differentia...

  9. Using frames to determine ordinary meaning in court cases: the case of “plant” and “vermin”

    Directory of Open Access Journals (Sweden)

    Terrence R Carney

    2016-05-01

    Full Text Available The South African judicial system has a variety of ways to determine the ordinary meaning of words, ranging from preceding court cases and academic publications to expert witnesses. However, one of the main resources in the interpretation of ordinary words is a dictionary. Much has already been published on both the use (and abuse of dictionaries in court cases and the ordinary meaning of words as a legal phenomenon. In continuation of this discourse, I propose that jurists consider using a conceptual approach to the interpretation of ordinary words as opposed to relying overly on dictionaries. One such conceptual approach is the use of frames, which deals with meaning in a way that is similar to Gestalt. In this article, I suggest the use of Barsalou’s (1992 frame structure that may be applied to a contested word in six steps. To illustrate the way Barsalou’s frame functions, I have applied it to two contested words taken from South African court cases. Building a frame in order to determine the ordinary meaning of certain words in court cases proves to be a possible alternative or an additional resource to dictionaries.

  10. Does antimatter fall with the same acceleration as ordinary matter?

    International Nuclear Information System (INIS)

    Adelberger, E.G.; Heckel, B.R.; Stubbs, C.W.; Su, Y.

    1991-01-01

    Equivalence-principle experiments with ordinary matter probe the gravivector acceleration of antimatter in the same way as do direct measurements of antimatter in free fall and set stringent upper limits on the gravivector acceleration of antimatter predicted by certain quantum-gravity models

  11. Design of a Negative Differential Resistance Circuit Element Using Single-Electron Transistors

    Science.gov (United States)

    Dixon, D. C.; Heij, C. P.; Hadley, P.; Mooij, J. E.

    1998-03-01

    Electronic circuit elements displaying negative differential resistance (NDR), such as tunnel diodes, have a wide variety of device applications, including oscillators, amplifiers, logic, and memory. We present a two-terminal device using two single-electron transistors (SET's) that demonstrates an NDR profile tuneable with gate voltages. If the capacitive coupling between the SET's is sufficiently larger than the junction capacitances, the device exhibits multiply-peaked NDR, allowing its use as a multi-valued digital element. We will also report recent experimental progress in measurements of such a device, fabricated using standard Al tunnel junctions, but with an additional overlap capacitor to allow the required inter-SET coupling.

  12. Influence of fly-ashes on properties of ordinary concretes

    Directory of Open Access Journals (Sweden)

    Rutkowska Gabriela

    2016-03-01

    Full Text Available Influence of fly-ashes on properties of ordinary concretes. Care of the environment in accordance with the principles of sustainable development introduces the possibility and need for waste recycling. The construction and building materials industry has the greatest potential for reuse of waste. The article presents the results of investigations of selected properties (consistency, water absorbability, compressive strength and tensile strength after 28 and 56 days of curing, depth of penetration of ordinary concretes and concretes containing fly-ashes - calcareous and siliceous ash − in their composition. To make the samples, the Portland cement CEM I 42.5 R and natural aggregate with graining of 0-16 mm were used. The concrete with siliceous and calcareous admixtures was made in three lots where the ash was added in the quantity of 15, 20 and 30% of the cement mass. After the tests, it was stated that the fly-ash admixture does not increase the air content in the mix, it increases the compressive strength in time and the siliceous ash improves the splitting tensile strength.

  13. Limiting precision in differential equation solvers. II Sources of trouble and starting a code

    International Nuclear Information System (INIS)

    Shampine, L.F.

    1978-01-01

    The reasons a class of codes for solving ordinary differential equations might want to use an extremely small step size are investigated. For this class the likelihood of precision difficulties is evaluated and remedies examined. The investigations suggests a way of selecting automatically an initial step size which should be reliably on scale

  14. Collage-based approaches for elliptic partial differential equations inverse problems

    Science.gov (United States)

    Yodzis, Michael; Kunze, Herb

    2017-01-01

    The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach's fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this paper, we explore and compare how the two different approaches perform for the estimation of the diffusivity for a steady-state heat equation.

  15. Generalized mechanics as a representation of the ordinary mechanics

    International Nuclear Information System (INIS)

    Knapecz, G.

    1974-01-01

    It is shown that the generalized mechanics of one masspoint may be interpreted as a special representation of the ordinary mechanics of a system of masspoints. The hormorphism of both representations is shown in the case of two masspoints coupled by a harmonic force. The new representation is applied in the special relativic meachanics of mass-points. (author)

  16. Methods of mathematical modelling continuous systems and differential equations

    CERN Document Server

    Witelski, Thomas

    2015-01-01

    This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

  17. Accelerated Genetic Algorithm Solutions Of Some Parametric Families Of Stochastic Differential Equations

    Directory of Open Access Journals (Sweden)

    Eman Ali Hussain

    2015-01-01

    Full Text Available Absract In this project A new method for solving Stochastic Differential Equations SDEs deriving by Wiener process numerically will be construct and implement using Accelerated Genetic Algorithm AGA. An SDE is a differential equation in which one or more of the terms and hence the solutions itself is a stochastic process. Solving stochastic differential equations requires going away from the recognizable deterministic setting of ordinary and partial differential equations into a world where the evolution of a quantity has an inherent random component and where the expected behavior of this quantity can be described in terms of probability distributions. We applied our method on the Ito formula which is equivalent to the SDE to find approximation solution of the SDEs. Numerical experiments illustrate the behavior of the proposed method.

  18. The numerical solution of linear multi-term fractional differential equations: systems of equations

    Science.gov (United States)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  19. The ethics of an ordinary medical technology.

    Science.gov (United States)

    van Manen, Michael A

    2015-07-01

    Some routinely applied hospital technologies may have unintended consequences for patients and their families. The neonatal cardiorespiratory monitor, a computer-like display used to show an infant's vital functions, is one such technology that may become part of a parent's day-to-day being with his or her hospitalized child. In this phenomenological study, I explored how the monitor may mediate parental sensibilities, reshaping the contact of parent and child. This exploration speaks to understanding the relational ethics of even the seemingly most ordinary of medical technologies in clinical contexts. © The Author(s) 2014.

  20. Comparison of SISEC code simulations with earthquake data of ordinary and base-isolated buildings

    International Nuclear Information System (INIS)

    Wang, C.Y.; Gvildys, J.

    1991-01-01

    At Argonne National Laboratory (ANL), a 3-D computer program SISEC (Seismic Isolation System Evaluation Code) is being developed for simulating the system response of isolated and ordinary structures (Wang et al. 1991). This paper describes comparison of SISEC code simulations with building response data of actual earthquakes. To ensure the accuracy of analytical simulations, recorded data of full-size reinforced concrete structures located in Sendai, Japan are used in this benchmark comparison. The test structures consist of two three-story buildings, one base-isolated and the other one ordinary founded. They were constructed side by side to investigate the effect of base isolation on the acceleration response. Among 20 earthquakes observed since April 1989, complete records of three representative earthquakes, no.2, no.6, and no.17, are used for the code validation presented in this paper. Correlations of observed and calculated accelerations at all instrument locations are made. Also, relative response characteristics of ordinary and isolated building structures are investigated. (J.P.N.)

  1. Rethinking Pedagogy for Second-Order Differential Equations: A Simplified Approach to Understanding Well-Posed Problems

    Science.gov (United States)

    Tisdell, Christopher C.

    2017-01-01

    Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching "well posedness" of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a…

  2. Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

    Directory of Open Access Journals (Sweden)

    Tarikul Islam

    2018-03-01

    Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

  3. On Robust Stability of Differential-Algebraic Equations with Structured Uncertainty

    Directory of Open Access Journals (Sweden)

    A. Kononov

    2018-03-01

    Full Text Available We consider a linear time-invariant system of differential-algebraic equations (DAE, which can be written as a system of ordinary differential equations with non-invertible coefficients matrices. An important characteristic of DAE is the unsolvability index, which reflects the complexity of the internal structure of the system. The question of the asymptotic stability of DAE containing the uncertainty given by the matrix norm is investigated. We consider a perturbation in the structured uncertainty case. It is assumed that the initial nominal system is asymptotically stable. For the analysis, the original equation is reduced to the structural form, in which the differential and algebraic subsystems are separated. This structural form is equivalent to the input system in the sense of coincidence of sets of solutions, and the operator transforming the DAE into the structural form possesses the inverse operator. The conversion to structural form does not use a change of variables. Regularity of matrix pencil of the source equation is the necessary and sufficient condition of structural form existence. Sufficient conditions have been obtained that perturbations do not break the internal structure of the nominal system. Under these conditions robust stability of the DAE with structured uncertainty is investigated. Estimates for the stability radius of the perturbed DAE system are obtained. The text of the article is from the simpler case, in which the perturbation is present only for an unknown function, to a more complex one, under which the perturbation is also present in the derivative of the unknown function. We used values of the real and the complex stability radii of explicit ordinary differential equations for obtaining the results. We consider the example illustrating the obtained results.

  4. Construction of Interval Wavelet Based on Restricted Variational Principle and Its Application for Solving Differential Equations

    OpenAIRE

    Mei, Shu-Li; Lv, Hong-Liang; Ma, Qin

    2008-01-01

    Based on restricted variational principle, a novel method for interval wavelet construction is proposed. For the excellent local property of quasi-Shannon wavelet, its interval wavelet is constructed, and then applied to solve ordinary differential equations. Parameter choices for the interval wavelet method are discussed and its numerical performance is demonstrated.

  5. Analytic, Algebraic and Geometric Aspects of Differential Equations

    CERN Document Server

    Haraoka, Yoshishige; Michalik, Sławomir

    2017-01-01

    This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of i...

  6. Numerical solution of second-order stochastic differential equations with Gaussian random parameters

    Directory of Open Access Journals (Sweden)

    Rahman Farnoosh

    2014-07-01

    Full Text Available In this paper, we present the numerical solution of ordinary differential equations (or SDEs, from each orderespecially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysisfor second-order equations in specially case of scalar linear second-order equations (damped harmonicoscillators with additive or multiplicative noises. Making stochastic differential equations system from thisequation, it could be approximated or solved numerically by different numerical methods. In the case oflinear stochastic differential equations system by Computing fundamental matrix of this system, it could becalculated based on the exact solution of this system. Finally, this stochastic equation is solved by numericallymethod like E.M. and Milstein. Also its Asymptotic stability and statistical concepts like expectationand variance of solutions are discussed.

  7. Optimal Control Strategies in a Two Dimensional Differential Game Using Linear Equation under a Perturbed System

    Directory of Open Access Journals (Sweden)

    Musa Danjuma SHEHU

    2008-06-01

    Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.

  8. Improved stochastic approximation methods for discretized parabolic partial differential equations

    Science.gov (United States)

    Guiaş, Flavius

    2016-12-01

    We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).

  9. Measurement of the Single Diffractive Differential Cross Section $d\\sigma/d\\tau$ at $\\sqrt{s} = 1.96$ TeV Using the D0 Forward Proton Detectors

    Energy Technology Data Exchange (ETDEWEB)

    Pal, Arnab [Univ. of Texas, Arlington, TX (United States)

    2011-08-01

    The analysis described in this dissertation uses the Forward Proton Detectors(FPD) installed at the DØ detector in Tevatron collider at Fermilab to measure the single diffractive differential cross section dσ/d|t| at √s = 1.96 TeV center of mass energy. The single diffractive events were selected using the DØ central detector and the Forward proton detectors and |t| of the forward protons are measured using the FPD system. The analysis presents the measurement of the differential cross section of the single di ractive events as a function of |t| in the range 0.2 < |t|< 1.3 GeV2. The differential cross section measurement is within the theoretical and experimental expectations. The total single diffractive cross section( σsd) in the region 0.0 < |t|< 1.3 GeV2 is found to be 9.682 0.048 (stat.) 1.219 (syst.) mb.

  10. Influence of oak planting on microelement composition (on example of Mn) of ordinary chernozem

    OpenAIRE

    Y. O. Tagunova

    2011-01-01

    Changes of Mn content in the ordinary chernozem of the forb-fescue-stipa steppeunder the influence of oak afforestation within the Prisamar’ya Dniprovske region were studied. The increase of the Mn content in the soil under the artificial oak plantation was noted. The average gross content of Mn in the root layer of the chernozem improved by forest was 541.2 mg/kg and 139.2 mg/kg in the ordinary chernozem. Average content of potentially available metal (mobile forms) in the root layer is 0.5 ...

  11. Quantum States as Ordinary Information

    Directory of Open Access Journals (Sweden)

    Ken Wharton

    2014-03-01

    Full Text Available Despite various parallels between quantum states and ordinary information, quantum no-go-theorems have convinced many that there is no realistic framework that might underly quantum theory, no reality that quantum states can represent knowledge about. This paper develops the case that there is a plausible underlying reality: one actual spacetime-based history, although with behavior that appears strange when analyzed dynamically (one time-slice at a time. By using a simple model with no dynamical laws, it becomes evident that this behavior is actually quite natural when analyzed “all-at-once” (as in classical action principles. From this perspective, traditional quantum states would represent incomplete information about possible spacetime histories, conditional on the future measurement geometry. Without dynamical laws imposing additional restrictions, those histories can have a classical probability distribution, where exactly one history can be said to represent an underlying reality.

  12. Local linearization methods for the numerical integration of ordinary differential equations: An overview

    International Nuclear Information System (INIS)

    Jimenez, J.C.

    2009-06-01

    Local Linearization (LL) methods conform a class of one-step explicit integrators for ODEs derived from the following primary and common strategy: the vector field of the differential equation is locally (piecewise) approximated through a first-order Taylor expansion at each time step, thus obtaining successive linear equations that are explicitly integrated. Hereafter, the LL approach may include some additional strategies to improve that basic affine approximation. Theoretical and practical results have shown that the LL integrators have a number of convenient properties. These include arbitrary order of convergence, A-stability, linearization preserving, regularity under quite general conditions, preservation of the dynamics of the exact solution around hyperbolic equilibrium points and periodic orbits, integration of stiff and high-dimensional equations, low computational cost, and others. In this paper, a review of the LL methods and their properties is presented. (author)

  13. Proceedings of the Nordic society for radiation protection 12. ordinary meeting

    DEFF Research Database (Denmark)

    The key themes of teh 12th ordinary general meeting of the Nordic Society for Radiation Protection were: RADIATION - ENVIRONMENT - INFORMATION. A number of outstanding international experts accepted to contribute on the meetings first day with invited presentations, which focussed on these themes...

  14. Effects of fullerol on the osteogenic differentiation of adipose-derived mesenchymal stem cells

    Directory of Open Access Journals (Sweden)

    Yan-ting TANG

    2016-09-01

    Full Text Available Objective  To investigate the effect of fullerol on the osteogenic differentiation of rat adipose-derived mesenchymal stem cells (rADSCs based on hanging drop culture. Methods  rADSC spheres were formed by hanging drop culture for 3 days, then the spheres were dissociated to single cell by trypsin (called rADSC sphere-derived cells. The rADSC sphere-derived cells were cultured in 2-D adherent cell cultures for 24 hours, then the ordinary culture medium was replaced by osteogenic induction medium (osteogenic medium, OM. OM without fullerol served as control group (CM; OM with 1.0μmol/L fullerol was used as the experimental group (OM+Ful1.0μmol/L. Two groups were induced to differentiation for 14d and 21d, using two methods of alizarin red staining and quantitative real-time PCR (qPCR to detecte the ability of rADSC sphere-derived cells differentiating into osteoblasts. Results  rADSCs could form a uniform size microspheres structure through hanging drop culture for 3 days; rADSC sphere-derived cells were obtained by dissipation of trypsin. Compared with OM group, OM+Ful1.0μmol/L can make rADSC sphere-derived cells form more mineralized calcium nodules, and enhance the expression of the relevant osteogenic gene Runx2, OCN and ColI. Conclusion  Fullerol can significantly enhance the osteogenic differentiation of rADSCs based on hanging drop culture, and it is helpful to improve the efficiency of osteogenic induction of rADSCs. DOI: 10.11855/j.issn.0577-7402.2016.08.03

  15. Differential manifolds

    CERN Document Server

    Kosinski, Antoni A

    2007-01-01

    The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.""How useful it is,"" noted the Bulletin of the American Mathematical Society, ""to have a single, sho

  16. Conjecturing via analogical reasoning constructs ordinary students into like gifted student

    Science.gov (United States)

    Supratman; Ratnaningsih, N.; Ryane, S.

    2017-12-01

    The purpose of this study is to reveal the development of knowledge of ordinary students to be like gifted students in the classroom based on Piaget's theory. In exposing it, students are given an open problem of classical analogy. Researchers explore students who conjecture via analogical reasoning in problem solving. Of the 32 students, through the method of think out loud and the interview was completed: 25 students conjecture via analogical reasoning. Of the 25 students, all of them have almost the same character in problem solving/knowledge construction. For that, a student is taken to analyze the thinking process while solving the problem/construction of knowledge based on Piaget's theory. Based on Piaget's theory in the development of the same knowledge, gifted students and ordinary students have similar structures in final equilibrium. They begin processing: assimilation and accommodation of problem, strategies, and relationships.

  17. Numerical solution of ordinary differential equations

    CERN Document Server

    Lapidus, Leon

    1971-01-01

    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

  18. Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator

    Directory of Open Access Journals (Sweden)

    Resat Yilmazer

    2016-02-01

    Full Text Available In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs. Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.

  19. Tracer kinetics: Modelling by partial differential equations of inhomogeneous compartments with age-dependent elimination rates. Pt. 2

    International Nuclear Information System (INIS)

    Winkler, E.

    1991-01-01

    The general theory of inhomogeneous compartments with age-dependent elimination rates is illustrated by examples. Mathematically, it turns out that models consisting of partial differential equations include ordinary, delayed and integro-differential equations, a general fact which is treated here in the context of linear tracer kinetics. The examples include standard compartments as a degenerate case, systems of standard compartments (compartment blocks), models resulting in special residence time distributions, models with pipes, and systems with heterogeneous particles. (orig./BBR) [de

  20. Stability by fixed point theory for functional differential equations

    CERN Document Server

    Burton, T A

    2006-01-01

    This book is the first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques. It contains an extensive collection of new and classical examples worked in detail and presented in an elementary manner. Most of this text relies on three principles: a complete metric space, the contraction mapping principle, and an elementary variation of parameters formula. The material is highly accessible to upper-level undergraduate students in the mathematical sciences, as well as working biologists, chemists, economists, engineers, mathematicia

  1. Zoology of condensed matter: framids, ordinary stuff, extra-ordinary stuff

    Energy Technology Data Exchange (ETDEWEB)

    Nicolis, Alberto; Penco, Riccardo [Physics Department and Institute for Strings, Cosmology, and Astroparticle Physics,Columbia University, New York, NY 10027 (United States); Piazza, Federico [Physics Department and Institute for Strings, Cosmology, and Astroparticle Physics,Columbia University, New York, NY 10027 (United States); Paris Center for Cosmological Physics and Laboratoire APC,Université Paris 7, 75205 Paris (France); CPT, Aix Marseille Université,UMR 7332, 13288 Marseille (France); Rattazzi, Riccardo [Institut de Théorie des Phénomènes Physiques,EPFL Lausanne (Switzerland)

    2015-06-23

    We classify condensed matter systems in terms of the spacetime symmetries they spontaneously break. In particular, we characterize condensed matter itself as any state in a Poincaré-invariant theory that spontaneously breaks Lorentz boosts while preserving at large distances some form of spatial translations, time-translations, and possibly spatial rotations. Surprisingly, the simplest, most minimal system achieving this symmetry breaking pattern — the framid — does not seem to be realized in Nature. Instead, Nature usually adopts a more cumbersome strategy: that of introducing internal translational symmetries — and possibly rotational ones — and of spontaneously breaking them along with their space-time counterparts, while preserving unbroken diagonal subgroups. This symmetry breaking pattern describes the infrared dynamics of ordinary solids, fluids, superfluids, and — if they exist — supersolids. A third, “extra-ordinary”, possibility involves replacing these internal symmetries with other symmetries that do not commute with the Poincaré group, for instance the galileon symmetry, supersymmetry or gauge symmetries. Among these options, we pick the systems based on the galileon symmetry, the “galileids”, for a more detailed study. Despite some similarity, all different patterns produce truly distinct physical systems with different observable properties. For instance, the low-energy 2→2 scattering amplitudes for the Goldstone excitations in the cases of framids, solids and galileids scale respectively as E{sup 2}, E{sup 4}, and E{sup 6}. Similarly the energy momentum tensor in the ground state is “trivial' for framids (ρ+p=0), normal for solids (ρ+p>0) and even inhomogenous for galileids.

  2. Kramers-Moyal expansion for stochastic differential equations with single and multiple delays: Applications to financial physics and neurophysics

    International Nuclear Information System (INIS)

    Frank, T.D.

    2007-01-01

    We present a generalized Kramers-Moyal expansion for stochastic differential equations with single and multiple delays. In particular, we show that the delay Fokker-Planck equation derived earlier in the literature is a special case of the proposed Kramers-Moyal expansion. Applications for bond pricing and a self-inhibitory neuron model are discussed

  3. Equivariant ordinary homology and cohomology

    CERN Document Server

    Costenoble, Steven R

    2016-01-01

    Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. The discussion is motivated by reference to a list of instructive “toy” examples and calculations in what is a relatively unexplored field. The authors also provide a reading path for the first-time reader less interested in working through sophisticated machinery but still desiring a rigorous understanding of the main concepts. The subject’s classical counterparts, ordinary homology and cohomology, dating back to the work of Henri Poincaré in topology, are calculational and theoretical tools which are important in many parts of mathematics and theoretical physics, particularly in the study of manifolds. Similarly powerful tools have been lacking, however, in the context of equivariant topology. Aimed at advanced graduate students and researchers in algebraic topology and related fields, the book assumes knowledge of basic algebraic topology and group act...

  4. Hochstadt-Lieberman Type Theorem for a Non-Symmetric System of First-Order Ordinary Differential Operators

    Science.gov (United States)

    Trooshin, Igor; Yamamoto, Masahiro

    2003-04-01

    We consider an eigenvalue problem for a nonsymmetric first order differential operator Au( x ; ) = ( {matrix { 0 & 1 ŗ1 & 0 ŗ} } ; ){{du} / {dx}}( x ; ) + Q( x ; )u( x ; ), 0 < x < 1 , where Q is a 2 × 2 matrix whose components are of C1 class on [0, 1]. Assuming that Q(x) is known in the half interval of (0, 1), we prove the uniqueness in an inverse eigenvalue problem of determining Q(x) from the spectra.

  5. Differentiation of malignant glioma and metastatic brain tumor by thallium-201 single photon emission computed tomography

    Energy Technology Data Exchange (ETDEWEB)

    Kojima, Yasuhiro; Kuwana, Nobumasa; Noji, Masato; Tosa, Junichi [Yokohama Minami Kyosai Hospital (Japan)

    1994-09-01

    The use of superdelayed thallium-201 single photon emission computed tomography ([sup 201]Tl SPECT) for differentiating malignant gliomas from cerebral metastases was investigated in 23 patients (7 with meningioma, 6 with glioma, 7 with cerebral metastasis, 1 with each of neurinoma, abscess, and necrosis). 4 mCi of [sup 201]Tl was injected intravenously, and gamma camera scans were performed after 10 minutes and 4, 24, 72, and 96 hours (superdelayed scan). The mean thallium index of meningiomas was significantly higher than those of gliomas and cerebral metastases after 10 minutes, while the mean thallium indices of meningiomas and gliomas were significantly higher than those of cerebral metastases after 96 hours. The combination of early and superdelayed [sup 201]Tl SPECT may be useful in differentiating malignant gliomas from cerebral metastases. (author).

  6. Fault detection and diagnosis in nonlinear systems a differential and algebraic viewpoint

    CERN Document Server

    Martinez-Guerra, Rafael

    2014-01-01

    The high reliability required in industrial processes has created the necessity of detecting abnormal conditions, called faults, while processes are operating. The term fault generically refers to any type of process degradation, or degradation in equipment performance because of changes in the process's physical characteristics, process inputs or environmental conditions. This book is about the fundamentals of fault detection and diagnosis in a variety of nonlinear systems which are represented by ordinary differential equations. The fault detection problem is approached from a differential algebraic viewpoint, using residual generators based upon high-gain nonlinear auxiliary systems (‘observers’). A prominent role is played by the type of mathematical tools that will be used, requiring knowledge of differential algebra and differential equations. Specific theorems tailored to the needs of the problem-solving procedures are developed and proved. Applications to real-world problems, both with constant an...

  7. Experimental study of chloride diffusivity in unsaturated ordinary Portland cement mortar

    NARCIS (Netherlands)

    Zhang, Y.; Ye, G.; Santhanam, M.

    2017-01-01

    Experiments are carried out to investigate the chloride diffusivity in partially saturated ordinary Portland cement mortars with water-to-cement (w/c) ratios of 0.4, 0.5 and 0.6. Based on resistivity measurement and Nernst-Einstein equation, the chloride diffusivities of cement mortars at various

  8. Identifying States along the Hematopoietic Stem Cell Differentiation Hierarchy with Single Cell Specificity via Raman Spectroscopy.

    Science.gov (United States)

    Ilin, Yelena; Choi, Ji Sun; Harley, Brendan A C; Kraft, Mary L

    2015-11-17

    A major challenge for expanding specific types of hematopoietic cells ex vivo for the treatment of blood cell pathologies is identifying the combinations of cellular and matrix cues that direct hematopoietic stem cells (HSC) to self-renew or differentiate into cell populations ex vivo. Microscale screening platforms enable minimizing the number of rare HSCs required to screen the effects of numerous cues on HSC fate decisions. These platforms create a strong demand for label-free methods that accurately identify the fate decisions of individual hematopoietic cells at specific locations on the platform. We demonstrate the capacity to identify discrete cells along the HSC differentiation hierarchy via multivariate analysis of Raman spectra. Notably, cell state identification is accurate for individual cells and independent of the biophysical properties of the functionalized polyacrylamide gels upon which these cells are cultured. We report partial least-squares discriminant analysis (PLS-DA) models of single cell Raman spectra enable identifying four dissimilar hematopoietic cell populations across the HSC lineage specification. Successful discrimination was obtained for a population enriched for long-term repopulating HSCs (LT-HSCs) versus their more differentiated progeny, including closely related short-term repopulating HSCs (ST-HSCs) and fully differentiated lymphoid (B cells) and myeloid (granulocytes) cells. The lineage-specific differentiation states of cells from these four subpopulations were accurately identified independent of the stiffness of the underlying biomaterial substrate, indicating subtle spectral variations that discriminated these populations were not masked by features from the culture substrate. This approach enables identifying the lineage-specific differentiation stages of hematopoietic cells on biomaterial substrates of differing composition and may facilitate correlating hematopoietic cell fate decisions with the extrinsic cues that

  9. Tribocorrosion Study of Ordinary and Laser-Melted Ti6Al4V Alloy

    Directory of Open Access Journals (Sweden)

    Danillo P. Silva

    2016-10-01

    Full Text Available Titanium alloys are used in biomedical implants, as well as in other applications, due to the excellent combination of corrosion resistance and mechanical properties. However, the tribocorrosion resistance of titanium alloy is normally not satisfactory. Therefore, surface modification is a way to improve this specific performance. In the present paper, laser surface-modified samples were tested in corrosion and pin-on-disk tribocorrosion testing in 0.90% NaCl under an average Hertzian pressure of 410 MPa against an alumina sphere. Laser-modified samples of Ti6Al4V were compared with ordinary Ti6Al4V alloy. Electrochemical impedance showed higher modulus for laser-treated samples than for ordinary Ti6Al4V ones. Moreover, atomic force microscopy revealed that laser-treated surfaces presented less wear than ordinary alloy for the initial exposure. For a further exposure to wear, i.e., when the wear depth is beyond the initial laser-affected layer, both materials showed similar corrosion behavior. Microstructure analysis and finite element method simulations revealed that the different behavior between the initial and the extensive rubbing was related to a fine martensite-rich external layer developed on the irradiated surface of the fusion zone.

  10. Zero singularities of codimension two and three in delay differential equations

    International Nuclear Information System (INIS)

    Campbell, Sue Ann; Yuan Yuan

    2008-01-01

    We give conditions under which a general class of delay differential equations has a point of Bogdanov–Takens or a triple zero bifurcation. We show how a centre manifold projection of the delay equations reduces the dynamics to two- or three-dimensional systems of ordinary differential equations. We put these equations in normal form and determine how the coefficients of the normal forms depend on the original parameters in the model. Finally we apply our results to two neural models and compare the predictions of the theory with numerical bifurcation analysis of the full equations. One model involves a transcritical bifurcation, hence we derive and analyse the appropriate unfoldings for this case

  11. Extension of the GroIMP modelling platform to allow easy specification of differential equations describing biological processes within plant models

    NARCIS (Netherlands)

    Hemmerling, R.; Evers, J.B.; Smolenova, K.; Buck-Sorlin, G.H.; Kurth, W.

    2013-01-01

    In simulation models of plant development, physiological processes taking place in plants are typically described in terms of ODEs (Ordinary Differential Equations). On the one hand, those processes drive the development of the plant structure and on the other hand, the developed structure again

  12. Was ordinary matter synthesized from mirror matter? An attempt to explain why ΩB≅0.2Ωdark

    International Nuclear Information System (INIS)

    Foot, R.; Volkas, R.R.

    2003-01-01

    The cosmological dust has begun to settle. A likely picture is a universe comprised (predominantly) of three components: ordinary baryons (Ω B ≅0.05), nonbaryonic dark matter (Ω dark ≅0.22) and dark energy (Ω Λ ≅0.7). We suggest that the observed similarity of the abundances of ordinary baryons and nonbaryonic dark matter (Ω B /Ω dark ≅0.20) hints at an underlying similarity between the fundamental properties of ordinary and dark matter particles. This is necessarily the case if dark matter is identified with mirror matter. We examine a specific mirror matter scenario where Ω B /Ω dark ≅0.20 is naturally obtained

  13. Single-Cell Gene Expression Analysis of a Human ESC Model of Pancreatic Endocrine Development Reveals Different Paths to β-Cell Differentiation.

    Science.gov (United States)

    Petersen, Maja Borup Kjær; Azad, Ajuna; Ingvorsen, Camilla; Hess, Katja; Hansson, Mattias; Grapin-Botton, Anne; Honoré, Christian

    2017-10-10

    The production of insulin-producing β cells from human embryonic stem cells (hESCs) in vitro represents a promising strategy for a cell-based therapy for type 1 diabetes mellitus. To explore the cellular heterogeneity and temporal progression of endocrine progenitors and their progeny, we performed single-cell qPCR on more than 500 cells across several stages of in vitro differentiation of hESCs and compared them with human islets. We reveal distinct subpopulations along the endocrine differentiation path and an early lineage bifurcation toward either polyhormonal cells or β-like cells. We uncover several similarities and differences with mouse development and reveal that cells can take multiple paths to the same differentiation state, a principle that could be relevant to other systems. Notably, activation of the key β-cell transcription factor NKX6.1 can be initiated before or after endocrine commitment. The single-cell temporal resolution we provide can be used to improve the production of functional β cells. Copyright © 2017 The Author(s). Published by Elsevier Inc. All rights reserved.

  14. Solving differential-algebraic equation systems by means of index reduction methodology

    DEFF Research Database (Denmark)

    Sørensen, Kim; Houbak, Niels; Condra, Thomas Joseph

    2006-01-01

    of a number of differential equations and algebraic equations - a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODE’s and index 1 DAE’s by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of Ordinary- Differential-Equations - ODE’s....

  15. Differential single-top-quark cross sections in t channel at 8 and 13 TeV with the CMS detector

    CERN Document Server

    Komm, Matthias

    2017-01-01

    The production of single top quarks in high energy collision events is a unique process to investigate the strength and structure of electroweak interactions. This thesis encompasses first measurements of differential single-top-quark cross sections in t channel which have been performed using data collected at center-of-mass energies of 8 and 13 TeV with the CMS detector at CERN, Switzerland. The electroweak coupling structure of the standard model of particle physics predicts only left-handed top quarks or right-handed top antiquarks to participate in electroweak interactions, resulting in the production of highly polarized top quarks via t channel. The degree of polarization is studied by measuring the cross section as a function of the polarization angle, defined as the angle between the charged lepton from the top quark decay and a spectator quark which is produced in association with the top quark. The differential cross section as a function of the polarization angle is measured in 8 TeV d...

  16. Differential-interference-contrast digital in-line holography microscopy based on a single-optical-element.

    Science.gov (United States)

    Zhang, Yuchao; Xie, Changqing

    2015-11-01

    Both digital in-line holography (DIH) and zone plate-based microscopy have received considerable interest as powerful imaging tools. However, the former suffers from a twin-image noise problem. The latter suffers from low efficiency and difficulty in fabrication. Here, we present an effective and efficient phase-contrast imaging approach, named differential-interference-contrast digital in-line holography (DIC-DIH), by using a single optical element to split the incident light into a plane wave and a converging spherical wave and generate a two-dimensional (2D) DIC effect simultaneously. Specifically, to improve image contrast, we present a new single optical element, termed 2D DIC compound photon sieves, by combining two overlaid binary gratings and a compound photon sieve through two logical XOR operations. The proof-of-concept experiments demonstrate that the proposed technique can eliminate the twin-image noise problem and improve image contrast with high efficiency. Additionally, we present an example of the phase-contrast imaging nonuniform thick photoresist development process.

  17. All-optical 1st- and 2nd-order differential equation solvers with large tuning ranges using Fabry-Pérot semiconductor optical amplifiers.

    Science.gov (United States)

    Chen, Kaisheng; Hou, Jie; Huang, Zhuyang; Cao, Tong; Zhang, Jihua; Yu, Yuan; Zhang, Xinliang

    2015-02-09

    We experimentally demonstrate an all-optical temporal computation scheme for solving 1st- and 2nd-order linear ordinary differential equations (ODEs) with tunable constant coefficients by using Fabry-Pérot semiconductor optical amplifiers (FP-SOAs). By changing the injection currents of FP-SOAs, the constant coefficients of the differential equations are practically tuned. A quite large constant coefficient tunable range from 0.0026/ps to 0.085/ps is achieved for the 1st-order differential equation. Moreover, the constant coefficient p of the 2nd-order ODE solver can be continuously tuned from 0.0216/ps to 0.158/ps, correspondingly with the constant coefficient q varying from 0.0000494/ps(2) to 0.006205/ps(2). Additionally, a theoretical model that combining the carrier density rate equation of the semiconductor optical amplifier (SOA) with the transfer function of the Fabry-Pérot (FP) cavity is exploited to analyze the solving processes. For both 1st- and 2nd-order solvers, excellent agreements between the numerical simulations and the experimental results are obtained. The FP-SOAs based all-optical differential-equation solvers can be easily integrated with other optical components based on InP/InGaAsP materials, such as laser, modulator, photodetector and waveguide, which can motivate the realization of the complicated optical computing on a single integrated chip.

  18. A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

    Science.gov (United States)

    Biala, T A; Jator, S N

    2015-01-01

    In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

  19. Differential equations and integrable models: the SU(3) case

    International Nuclear Information System (INIS)

    Dorey, Patrick; Tateo, Roberto

    2000-01-01

    We exhibit a relationship between the massless a 2 (2) integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schroedinger equation. This forms part of a more general correspondence involving A 2 -related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the non-linear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators phi 12 , phi 21 and phi 15 . This is checked against previous results obtained using the thermodynamic Bethe ansatz

  20. The Relationship between Knowledge Management and Organizational Learning with the Effectiveness of Ordinary and Smart Secondary School Principals

    Science.gov (United States)

    Khammar, Zahra; Heidarzadegan, Alireza; Balaghat, Seyed Reza; Salehi, Hadi

    2013-01-01

    This study aimed to investigate the relationship between knowledge management and organizational learning with the effectiveness of ordinary and smart high school principals in Zahedan Pre-province. The statistical community of this research is 1350 male and female teachers teaching in ordinary and smart students of high schools in that 300 ones…

  1. A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    Sufia Zulfa Ahmad

    2016-01-01

    Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

  2. Probabilistic assessment of steel moment frames incremental collapse (ordinary, intermediate and special under earthquake

    Directory of Open Access Journals (Sweden)

    Kourosh Mehdizadeh

    2017-11-01

    Full Text Available Building collapse is a level of the structure performance in which the amount of financial and life loss is maximized, so this event could be the worst incident in the construction. Regarding to the possibility of destructive earthquakes in different parts of the world, detailed assessment of the structure's collapse has been one of the major challenges of the structural engineering. In this regard, offering models based on laboratory studies, considering the effective parameters and appropriate earthquakes could be a step towards achieving this goal. In this research, a five-story steel structure with a system of ordinary, intermediate and special moment frame (low, intermediate and high ductility has been designed based on the local regulations. In this study, the effect of resistance and stiffness deterioration of the structural elements based on the results of the laboratory models have been considered and the ductility role in the collapse capacity of steel moment frames has been investigated as probabilistic matter. For this purpose, incremental dynamic analysis has been done under 50 pairs of earthquake records proposing FEMA P695 instruction and fragility curves of various performance levels are developed. Results showed higher collapse capacity of special moment steel frame than the intermediate and ordinary moment frames. In the 50 percent probability level, the collapse capacity of special moment frame increased 34 % compared to the intermediate moment frame and 66 % to the ordinary moment frame. Also, the results showed that for different collapse spectral accelerations, the use of special moment frame instead of intermediate and ordinary moment frames reduces the collapse probability to 30 and 50 % respectively.

  3. Comparison of Body Composition and Energy Intake of Young Female Ballet Dancers and Ordinary School Girls

    OpenAIRE

    Kalniņa Līga; Selga Guntars; Sauka Melita; Randoha Aija; Krasovska Eva; Lāriņš Viesturs

    2017-01-01

    The aim of this study is to assess body fat level, energy and nutrient intake of adolescent ballet dancers and to compare these results with those of adolescents from ordinary school. Participants included 39 ballet dancers and 70 adolescents from ordinary school. Body composition was measured using a multi-frequency 8-polar bioelectrical impedance leg-to-hand analyser (X-Scan Plus II, Korea). Dietary intakes were assessed using a three-day estimated food record. Nutritional intake was calcul...

  4. Differential Equations Models to Study Quorum Sensing.

    Science.gov (United States)

    Pérez-Velázquez, Judith; Hense, Burkhard A

    2018-01-01

    Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

  5. A Layer Framework to Investigate Student Understanding and Application of the Existence and Uniqueness Theorems of Differential Equations

    Science.gov (United States)

    Raychaudhuri, D.

    2007-01-01

    The focus of this paper is on student interpretation and usage of the existence and uniqueness theorems for first-order ordinary differential equations. The inherent structure of the theorems is made explicit by the introduction of a framework of layers concepts-conditions-connectives-conclusions, and we discuss the manners in which students'…

  6. Immunohistochemical study of hepatocyte, cholangiocyte and stem cell markers of hepatocellular carcinoma: the second report: relationship with tumor size and cell differentiation.

    Science.gov (United States)

    Kumagai, Arisa; Kondo, Fukuo; Sano, Keiji; Inoue, Masafumi; Fujii, Takeshi; Hashimoto, Masaji; Watanabe, Masato; Soejima, Yurie; Ishida, Tsuyoshi; Tokairin, Takuo; Saito, Koji; Sasajima, Yuko; Takahashi, Yoshihisa; Uozaki, Hiroshi; Fukusato, Toshio

    2016-07-01

    The purpose of this study is to investigate whether ordinary hepatocellular carcinomas (HCCs) show positivity of stem/progenitor cell markers and cholangiocyte markers during the process of tumor progression. Ninety-four HCC lesions no larger than 8 cm from 94 patients were immuno-histochemically studied using two hepatocyte markers (Hep par 1 and α-fetoprotein), five cholangiocyte markers (cytokeratin CK7, CK19, Muc1, epithelial membrane antigen and carcinoembryonic antigen) and three hepatic stem/progenitor cell markers (CD56, c-Kit and EpCAM). The tumors were classified into three groups by tumor size: S1, tumors were also classified according to tumor differentiation: well, moderately and poorly differentiated. The relationship between the positive ratios of these markers, tumor size and tumor differentiation was examined. The positive ratios of cholangiocyte markers tended to be higher in larger sized and more poorly differentiated tumors (except for CK7). The positive ratios of stem/progenitor cell markers tended to be higher in larger sized and more poorly differentiated tumors (except for c-Kit). Ordinary HCC can acquire the characteristic of positivity of cholangiocyte and stem/progenitor cell markers during the process of tumor progression. © 2016 The Authors. Journal of Hepato-Biliary-Pancreatic Sciences published by John Wiley & Sons Australia, Ltd on behalf of Japanese Society of Hepato-Biliary-Pancreatic Surgery.

  7. A new power mapping method based on ordinary kriging and determination of optimal detector location strategy

    International Nuclear Information System (INIS)

    Peng, Xingjie; Wang, Kan; Li, Qing

    2014-01-01

    Highlights: • A new power mapping method based on Ordinary Kriging (OK) is proposed. • Measurements from DayaBay Unit 1 PWR are used to verify the OK method. • The OK method performs better than the CECOR method. • An optimal neutron detector location strategy based on ordinary kriging and simulated annealing is proposed. - Abstract: The Ordinary Kriging (OK) method is presented that is designed for a core power mapping calculation of pressurized water reactors (PWRs). Measurements from DayaBay Unit 1 PWR are used to verify the accuracy of the OK method. The root mean square (RMS) reconstruction errors are kept at less than 0.35%, and the maximum reconstruction relative errors (RE) are kept at less than 1.02% for the entire operating cycle. The reconstructed assembly power distribution results show that the OK method is fit for core power distribution monitoring. The quality of power distribution obtained by the OK method is partly determined by the neutron detector locations, and the OK method is also applied to solve the optimal neutron detector location problem. The spatially averaged ordinary kriging variance (AOKV) is minimized using simulated annealing, and then, the optimal in-core neutron detector locations are obtained. The result shows that the current neutron detector location of DayaBay Unit 1 reactor is near-optimal

  8. Differential equations with Matlab exploration, applications, and theory

    CERN Document Server

    McKibben, Mark

    2014-01-01

    ORDINARY DIFFERENTIAL EQUATIONS Welcome! Introduction This Book Is a Field Guide. What Does That Mean for YOU? Mired in Jargon - A Quick Language Lesson! Introducing MATLAB A First Look at Some Elementary Mathematical Models A Basic Analysis Toolbox Some Basic Mathematical Shorthand Set Algebra Functions The Space (R; j_j) A Closer Look at Sequences in (R; j_j) The Spaces (RN; k_kRN ) and (MN(R); k_kMN(R)Calculus of RN-valued and MN(R)-valued FunctionsSome Elementary ODEs Looking Ahead A First Wave of Mathematical Models Newton's Law of Heating and Cooling-Revisited Pharmocokinetics Uniform Mi

  9. International Conference on Differential Equations and Mathematical Physics

    CERN Document Server

    Saitō, Yoshimi

    1987-01-01

    The meeting in Birmingham, Alabama, provided a forum for the discussion of recent developments in the theory of ordinary and partial differential equations, both linear and non-linear, with particular reference to work relating to the equations of mathematical physics. The meeting was attended by about 250 mathematicians from 22 countries. The papers in this volume all involve new research material, with at least outline proofs; some papers also contain survey material. Topics covered include: Schrödinger theory, scattering and inverse scattering, fluid mechanics (including conservative systems and inertial manifold theory attractors), elasticity, non-linear waves, and feedback control theory.

  10. The convergence of the order sequence and the solution function sequence on fractional partial differential equation

    Science.gov (United States)

    Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.

    2018-03-01

    One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).

  11. An extension of PPLS-DA for classification and comparison to ordinary PLS-DA.

    Directory of Open Access Journals (Sweden)

    Anna Telaar

    Full Text Available Classification studies are widely applied, e.g. in biomedical research to classify objects/patients into predefined groups. The goal is to find a classification function/rule which assigns each object/patient to a unique group with the greatest possible accuracy (classification error. Especially in gene expression experiments often a lot of variables (genes are measured for only few objects/patients. A suitable approach is the well-known method PLS-DA, which searches for a transformation to a lower dimensional space. Resulting new components are linear combinations of the original variables. An advancement of PLS-DA leads to PPLS-DA, introducing a so called 'power parameter', which is maximized towards the correlation between the components and the group-membership. We introduce an extension of PPLS-DA for optimizing this power parameter towards the final aim, namely towards a minimal classification error. We compare this new extension with the original PPLS-DA and also with the ordinary PLS-DA using simulated and experimental datasets. For the investigated data sets with weak linear dependency between features/variables, no improvement is shown for PPLS-DA and for the extensions compared to PLS-DA. A very weak linear dependency, a low proportion of differentially expressed genes for simulated data, does not lead to an improvement of PPLS-DA over PLS-DA, but our extension shows a lower prediction error. On the contrary, for the data set with strong between-feature collinearity and a low proportion of differentially expressed genes and a large total number of genes, the prediction error of PPLS-DA and the extensions is clearly lower than for PLS-DA. Moreover we compare these prediction results with results of support vector machines with linear kernel and linear discriminant analysis.

  12. Coming in from the Margin: Research Practices, Representation and the Ordinary

    Science.gov (United States)

    Greiner, Karen P.

    2010-01-01

    This essay explores issues of marginality and representation in research, which emerged during life history interviews with Tammi, an "ordinary" woman living in Appalachia. I examine how my research practices, namely my thirst for drama and marginality, nearly silenced the preferred stories of the woman who shared her life with me. I…

  13. Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks

    Directory of Open Access Journals (Sweden)

    Raheleh Jafari

    2017-01-01

    Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations or fuzzy differential equations (FDEs by incorporating the fuzzy set theory. The solutions of them are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by two types of Bernstein neural networks. Here, the uncertainties are in the sense of Z-numbers. Initially the FDE is transformed into four ordinary differential equations (ODEs with Hukuhara differentiability. Then neural models are constructed with the structure of ODEs. With modified back propagation method for Z- number variables, the neural networks are trained. The theory analysis and simulation results show that these new models, Bernstein neural networks, are effective to estimate the solutions of FDEs based on Z-numbers.

  14. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  15. Block Hybrid Collocation Method with Application to Fourth Order Differential Equations

    Directory of Open Access Journals (Sweden)

    Lee Ken Yap

    2015-01-01

    Full Text Available The block hybrid collocation method with three off-step points is proposed for the direct solution of fourth order ordinary differential equations. The interpolation and collocation techniques are applied on basic polynomial to generate the main and additional methods. These methods are implemented in block form to obtain the approximation at seven points simultaneously. Numerical experiments are conducted to illustrate the efficiency of the method. The method is also applied to solve the fourth order problem from ship dynamics.

  16. Pairing fluctuation effects on the single-particle spectra for the superconducting state

    International Nuclear Information System (INIS)

    Pieri, P.; Pisani, L.; Strinati, G.C.

    2004-01-01

    Single-particle spectra are calculated in the superconducting state for a fermionic system with an attractive interaction, as functions of temperature and coupling strength from weak to strong. The fermionic system is described by a single-particle self-energy that includes pairing-fluctuation effects in the superconducting state. The theory reduces to the ordinary BCS approximation in weak coupling and to the Bogoliubov approximation for the composite bosons in strong coupling. Several features of the single-particle spectral function are shown to compare favorably with experimental data for cuprate superconductors

  17. Real-effectiveness medicine--pursuing the best effectiveness in the ordinary care of patients.

    Science.gov (United States)

    Malmivaara, Antti

    2013-03-01

    Clinical know-how and skills as well as up-to-date scientific evidence are cornerstones for providing effective treatment for patients. However, in order to improve the effectiveness of treatment in ordinary practice, also appropriate documentation of care at the health care units and benchmarking based on this documentation are needed. This article presents the new concept of real-effectiveness medicine (REM) which pursues the best effectiveness of patient care in the real-world setting. In order to reach the goal, four layers of information are utilized: 1) good medical know-how and skills combined with the patient view, 2) up-to-date scientific evidence, 3) continuous documentation of performance in ordinary settings, and 4) benchmarking between providers. The new framework is suggested for clinicians, organizations, policy-makers, and researchers.

  18. A Tutorial on RxODE: Simulating Differential Equation Pharmacometric Models in R.

    Science.gov (United States)

    Wang, W; Hallow, K M; James, D A

    2016-01-01

    This tutorial presents the application of an R package, RxODE, that facilitates quick, efficient simulations of ordinary differential equation models completely within R. Its application is illustrated through simulation of design decision effects on an adaptive dosing regimen. The package provides an efficient, versatile way to specify dosing scenarios and to perform simulation with variability with minimal custom coding. Models can be directly translated to Rshiny applications to facilitate interactive, real-time evaluation/iteration on simulation scenarios.

  19. Chemical zoning and homogenization of olivines in ordinary chondrites and implications for thermal histories of chondrules

    Science.gov (United States)

    Miyamoto, Masamichi; Mckay, David S.; Mckay, Gordon A.; Duke, Michael B.

    1986-01-01

    The extent and degree of homogenization of chemical zoning of olivines in type 3 ordinary chondrites is studied in order to obtain some constraints on cooling histories of chondrites. Based on Mg-Fe and CaO zoning, olivines in type 3 chondrites are classified into four types. A single chondrule usually contains olivines with the same type of zoning. Microporphyritic olivines show all four zoning types. Barred olivines usually show almost homogenized chemical zoning. The cooling rates or burial depths needed to homogenize the chemical zoning are calculated by solving the diffusion equation, using the zoning profiles as an initial condition. Mg-Fe zoning of olivine may be altered during initial cooling, whereas CaO zoning is hardly changed. Barred olivines may be homogenized during initial cooling because their size is relatively small. To simulated microporphyritic olivine chondrules, cooling from just below the liquidus at moderately high rates is preferable to cooling from above the liquidus at low rates. For postaccumulation metamorphism of type 3 chondrites to keep Mg-Fe zoning unaltered, the maximum metamorphic temperature must be less than about 400 C if cooling rates based on Fe-Ni data are assumed. Calculated cooling rates for both Fa and CaO homogenization are consistent with those by Fe-Ni data for type 4 chondrites. A hot ejecta blanket several tens of meters thick on the surface of a parent body is sufficient to homogenize Mg-Fe zoning if the temperature of the blanket is 600-700 C. Burial depths for petrologic types of ordinary chondrites in a parent body heated by Al-26 are broadly consistent with those previously proposed.

  20. Assessment of modal-pushover-based scaling procedure for nonlinear response history analysis of ordinary standard bridges

    Science.gov (United States)

    Kalkan, E.; Kwong, N.

    2012-01-01

    The earthquake engineering profession is increasingly utilizing nonlinear response history analyses (RHA) to evaluate seismic performance of existing structures and proposed designs of new structures. One of the main ingredients of nonlinear RHA is a set of ground motion records representing the expected hazard environment for the structure. When recorded motions do not exist (as is the case in the central United States) or when high-intensity records are needed (as is the case in San Francisco and Los Angeles), ground motions from other tectonically similar regions need to be selected and scaled. The modal-pushover-based scaling (MPS) procedure was recently developed to determine scale factors for a small number of records such that the scaled records provide accurate and efficient estimates of “true” median structural responses. The adjective “accurate” refers to the discrepancy between the benchmark responses and those computed from the MPS procedure. The adjective “efficient” refers to the record-to-record variability of responses. In this paper, the accuracy and efficiency of the MPS procedure are evaluated by applying it to four types of existing Ordinary Standard bridges typical of reinforced concrete bridge construction in California. These bridges are the single-bent overpass, multi-span bridge, curved bridge, and skew bridge. As compared with benchmark analyses of unscaled records using a larger catalog of ground motions, it is demonstrated that the MPS procedure provided an accurate estimate of the engineering demand parameters (EDPs) accompanied by significantly reduced record-to-record variability of the EDPs. Thus, it is a useful tool for scaling ground motions as input to nonlinear RHAs of Ordinary Standard bridges.